Mathematics & Statistics (School of)
http://hdl.handle.net/10023/28
Tue, 25 Jul 2017 06:52:48 GMT2017-07-25T06:52:48ZMathematics & Statistics (School of)http://research-repository.st-andrews.ac.uk:80/bitstream/id/13/Mathematics and statistics.gif
http://hdl.handle.net/10023/28
Decision problems for word-hyperbolic semigroups
http://hdl.handle.net/10023/11263
This paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be strengthened slightly in order to define a unique semigroup up to isomorphism. The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the situation for word-hyperbolic groups). It is proved that it is undecidable whether a word-hyperbolic semigroup is automatic, asynchronously automatic, biautomatic, or asynchronously biautomatic. (These properties do not hold in general for word-hyperbolic semigroups.) It is proved that the uniform word problem for word-hyperbolic semigroup is solvable in polynomial time (improving on the previous exponential-time algorithm). Algorithms are presented for deciding whether a word-hyperbolic semigroup is a monoid, a group, a completely simple semigroup, a Clifford semigroup, or a free semigroup.
Fri, 22 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/112632016-07-22T00:00:00ZCain, Alan JamesPfeiffer, Markus JohannesThis paper studies decision problems for semigroups that are word-hyperbolic in the sense of Duncan & Gilman. A fundamental investigation reveals that the natural definition of a `word-hyperbolic structure' has to be strengthened slightly in order to define a unique semigroup up to isomorphism. The isomorphism problem is proven to be undecidable for word-hyperbolic semigroups (in contrast to the situation for word-hyperbolic groups). It is proved that it is undecidable whether a word-hyperbolic semigroup is automatic, asynchronously automatic, biautomatic, or asynchronously biautomatic. (These properties do not hold in general for word-hyperbolic semigroups.) It is proved that the uniform word problem for word-hyperbolic semigroup is solvable in polynomial time (improving on the previous exponential-time algorithm). Algorithms are presented for deciding whether a word-hyperbolic semigroup is a monoid, a group, a completely simple semigroup, a Clifford semigroup, or a free semigroup.Marine mammals and sonar : dose-response studies, the risk-disturbance hypothesis and the role of exposure context
http://hdl.handle.net/10023/11259
1. Marine mammals may be negatively affected by anthropogenic noise. Behavioural response studies (BRSs) aim to establish a relationship between the exposure dose of a stressor and associated behavioural responses of animals. A recent series of BRSs have focused on the effects of naval sonar on cetaceans. Here we review the current state of understanding of the impact of sonar on marine mammals and highlight knowledge gaps and future research priorities. 2. Many marine mammal species exhibit responses to naval sonar. However, responses are highly variable between and within individuals, species and populations, highlighting the importance of context in modulating dose-response relationships. 3. There is increasing support for the risk-disturbance hypothesis as an underlying response mechanism. This hypothesis proposes that sonar sounds may be perceived by animals as a threat, evoking an evolved anti-predator response. An understanding of responses within both the dose-response and risk-disturbance frameworks may enhance our ability to predict responsiveness for unstudied species and populations. 4. Many observed behavioural responses are energetically costly, but the way in which these responses may lead to long-term individual and population level impacts is poorly understood. Synthesis and Applications Behavioural response studies have greatly enhanced our understanding of the potential effects of navy sonar on marine mammals. Despite data gaps, we believe a dose-response approach within a risk-disturbance framework will enhance our ability to predict responsiveness for unstudied species and populations. We advocate for (1) regulatory frameworks to utilise recent peer-reviewed research findings when making predictions of impact (where feasible within assessment cycles), (2) regulatory frameworks to account for the inherent uncertainty in predictions of impact, and (3) investment in monitoring programmes that are both directed by recent research and offer opportunities for validation of predictions at the individual and population level.
This manuscript was written following the Behavioral Response Research Evaluation Workshop (BRREW), jointly sponsored by the US Office of Naval Research, US Navy Living Marine Resources, and US National Oceanic and Atmospheric Administration - National Marine Fisheries Service. PLT acknowledges funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland). MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Thu, 20 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/112592017-07-20T00:00:00ZHarris, Catriona MThomas, LenFalcone, ErinHildebrand, JohnHouser, DorianKvadsheim, PetterLam, Frans-Peter A.Miller, PatrickMoretti, David J.Read, AndrewSlabbekoorn, HansSouthall, Brandon L.Tyack, Peter LloydWartzok, DouglasJanik, Vincent M.1. Marine mammals may be negatively affected by anthropogenic noise. Behavioural response studies (BRSs) aim to establish a relationship between the exposure dose of a stressor and associated behavioural responses of animals. A recent series of BRSs have focused on the effects of naval sonar on cetaceans. Here we review the current state of understanding of the impact of sonar on marine mammals and highlight knowledge gaps and future research priorities. 2. Many marine mammal species exhibit responses to naval sonar. However, responses are highly variable between and within individuals, species and populations, highlighting the importance of context in modulating dose-response relationships. 3. There is increasing support for the risk-disturbance hypothesis as an underlying response mechanism. This hypothesis proposes that sonar sounds may be perceived by animals as a threat, evoking an evolved anti-predator response. An understanding of responses within both the dose-response and risk-disturbance frameworks may enhance our ability to predict responsiveness for unstudied species and populations. 4. Many observed behavioural responses are energetically costly, but the way in which these responses may lead to long-term individual and population level impacts is poorly understood. Synthesis and Applications Behavioural response studies have greatly enhanced our understanding of the potential effects of navy sonar on marine mammals. Despite data gaps, we believe a dose-response approach within a risk-disturbance framework will enhance our ability to predict responsiveness for unstudied species and populations. We advocate for (1) regulatory frameworks to utilise recent peer-reviewed research findings when making predictions of impact (where feasible within assessment cycles), (2) regulatory frameworks to account for the inherent uncertainty in predictions of impact, and (3) investment in monitoring programmes that are both directed by recent research and offer opportunities for validation of predictions at the individual and population level.Diffusion driven oscillations in gene regulatory networks
http://hdl.handle.net/10023/11258
Gene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact - typically by feedback. In many GRNs, proteins bind to gene-sites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf-bifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator-repressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics.
Fri, 21 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/112582016-10-21T00:00:00ZMacnamara, Cicely KrystynaChaplain, Mark Andrew JosephGene regulatory networks (GRNs) play an important role in maintaining cellular function by correctly timing key processes such as cell division and apoptosis. GRNs are known to contain similar structural components, which describe how genes and proteins within a network interact - typically by feedback. In many GRNs, proteins bind to gene-sites in the nucleus thereby altering the transcription rate. If the binding reduces the transcription rate there is a negative feedback leading to oscillatory behaviour in mRNA and protein levels, both spatially (e.g. by observing fluorescently labelled molecules in single cells) and temporally (e.g. by observing protein/mRNA levels over time). Mathematical modelling of GRNs has focussed on such oscillatory behaviour. Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs, while it has been proved rigorously that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf-bifurcation. In this paper we consider the spatial aspect further by considering the specific location of gene and protein production, showing that there is an optimum range for the distance between an mRNA gene-site and a protein production site in order to achieve oscillations. We first present a model of a well-known GRN, the Hes1 system, and then extend the approach to examine spatio-temporal models of synthetic GRNs e.g. n-gene repressilator and activator-repressor systems. By incorporating the idea of production sites into such models we show that the spatial component is vital to fully understand GRN dynamics.Improving the usability of spatial point processes methodology : an interdisciplinary dialogue between statistics and ecology
http://hdl.handle.net/10023/11253
The last few decades have seen an increasing interest and strong development in spatial point process methodology, and associated software that facilitates model fitting has become available. A lot of this progress has made these approaches more accessible to users, through freely available software. However, in the ecological user community the methodology has only been slowly picked up despite its obvious relevance to the field. This paper reflects on this development, highlighting mutual benefits of interdisciplinary dialogue for both statistics and ecology. We detail the contribution point process methodology has made to research on biodiversity theory as a result of this dialogue and reflect on reasons for the slow take-up of the methodology. This primarily concerns the current lack of consideration of the usability of the approaches, which we discuss in detail, presenting current discussions as well as indicating future directions.
Fri, 14 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/112532017-07-14T00:00:00ZIllian, Janine BarbelBurslem, DavidThe last few decades have seen an increasing interest and strong development in spatial point process methodology, and associated software that facilitates model fitting has become available. A lot of this progress has made these approaches more accessible to users, through freely available software. However, in the ecological user community the methodology has only been slowly picked up despite its obvious relevance to the field. This paper reflects on this development, highlighting mutual benefits of interdisciplinary dialogue for both statistics and ecology. We detail the contribution point process methodology has made to research on biodiversity theory as a result of this dialogue and reflect on reasons for the slow take-up of the methodology. This primarily concerns the current lack of consideration of the usability of the approaches, which we discuss in detail, presenting current discussions as well as indicating future directions.The theory of rational integral functions of several sets of variables and associated linear transformations
http://hdl.handle.net/10023/11212
The theme of this paper is the unification of two theories which arose and were developed independently of one another in the latter part of the 19th century and the beginning of the 20th, namely the theory of series expansion of rational integral functions of several sets of variables, homogeneous in the variables of each set, that is the series expansion of algebraic forms in several sets of variables, and the theory of induces linear transformations, or invariant matrices. I have divided the work into five chapters of which the first and third are purely historical; Chapter I is an account of various methods, devised before the introduction of the ideas of standard order and standard tableaux, of forming series expansions of algebraic forms, while Chapter III is mainly occupied by an account of Schnur’s work on invariant matrices. Chapters II, IV and V establish the link between the two theories and, at the expense of one or two points of repetition of definitions, are self-contained and may be read consecutively, more or less without reference to the other two chapters.
Fri, 01 Apr 1949 00:00:00 GMThttp://hdl.handle.net/10023/112121949-04-01T00:00:00ZWallace, Andrew HughThe theme of this paper is the unification of two theories which arose and were developed independently of one another in the latter part of the 19th century and the beginning of the 20th, namely the theory of series expansion of rational integral functions of several sets of variables, homogeneous in the variables of each set, that is the series expansion of algebraic forms in several sets of variables, and the theory of induces linear transformations, or invariant matrices. I have divided the work into five chapters of which the first and third are purely historical; Chapter I is an account of various methods, devised before the introduction of the ideas of standard order and standard tableaux, of forming series expansions of algebraic forms, while Chapter III is mainly occupied by an account of Schnur’s work on invariant matrices. Chapters II, IV and V establish the link between the two theories and, at the expense of one or two points of repetition of definitions, are self-contained and may be read consecutively, more or less without reference to the other two chapters.James Gregory : a survey of his work in mathematical analysis
http://hdl.handle.net/10023/11211
Mon, 01 May 1933 00:00:00 GMThttp://hdl.handle.net/10023/112111933-05-01T00:00:00ZInglis, AlexanderMapMySmoke : feasibility of a new quit cigarette smoking mobile phone application using integrated geo-positioning technology, and motivational messaging within a primary care setting
http://hdl.handle.net/10023/11205
Background: Approximately 11,000 people die in Scotland each year as a result of smoking-related causes. Quitting smoking is relatively easy; maintaining a quit attempt is a very difficult task with success rates for unaided quit attempts stubbornly remaining in the single digits. Pharmaceutical treatment can improve these rates by lowering the overall reward factor of nicotine. However, these and related nicotine replacement therapies do not operate on, or address, the spatial and contextual aspects of smoking behaviour. With the ubiquity of smartphones that can log spatial, quantitative and qualitative data related to smoking behaviour, there exists a person-centred clinical opportunity to support smokers attempting to quit by first understanding their smoking behaviour and subsequently sending them dynamic messages to encourage health behaviour change within a situational context. Methods: We have built a smartphone app—MapMySmoke—that works on Android and iOS platforms. The deployment of this app within a clinical National Health Service (NHS) setting has two distinct phases: (1) a 2-week logging phase where pre-quit patients log all of their smoking and craving events; and (2) a post-quit phase where users receive dynamic support messages and can continue to log craving events, and should they occur, relapse events. Following the initial logging phase, patients consult with their general practitioner (GP) or healthcare provider to review their smoking patterns and to outline a precise, individualised quit attempt plan. Our feasibility study consists of assessment of an initial app version during and after use by eight patients recruited from an NHS Fife GP practice. In addition to evaluation of the app as a potential smoking cessation aid, we have assessed the user experience, technological requirements and security of the data flow. Results: In an initial feasibility study, we have deployed the app for a small number of patients within one GP practice in NHS Fife. We recruited eight patients within one surgery, four of whom actively logged information about their smoking behaviour. Initial feedback was very positive, and users indicated a willingness to log their craving and smoking events. In addition, two out of three patients who completed follow-up interviews noted that the app helped them reduce the number of cigarettes they smoked per day, while the third indicated that it had helped them quit. The study highlighted the use of pushed notifications as a potential technology for maintaining quit attempts, and the security of collection of data was audited. These initial results influenced the design of a planned second larger study, comprised of 100 patients, the primary objectives of which are to use statistical modelling to identify times and places of probable switches into smoking states, and to target these times with dynamic health behaviour messaging. Conclusions: While the health benefits of quitting smoking are unequivocal, such behaviour change is very difficult to achieve. Many factors are likely to contribute to maintaining smoking behaviour, yet the precise role of cues derived from the spatial environment remains unclear. The rise of smartphones, therefore, allows clinicians the opportunity to better understand the spatial aspects of smoking behaviour and affords them the opportunity to push targeted individualised health support messages at vulnerable times and places.
This work was funded in part by an NHS Fife Research and Development Bursary Award to all authors. In addition, we have received funding from the University of St Andrews’ EPSRC Impact Acceleration Account. In 2013, Schick received a LEADERS award from the Scottish Universities Life Sciences Alliance that started this project.
Fri, 14 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/112052017-07-14T00:00:00ZSchick, Robert S.Kelsey, Thomas W.Marston, JohnSampson, KayHumphris, Gerald M.Background: Approximately 11,000 people die in Scotland each year as a result of smoking-related causes. Quitting smoking is relatively easy; maintaining a quit attempt is a very difficult task with success rates for unaided quit attempts stubbornly remaining in the single digits. Pharmaceutical treatment can improve these rates by lowering the overall reward factor of nicotine. However, these and related nicotine replacement therapies do not operate on, or address, the spatial and contextual aspects of smoking behaviour. With the ubiquity of smartphones that can log spatial, quantitative and qualitative data related to smoking behaviour, there exists a person-centred clinical opportunity to support smokers attempting to quit by first understanding their smoking behaviour and subsequently sending them dynamic messages to encourage health behaviour change within a situational context. Methods: We have built a smartphone app—MapMySmoke—that works on Android and iOS platforms. The deployment of this app within a clinical National Health Service (NHS) setting has two distinct phases: (1) a 2-week logging phase where pre-quit patients log all of their smoking and craving events; and (2) a post-quit phase where users receive dynamic support messages and can continue to log craving events, and should they occur, relapse events. Following the initial logging phase, patients consult with their general practitioner (GP) or healthcare provider to review their smoking patterns and to outline a precise, individualised quit attempt plan. Our feasibility study consists of assessment of an initial app version during and after use by eight patients recruited from an NHS Fife GP practice. In addition to evaluation of the app as a potential smoking cessation aid, we have assessed the user experience, technological requirements and security of the data flow. Results: In an initial feasibility study, we have deployed the app for a small number of patients within one GP practice in NHS Fife. We recruited eight patients within one surgery, four of whom actively logged information about their smoking behaviour. Initial feedback was very positive, and users indicated a willingness to log their craving and smoking events. In addition, two out of three patients who completed follow-up interviews noted that the app helped them reduce the number of cigarettes they smoked per day, while the third indicated that it had helped them quit. The study highlighted the use of pushed notifications as a potential technology for maintaining quit attempts, and the security of collection of data was audited. These initial results influenced the design of a planned second larger study, comprised of 100 patients, the primary objectives of which are to use statistical modelling to identify times and places of probable switches into smoking states, and to target these times with dynamic health behaviour messaging. Conclusions: While the health benefits of quitting smoking are unequivocal, such behaviour change is very difficult to achieve. Many factors are likely to contribute to maintaining smoking behaviour, yet the precise role of cues derived from the spatial environment remains unclear. The rise of smartphones, therefore, allows clinicians the opportunity to better understand the spatial aspects of smoking behaviour and affords them the opportunity to push targeted individualised health support messages at vulnerable times and places.An analysis of pilot whale vocalization activity using hidden Markov models
http://hdl.handle.net/10023/11194
Vocalizations of cetaceans form a key component of their social interactions. Such vocalization activity is driven by the behavioral states of the whales, which are not directly observable, so that latent-state models are natural candidates for modeling empirical data on vocalizations. In this paper, we use hidden Markov models to analyze calling activity of long-finned pilot whales (Globicephala melas) recorded over three years in the Vestfjord basin off Lofoten, Norway. Baseline models are used to motivate the use of three states, while more complex models are fit to study the influence of covariates on the state-switching dynamics. Our analysis demonstrates the potential usefulness of hidden Markov models in concisely yet accurately describing the stochastic patterns found in animal communication data, thereby providing a framework for drawing meaningful biological inference.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/111942017-01-01T00:00:00ZPopov, Valentin MinaLangrock, RolandDe Ruiter, Stacy LynnVisser, FleurVocalizations of cetaceans form a key component of their social interactions. Such vocalization activity is driven by the behavioral states of the whales, which are not directly observable, so that latent-state models are natural candidates for modeling empirical data on vocalizations. In this paper, we use hidden Markov models to analyze calling activity of long-finned pilot whales (Globicephala melas) recorded over three years in the Vestfjord basin off Lofoten, Norway. Baseline models are used to motivate the use of three states, while more complex models are fit to study the influence of covariates on the state-switching dynamics. Our analysis demonstrates the potential usefulness of hidden Markov models in concisely yet accurately describing the stochastic patterns found in animal communication data, thereby providing a framework for drawing meaningful biological inference.Generalized Bernstein polynomials and total positivity
http://hdl.handle.net/10023/11183
"This thesis submitted for Ph.D. degree deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a one-parameter family of polynomials. It also provides a triangular decomposition and 1-banded factorization of the Vandermonde matrix.
We first establish the generalized Bernstein polynomials for monomials, which leads to a definition of Stirling polynomials of the second kind. These are q-analogues of Stirling numbers of the second kind. Some of the properties of the Stirling numbers are generalized to their q-analogues.
We show that the generalized Bernstein polynomials are monotonic in degree n when the function ƒ is convex...
Shape preserving properties of the generalized Bernstein polynomials are studied by making use of the concept of total positivity. It is proved that monotonic and convex functions produce monotonic and convex generalized Bernstein polynomials. It is also shown that the generalized Bernstein polynomials are monotonic in the parameter q
for the class of convex functions.
Finally, we look into the degree elevation and degree reduction processes on the generalized Bernstein polynomials." -- from the Abstract.
Fri, 01 Jan 1999 00:00:00 GMThttp://hdl.handle.net/10023/111831999-01-01T00:00:00ZOruç, Halil"This thesis submitted for Ph.D. degree deals mainly with geometric properties of generalized Bernstein polynomials which replace the single Bernstein polynomial by a one-parameter family of polynomials. It also provides a triangular decomposition and 1-banded factorization of the Vandermonde matrix.
We first establish the generalized Bernstein polynomials for monomials, which leads to a definition of Stirling polynomials of the second kind. These are q-analogues of Stirling numbers of the second kind. Some of the properties of the Stirling numbers are generalized to their q-analogues.
We show that the generalized Bernstein polynomials are monotonic in degree n when the function ƒ is convex...
Shape preserving properties of the generalized Bernstein polynomials are studied by making use of the concept of total positivity. It is proved that monotonic and convex functions produce monotonic and convex generalized Bernstein polynomials. It is also shown that the generalized Bernstein polynomials are monotonic in the parameter q
for the class of convex functions.
Finally, we look into the degree elevation and degree reduction processes on the generalized Bernstein polynomials." -- from the Abstract.Mathematical modelling of cancer invasion : the multiple roles of TGF-β pathway on tumour proliferation and cell adhesion
http://hdl.handle.net/10023/11162
In this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell–cell adhesion and cell–matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.
VB acknowledges support from an Engineering and Physical Sciences Research Council (UK) grant number EP/L504932/1. RE was partially supported by an Engineering and Physical Sciences Research Council (UK) grant number EP/K033689/1.
Thu, 06 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/111622017-07-06T00:00:00ZBitsouni, VasilikiChaplain, Mark Andrew JosephEftimie, RalucaIn this paper, we develop a non-local mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell–cell adhesion and cell–matrix adhesion, and transforming growth factor-beta (TGF-β) effect on cell proliferation and adhesion, for two cancer cell populations with different levels of mutation. The model consists of partial integro-differential equations describing the dynamics of two cancer cell populations, coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins, and with a parabolic PDE governing the evolution of TGF-β concentration. We prove the global existence of weak solutions to the model. We then use our model to explore numerically the role of TGF-β in cell aggregation and movement.The characteristics of billows generated by internal solitary waves
http://hdl.handle.net/10023/11156
The spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/111562017-02-01T00:00:00ZCarr, MagdaFranklin, JamesKing, Stuart EdwardDavies, PeterGrue, JohnDritschel, David GerardThe spatial and temporal development of shear-induced overturning billows associated with breaking internal solitary waves is studied by means of a combined laboratory and numerical investigation. The waves are generated in the laboratory by a lock exchange mechanism and they are simulated numerically via a contour-advective semi-Lagrangian method. The properties of individual billows (maximum height attained, time of collapse, growth rate, speed, wavelength, Thorpe scale) are determined in each case, and the billow interaction processes are studied and classified. For broad flat waves, similar characteristics are seen to those in parallel shear flow, but, for waves not at the conjugate flow limit, billow characteristics are affected by the spatially varying wave-induced shear flow. Wave steepness and wave amplitude are shown to have a crucial influence on determining the type of interaction that occurs between billows and whether billow overturning can be arrested. Examples are given in which billows (i) evolve independently of one another, (ii) pair with one another, (iii) engulf/entrain one another and (iv) fail to completely overturn. It is shown that the vertical extent a billow can attain (and the associated Thorpe scale of the billow) is dependent on wave amplitude but that its value saturates once a given amplitude is reached. It is interesting to note that this amplitude is less than the conjugate flow limit amplitude. The number of billows that form on a wave is shown to be dependent on wavelength; shorter waves support fewer but larger billows than their long-wave counterparts for a given stratification.Solar coronal jets : observations, theory, and modeling
http://hdl.handle.net/10023/11148
Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While the energy involved in a jet-like event is smaller than that of “nominal” solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the size-spectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solar-heliospheric problems.
S. Patsourakos acknowledges support from an FP7 Marie Curie Grant (FP7-PEOPLE-2010-RG/268288) as well as European Union (European Social Fund—ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF)—Research Funding Program: Thales. A.C. Sterling was supported by funding from the Heliophysics Division of NASA’s Science Mission Directorate through the Living With a Star Targeted Research and Technology Program, and by funding from the Hinode Project Office at NASA/MSFC. P.R. Young acknowledges funding from National Science Foundation grant AGS-1159353. T. Török was supported by NASA’s HSR and LWS programs. K. Dalmasse acknowledges support from the Computational and Information Systems Laboratory and from the HAO, as well as support from the AFOSR under award FA9550-15-1-0030.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/111482016-11-01T00:00:00ZRaouafi, N. E.Patsourakos, S.Pariat, E.Young, P. R.Sterling, A. C.Savcheva, A.Shimojo, M.Moreno-Insertis, F.DeVore, C. R.Archontis, V.Török, T.Mason, H.Curdt, W.Meyer, K.Dalmasse, K.Matsui, Y.Coronal jets represent important manifestations of ubiquitous solar transients, which may be the source of significant mass and energy input to the upper solar atmosphere and the solar wind. While the energy involved in a jet-like event is smaller than that of “nominal” solar flares and coronal mass ejections (CMEs), jets share many common properties with these phenomena, in particular, the explosive magnetically driven dynamics. Studies of jets could, therefore, provide critical insight for understanding the larger, more complex drivers of the solar activity. On the other side of the size-spectrum, the study of jets could also supply important clues on the physics of transients close or at the limit of the current spatial resolution such as spicules. Furthermore, jet phenomena may hint to basic process for heating the corona and accelerating the solar wind; consequently their study gives us the opportunity to attack a broad range of solar-heliospheric problems.Interaction between a quasi-geostrophic buoyancy filament and a heton
http://hdl.handle.net/10023/11138
We investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite sign lying at different depths. Such structures have a self-induced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation modifies locally the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large.
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/111382017-09-01T00:00:00ZReinaud, Jean NoelCarton, XavierDritschel, David GerardWe investigate the interaction between a heton and a current generated by a filament of buoyancy anomaly at the surface. Hetons are baroclinic dipoles consisting of a pair of vortices of opposite sign lying at different depths. Such structures have a self-induced motion whenever the pair of vortices are offset horizontally. A surface buoyancy filament generates a shear flow since the density perturbation modifies locally the pressure field. The vertical shear induced by the filament offsets the vortices of the heton if vertically aligned initially. Moreover, if the vortex nearer the surface is in adverse horizontal shear with the buoyancy filament the heton tends to move towards the filament. Conversely, if the upper vortex is in cooperative horizontal shear with the buoyancy filament, the heton moves away from it. The filament is also naturally unstable and eventually breaks into a series of billows as it is perturbed by the heton. Moderate to large intensity surface buoyancy distributions separate the vortices of the heton, limiting its advection as a baroclinic dipole. Instead, the vortices of the heton start to interact strongly with surface billows. Additionally, the vortices of the heton can be partially destroyed by the filament if the shear it induces is sufficiently large.Between primitive and 2-transitive : synchronization and its friends
http://hdl.handle.net/10023/11134
An automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the Černý conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing n-state automaton has a reset word of length at most (n − 1)2 . The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchronizing if the transitions generate a constant map. A permutation group G on a set Ω is said to synchronize a map f if the monoid hG, fi generated by G and f is synchronizing in the above sense; we say G is synchronizing if it synchronizes every non-permutation. The classes of synchronizing groups and friends form an hierarchy of natural and elegant classes of groups lying strictly between the classes of primitive and 2-homogeneous groups. These classes have been floating around for some years and it is now time to provide a unified reference on them. The study of all these classes has been prompted by the Černý conjecture, but it is of independent interest since it involves a rich mix of group theory, combinatorics, graph endomorphisms, semigroup theory, finite geometry, and representation theory, and has interesting computational aspects as well. So as to make the paper self-contained, we have provided background material on these topics. Our purpose here is to present recent work on synchronizing groups and related topics. In addition to the results that show the connections between the various areas of mathematics mentioned above, we include a new result on the Černý conjecture (a strengthening of a theorem of Rystsov), some challenges to finite geometers (which classical polar spaces can be partitioned into ovoids?), some thoughts about infinite analogues, and a long list of open problems to stimulate further work.
The second author was supported by the Fundação para a Ciência e Tecnologia (Portuguese Foundation for Science and Technology) through the project CEMAT-CIÊNCIAS UID/Multi/ 04621/2013
Thu, 15 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/111342017-06-15T00:00:00ZAraújo, JoãoCameron, Peter JephsonSteinberg, BenjaminAn automaton (consisting of a finite set of states with given transitions) is said to be synchronizing if there is a word in the transitions which sends all states of the automaton to a single state. Research on this topic has been driven by the Černý conjecture, one of the oldest and most famous problems in automata theory, according to which a synchronizing n-state automaton has a reset word of length at most (n − 1)2 . The transitions of an automaton generate a transformation monoid on the set of states, and so an automaton can be regarded as a transformation monoid with a prescribed set of generators. In this setting, an automaton is synchronizing if the transitions generate a constant map. A permutation group G on a set Ω is said to synchronize a map f if the monoid hG, fi generated by G and f is synchronizing in the above sense; we say G is synchronizing if it synchronizes every non-permutation. The classes of synchronizing groups and friends form an hierarchy of natural and elegant classes of groups lying strictly between the classes of primitive and 2-homogeneous groups. These classes have been floating around for some years and it is now time to provide a unified reference on them. The study of all these classes has been prompted by the Černý conjecture, but it is of independent interest since it involves a rich mix of group theory, combinatorics, graph endomorphisms, semigroup theory, finite geometry, and representation theory, and has interesting computational aspects as well. So as to make the paper self-contained, we have provided background material on these topics. Our purpose here is to present recent work on synchronizing groups and related topics. In addition to the results that show the connections between the various areas of mathematics mentioned above, we include a new result on the Černý conjecture (a strengthening of a theorem of Rystsov), some challenges to finite geometers (which classical polar spaces can be partitioned into ovoids?), some thoughts about infinite analogues, and a long list of open problems to stimulate further work.Heating by transverse waves in simulated coronal loops
http://hdl.handle.net/10023/11122
Context. Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The nonlinear nature of the mechanism has been examined alongside the Kelvin-Helmholtz instability,which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. Aims. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Methods. Using the MPI-AMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. Results. We have observed the development of Kelvin-Helmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.
K.K. was funded by GOA-2015-014 (KU Leuven). T.V.D was supported by the IAP P7/08 CHARM (Belspo) and the GOA-2015-014 (KU Leuven). P.A. acknowledges funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Sat, 27 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/111222017-05-27T00:00:00ZKarampelas, K.Van Doorsselaere, T.Antolin, P.Context. Recent numerical studies of oscillating flux tubes have established the significance of resonant absorption in the damping of propagating transverse oscillations in coronal loops. The nonlinear nature of the mechanism has been examined alongside the Kelvin-Helmholtz instability,which is expected to manifest in the resonant layers at the edges of the flux tubes. While these two processes have been hypothesized to heat coronal loops through the dissipation of wave energy into smaller scales, the occurring mixing with the hotter surroundings can potentially hide this effect. Aims. We aim to study the effects of wave heating from driven and standing kink waves in a coronal loop. Methods. Using the MPI-AMRVAC code, we perform ideal, three dimensional magnetohydrodynamic (MHD) simulations of both (a) footpoint driven and (b) free standing oscillations in a straight coronal flux tube, in the presence of numerical resistivity. Results. We have observed the development of Kelvin-Helmholtz eddies at the loop boundary layer of all three models considered here, as well as an increase of the volume averaged temperature inside the loop. The main heating mechanism in our setups was Ohmic dissipation, as indicated by the higher values for the temperatures and current densities located near the footpoints. The introduction of a temperature gradient between the inner tube and the surrounding plasma, suggests that the mixing of the two regions, in the case of hotter environment, greatly increases the temperature of the tube at the site of the strongest turbulence, beyond the contribution of the aforementioned wave heating mechanism.Algorithms for detecting dependencies and rigid subsystems for CAD
http://hdl.handle.net/10023/11110
Automated approaches for detecting dependencies in structures created with Computer Aided Design software are critical for developing robust solvers and providing informative user feedback. We model a set of geometric constraints with a bi-colored multigraph and give a graph-based pebble game algorithm that allows us to determine combinatorially if there are generic dependencies. We further use the pebble game to yield a decomposition of the graph into factor graphs which may be used to give a user detailed feedback about dependent substructures in a specific realization of a system of CAD constraints with non-generic properties.
Louis Theran is partially supported by the European Research Council under the European Union’s Seventh Framework Programme (FP7/2007–2013)/ERC grant agreement No. 247029-SDModels, Academy of Finland (AKA) project COALESCE, and the Hutchcroft fund.
Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/111102016-10-01T00:00:00ZFarre, JamesKleinschmidt, HelenaSidman, JessicaJohn, Audrey St.Stark, StephanieTheran, LouisYu, XilinAutomated approaches for detecting dependencies in structures created with Computer Aided Design software are critical for developing robust solvers and providing informative user feedback. We model a set of geometric constraints with a bi-colored multigraph and give a graph-based pebble game algorithm that allows us to determine combinatorially if there are generic dependencies. We further use the pebble game to yield a decomposition of the graph into factor graphs which may be used to give a user detailed feedback about dependent substructures in a specific realization of a system of CAD constraints with non-generic properties.Comparison of variational balance models for the rotating shallow water equations
http://hdl.handle.net/10023/11100
We present an extensive numerical comparison of a family of balance models appropriate to the semi-geostrophic limit of the rotating shallow water equations, and derived by variational asymptotics in Oliver (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers Ro . This family of generalized large-scale semi-geostrophic (GLSG) models contains the L 1-model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431-444) as a special case. We use these models to produce balanced initial states for the full shallow water equations. We then numerically investigate how well these models capture the dynamics of an initially balanced shallow water flow. It is shown that, whereas the L 1-member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of O ( 1/Ro ) very well, all other members develop significant unphysical high wave number contributions in the ageostrophic vorticity which spoil the dynamics.
Funding through the TRR 181 is gratefully acknowledged. GAG’s initial work was funded by the Australian Research Council grant DP0452147. All three authors received support for this research from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Sat, 01 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/111002017-07-01T00:00:00ZDritschel, David GerardGottwald, GeorgOliver, MarcelWe present an extensive numerical comparison of a family of balance models appropriate to the semi-geostrophic limit of the rotating shallow water equations, and derived by variational asymptotics in Oliver (J. Fluid Mech., vol. 551, 2006, pp. 197–234) for small Rossby numbers Ro . This family of generalized large-scale semi-geostrophic (GLSG) models contains the L 1-model introduced by Simon (J. Fluid. Mech., vol. 132, pp. 431-444) as a special case. We use these models to produce balanced initial states for the full shallow water equations. We then numerically investigate how well these models capture the dynamics of an initially balanced shallow water flow. It is shown that, whereas the L 1-member of the GLSG family is able to reproduce the balanced dynamics of the full shallow water equations on time scales of O ( 1/Ro ) very well, all other members develop significant unphysical high wave number contributions in the ageostrophic vorticity which spoil the dynamics.Flatness, extension and amalgamation in monoids, semigroups and rings
http://hdl.handle.net/10023/11071
We begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in the category of S-sets.
Chapter II introduces the important concept of free extensions and uses this to describe the amalgamated free product.
In Chapter III we define the extension property and the notion of purity. We show that many of the important notions in semigroup amalgams are intimately connected to these. In Section 2 we deduce that 'the extension property implies amalgamation' and more
surprisingly that a semigroup U is an amalgamation base if and only if it has the extension property in every containing semigroup.
Chapter IV revisits the idea of flatness and after some technical results we prove a result, similar to one for rings, on flat amalgams.
In Chapter V we show that the results of Hall and Howie on perfect amalgams can be proved using the same techniques as those used in Chapters III and IV.
We conclude the thesis with a look at the case of rings. We show that almost all of the results for semi group amalgams examined in the previous chapters, also hold for ring amalgams.
Wed, 01 Jan 1986 00:00:00 GMThttp://hdl.handle.net/10023/110711986-01-01T00:00:00ZRenshaw, James HenryWe begin our study of amalgamations by examining some ideas which are well-known for the category of R-modules. In particular we look at such notions as direct limits, pushouts, pullbacks, tensor products and flatness in the category of S-sets.
Chapter II introduces the important concept of free extensions and uses this to describe the amalgamated free product.
In Chapter III we define the extension property and the notion of purity. We show that many of the important notions in semigroup amalgams are intimately connected to these. In Section 2 we deduce that 'the extension property implies amalgamation' and more
surprisingly that a semigroup U is an amalgamation base if and only if it has the extension property in every containing semigroup.
Chapter IV revisits the idea of flatness and after some technical results we prove a result, similar to one for rings, on flat amalgams.
In Chapter V we show that the results of Hall and Howie on perfect amalgams can be proved using the same techniques as those used in Chapters III and IV.
We conclude the thesis with a look at the case of rings. We show that almost all of the results for semi group amalgams examined in the previous chapters, also hold for ring amalgams.3D pic simulations of collisionless shocks at lunar magnetic anomalies and their role in forming lunar swirls
http://hdl.handle.net/10023/11067
Investigation of the lunar crustal magnetic anomalies offers a comprehensive long-term data set of observations of small-scale magnetic fields and their interaction with the solar wind. In this paper a review of the observations of lunar mini-magnetospheres is compared quantifiably with theoretical kinetic-scale plasma physics and 3D particle-in-cell simulations. The aim of this paper is to provide a complete picture of all the aspects of the phenomena and to show how the observations from all the different and international missions interrelate. The analysis shows that the simulations are consistent with the formation of miniature (smaller than the ion Larmor orbit) collisionless shocks and miniature magnetospheric cavities, which has not been demonstrated previously. The simulations reproduce the finesse and form of the differential proton patterns that are believed to be responsible for the creation of both the "lunar swirls" and "dark lanes." Using a mature plasma physics code like OSIRIS allows us, for the first time, to make a side-by-side comparison between model and space observations. This is shown for all of the key plasma parameters observed to date by spacecraft, including the spectral imaging data of the lunar swirls. The analysis of miniature magnetic structures offers insight into multi-scale mechanisms and kinetic-scale aspects of planetary magnetospheres.
The authors would like to thank the Science and Technology Facilities Council for fundamental physics and computing resources that were provided by funding from STFC’s Scientific Computing Department, and would like to thank the European Research Council (ERC 2010 AdG Grant 267841) and FCT (Portugal) grants SFRH/BD/75558/2010 for support.
Tue, 18 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/110672016-10-18T00:00:00ZBamford, R. A.Alves, E. P.Cruz, F.Kellett, B. J.Fonsesca, R. A.Silva, L. O.Trines, R. M. G. M.Halekas, J. S.Kamer, G.Harnett, E.Cairns, Robert AlanBingham, R.Investigation of the lunar crustal magnetic anomalies offers a comprehensive long-term data set of observations of small-scale magnetic fields and their interaction with the solar wind. In this paper a review of the observations of lunar mini-magnetospheres is compared quantifiably with theoretical kinetic-scale plasma physics and 3D particle-in-cell simulations. The aim of this paper is to provide a complete picture of all the aspects of the phenomena and to show how the observations from all the different and international missions interrelate. The analysis shows that the simulations are consistent with the formation of miniature (smaller than the ion Larmor orbit) collisionless shocks and miniature magnetospheric cavities, which has not been demonstrated previously. The simulations reproduce the finesse and form of the differential proton patterns that are believed to be responsible for the creation of both the "lunar swirls" and "dark lanes." Using a mature plasma physics code like OSIRIS allows us, for the first time, to make a side-by-side comparison between model and space observations. This is shown for all of the key plasma parameters observed to date by spacecraft, including the spectral imaging data of the lunar swirls. The analysis of miniature magnetic structures offers insight into multi-scale mechanisms and kinetic-scale aspects of planetary magnetospheres.Cell population heterogeneity and evolution towards drug resistance in cancer : biological and mathematical assessment, theoretical treatment optimisation
http://hdl.handle.net/10023/11036
Background. Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review. We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions. Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/110362016-11-01T00:00:00ZChisholm, Rebecca H.Lorenzi, TommasoClairambault, JeanBackground. Drug-induced drug resistance in cancer has been attributed to diverse biological mechanisms at the individual cell or cell population scale, relying on stochastically or epigenetically varying expression of phenotypes at the single cell level, and on the adaptability of tumours at the cell population level. Scope of review. We focus on intra-tumour heterogeneity, namely between-cell variability within cancer cell populations, to account for drug resistance. To shed light on such heterogeneity, we review evolutionary mechanisms that encompass the great evolution that has designed multicellular organisms, as well as smaller windows of evolution on the time scale of human disease. We also present mathematical models used to predict drug resistance in cancer and optimal control methods that can circumvent it in combined therapeutic strategies. Major conclusions. Plasticity in cancer cells, i.e., partial reversal to a stem-like status in individual cells and resulting adaptability of cancer cell populations, may be viewed as backward evolution making cancer cell populations resistant to drug insult. This reversible plasticity is captured by mathematical models that incorporate between-cell heterogeneity through continuous phenotypic variables. Such models have the benefit of being compatible with optimal control methods for the design of optimised therapeutic protocols involving combinations of cytotoxic and cytostatic treatments with epigenetic drugs and immunotherapies. General significance. Gathering knowledge from cancer and evolutionary biology with physiologically based mathematical models of cell population dynamics should provide oncologists with a rationale to design optimised therapeutic strategies to circumvent drug resistance, that still remains a major pitfall of cancer therapeutics. This article is part of a Special Issue entitled "System Genetics" Guest Editor: Dr. Yudong Cai and Dr. Tao Huang.Dimension theory of random self-similar and self-affine constructions
http://hdl.handle.net/10023/11033
This thesis is structured as follows.
Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory.
In Chapter 2 we give an overview of both deterministic and stochastic sets obtained from iterated function systems.
We summarise classical results and set most of the basic notation.
This is followed by the introduction of random graph directed systems in Chapter 3, based on the single authored paper [T1] to be published in Journal of Fractal Geometry. We prove that these attractors have equal Hausdorff and upper box-counting dimension irrespective of overlaps. It follows that the same holds for the classical models introduced in Chapter 2. This chapter also contains results about the Assouad dimensions for these random sets.
Chapter 4 is based on the single authored paper [T2] and establishes the box-counting dimension for random box-like self-affine sets using some of the results and the notation developed in Chapter 3. We give some examples to illustrate the results.
In Chapter 5 we consider the Hausdorff and packing measure of random attractors and show that for reasonable random systems the Hausdorff measure is zero almost surely. We further establish bounds on the gauge functions necessary to obtain positive or finite Hausdorff measure for random homogeneous systems.
Chapter 6 is based on a joint article with J. M. Fraser and J.-J. Miao [FMT] to appear in Ergodic Theory and Dynamical Systems. It is chronologically the first and contains results that were extended in the paper on which Chapter 3 is based.
However, we will give some simpler, alternative proofs in this section and crucially also find the Assouad dimension of some random self-affine carpets and show that the Assouad dimension is always `maximal' in both measure theoretic and topological meanings.
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/110332017-06-23T00:00:00ZTroscheit, SaschaThis thesis is structured as follows.
Chapter 1 introduces fractal sets before recalling basic mathematical concepts from dynamical systems, measure theory, dimension theory and probability theory.
In Chapter 2 we give an overview of both deterministic and stochastic sets obtained from iterated function systems.
We summarise classical results and set most of the basic notation.
This is followed by the introduction of random graph directed systems in Chapter 3, based on the single authored paper [T1] to be published in Journal of Fractal Geometry. We prove that these attractors have equal Hausdorff and upper box-counting dimension irrespective of overlaps. It follows that the same holds for the classical models introduced in Chapter 2. This chapter also contains results about the Assouad dimensions for these random sets.
Chapter 4 is based on the single authored paper [T2] and establishes the box-counting dimension for random box-like self-affine sets using some of the results and the notation developed in Chapter 3. We give some examples to illustrate the results.
In Chapter 5 we consider the Hausdorff and packing measure of random attractors and show that for reasonable random systems the Hausdorff measure is zero almost surely. We further establish bounds on the gauge functions necessary to obtain positive or finite Hausdorff measure for random homogeneous systems.
Chapter 6 is based on a joint article with J. M. Fraser and J.-J. Miao [FMT] to appear in Ergodic Theory and Dynamical Systems. It is chronologically the first and contains results that were extended in the paper on which Chapter 3 is based.
However, we will give some simpler, alternative proofs in this section and crucially also find the Assouad dimension of some random self-affine carpets and show that the Assouad dimension is always `maximal' in both measure theoretic and topological meanings.Automatic generation of generalised regular factorial designs
http://hdl.handle.net/10023/11025
The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.
Open Access for this article was paid for by the French Research Agency (ANR), project Escapade (ANR-12-AGRO-0003).
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/110252017-09-01T00:00:00ZKobilinsky, AndréMonod, HervéBailey, R. A.The R package planor enables the user to search for, and construct, factorial designs satisfying given conditions. The user specifies the factors and their numbers of levels, the factorial terms which are assumed to be non-zero, and the subset of those which are to be estimated. Both block and treatment factors can be allowed for, and they may have either fixed or random effects, as well as hierarchy relationships. The designs are generalised regular designs, which means that each one is constructed by using a design key and that the underlying theory is that of finite abelian groups. The main theoretical results and algorithms on which planor is based are developed and illustrated, with the emphasis on mathematical rather than programming details. Sections 3–5 are dedicated to the elementary case, when the numbers of levels of all factors are powers of the same prime. The ineligible factorial terms associated with users’ specifications are defined and it is shown how they can be used to search for a design key by a backtrack algorithm. Then the results are extended to the case when different primes are involved, by making use of the Sylow decomposition of finite abelian groups. The proposed approach provides a unified framework for a wide range of factorial designs.Restricted permutations, antichains, atomic classes and stack sorting
http://hdl.handle.net/10023/11023
Involvement is a partial order on all finite permutations, of infinite dimension and having subsets isomorphic to every countable partial order with finite descending chains. It has attracted the attention of some celebrated mathematicians including Paul Erdős and, due to its close links with sorting devices, Donald Knuth.
We compare and contrast two presentations of closed classes that depend on the partial order of involvement: Basis or Avoidance Set, and Union of Atomic Classes. We examine how the basis is affected by a comprehensive list of closed class constructions and decompositions.
The partial order of involvement contains infinite antichains. We develop the concept of a fundamental antichain. We compare the concept of 'fundamental' with other definitions of minimality for antichains, and compare fundamental permutation antichains with fundamental antichains in graph theory. The justification for investigating fundamental antichains is the nice patterns they produce. We forward the case for classifying the fundamental permutation antichains.
Sorting devices have close links with closed classes. We consider two sorting devices, constructed from stacks in series, in detail.
We give a comment on an enumerative conjecture by Ira Gessel.
We demonstrate, with a remarkable example, that there exist two closed classes, equinumerous, one of which has a single basis element, the other infinitely many basis elements.
We present this paper as a comprehensive analysis of the partial order of permutation involvement. We regard the main research contributions offered here to be the examples that demonstrate what is, and what is not, possible; although there are numerous structure results that do not fall under this category. We propose the classification of fundamental permutation antichains as one of the principal problems for closed classes today, and consider this as a problem whose solution will have wide significance for the study of partial orders, and mathematics as a whole.
Wed, 01 Jan 2003 00:00:00 GMThttp://hdl.handle.net/10023/110232003-01-01T00:00:00ZMurphy, Maximilian M.Involvement is a partial order on all finite permutations, of infinite dimension and having subsets isomorphic to every countable partial order with finite descending chains. It has attracted the attention of some celebrated mathematicians including Paul Erdős and, due to its close links with sorting devices, Donald Knuth.
We compare and contrast two presentations of closed classes that depend on the partial order of involvement: Basis or Avoidance Set, and Union of Atomic Classes. We examine how the basis is affected by a comprehensive list of closed class constructions and decompositions.
The partial order of involvement contains infinite antichains. We develop the concept of a fundamental antichain. We compare the concept of 'fundamental' with other definitions of minimality for antichains, and compare fundamental permutation antichains with fundamental antichains in graph theory. The justification for investigating fundamental antichains is the nice patterns they produce. We forward the case for classifying the fundamental permutation antichains.
Sorting devices have close links with closed classes. We consider two sorting devices, constructed from stacks in series, in detail.
We give a comment on an enumerative conjecture by Ira Gessel.
We demonstrate, with a remarkable example, that there exist two closed classes, equinumerous, one of which has a single basis element, the other infinitely many basis elements.
We present this paper as a comprehensive analysis of the partial order of permutation involvement. We regard the main research contributions offered here to be the examples that demonstrate what is, and what is not, possible; although there are numerous structure results that do not fall under this category. We propose the classification of fundamental permutation antichains as one of the principal problems for closed classes today, and consider this as a problem whose solution will have wide significance for the study of partial orders, and mathematics as a whole.Scaling theory for vortices in the two-dimensional inverse energy cascade
http://hdl.handle.net/10023/11014
We propose a new similarity theory for the two-dimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that E∼t yield three length scales, lω, lE and lψ, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, t1/2, t and t3/2, respectively. We thus predict that vortex areas grow linearly in time, A∼l2ω∼t, while the spectral peak wavenumber kE ≡ 2πl−1E ∼ t−1. We construct a theoretical framework involving a three-part, time-evolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcing-equilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘self-energy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in A-space intervals [μA0(t), A0(t)] comoving with the growth in vortex area, A0(t) ∼ t. In this range, α1 = 0 and n(A) ∼ A−3. At intermediate scales (i = 2) sufficiently far from the forcing and the largest vortex, there is a range with a scale-invariant vortex size distribution. We predict that in this range the vortex enstrophy Zvcm = (2D)−1∫ ωv2An(A)dA is conserved and n(A) ∼ t−1A−1. The final range (i = 3), which extends over the largest vortex-containing scales, conserves σvcm = (2D)−1∫ ωv2n(A)dA. If ωv2 is constant in time, this is equivalent to conservation of vortex number Nvcm =∫ n(A)dA. This regime represents a ‘front’ of sparse vortices, which are effectively point-like; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for time-varying ωv2 results in a small but significant correction to these temporal dependences. High-resolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum E(k) past the classical k−5/3 scaling in the range k ∈ [kf , kv], where kv is the wavenumber associated with the largest vortex, while at larger scales the slope approaches −5/3. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.
B.H.B. is supported by the Natural Environment Research Council grant NE/M014983/1.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/110142017-01-01T00:00:00ZBurgess, B. H.Scott, R. K.We propose a new similarity theory for the two-dimensional inverse energy cascade and the coherent vortex population it contains when forced at intermediate scales. Similarity arguments taking into account enstrophy conservation and a prescribed constant energy injection rate such that E∼t yield three length scales, lω, lE and lψ, associated with the vorticity field, energy peak and streamfunction, and predictions for their temporal evolutions, t1/2, t and t3/2, respectively. We thus predict that vortex areas grow linearly in time, A∼l2ω∼t, while the spectral peak wavenumber kE ≡ 2πl−1E ∼ t−1. We construct a theoretical framework involving a three-part, time-evolving vortex number density distribution, n(A) ∼ tαiA−ri, i ∈ 1,2,3. Just above the forcing scale (i =1) there is a forcing-equilibrated scaling range in which the number of vortices at fixed A is constant and vortex ‘self-energy’ Evcm = (2D)−1∫ωv2A2n(A) dA is conserved in A-space intervals [μA0(t), A0(t)] comoving with the growth in vortex area, A0(t) ∼ t. In this range, α1 = 0 and n(A) ∼ A−3. At intermediate scales (i = 2) sufficiently far from the forcing and the largest vortex, there is a range with a scale-invariant vortex size distribution. We predict that in this range the vortex enstrophy Zvcm = (2D)−1∫ ωv2An(A)dA is conserved and n(A) ∼ t−1A−1. The final range (i = 3), which extends over the largest vortex-containing scales, conserves σvcm = (2D)−1∫ ωv2n(A)dA. If ωv2 is constant in time, this is equivalent to conservation of vortex number Nvcm =∫ n(A)dA. This regime represents a ‘front’ of sparse vortices, which are effectively point-like; in this range we predict n(A) ∼ tr3−1A−r3. Allowing for time-varying ωv2 results in a small but significant correction to these temporal dependences. High-resolution numerical simulations verify the predicted vortex and spectral peak growth rates, as well as the theoretical picture of the three scaling ranges in the vortex population. Vortices steepen the energy spectrum E(k) past the classical k−5/3 scaling in the range k ∈ [kf , kv], where kv is the wavenumber associated with the largest vortex, while at larger scales the slope approaches −5/3. Though vortices disrupt the classical scaling, their number density distribution and evolution reveal deeper and more complex scale invariance, and suggest an effective theory of the inverse cascade in terms of vortex interactions.A robust and efficient adaptive multigrid solver for the optimal control of phase field formulations of geometric evolution laws
http://hdl.handle.net/10023/10909
We propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.
All authors acknowledge support from the Leverhulme Trust Research Project Grant (RPG-2014-149). The work of CV, VS and AMwas partially supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1). This work (AM) has also received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. The work of CV is partially supported by an EPSRC Impact Accelerator Account award. The authors (FWY, CV, VS, AM) thank the Isaac Newton Institute for Mathematical Sciences for its hospitality during the programme (Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation; EPSRC EP/K032208/1). AM was partially supported by Fellowships from the Simons Foundation.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/109092017-01-01T00:00:00ZYang, Feng WeiVenkataraman, ChandrasekharStyles, VanessaMadzvamuse, AnotidaWe propose and investigate a novel solution strategy to efficiently and accurately compute approximate solutions to semilinear optimal control problems, focusing on the optimal control of phase field formulations of geometric evolution laws. The optimal control of geometric evolution laws arises in a number of applications in fields including material science, image processing, tumour growth and cell motility. Despite this, many open problems remain in the analysis and approximation of such problems. In the current work we focus on a phase field formulation of the optimal control problem, hence exploiting the well developed mathematical theory for the optimal control of semilinear parabolic partial differential equations. Approximation of the resulting optimal control problem is computationally challenging, requiring massive amounts of computational time and memory storage. The main focus of this work is to propose, derive, implement and test an efficient solution method for such problems. The solver for the discretised partial differential equations is based upon a geometric multigrid method incorporating advanced techniques to deal with the nonlinearities in the problem and utilising adaptive mesh refinement. An in-house two grid solution strategy for the forward and adjoint problems, that significantly reduces memory requirements and CPU time, is proposed and investigated computationally. Furthermore, parallelisation as well as an adaptive-step gradient update for the control are employed to further improve efficiency. Along with a detailed description of our proposed solution method together with its implementation we present a number of computational results that demonstrate and evaluate our algorithms with respect to accuracy and efficiency. A highlight of the present work is simulation results on the optimal control of phase field formulations of geometric evolution laws in 3-D which would be computationally infeasible without the solution strategies proposed in the present work.Particle acceleration in collapsing magnetic traps with a braking plasma jet
http://hdl.handle.net/10023/10896
Collapsing magnetic traps (CMTs) are one proposed mechanism for generating non-thermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lower-energy configuration, which is believed to happen as a by-product of magnetic reconnection. A similar mechanism for energising particles has also been found to operate in the Earth's magnetotail. One particular feature proposed to be of importance for particle acceleration in the magnetotail is that of a braking plasma jet, i.e. a localised region of strong flow encountering stronger magnetic field which causes the jet to slow down and stop. Such a feature has not been included in previously proposed analytical models of CMTs for solar flares. In this work we incorporate a braking plasma jet into a well studied CMT model for the first time. We present results of test particle calculations in this new CMT model. We observe and characterise new types of particle behaviour caused by the magnetic structure of the jet braking region, which allows electrons to be trapped both in the braking jet region and the loop legs. We compare and contrast the behaviour of particle orbits for various parameter regimes of the underlying trap by examining particle trajectories, energy gains and the frequency with which different types of particle orbit are found for each parameter regime.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/108962016-01-01T00:00:00ZBorissov, AlexeiNeukirch, ThomasThrelfall, James WilliamCollapsing magnetic traps (CMTs) are one proposed mechanism for generating non-thermal particle populations in solar flares. CMTs occur if an initially stretched magnetic field structure relaxes rapidly into a lower-energy configuration, which is believed to happen as a by-product of magnetic reconnection. A similar mechanism for energising particles has also been found to operate in the Earth's magnetotail. One particular feature proposed to be of importance for particle acceleration in the magnetotail is that of a braking plasma jet, i.e. a localised region of strong flow encountering stronger magnetic field which causes the jet to slow down and stop. Such a feature has not been included in previously proposed analytical models of CMTs for solar flares. In this work we incorporate a braking plasma jet into a well studied CMT model for the first time. We present results of test particle calculations in this new CMT model. We observe and characterise new types of particle behaviour caused by the magnetic structure of the jet braking region, which allows electrons to be trapped both in the braking jet region and the loop legs. We compare and contrast the behaviour of particle orbits for various parameter regimes of the underlying trap by examining particle trajectories, energy gains and the frequency with which different types of particle orbit are found for each parameter regime.A complex solar coronal jet with two phases
http://hdl.handle.net/10023/10893
Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an opposite-polarity fragment between them.
This work was partly supported by National Natural Science Foundation of China (grant Nos. 11303048, 11673033, 11373040, 11427901). This work was also partly supported by an International Exchanges cost share award with NSFC for overseas travel between collaborators in the UK and China, and State Key Laboratory for Space Weather, Center for Space Science and Applied Research, Chinese Academy of Sciences.
Thu, 04 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/108932017-05-04T00:00:00ZChen, JieSu, JiangtaoDeng, YuanyongPriest, E. R.Jets often occur repeatedly from almost the same location. In this paper, a complex solar jet was observed with two phases to the west of NOAA AR 11513 on 2012 July 2. If it had been observed at only moderate resolution, the two phases and their points of origin would have been regarded as identical. However, at high resolution we find that the two phases merge into one another and the accompanying footpoint brightenings occur at different locations. The phases originate from different magnetic patches rather than being one phase originating from the same patch. Photospheric line of sight (LOS) magnetograms show that the bases of the two phases lie in two different patches of magnetic flux that decrease in size during the occurrence of the two phases. Based on these observations, we suggest that the driving mechanism of the two successive phases is magnetic cancellation of two separate magnetic fragments with an opposite-polarity fragment between them.Estimation bias under model selection for distance sampling detection functions
http://hdl.handle.net/10023/10890
Many simulation studies have examined the properties of distance sampling estimators of wildlife population size. When assumptions hold, if distances are generated from a detection model and fitted using the same model, they are known to perform well. However, in practice, the true model is unknown. Therefore, standard practice includes model selection, typically using model comparison tools like Akaike Information Criterion. Here we examine the performance of standard distance sampling estimators under model selection. We compare line and point transect estimators with distances simulated from two detection functions, hazard-rate and exponential power series (EPS), over a range of sample sizes. To mimic the real-world context where the true model may not be part of the candidate set, EPS models were not included as candidates, except for the half-normal parameterization. We found median bias depended on sample size (being asymptotically unbiased) and on the form of the true detection function: negative bias (up to 15% for line transects and 30% for point transects) when the shoulder of maximum detectability was narrow, and positive bias (up to 10% for line transects and 15% for point transects) when it was wide. Generating unbiased simulations requires careful choice of detection function or very large datasets. Practitioners should collect data that result in detection functions with a shoulder similar to a half-normal and use the monotonicity constraint. Narrow-shouldered detection functions can be avoided through good field procedures and those with wide shoulder are unlikely to occur, due to heterogeneity in detectability.
TAM thanks support by CEAUL (funded by FCT—Fundação para a Ciência e a Tecnologia, Portugal, through the Project UID/MAT/00006/2013)
Fri, 26 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/108902017-05-26T00:00:00ZPrieto Gonzalez, RocioThomas, Leonard JosephMarques, Tiago Andre Lamas OliveiraMany simulation studies have examined the properties of distance sampling estimators of wildlife population size. When assumptions hold, if distances are generated from a detection model and fitted using the same model, they are known to perform well. However, in practice, the true model is unknown. Therefore, standard practice includes model selection, typically using model comparison tools like Akaike Information Criterion. Here we examine the performance of standard distance sampling estimators under model selection. We compare line and point transect estimators with distances simulated from two detection functions, hazard-rate and exponential power series (EPS), over a range of sample sizes. To mimic the real-world context where the true model may not be part of the candidate set, EPS models were not included as candidates, except for the half-normal parameterization. We found median bias depended on sample size (being asymptotically unbiased) and on the form of the true detection function: negative bias (up to 15% for line transects and 30% for point transects) when the shoulder of maximum detectability was narrow, and positive bias (up to 10% for line transects and 15% for point transects) when it was wide. Generating unbiased simulations requires careful choice of detection function or very large datasets. Practitioners should collect data that result in detection functions with a shoulder similar to a half-normal and use the monotonicity constraint. Narrow-shouldered detection functions can be avoided through good field procedures and those with wide shoulder are unlikely to occur, due to heterogeneity in detectability.A new class of vacillations of the stratospheric polar vortex
http://hdl.handle.net/10023/10887
A new class of persistent vacillations of the winter polar vortex, under the action of topographic wave forcing and radiative cooling, is identified in numerical integrations of the rotating shallow water equations. The vacillations are obtained provided only that care is taken to prevent the unconstrained growth of tropical easterlies that otherwise develop as the result of persistent angular momentum deposition at low latitudes. The vacillation cycle involves purely barotropic dynamics and is characterized by a dynamically controlled rapid splitting and rapid reformation of the vortex followed by a more gradual period of vortex intensification under the influence of radiative relaxation. The onset of the splitting occurs when the frequency of the free mode of the vortex approaches that of the forcing and resembles a resonant excitation. Experiments with an alternative basic state suggest that the vacillations are a robust feature of the topographically forced and radiatively relaxed vortex. In contrast to the behavior found in models with vertical structure, the period of the vacillation cycles here increases with increasing forcing amplitude. A wide range of forcing amplitude exists over which the vortex exhibits distinct regime transitions between a strong, vacillating state and a state in which the vortex is weak and the zonal mean polar flow nearly zero. Comparison with observational reanalysis suggest that the vacillation cycles obtained here may be relevant to the dynamics of some sudden warming events and that the onset of a radiatively dominated regime may be usefully linked to the loss of vortex area following such an event.
Fri, 01 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/108872016-07-01T00:00:00ZScott, Richard KirknessA new class of persistent vacillations of the winter polar vortex, under the action of topographic wave forcing and radiative cooling, is identified in numerical integrations of the rotating shallow water equations. The vacillations are obtained provided only that care is taken to prevent the unconstrained growth of tropical easterlies that otherwise develop as the result of persistent angular momentum deposition at low latitudes. The vacillation cycle involves purely barotropic dynamics and is characterized by a dynamically controlled rapid splitting and rapid reformation of the vortex followed by a more gradual period of vortex intensification under the influence of radiative relaxation. The onset of the splitting occurs when the frequency of the free mode of the vortex approaches that of the forcing and resembles a resonant excitation. Experiments with an alternative basic state suggest that the vacillations are a robust feature of the topographically forced and radiatively relaxed vortex. In contrast to the behavior found in models with vertical structure, the period of the vacillation cycles here increases with increasing forcing amplitude. A wide range of forcing amplitude exists over which the vortex exhibits distinct regime transitions between a strong, vacillating state and a state in which the vortex is weak and the zonal mean polar flow nearly zero. Comparison with observational reanalysis suggest that the vacillation cycles obtained here may be relevant to the dynamics of some sudden warming events and that the onset of a radiatively dominated regime may be usefully linked to the loss of vortex area following such an event.Rebuilding beluga stocks in West Greenland
http://hdl.handle.net/10023/10882
Decisions about sustainable exploitation levels of marine resources are often based on inadequate data, but are nevertheless required for practical purposes. We describe one exception where abundance estimates spanning 30 years and catch data spanning more than 40 years were used in a Bayesian assessment model of belugas Delphinapterus leucas off West Greenland. The model was updated with data from a visual aerial survey on the wintering ground in 2012. Methods that take account of stochastic animal availability by using independent estimates of forward and perpendicular sighting distances were used to estimate beluga abundance. A model that appears to be robust to the presence of a few large groups yielded an estimate of 7456 belugas (cv = 0.44), similar to a conventional distance-sampling estimate. A mark–recapture distance analysis that corrects for perception and availability bias estimated the abundance to be 9072 whales (cv = 0.32). Increasing distance of beluga sightings from shore was correlated with decreasing sea ice cover, suggesting that belugas expand their distribution offshore (i.e. westward in this context) with the reduction of coastal sea ice. A model with high (0.98) adult survival estimated a decline from 18 600 (90% CI: 13 400, 26 000) whales in 1970 to 8000 (90% CI: 5830, 11 200) in 2004. The decline was probably a result of a period with exceptionally large catches. Following the introduction of catch limits in 2004, the model projects an increase to 11 600 (90% CI: 6760, 17 600) individuals in 2020 (assuming annual removals of 294 belugas after 2014). If the annual removal level is fixed at 300 individuals, a low-survival (0.97) model predicts a 75% probability of an increasing population during 2015–2020. Reduced removal rates due to catch limits and the more offshore, less accessible distribution of the whales are believed to be responsible for the initial signs of population recovery.
This study was funded by the Greenland Bureau of Minerals and Petroleum, the Danish Cooperation of the Environment in the Arctic (DANCEA, Danish Ministry of the Environment) and the Greenland Institute of Natural Resources.
Fri, 11 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/108822016-11-11T00:00:00ZHeide-Jørgensen, M. P.Hansen, R. G.Fossette, S.Nielsen, N. H.Borchers, D. L.Stern, H.Witting, L.Decisions about sustainable exploitation levels of marine resources are often based on inadequate data, but are nevertheless required for practical purposes. We describe one exception where abundance estimates spanning 30 years and catch data spanning more than 40 years were used in a Bayesian assessment model of belugas Delphinapterus leucas off West Greenland. The model was updated with data from a visual aerial survey on the wintering ground in 2012. Methods that take account of stochastic animal availability by using independent estimates of forward and perpendicular sighting distances were used to estimate beluga abundance. A model that appears to be robust to the presence of a few large groups yielded an estimate of 7456 belugas (cv = 0.44), similar to a conventional distance-sampling estimate. A mark–recapture distance analysis that corrects for perception and availability bias estimated the abundance to be 9072 whales (cv = 0.32). Increasing distance of beluga sightings from shore was correlated with decreasing sea ice cover, suggesting that belugas expand their distribution offshore (i.e. westward in this context) with the reduction of coastal sea ice. A model with high (0.98) adult survival estimated a decline from 18 600 (90% CI: 13 400, 26 000) whales in 1970 to 8000 (90% CI: 5830, 11 200) in 2004. The decline was probably a result of a period with exceptionally large catches. Following the introduction of catch limits in 2004, the model projects an increase to 11 600 (90% CI: 6760, 17 600) individuals in 2020 (assuming annual removals of 294 belugas after 2014). If the annual removal level is fixed at 300 individuals, a low-survival (0.97) model predicts a 75% probability of an increasing population during 2015–2020. Reduced removal rates due to catch limits and the more offshore, less accessible distribution of the whales are believed to be responsible for the initial signs of population recovery.On the correspondence from Bayesian log-linear modelling to logistic regression modelling with g-priors
http://hdl.handle.net/10023/10854
Consider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Within the Bayesian framework, the g-prior and mixtures of g-priors are commonly assigned to the parameters of a generalized linear model. We prove that assigning a g-prior (or a mixture of g-priors) to the parameters of a certain log-linear model designates a g-prior (or a mixture of g-priors) on the parameters of the corresponding logistic regression. By deriving an asymptotic result, and with numerical illustrations, we demonstrate that when a g-prior is adopted, this correspondence extends to the posterior distribution of the model parameters. Thus, it is valid to translate inferences from fitting a log-linear model to inferences within the logistic regression framework, with regard to the presence of main effects and interaction terms.
Thu, 18 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/108542017-05-18T00:00:00ZPapathomas, MichailConsider a set of categorical variables where at least one of them is binary. The log-linear model that describes the counts in the resulting contingency table implies a specific logistic regression model, with the binary variable as the outcome. Within the Bayesian framework, the g-prior and mixtures of g-priors are commonly assigned to the parameters of a generalized linear model. We prove that assigning a g-prior (or a mixture of g-priors) to the parameters of a certain log-linear model designates a g-prior (or a mixture of g-priors) on the parameters of the corresponding logistic regression. By deriving an asymptotic result, and with numerical illustrations, we demonstrate that when a g-prior is adopted, this correspondence extends to the posterior distribution of the model parameters. Thus, it is valid to translate inferences from fitting a log-linear model to inferences within the logistic regression framework, with regard to the presence of main effects and interaction terms.Topological graph inverse semigroups
http://hdl.handle.net/10023/10847
To every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E . These semigroups generalize polycyclic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, graph C⁎C⁎-algebras, and Toeplitz C⁎-algebras. We investigate topologies that turn G(E) into a topological semigroup. For instance, we show that in any such topology that is Hausdorff, G(E)∖{0} must be discrete for any directed graph E . On the other hand, G(E) need not be discrete in a Hausdorff semigroup topology, and for certain graphs E , G(E) admits a T1 semigroup topology in which G(E)∖{0} is not discrete. We also describe, in various situations, the algebraic structure and possible cardinality of the closure of G(E) in larger topological semigroups.
Michał Morayne was partially supported by NCN grant DEC-2011/01/B/ST1/01439 while this work was performed.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/108472016-08-01T00:00:00ZMesyan, Z.Mitchell, J. D.Morayne, M.Péresse, Y. H.To every directed graph E one can associate a graph inverse semigroup G(E), where elements roughly correspond to possible paths in E . These semigroups generalize polycyclic monoids, and they arise in the study of Leavitt path algebras, Cohn path algebras, graph C⁎C⁎-algebras, and Toeplitz C⁎-algebras. We investigate topologies that turn G(E) into a topological semigroup. For instance, we show that in any such topology that is Hausdorff, G(E)∖{0} must be discrete for any directed graph E . On the other hand, G(E) need not be discrete in a Hausdorff semigroup topology, and for certain graphs E , G(E) admits a T1 semigroup topology in which G(E)∖{0} is not discrete. We also describe, in various situations, the algebraic structure and possible cardinality of the closure of G(E) in larger topological semigroups.ℤ4-codes and their Gray map images as orthogonal arrays
http://hdl.handle.net/10023/10804
A classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over ℤ4 and their (usually non-linear) binary Gray map images.We show that Delsarte's observation extends to codes over arbitrary finite commutative rings with identity. Also, we show that the strength of the Gray map image of a ℤ4 code is one less than the minimum Lee weight of its Gray map image.
Sat, 01 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/108042017-07-01T00:00:00ZCameron, Peter JephsonKusuma, JosephineSolé, PatrickA classic result of Delsarte connects the strength (as orthogonal array) of a linear code with the minimum weight of its dual: the former is one less than the latter.Since the paper of Hammons et al., there is a lot of interest in codes over rings, especially in codes over ℤ4 and their (usually non-linear) binary Gray map images.We show that Delsarte's observation extends to codes over arbitrary finite commutative rings with identity. Also, we show that the strength of the Gray map image of a ℤ4 code is one less than the minimum Lee weight of its Gray map image.Rare events for the Manneville-Pomeau map
http://hdl.handle.net/10023/10742
We prove a dichotomy for Manneville-Pomeau maps ƒ : [0, 1] → [0, 1] : given any point ζ ε [0, 1] , either the Rare Events Point Processes (REPP), counting the number of exceedances, which correspond to entrances in balls around ζ, converge in distribution to a Poisson process; or the point ζ is periodic and the REPP converge in distribution to a compound Poisson process. Our method is to use inducing techniques for all points except 0 and its preimages, extending a recent result [HWZ14], and then to deal with the remaining points separately. The preimages of 0 are dealt with applying recent results in [AFV14]. The point ζ = 0 is studied separately because the tangency with the identity map at this point creates too much dependence, which causes severe clustering of exceedances. The Extremal Index, which measures the intensity of clustering, is equal to 0 at ζ = 0 , which ultimately leads to a degenerate limit distribution for the partial maxima of stochastic processes arising from the dynamics and for the usual normalising sequences. We prove that using adapted normalising sequences we can still obtain non-degenerate limit distributions at ζ = 0 .
Funding: CMUP (UID/MAT/00144/2013), which is funded by FCT (Portugal) with national (MEC) and European structural funds through the programs FEDER, under the partnership agreement PT2020.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/107422016-11-01T00:00:00ZFreitas, Ana Cristina MoreiraFreitas, JorgeTodd, MikeVaienti, SandroWe prove a dichotomy for Manneville-Pomeau maps ƒ : [0, 1] → [0, 1] : given any point ζ ε [0, 1] , either the Rare Events Point Processes (REPP), counting the number of exceedances, which correspond to entrances in balls around ζ, converge in distribution to a Poisson process; or the point ζ is periodic and the REPP converge in distribution to a compound Poisson process. Our method is to use inducing techniques for all points except 0 and its preimages, extending a recent result [HWZ14], and then to deal with the remaining points separately. The preimages of 0 are dealt with applying recent results in [AFV14]. The point ζ = 0 is studied separately because the tangency with the identity map at this point creates too much dependence, which causes severe clustering of exceedances. The Extremal Index, which measures the intensity of clustering, is equal to 0 at ζ = 0 , which ultimately leads to a degenerate limit distribution for the partial maxima of stochastic processes arising from the dynamics and for the usual normalising sequences. We prove that using adapted normalising sequences we can still obtain non-degenerate limit distributions at ζ = 0 .Bombs and flares at the surface and lower atmosphere of the Sun
http://hdl.handle.net/10023/10741
A spectacular manifestation of solar activity is the appearance of transient brightenings in the far wings of the Hα line, known as Ellerman bombs (EBs). Recent observations obtained by the Interface Region Imaging Spectrograph have revealed another type of plasma "bombs" (UV bursts) with high temperatures of perhaps up to 8 ×104 K within the cooler lower solar atmosphere. Realistic numerical modeling showing such events is needed to explain their nature. Here, we report on 3D radiative magnetohydrodynamic simulations of magnetic flux emergence in the solar atmosphere. We find that ubiquitous reconnection between emerging bipolar magnetic fields can trigger EBs in the photosphere, UV bursts in the mid/low chromosphere and small (nano-/micro-) flares (106 K) in the upper chromosphere. These results provide new insights into the emergence and build up of the coronal magnetic field and the dynamics and heating of the solar surface and lower atmosphere.
This research was supported by the Research Council of Norway and by the European Research Council under the European Union's Seventh Framework Programme (FP7/2007–2013)/ERC Grant agreement no. 291058.
Mon, 10 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/107412017-04-10T00:00:00ZHansteen, V. H.Archontis, V.Pereira, T. M. D.Carlsson, M.Rouppe van der Voort, L.Leenaarts, J.A spectacular manifestation of solar activity is the appearance of transient brightenings in the far wings of the Hα line, known as Ellerman bombs (EBs). Recent observations obtained by the Interface Region Imaging Spectrograph have revealed another type of plasma "bombs" (UV bursts) with high temperatures of perhaps up to 8 ×104 K within the cooler lower solar atmosphere. Realistic numerical modeling showing such events is needed to explain their nature. Here, we report on 3D radiative magnetohydrodynamic simulations of magnetic flux emergence in the solar atmosphere. We find that ubiquitous reconnection between emerging bipolar magnetic fields can trigger EBs in the photosphere, UV bursts in the mid/low chromosphere and small (nano-/micro-) flares (106 K) in the upper chromosphere. These results provide new insights into the emergence and build up of the coronal magnetic field and the dynamics and heating of the solar surface and lower atmosphere.Uniform scaling limits for ergodic measures
http://hdl.handle.net/10023/10724
We provide an elementary proof that ergodic measures on one-sided shift spaces are ‘uniformly scaling’ in the following sense: at almost every point the scenery distributions weakly converge to a common distribution on the space of measures. Moreover, we show how the limiting distribution can be expressed in terms of, and derived from, a 'reverse Jacobian’ function associated with the corresponding measure on the space of left infinite sequences. Finally we specialise to the setting of Gibbs measures, discuss some statistical properties, and prove a Central Limit Theorem for ergodic Markov measures.
J. M. Fraser and M. Pollicott were financially supported in part by the EPSRC grant EP/J013560/1.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/107242017-01-01T00:00:00ZFraser, Jonathan MacDonaldPollicott, MarkWe provide an elementary proof that ergodic measures on one-sided shift spaces are ‘uniformly scaling’ in the following sense: at almost every point the scenery distributions weakly converge to a common distribution on the space of measures. Moreover, we show how the limiting distribution can be expressed in terms of, and derived from, a 'reverse Jacobian’ function associated with the corresponding measure on the space of left infinite sequences. Finally we specialise to the setting of Gibbs measures, discuss some statistical properties, and prove a Central Limit Theorem for ergodic Markov measures.Foraging behaviour, swimming performance and malformations of early stages of commercially important fishes under ocean acidification and warming
http://hdl.handle.net/10023/10703
Early life stages of many marine organisms are being challenged by climate change, but little is known about their capacity to tolerate future ocean conditions. Here we investigated a comprehensive set of biological responses of larvae of two commercially important teleost fishes, Sparus aurata (gilthead seabream) and Argyrosomus regius (meagre), after exposure to future predictions of ocean warming (+4 °C) and acidification (ΔpH = 0.5). The combined effect of warming and hypercapnia elicited a decrease in the hatching success (by 26.4 and 14.3 % for S. aurata and A. regius, respectively) and larval survival (by half) in both species. The length for newly-hatched larvae was not significantly affected, but a significant effect of hypercapnia was found on larval growth. However, while S. aurata growth was reduced (24.8–36.4 % lower), A. regius growth slightly increased (3.2–12.9 % higher) under such condition. Under acidification, larvae of both species spent less time swimming, and displayed reduced attack and capture rates of prey. The impact of warming on these behavioural traits was opposite but less evident. While not studied in A. regius, the incidence of body malformations in S. aurata larvae increased significantly (more than tripled) under warmer and hypercapnic conditions. These morphological impairments and behavioural changes are expected to affect larval performance and recruitment success, and further influence the abundance of fish stocks and the population structure of these commercially important fish species. However, given the pace of ocean climate change, it is important not to forget that species may have the opportunity to acclimate and adapt.
The Portuguese Foundation for Science and Technology (FCT) supported this study through doctoral grants to M.S.P. and G.D. (SFRH/BD/81928/2011 and SFRH/BD/73205/2010, respectively), a post-doc grant to F.F. (SFRH/BPD/79038/2011), and project grants to P.P.F. (AQUACOR-PROMAR31-03-05FEP-003) and R.R. (PTDC/MAR/0908066/2008 and PTDC/AAGGLO/3342/2012).
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/107032016-08-01T00:00:00ZPimentel, Marta S.Faleiro, FilipaMarques, TiagoBispo, ReginaDionísio, GiselaFaria, Ana M.Machado, JorgePeck, Myron A.Pörtner, HansPousão-Ferreira, PedroGonçalves, Emanuel J.Rosa, RuiEarly life stages of many marine organisms are being challenged by climate change, but little is known about their capacity to tolerate future ocean conditions. Here we investigated a comprehensive set of biological responses of larvae of two commercially important teleost fishes, Sparus aurata (gilthead seabream) and Argyrosomus regius (meagre), after exposure to future predictions of ocean warming (+4 °C) and acidification (ΔpH = 0.5). The combined effect of warming and hypercapnia elicited a decrease in the hatching success (by 26.4 and 14.3 % for S. aurata and A. regius, respectively) and larval survival (by half) in both species. The length for newly-hatched larvae was not significantly affected, but a significant effect of hypercapnia was found on larval growth. However, while S. aurata growth was reduced (24.8–36.4 % lower), A. regius growth slightly increased (3.2–12.9 % higher) under such condition. Under acidification, larvae of both species spent less time swimming, and displayed reduced attack and capture rates of prey. The impact of warming on these behavioural traits was opposite but less evident. While not studied in A. regius, the incidence of body malformations in S. aurata larvae increased significantly (more than tripled) under warmer and hypercapnic conditions. These morphological impairments and behavioural changes are expected to affect larval performance and recruitment success, and further influence the abundance of fish stocks and the population structure of these commercially important fish species. However, given the pace of ocean climate change, it is important not to forget that species may have the opportunity to acclimate and adapt.Elongation of flare ribbons
http://hdl.handle.net/10023/10686
We present an analysis of the apparent elongation motion of flare ribbons along the polarity inversion line (PIL), as well as the shear of flare loops in several two-ribbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s-1. The shear measured from conjugate footpoints is consistent with the measurement from flare loops, and both show the decrease of shear toward a potential field as a flare evolves and ribbons and loops spread along the PIL. Flares exhibiting fast bidirectional elongation appear to have a strong shear, which may indicate a large magnetic guide field relative to the reconnection field in the coronal current sheet. We discuss how the analysis of ribbon motion could help infer properties in the corona where reconnection takes place.
J.Q., D.W.L., and P.A.C. gratefully acknowledge support by NSF SHINE collaborative grant AGS-1460059.
Mon, 20 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/106862017-03-20T00:00:00ZQiu, JiongLongcope, Dana W.Cassak, Paul A.Priest, Eric R.We present an analysis of the apparent elongation motion of flare ribbons along the polarity inversion line (PIL), as well as the shear of flare loops in several two-ribbon flares. Flare ribbons and loops spread along the PIL at a speed ranging from a few to a hundred km s-1. The shear measured from conjugate footpoints is consistent with the measurement from flare loops, and both show the decrease of shear toward a potential field as a flare evolves and ribbons and loops spread along the PIL. Flares exhibiting fast bidirectional elongation appear to have a strong shear, which may indicate a large magnetic guide field relative to the reconnection field in the coronal current sheet. We discuss how the analysis of ribbon motion could help infer properties in the corona where reconnection takes place.The role of spatial variations of abiotic factors in mediating intratumour phenotypic heterogeneity
http://hdl.handle.net/10023/10685
A growing body of evidence indicates that the progression of cancer can be viewed as an eco-evolutionary process. Under this perspective, we present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours.
CV wishes to acknowledge partial support from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. AL was supported by King Abdullah University of Science and Technology (KAUST) baseline and start-up funds (BAS/1/1648-01-01 and BAS/1/1648-01-02). MAJC gratefully acknowledge support of EPSRC grant no. EP/N014642/1.
Thu, 20 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/106852017-04-20T00:00:00ZLorenzi, TommasoVenkataraman, ChandrasekharLorz, AlexanderChaplain, Mark A. J.A growing body of evidence indicates that the progression of cancer can be viewed as an eco-evolutionary process. Under this perspective, we present here a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of abiotic components of the tumour microenvironment in mediating phenotypic selection of cancer cells. Numerical simulations are performed both on the 3D geometry of an in silico multicellular tumour spheroid and on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. The results obtained show that inhomogeneities in the spatial distribution of oxygen, currently observed in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. This process fosters the emergence of stable phenotypic heterogeneity and supports the presence of hypoxic cells resistant to cytotoxic therapy prior to treatment. Our theoretical results demonstrate the importance of integrating spatial data with ecological principles when evaluating the therapeutic response of solid tumours.Extrapolating cetacean densities to quantitatively assess human impacts on populations in the high seas
http://hdl.handle.net/10023/10682
As human activities expand beyond national jurisdictions to the high seas, there is an increasing need to consider anthropogenic impacts to species inhabiting these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of population-level impacts of these activities. We developed plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extended from a well-surveyed region within the U.S. Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa with available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we mapped where predictions were made outside sampled covariate ranges, examined alternate models, and compared predicted densities with maps of sightings from sources that could not be integrated into our models. Confidence levels in model results depended on the taxon and geographic area and highlighted the need for additional surveying in environmentally distinct areas. With application of necessary caution, our density estimates can inform management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, and deep-sea mining and be used to delineate areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse.
Funding for this study came from the U.S. Fleet Forces Command (Cooperative Agreement N62470-13-2-8008), NASA (NNX08AK73G) and NOAA/NMFS (EE-133F-14-SE-3558).
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/106822017-06-01T00:00:00ZMannocci, LauraRoberts, Jason J.Miller, David L.Halpin, Patrick N.As human activities expand beyond national jurisdictions to the high seas, there is an increasing need to consider anthropogenic impacts to species inhabiting these waters. The current scarcity of scientific observations of cetaceans in the high seas impedes the assessment of population-level impacts of these activities. We developed plausible density estimates to facilitate a quantitative assessment of anthropogenic impacts on cetacean populations in these waters. Our study region extended from a well-surveyed region within the U.S. Exclusive Economic Zone into a large region of the western North Atlantic sparsely surveyed for cetaceans. We modeled densities of 15 cetacean taxa with available line transect survey data and habitat covariates and extrapolated predictions to sparsely surveyed regions. We formulated models to reduce the extent of extrapolation beyond covariate ranges, and constrained them to model simple and generalizable relationships. To evaluate confidence in the predictions, we mapped where predictions were made outside sampled covariate ranges, examined alternate models, and compared predicted densities with maps of sightings from sources that could not be integrated into our models. Confidence levels in model results depended on the taxon and geographic area and highlighted the need for additional surveying in environmentally distinct areas. With application of necessary caution, our density estimates can inform management needs in the high seas, such as the quantification of potential cetacean interactions with military training exercises, shipping, fisheries, and deep-sea mining and be used to delineate areas of special biological significance in international waters. Our approach is generally applicable to other marine taxa and geographic regions for which management will be implemented but data are sparse.Highest rank of a polytope for An
http://hdl.handle.net/10023/10678
We prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n=5, 4 if n=9, 5 if n=10, 6 if n=11, and ⌊(n−1)/2⌋ if n⩾12. Moreover, if n=3,4,6,7, or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.
This research was supported by a Marsden grant (UOA1218) of the Royal Society of New Zealand, and by the Portuguese Foundation for Science and Technology (FCT-Fundação para a Ciência e a Tecnologia), through CIDMA - Center for Research and Development in Mathematics and Applications, within project UID/MAT/04106/2013.
Tue, 04 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/106782017-07-04T00:00:00ZCameron, Peter J.Fernandes, Maria ElisaLeemans, DimitriMixer, MarkWe prove that the highest rank of a string C-group constructed from an alternating group An is 3 if n=5, 4 if n=9, 5 if n=10, 6 if n=11, and ⌊(n−1)/2⌋ if n⩾12. Moreover, if n=3,4,6,7, or 8, the group An is not a string C-group. This solves a conjecture made by the last three authors in 2012.Multifractal zeta functions
http://hdl.handle.net/10023/10637
Multifractals have during the past 20 − 25 years been the focus of enormous attention in the mathematical literature. Loosely speaking there are two main ingredients in multifractal analysis: the multifractal spectra and the Renyi dimensions. One of the main goals in multifractal analysis is to understand these two ingredients and their relationship with each other. Motivated by the powerful techniques provided by the use of the Artin-Mazur zeta-functions in number theory and the use of the Ruelle zeta-functions in dynamical systems, Lapidus and collaborators (see books by Lapidus & van Frankenhuysen [32, 33] and the references therein) have introduced and pioneered use of zeta-functions in fractal geometry. Inspired by this development, within the past 7−8 years several authors have paralleled this development by introducing zeta-functions into multifractal geometry. Our result inspired by this work will be given in section 2.2.2. There we introduce geometric multifractal zeta-functions providing precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. Results in that section are based on paper [37].
Dynamical zeta-functions have been introduced and developed by Ruelle [63, 64] and others, (see, for example, the surveys and books [3, 54, 55] and the references therein). It has been a major challenge to introduce and develop a natural and meaningful theory of dynamical multifractal zeta-functions paralleling existing theory of dynamical zeta functions. In particular, in the setting of self-conformal constructions, Olsen [49] introduced a family of dynamical multifractal zeta-functions designed to provide precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. However, recently it has been recognised that while self-conformal constructions provide a useful and important framework for studying fractal and multifractal geometry, the more general notion of graph-directed self-conformal constructions provide a substantially more flexible and useful framework, see, for example, [36] for an elaboration of this. In recognition of this viewpoint, in section 2.3.11 we provide main definitions of the multifractal pressure and the multifractal dynamical zeta-functions and we state our main results. This section is based on paper [38].
Setting we are working unifies various different multifractal spectra including fine multifractal spectra of self-conformal measures or Birkhoff averages of continuous function. It was introduced by Olsen in [43]. In section 2.1 we propose answer to problem of defining Renyi spectra in more general settings and provide slight improvement of result regrading multifractal spectra in the case of Subshift of finite type.
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/106372017-06-23T00:00:00ZMijović, VuksanMultifractals have during the past 20 − 25 years been the focus of enormous attention in the mathematical literature. Loosely speaking there are two main ingredients in multifractal analysis: the multifractal spectra and the Renyi dimensions. One of the main goals in multifractal analysis is to understand these two ingredients and their relationship with each other. Motivated by the powerful techniques provided by the use of the Artin-Mazur zeta-functions in number theory and the use of the Ruelle zeta-functions in dynamical systems, Lapidus and collaborators (see books by Lapidus & van Frankenhuysen [32, 33] and the references therein) have introduced and pioneered use of zeta-functions in fractal geometry. Inspired by this development, within the past 7−8 years several authors have paralleled this development by introducing zeta-functions into multifractal geometry. Our result inspired by this work will be given in section 2.2.2. There we introduce geometric multifractal zeta-functions providing precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. Results in that section are based on paper [37].
Dynamical zeta-functions have been introduced and developed by Ruelle [63, 64] and others, (see, for example, the surveys and books [3, 54, 55] and the references therein). It has been a major challenge to introduce and develop a natural and meaningful theory of dynamical multifractal zeta-functions paralleling existing theory of dynamical zeta functions. In particular, in the setting of self-conformal constructions, Olsen [49] introduced a family of dynamical multifractal zeta-functions designed to provide precise information of very general classes of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. However, recently it has been recognised that while self-conformal constructions provide a useful and important framework for studying fractal and multifractal geometry, the more general notion of graph-directed self-conformal constructions provide a substantially more flexible and useful framework, see, for example, [36] for an elaboration of this. In recognition of this viewpoint, in section 2.3.11 we provide main definitions of the multifractal pressure and the multifractal dynamical zeta-functions and we state our main results. This section is based on paper [38].
Setting we are working unifies various different multifractal spectra including fine multifractal spectra of self-conformal measures or Birkhoff averages of continuous function. It was introduced by Olsen in [43]. In section 2.1 we propose answer to problem of defining Renyi spectra in more general settings and provide slight improvement of result regrading multifractal spectra in the case of Subshift of finite type.Planar self-affine sets with equal Hausdorff, box and affinity dimensions
http://hdl.handle.net/10023/10634
Using methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.
Thu, 20 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/106342016-10-20T00:00:00ZFalconer, KennethKempton, Thomas Michael WilliamUsing methods from ergodic theory along with properties of the Furstenberg measure we obtain conditions under which certain classes of plane self-affine sets have Hausdorff or box-counting dimensions equal to their affinity dimension. We exhibit some new specific classes of self-affine sets for which these dimensions are equal.Estimating Key Largo woodrat abundance using spatially explicit capture–recapture and trapping point transects
http://hdl.handle.net/10023/10625
The Key Largo woodrat (Neotoma floridana smalli) is an endangered rodent with a restricted geographic range and small population size. Establishing an efficient monitoring program of its abundance has been problematic; previous trapping designs have not worked well because the species is sparsely distributed. We compared Key Largo woodrat abundance estimates in Key Largo, Florida, USA, obtained using trapping point transects (TPT) and spatially explicit capture–recapture (SECR) based on statistical properties, survey effort, practicality, and cost. Both methods combine aspects of distance sampling with capture–recapture, but TPT relies on radiotracking individuals to estimate detectability and SECR relies on repeat capture information to estimate densities of home ranges. Abundance estimates using TPT in the spring of 2007 and 2008 were 333 woodrats (CV = 0.46) and 696 (CV = 0.43), respectively. Abundance estimates using SECR in the spring, summer, and winter of 2007 were 97 (CV = 0.31), 334 (CV = 0.26), and 433 (CV = 0.20) animals, respectively. Trapping point transects used approximately 960 person-hours and 1,010 trap-nights/season. Spatially explicit capture–recapture used approximately 500 person-hours and 6,468 trap-nights/season. Significant time was saved in the SECR survey by setting large numbers of traps close together, minimizing time walking between traps. Trapping point transects were practical to implement in the field, and valuable auxiliary information on Key Largo woodrat behavior was obtained via radiocollaring. In this particular study, detectability of the woodrat using TPT was very low and consequently the SECR method was more efficient. Both methods require a substantial investment in survey effort to detect any change in abundance because of large uncertainty in estimates.
JMP was funded by Disney's Animal Programs, the US Fish and Wildlife Service and University of St Andrews.
Sun, 17 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/106252016-04-17T00:00:00ZPotts, Joanne MarieBuckland, Stephen TerrenceThomas, LenSavage, AnneThe Key Largo woodrat (Neotoma floridana smalli) is an endangered rodent with a restricted geographic range and small population size. Establishing an efficient monitoring program of its abundance has been problematic; previous trapping designs have not worked well because the species is sparsely distributed. We compared Key Largo woodrat abundance estimates in Key Largo, Florida, USA, obtained using trapping point transects (TPT) and spatially explicit capture–recapture (SECR) based on statistical properties, survey effort, practicality, and cost. Both methods combine aspects of distance sampling with capture–recapture, but TPT relies on radiotracking individuals to estimate detectability and SECR relies on repeat capture information to estimate densities of home ranges. Abundance estimates using TPT in the spring of 2007 and 2008 were 333 woodrats (CV = 0.46) and 696 (CV = 0.43), respectively. Abundance estimates using SECR in the spring, summer, and winter of 2007 were 97 (CV = 0.31), 334 (CV = 0.26), and 433 (CV = 0.20) animals, respectively. Trapping point transects used approximately 960 person-hours and 1,010 trap-nights/season. Spatially explicit capture–recapture used approximately 500 person-hours and 6,468 trap-nights/season. Significant time was saved in the SECR survey by setting large numbers of traps close together, minimizing time walking between traps. Trapping point transects were practical to implement in the field, and valuable auxiliary information on Key Largo woodrat behavior was obtained via radiocollaring. In this particular study, detectability of the woodrat using TPT was very low and consequently the SECR method was more efficient. Both methods require a substantial investment in survey effort to detect any change in abundance because of large uncertainty in estimates.Bystander effects and their implications for clinical radiation therapy : insights from multiscale in silico experiments
http://hdl.handle.net/10023/10615
Radiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this article, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiation-induced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses that are not obtained using a traditional radiobiological model.
GGP and MAJC thank University of Dundee, where this research was carried out. The authors gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, M5CGS - From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread. AJM Acknowledges support from EU BIOMICS Project DG-CNECT Contract 318202.
Thu, 21 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/106152016-07-21T00:00:00ZPowathil, GibinMunro, Alastair JohnChaplain, Mark Andrew JosephSwat, MaciejRadiotherapy is a commonly used treatment for cancer and is usually given in varying doses. At low radiation doses relatively few cells die as a direct response to radiation but secondary radiation effects, such as DNA mutation or bystander phenomena, may affect many cells. Consequently it is at low radiation levels where an understanding of bystander effects is essential in designing novel therapies with superior clinical outcomes. In this article, we use a hybrid multiscale mathematical model to study the direct effects of radiation as well as radiation-induced bystander effects on both tumour cells and normal cells. We show that bystander responses play a major role in mediating radiation damage to cells at low-doses of radiotherapy, doing more damage than that due to direct radiation. The survival curves derived from our computational simulations showed an area of hyper-radiosensitivity at low-doses that are not obtained using a traditional radiobiological model.Late summer distribution and abundance of ice-associated whales in the Norwegian High Arctic
http://hdl.handle.net/10023/10595
The Arctic is experiencing rapid warming, and resultant sea ice losses represent a serious threat to ice-associated species in the region. This study explored the distribution and abundance of the 3 Arctic resident whale species: narwhals, bowhead and white whales, in the marginal ice zone and into the sea ice north of the Svalbard Archipelago. Line-transect surveys were conducted using a combination of helicopter-based and ship-based efforts in August 2015. Twenty-six sightings, involving 27 bowhead whales and 58 narwhals, occurred along the helicopter transects, while no whales were recorded along ship transects. No white whales were observed during these surveys. After correcting for surface availability, distance sampling produced abundance estimates of 343 (CV = 0.488) bowhead whales and 837 (CV = 0.501) narwhals within the 52 919 km(2) study area. Bowhead whales were predominantly seen close to the ice-edge, whereas narwhals were located deeper into the ice. To contextualize these results within the broader Svalbard cetacean community, all whale sightings from the Norwegian Polar Institute's Svalbard Marine Mammal Sighting Data Base, from the period of the survey, were mapped to compare general distributions. These opportunistic sightings included numerous cetacean species, especially seasonally occurring ones. However, white whales dominated in terms of the numbers of individuals reported. Our results suggest little spatial overlap between seasonally occurring whales and the 3 Arctic resident whales. Bowhead whales and narwhals were tightly associated with sea ice, and white whales were tightly coastal. In contrast, the seasonally occurring species were found over the shelf and along its edges.
This study was financed by the Norwegian Research Council ICE whales grant (No. 244488/E10), The Foreign Ministry of Norway (Norwegian-Russian programme), WWF Sweden and the Norwegian Polar Institute. T.A.M. was supported in part by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013).
Tue, 07 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/105952017-02-07T00:00:00ZVacquié-Garcia, JadeLydersen, ChristianMarques, Tiago A.Aars, JonAhonen, HeidiSkern-Mauritzen, MetteØien, NilsKovacs, Kit M.The Arctic is experiencing rapid warming, and resultant sea ice losses represent a serious threat to ice-associated species in the region. This study explored the distribution and abundance of the 3 Arctic resident whale species: narwhals, bowhead and white whales, in the marginal ice zone and into the sea ice north of the Svalbard Archipelago. Line-transect surveys were conducted using a combination of helicopter-based and ship-based efforts in August 2015. Twenty-six sightings, involving 27 bowhead whales and 58 narwhals, occurred along the helicopter transects, while no whales were recorded along ship transects. No white whales were observed during these surveys. After correcting for surface availability, distance sampling produced abundance estimates of 343 (CV = 0.488) bowhead whales and 837 (CV = 0.501) narwhals within the 52 919 km(2) study area. Bowhead whales were predominantly seen close to the ice-edge, whereas narwhals were located deeper into the ice. To contextualize these results within the broader Svalbard cetacean community, all whale sightings from the Norwegian Polar Institute's Svalbard Marine Mammal Sighting Data Base, from the period of the survey, were mapped to compare general distributions. These opportunistic sightings included numerous cetacean species, especially seasonally occurring ones. However, white whales dominated in terms of the numbers of individuals reported. Our results suggest little spatial overlap between seasonally occurring whales and the 3 Arctic resident whales. Bowhead whales and narwhals were tightly associated with sea ice, and white whales were tightly coastal. In contrast, the seasonally occurring species were found over the shelf and along its edges.Assigning stranded bottlenose dolphins to source stocks using stable isotope ratios following the Deepwater Horizon oil spill
http://hdl.handle.net/10023/10588
The potential for stranded dolphins to serve as a tool for monitoring free-ranging populations would be enhanced if their stocks of origin were known. We used stable isotopes of carbon, nitrogen, and sulfur from skin to assign stranded bottlenose dolphins Tursiops truncatus to different habitats, as a proxy for stocks (demographically independent populations), following the Deepwater Horizon oil spill. Model results from biopsy samples collected from dolphins from known habitats (n = 205) resulted in an 80.5% probability of correct assignment. These results were applied to data from stranded dolphins (n = 217), resulting in predicted assignment probabilities of 0.473, 0.172, and 0.355 to Estuarine, Barrier Island (BI), and Coastal stocks, respectively. Differences were found west and east of the Mississippi River, with more Coastal dolphins stranding in western Louisiana and more Estuarine dolphins stranding in Mississippi. Within the Estuarine East Stock, 2 groups were identified, one predominantly associated with Mississippi and Alabama estuaries and another with western Florida. δ15N values were higher in stranded samples for both Estuarine and BI stocks, potentially indicating nutritional stress. High probabilities of correct assignment of the biopsy samples indicate predictable variation in stable isotopes and fidelity to habitat. The power of δ34S to discriminate habitats relative to salinity was essential. Stable isotopes may provide guidance regarding where additional testing is warranted to confirm demographic independence and aid in determining the source habitat of stranded dolphins, thus increasing the value of biological data collected from stranded individuals.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/105882017-01-31T00:00:00ZHohn, A. A.Thomas, L.Carmichael, R. H.Litz, J.Clemons-Chevis, C.Shippee, S. F.Sinclair, C.Smith, S.Speakman, T. R.Tumlin, M. C.Zolman, E. S.The potential for stranded dolphins to serve as a tool for monitoring free-ranging populations would be enhanced if their stocks of origin were known. We used stable isotopes of carbon, nitrogen, and sulfur from skin to assign stranded bottlenose dolphins Tursiops truncatus to different habitats, as a proxy for stocks (demographically independent populations), following the Deepwater Horizon oil spill. Model results from biopsy samples collected from dolphins from known habitats (n = 205) resulted in an 80.5% probability of correct assignment. These results were applied to data from stranded dolphins (n = 217), resulting in predicted assignment probabilities of 0.473, 0.172, and 0.355 to Estuarine, Barrier Island (BI), and Coastal stocks, respectively. Differences were found west and east of the Mississippi River, with more Coastal dolphins stranding in western Louisiana and more Estuarine dolphins stranding in Mississippi. Within the Estuarine East Stock, 2 groups were identified, one predominantly associated with Mississippi and Alabama estuaries and another with western Florida. δ15N values were higher in stranded samples for both Estuarine and BI stocks, potentially indicating nutritional stress. High probabilities of correct assignment of the biopsy samples indicate predictable variation in stable isotopes and fidelity to habitat. The power of δ34S to discriminate habitats relative to salinity was essential. Stable isotopes may provide guidance regarding where additional testing is warranted to confirm demographic independence and aid in determining the source habitat of stranded dolphins, thus increasing the value of biological data collected from stranded individuals.Quantifying injury to common bottlenose dolphins from the Deepwater Horizon oil spill using an age-, sex- and class-structured population model
http://hdl.handle.net/10023/10587
Field studies documented increased mortality, adverse health effects, and reproductive failure in common bottlenose dolphins Tursiops truncatus following the Deepwater Horizon (DWH) oil spill. In order to determine the appropriate type and amount of restoration needed to compensate for losses, the overall extent of injuries to dolphins had to be quantified. Simply counting dead individuals does not consider long-term impacts to populations, such as the loss of future reproductive potential from mortality of females, or the chronic health effects that continue to compromise survival long after acute effects subside. Therefore, we constructed a sex- and agestructured model of population growth and included additional class structure to represent dolphins exposed and unexposed to DWH oil. The model was applied for multiple stocks to predict injured population trajectories using estimates of post-spill survival and reproductive rates. Injured trajectories were compared to baseline trajectories that were expected had the DWH incident not occurred. Two principal measures of injury were computed: (1) lost cetacean years (LCY); the difference between baseline and injured population size, summed over the modeled time period, and (2) time to recovery; the number of years for the stock to recover to within 95% of baseline. For the dolphin stock in Barataria Bay, Louisiana, the estimated LCY was substantial: 30 347 LCY (95% CI: 11 511 to 89 746). Estimated time to recovery was 39 yr (95% CI: 24 to 80). Similar recovery timelines were predicted for stocks in the Mississippi River Delta, Mississippi Sound, Mobile Bay and the Northern Coastal Stock.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/105872017-01-31T00:00:00ZSchwacke, Lori H.Thomas, LenWells, Randall S.McFee, Wayne E.Hohn, Aleta A.Mullin, Keith D.Zolman, Eric S.Quigley, Brian M.Rowles, Teri K.Schwacke, John H.Field studies documented increased mortality, adverse health effects, and reproductive failure in common bottlenose dolphins Tursiops truncatus following the Deepwater Horizon (DWH) oil spill. In order to determine the appropriate type and amount of restoration needed to compensate for losses, the overall extent of injuries to dolphins had to be quantified. Simply counting dead individuals does not consider long-term impacts to populations, such as the loss of future reproductive potential from mortality of females, or the chronic health effects that continue to compromise survival long after acute effects subside. Therefore, we constructed a sex- and agestructured model of population growth and included additional class structure to represent dolphins exposed and unexposed to DWH oil. The model was applied for multiple stocks to predict injured population trajectories using estimates of post-spill survival and reproductive rates. Injured trajectories were compared to baseline trajectories that were expected had the DWH incident not occurred. Two principal measures of injury were computed: (1) lost cetacean years (LCY); the difference between baseline and injured population size, summed over the modeled time period, and (2) time to recovery; the number of years for the stock to recover to within 95% of baseline. For the dolphin stock in Barataria Bay, Louisiana, the estimated LCY was substantial: 30 347 LCY (95% CI: 11 511 to 89 746). Estimated time to recovery was 39 yr (95% CI: 24 to 80). Similar recovery timelines were predicted for stocks in the Mississippi River Delta, Mississippi Sound, Mobile Bay and the Northern Coastal Stock.Where were they from? Modelling the source stock of dolphins stranded after the Deepwater Horizon oil spill using genetic and stable isotope data
http://hdl.handle.net/10023/10586
Understanding the source stock of common bottlenose dolphins Tursiops truncatus that stranded in the northern Gulf of Mexico subsequent to the Deepwater Horizon oil spill was essential to accurately quantify injury and apportion individuals to the appropriate stock. The aim of this study, part of the Natural Resource Damage Assessment (NRDA), was to estimate the proportion of the 932 recorded strandings between May 2010 and June 2014 that came from coastal versus bay, sound and estuary (BSE) stocks. Four sources of relevant information were available on overlapping subsets totaling 336 (39%) of the strandings: genetic stock assignment, stable isotope ratios, photo-ID and individual genetic-ID. We developed a hierarchical Bayesian model for combining these sources that weighted each data source for each stranding according to a measure of estimated precision: the effective sample size (ESS). The photo- and genetic-ID data were limited and considered to potentially introduce biases, so these data sources were excluded from analyses used in the NRDA. Estimates were calculated separately in 3 regions: East (of the Mississippi outflow), West (of the Mississippi outflow through Vermilion Bay, Louisiana) and Western Louisiana (west of Vermilion Bay to the Texas-Louisiana border); the estimated proportions of coastal strandings were, respectively 0.215 (95% CI: 0.169-0.263), 0.016 (0.036-0.099) and 0.622 (0.487-0.803). This method represents a general approach for integrating multiple sources of information that have differing uncertainties.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/105862017-01-31T00:00:00ZThomas, L.Booth, C. G.Rosel, P. E.Hohn, A.Litz, J.Schwacke, L. H.Understanding the source stock of common bottlenose dolphins Tursiops truncatus that stranded in the northern Gulf of Mexico subsequent to the Deepwater Horizon oil spill was essential to accurately quantify injury and apportion individuals to the appropriate stock. The aim of this study, part of the Natural Resource Damage Assessment (NRDA), was to estimate the proportion of the 932 recorded strandings between May 2010 and June 2014 that came from coastal versus bay, sound and estuary (BSE) stocks. Four sources of relevant information were available on overlapping subsets totaling 336 (39%) of the strandings: genetic stock assignment, stable isotope ratios, photo-ID and individual genetic-ID. We developed a hierarchical Bayesian model for combining these sources that weighted each data source for each stranding according to a measure of estimated precision: the effective sample size (ESS). The photo- and genetic-ID data were limited and considered to potentially introduce biases, so these data sources were excluded from analyses used in the NRDA. Estimates were calculated separately in 3 regions: East (of the Mississippi outflow), West (of the Mississippi outflow through Vermilion Bay, Louisiana) and Western Louisiana (west of Vermilion Bay to the Texas-Louisiana border); the estimated proportions of coastal strandings were, respectively 0.215 (95% CI: 0.169-0.263), 0.016 (0.036-0.099) and 0.622 (0.487-0.803). This method represents a general approach for integrating multiple sources of information that have differing uncertainties.Survival, density, and abundance of common bottlenose dolphins in Barataria Bay (USA) following the Deepwater Horizon oil spill
http://hdl.handle.net/10023/10580
To assess potential impacts of the Deepwater Horizon oil spill in April 2010, we conducted boat-based photo-identification surveys for common bottlenose dolphins Tursiops truncatus in Barataria Bay, Louisiana, USA (~230 km2, located 167 km WNW of the spill center). Crews logged 838 h of survey effort along pre-defined routes on 10 occasions between late June 2010 and early May 2014. We applied a previously unpublished spatial version of the robust design capture-recapture model to estimate survival and density. This model used photo locations to estimate density in the absence of study area boundaries and to separate mortality from permanent emigration. To estimate abundance, we applied density estimates to saltwater (salinity > ~8 ppt) areas of the bay where telemetry data suggested that dolphins reside. Annual dolphin survival varied between 0.80 and 0.85 (95% CIs varied from 0.77 to 0.90) over 3 yr following the Deepwater Horizon spill. In 2 non-oiled bays (in Florida and North Carolina), historic survival averages approximately 0.95. From June to November 2010, abundance increased from 1300 (95% CI ± ~130) to 3100 (95% CI ± ~400), then declined and remained between ~1600 and ~2400 individuals until spring 2013. In fall 2013 and spring 2014, abundance increased again to approximately 3100 individuals. Dolphin abundance prior to the spill was unknown, but we hypothesize that some dolphins moved out of the sampled area, probably northward into marshes, prior to initiation of our surveys in late June 2010, and later immigrated back into the sampled area.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/105802017-01-31T00:00:00ZMcDonald, Trent L.Hornsby, Fawn E.Speakman, Todd R.Zolman, Eric S.Mullin, Keith D.Sinclair, CarrieRosel, Patricia E.Thomas, LenSchwacke, Lori H.To assess potential impacts of the Deepwater Horizon oil spill in April 2010, we conducted boat-based photo-identification surveys for common bottlenose dolphins Tursiops truncatus in Barataria Bay, Louisiana, USA (~230 km2, located 167 km WNW of the spill center). Crews logged 838 h of survey effort along pre-defined routes on 10 occasions between late June 2010 and early May 2014. We applied a previously unpublished spatial version of the robust design capture-recapture model to estimate survival and density. This model used photo locations to estimate density in the absence of study area boundaries and to separate mortality from permanent emigration. To estimate abundance, we applied density estimates to saltwater (salinity > ~8 ppt) areas of the bay where telemetry data suggested that dolphins reside. Annual dolphin survival varied between 0.80 and 0.85 (95% CIs varied from 0.77 to 0.90) over 3 yr following the Deepwater Horizon spill. In 2 non-oiled bays (in Florida and North Carolina), historic survival averages approximately 0.95. From June to November 2010, abundance increased from 1300 (95% CI ± ~130) to 3100 (95% CI ± ~400), then declined and remained between ~1600 and ~2400 individuals until spring 2013. In fall 2013 and spring 2014, abundance increased again to approximately 3100 individuals. Dolphin abundance prior to the spill was unknown, but we hypothesize that some dolphins moved out of the sampled area, probably northward into marshes, prior to initiation of our surveys in late June 2010, and later immigrated back into the sampled area.Markov-switching generalized additive models
http://hdl.handle.net/10023/10578
We consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/105782017-01-01T00:00:00ZLangrock, RolandKneib, ThomasGlennie, RichardMichelot, ThéoWe consider Markov-switching regression models, i.e. models for time series regression analyses where the functional relationship between covariates and response is subject to regime switching controlled by an unobservable Markov chain. Building on the powerful hidden Markov model machinery and the methods for penalized B-splines routinely used in regression analyses, we develop a framework for nonparametrically estimating the functional form of the effect of the covariates in such a regression model, assuming an additive structure of the predictor. The resulting class of Markov-switching generalized additive models is immensely flexible, and contains as special cases the common parametric Markov-switching regression models and also generalized additive and generalized linear models. The feasibility of the suggested maximum penalized likelihood approach is demonstrated by simulation. We further illustrate the approach using two real data applications, modelling (i) how sales data depend on advertising spending and (ii) how energy price in Spain depends on the Euro/Dollar exchange rate.Generating sets of finite groups
http://hdl.handle.net/10023/10576
We investigate the extent to which the exchange relation holds in finite groups G. We define a new equivalence relation ≡m, where two elements are equivalent if each can be substituted for the other in any generating set for G. We then refine this to a new sequence ≡(r)/m of equivalence relations by saying that x≡(r)/m y if each can be substituted for the other in any r-element generating set. The relations ≡(r)/m become finer as r increases, and we define a new group invariant ψ(G) to be the value of r at which they stabilise to ≡m. Remarkably, we are able to prove that if G is soluble then ψ(G) ∈ {d(G),d(G)+1}, where d(G) is the minimum number of generators of G, and to classify the finite soluble groups G for which ψ(G)=d(G). For insoluble G, we show that d(G) ≤ ψ(G) ≤ d(G)+5. However, we know of no examples of groups G for which ψ(G) > d(G)+1. As an application, we look at the generating graph of G, whose vertices are the elements of G, the edges being the 2-element generating sets. Our relation ≡(2)m enables us to calculate Aut(Γ(G)) for all soluble groups G of nonzero spread, and give detailed structural information about Aut(Γ(G)) in the insoluble case.
Sun, 02 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/105762017-04-02T00:00:00ZCameron, Peter JephsonLucchini, AndreaRoney-Dougal, Colva MaryWe investigate the extent to which the exchange relation holds in finite groups G. We define a new equivalence relation ≡m, where two elements are equivalent if each can be substituted for the other in any generating set for G. We then refine this to a new sequence ≡(r)/m of equivalence relations by saying that x≡(r)/m y if each can be substituted for the other in any r-element generating set. The relations ≡(r)/m become finer as r increases, and we define a new group invariant ψ(G) to be the value of r at which they stabilise to ≡m. Remarkably, we are able to prove that if G is soluble then ψ(G) ∈ {d(G),d(G)+1}, where d(G) is the minimum number of generators of G, and to classify the finite soluble groups G for which ψ(G)=d(G). For insoluble G, we show that d(G) ≤ ψ(G) ≤ d(G)+5. However, we know of no examples of groups G for which ψ(G) > d(G)+1. As an application, we look at the generating graph of G, whose vertices are the elements of G, the edges being the 2-element generating sets. Our relation ≡(2)m enables us to calculate Aut(Γ(G)) for all soluble groups G of nonzero spread, and give detailed structural information about Aut(Γ(G)) in the insoluble case.Mixed moments and local dimensions of measures
http://hdl.handle.net/10023/10568
We analyse the asymptotic behaviour of the mixed moments of Borel probability measures on [0,1]d. In particular, we prove that the asymptotic behaviour of the mixed moments of a measure is intimately related to the local dimensions of the measure.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/105682016-09-01T00:00:00ZOlsen, Lars Ole RonnowWe analyse the asymptotic behaviour of the mixed moments of Borel probability measures on [0,1]d. In particular, we prove that the asymptotic behaviour of the mixed moments of a measure is intimately related to the local dimensions of the measure.Particle acceleration due to coronal non-null magnetic reconnection
http://hdl.handle.net/10023/10551
Various topological features, for example magnetic null-points and separators, have been inferred as likely sites of magnetic reconnection and particle acceleration in the solar atmosphere. In fact, magnetic reconnection is not constrained to solely take place at or near such topological features and may also take place in the absence of such features. Studies of particle acceleration using non-topological reconnection experiments embedded in the solar atmosphere are uncommon. We aim to investigate and characterise particle behaviour in a model of magnetic reconnection which causes an arcade of solar coronal magnetic field to twist and form an erupting flux rope, crucially in the absence of any common topological features where reconnection is often thought to occur. We use a numerical scheme which evolves the gyro-averaged orbit equations of single electrons and protons in time and space, and simulate the gyromotion of particles in a fully analytical global field model. We observe and discuss how the magnetic and electric fields of the model and the initial conditions of each orbit may lead to acceleration of protons and electrons up to 2 MeV in energy (depending on model parameters). We describe the morphology of time-dependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of three-dimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during two-ribbon flare events.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/105512017-03-01T00:00:00ZThrelfall, James WilliamNeukirch, ThomasParnell, Clare ElizabethVarious topological features, for example magnetic null-points and separators, have been inferred as likely sites of magnetic reconnection and particle acceleration in the solar atmosphere. In fact, magnetic reconnection is not constrained to solely take place at or near such topological features and may also take place in the absence of such features. Studies of particle acceleration using non-topological reconnection experiments embedded in the solar atmosphere are uncommon. We aim to investigate and characterise particle behaviour in a model of magnetic reconnection which causes an arcade of solar coronal magnetic field to twist and form an erupting flux rope, crucially in the absence of any common topological features where reconnection is often thought to occur. We use a numerical scheme which evolves the gyro-averaged orbit equations of single electrons and protons in time and space, and simulate the gyromotion of particles in a fully analytical global field model. We observe and discuss how the magnetic and electric fields of the model and the initial conditions of each orbit may lead to acceleration of protons and electrons up to 2 MeV in energy (depending on model parameters). We describe the morphology of time-dependent acceleration and impact sites for each particle species and compare our findings to those recovered by topologically based studies of three-dimensional (3D) reconnection and particle acceleration. We also broadly compare aspects of our findings to general observational features typically seen during two-ribbon flare events.Blockage of saline intrusions in restricted, two-layer exchange flows across a submerged sill obstruction
http://hdl.handle.net/10023/10543
Results are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.
The work has been supported by European Community’s Seventh Framework Programme through the grant to the budget of the Integrating Activity HYDRALAB IV within the Transnational Access Activities, Contract No. 261520.
Thu, 23 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/105432017-03-23T00:00:00ZCuthbertson, AlanLaanearu, JanekCarr, MagdaSommeria, JoelViboud, SamuelResults are presented from a series of large-scale experiments investigating the internal and near-bed dynamics of bi-directional stratified flows with a net-barotropic component across a submerged, trapezoidal, sill obstruction. High-resolution velocity and density profiles are obtained in the vicinity of the obstruction to observe internal-flow dynamics under a range of parametric forcing conditions (i.e. variable saline and fresh water volume fluxes; density differences; sill obstruction submergence depths). Detailed synoptic velocity fields are measured across the sill crest using 2D particle image velocimetry, while the density structure of the two-layer exchange flows is measured using micro-conductivity probes at several sill locations. These measurements are designed to aid qualitative and quantitative interpretation of the internal-flow processes associated with the lower saline intrusion layer blockage conditions, and indicate that the primary mechanism for this blockage is mass exchange from the saline intrusion layer due to significant interfacial mixing and entrainment under dominant, net-barotropic, flow conditions in the upper freshwater layer. This interfacial mixing is quantified by considering both the isopycnal separation of vertically-sorted density profiles across the sill, as well as calculation of corresponding Thorpe overturning length scales. Analysis of the synoptic velocity fields and density profiles also indicates that the net exchange flow conditions remain subcritical (G < 1) across the sill for all parametric conditions tested. An analytical two-layer exchange flow model is then developed to include frictional and entrainment effects, both of which are needed to account for turbulent stresses and saline entrainment into the upper freshwater layer. The experimental results are used to validate two key model parameters: (1) the internal-flow head loss associated with boundary friction and interfacial shear; and (2) the mass exchange from the lower saline layer into the upper fresh layer due to entrainment.On the generating graph of a simple group
http://hdl.handle.net/10023/10539
The generating graph Γ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Γ(G) ≅ Γ(H) for a finite group G, then G ≅ H. We also prove that the generating graph of a symmetric group determines the group.
The authors were supported by Universita di Padova (Progetto di Ricerca di Ateneo: Invariable generation of groups). The second author was also supported by an Alexander von Humboldt Fellowship for Experienced Researchers, by OTKA grants K84233 and K115799, and by the MTA Renyi Lendulet Groups and Graphs Research Group.
Mon, 26 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/105392016-09-26T00:00:00ZLucchini, AndreaMaroti, AttilaRoney-Dougal, Colva MaryThe generating graph Γ(H) of a finite group H is the graph defined on the elements of H, with an edge between two vertices if and only if they generate H. We show that if H is a sufficiently large simple group with Γ(G) ≅ Γ(H) for a finite group G, then G ≅ H. We also prove that the generating graph of a symmetric group determines the group.Contribution of mode-coupling and phase-mixing of Alfvén waves to coronal heating
http://hdl.handle.net/10023/10517
Context. Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small-scale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the million-degree hot solar corona. Aims. The aim of this work is to assess how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona. Methods. To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phase-mix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver. Results. When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that i) phase-mixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell, ii) this energy is able to balance the radiative losses only in the localised region involved in the heating, and iii) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system. Conclusions. Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phase-mixing can contribute on a global scale to the heating of the solar corona.
This research has received funding from the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation programme (grant agreement No. 647214) and from the UK Science and Technology Facilities Council. This work used the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University.
Fri, 12 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/105172017-05-12T00:00:00ZPagano, P.De Moortel, I.Context. Phase-mixing of Alfvén waves in the solar corona has been identified as one possible candidate to explain coronal heating. While this scenario is supported by observations of ubiquitous oscillations in the corona carrying sufficient wave energy and by theoretical models that have described the concentration of energy in small-scale structures, it is still unclear whether this wave energy can be converted into thermal energy in order to maintain the million-degree hot solar corona. Aims. The aim of this work is to assess how much energy can be converted into thermal energy by a phase-mixing process triggered by the propagation of Alfvénic waves in a cylindric coronal structure, such as a coronal loop, and to estimate the impact of this conversion on the coronal heating and thermal structure of the solar corona. Methods. To this end, we ran 3D MHD simulations of a magnetised cylinder where the Alfvén speed varies through a boundary shell, and a footpoint driver is set to trigger kink modes that mode couple to torsional Alfvén modes in the boundary shell. These Alfvén waves are expected to phase-mix, and the system allows us to study the subsequent thermal energy deposition. We ran a reference simulation to explain the main process and then we varied the simulation parameters, such as the size of the boundary shell, its structure, and the persistence of the driver. Results. When we take high values of magnetic resistivity and strong footpoint drivers into consideration, we find that i) phase-mixing leads to a temperature increase of the order of 105 K or less, depending on the structure of the boundary shell, ii) this energy is able to balance the radiative losses only in the localised region involved in the heating, and iii) we can determine the influence of the boundary layer and the persistence of the driver on the thermal structure of the system. Conclusions. Our conclusion is that as a result of the extreme physical parameters we adopted and the moderate impact on the heating of the system, it is unlikely that phase-mixing can contribute on a global scale to the heating of the solar corona.Delphinid echolocation click detection probability on near-seafloor sensors
http://hdl.handle.net/10023/10512
The probability of detecting echolocating delphinids on a near-seafloor sensor was estimated using two Monte Carlo simulation methods. One method estimated the probability of detecting a single click (cue counting); the other estimated the probability of detecting a group of delphinids (group counting). Echolocation click beam pattern and source level assumptions strongly influenced detectability predictions by the cue counting model. Group detectability was also influenced by assumptions about group behaviors. Model results were compared to in situ recordings of encounters with Risso's dolphin (Grampus griseus) and presumed pantropical spotted dolphin (Stenella attenuata) from a near-seafloor four-channel tracking sensor deployed in the Gulf of Mexico (25.537°N 84.632°W, depth 1220 m). Horizontal detection range, received level and estimated source level distributions from localized encounters were compared with the model predictions. Agreement between in situ results and model predictions suggests that simulations can be used to estimate detection probabilities when direct distance estimation is not available.
Funding for HARP data collection and analysis was provided by the Natural Resource Damage Assessment partners (20105138) and the Center for the Integrated Modeling and Analysis of the Gulf Ecosystem (C-IMAGE) Consortium of the BP/Gulf of Mexico Research Initiative (SA 12-10/GoMRI-007). The analyses and opinions expressed are those of the authors and not necessarily those of the funding entities. This research was made possible by a grant from The Gulf of Mexico Research Initiative/C-IMAGE II.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/105122016-09-01T00:00:00ZFrasier, Kaitlin E.Wiggins, Sean M.Harris, DanielleMarques, Tiago A.Thomas, LenHildebrand, John A.The probability of detecting echolocating delphinids on a near-seafloor sensor was estimated using two Monte Carlo simulation methods. One method estimated the probability of detecting a single click (cue counting); the other estimated the probability of detecting a group of delphinids (group counting). Echolocation click beam pattern and source level assumptions strongly influenced detectability predictions by the cue counting model. Group detectability was also influenced by assumptions about group behaviors. Model results were compared to in situ recordings of encounters with Risso's dolphin (Grampus griseus) and presumed pantropical spotted dolphin (Stenella attenuata) from a near-seafloor four-channel tracking sensor deployed in the Gulf of Mexico (25.537°N 84.632°W, depth 1220 m). Horizontal detection range, received level and estimated source level distributions from localized encounters were compared with the model predictions. Agreement between in situ results and model predictions suggests that simulations can be used to estimate detection probabilities when direct distance estimation is not available.The Assouad dimension of randomly generated fractals
http://hdl.handle.net/10023/10511
We consider several dierent models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire typical Assouad dimension and consider some illustrative examples. Our results reveal a phenomenon common to each of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdor or packing dimension.
JMF was financially supported by the EPSRC grant EP/J013560/1 whilst employed at the University of Warwick. JJM was partially supported by the NNSF of China (no. 11201152), the Fund for the Doctoral Program of Higher Education of China (no. 20120076120001) and SRF for ROCS, SEM (no. 01207427) ST was financially supported by the EPSRC Doctoral Training Grant EP/K503162/1.
Thu, 22 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/105112016-09-22T00:00:00ZFraser, Jonathan MacDonaldMiao, Jun JieTroscheit, SaschaWe consider several dierent models for generating random fractals including random self-similar sets, random self-affine carpets, and Mandelbrot percolation. In each setting we compute either the almost sure or the Baire typical Assouad dimension and consider some illustrative examples. Our results reveal a phenomenon common to each of our models: the Assouad dimension of a randomly generated fractal is generically as big as possible and does not depend on the measure theoretic or topological structure of the sample space. This is in stark contrast to the other commonly studied notions of dimension like the Hausdor or packing dimension.Imaging observations of magnetic reconnection in a solar eruptive flare
http://hdl.handle.net/10023/10486
Solar flares are among the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extreme-ultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence of magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tether-cutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops.
Tue, 31 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/104862017-01-31T00:00:00ZLi, Y.Sun, X.Ding, M. D.Qiu, J.Priest, E. R.Solar flares are among the most energetic events in the solar atmosphere. It is widely accepted that flares are powered by magnetic reconnection in the corona. An eruptive flare is usually accompanied by a coronal mass ejection, both of which are probably driven by the eruption of a magnetic flux rope (MFR). Here we report an eruptive flare on 2016 March 23 observed by the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory. The extreme-ultraviolet imaging observations exhibit the clear rise and eruption of an MFR. In particular, the observations reveal solid evidence of magnetic reconnection from both the corona and chromosphere during the flare. Moreover, weak reconnection is observed before the start of the flare. We find that the preflare weak reconnection is of tether-cutting type and helps the MFR to rise slowly. Induced by a further rise of the MFR, strong reconnection occurs in the rise phases of the flare, which is temporally related to the MFR eruption. We also find that the magnetic reconnection is more of 3D-type in the early phase, as manifested in a strong-to-weak shear transition in flare loops, and becomes more 2D-like in the later phase, as shown by the apparent rising motion of an arcade of flare loops.The effects of resistivity and viscosity on the Kelvin-Helmholtz instability in oscillating coronal loops
http://hdl.handle.net/10023/10450
Aims. Investigate the effects of resistivity and viscosity on the onset and growth of the Kelvin-Helmholtz instability (KHI) in an oscillating coronal loop. Methods. We modelled a standing kink wave in a density-enhanced loop with the three dimensional (3-D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI. Results. Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of ν and η delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instability-suppressed regime (using uniform resistivity). Conclusions. From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν.
The research leading to these results has received funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Fri, 16 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/104502017-06-16T00:00:00ZHowson, T. A.De Moortel, I.Antolin, P.Aims. Investigate the effects of resistivity and viscosity on the onset and growth of the Kelvin-Helmholtz instability (KHI) in an oscillating coronal loop. Methods. We modelled a standing kink wave in a density-enhanced loop with the three dimensional (3-D), resistive magnetohydrodynamics code, Lare3d. We conducted a parameter study on the viscosity and resistivity coefficients to examine the effects of dissipation on the KHI. Results. Enhancing the viscosity (ν) and resistivity (η) acts to suppress the KHI. Larger values of ν and η delay the formation of the instability and, in some cases, prevent the onset completely. This leads to the earlier onset of heating for smaller values of the transport coefficients. We note that viscosity has a greater effect on the development of the KHI than resistivity. Furthermore, when using anomalous resistivity, the Ohmic heating rate associated with the KHI may be greater than that associated with the phase mixing that occurs in an instability-suppressed regime (using uniform resistivity). Conclusions. From our study, it is clear that the heating rate crucially depends on the formation of small length scales (influenced by the numerical resolution) as well as the values of resistivity and viscosity. As larger values of the transport coefficients suppress the KHI, the onset of heating is delayed but the heating rate is larger. As increased numerical resolution allows smaller length scales to develop, the heating rate will be higher even for the same values of η and ν.Low tortoise abundances in pine forest plantations in forest-shrubland transition areas
http://hdl.handle.net/10023/10435
In the transition between Mediterranean forest and the arid subtropical shrublands of the southeastern Iberian Peninsula, humans have transformed habitat since ancient times. Understanding the role of the original mosaic landscapes in wildlife species and the effects of the current changes as pine forest plantations, performed even outside the forest ecological boundaries, are important conservation issues. We studied variation in the density of the endangered spur-thighed tortoise (Testudo graeca) in three areas that include the four most common land types within the species’ range (pine forests, natural shrubs, dryland crop fields, and abandoned crop fields). Tortoise densities were estimated using a two-stage modeling approach with line transect distance sampling. Densities in dryland crop fields, abandoned crop fields and natural shrubs were higher (>6 individuals/ha) than in pine forests (1.25 individuals/ha). We also found large variation in density in the pine forests. Recent pine plantations showed higher densities than mature pine forests where shrub and herbaceous cover was taller and thicker. We hypothesize that mature pine forest might constrain tortoise activity by acting as partial barriers to movements. This issue is relevant for management purposes given that large areas in the tortoise’s range have recently been converted to pine plantations.
The Spanish Ministry of Science and European Regional Development Fund funded this work through Projects CGL2012-33536 and CGL2015- 64144; MINECIO/FEDER. Regional Government of the Community of Valencia supported R.R-C. by a postgraduate grant (ACIF/2010/133) and E.G. by a postdoctoral grant (APOSTD/2015/048).
Wed, 08 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/104352017-03-08T00:00:00ZRodríguez-Caro, Roberto C.Oedekoven, Cornelia S.Graciá, EvaAnadón, José D.Buckland, Stephen T.Esteve-Selma, Miguel A.Martinez, JuliaGiménez, AndrésIn the transition between Mediterranean forest and the arid subtropical shrublands of the southeastern Iberian Peninsula, humans have transformed habitat since ancient times. Understanding the role of the original mosaic landscapes in wildlife species and the effects of the current changes as pine forest plantations, performed even outside the forest ecological boundaries, are important conservation issues. We studied variation in the density of the endangered spur-thighed tortoise (Testudo graeca) in three areas that include the four most common land types within the species’ range (pine forests, natural shrubs, dryland crop fields, and abandoned crop fields). Tortoise densities were estimated using a two-stage modeling approach with line transect distance sampling. Densities in dryland crop fields, abandoned crop fields and natural shrubs were higher (>6 individuals/ha) than in pine forests (1.25 individuals/ha). We also found large variation in density in the pine forests. Recent pine plantations showed higher densities than mature pine forests where shrub and herbaceous cover was taller and thicker. We hypothesize that mature pine forest might constrain tortoise activity by acting as partial barriers to movements. This issue is relevant for management purposes given that large areas in the tortoise’s range have recently been converted to pine plantations.Geostrophic tripolar vortices in a two-layer fluid : linear stability and nonlinear evolution of equilibria
http://hdl.handle.net/10023/10411
We investgate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate of the nonlinear evolution of a few selected cases of tripoles.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/104112017-03-01T00:00:00ZReinaud, Jean NoelSokolovskiy, MikhailCarton, XavierWe investgate equilibrium solutions for tripolar vortices in a two-layer quasi-geostrophic flow. Two of the vortices are like-signed and lie in one layer. An opposite-signed vortex lies in the other layer. The families of equilibria can be spanned by the distance (called separation) between the two like-signed vortices. Two equilibrium configurations are possible when the opposite-signed vortex lies between the two other vortices. In the first configuration (called ordinary roundabout), the opposite signed vortex is equidistant to the two other vortices. In the second configuration (eccentric roundabouts), the distances are unequal. We determine the equilibria numerically and describe their characteristics for various internal deformation radii. The two branches of equilibria can co-exist and intersect for small deformation radii. Then, the eccentric roundabouts are stable while unstable ordinary roundabouts can be found. Indeed, ordinary roundabouts exist at smaller separations than eccentric roundabouts do, thus inducing stronger vortex interactions. However, for larger deformation radii, eccentric roundabouts can also be unstable. Then, the two branches of equilibria do not cross. The branch of eccentric roundabouts only exists for large separations. Near the end of the branch of eccentric roundabouts (at the smallest separation), one of the like-signed vortices exhibits a sharp inner corner where instabilities can be triggered. Finally, we investigate of the nonlinear evolution of a few selected cases of tripoles.A simulation approach to assessing environmental risk of sound exposure to marine mammals
http://hdl.handle.net/10023/10382
Intense underwater sounds caused by military sonar, seismic surveys, and pile driving can harm acoustically sensitive marine mammals. Many jurisdictions require such activities to undergo marine mammal impact assessments to guide mitigation. However, the ability to assess impacts in a rigorous, quantitative way is hindered by large knowledge gaps concerning hearing ability, sensitivity, and behavioral responses to noise exposure. We describe a simulation-based framework, called SAFESIMM (Statistical Algorithms For Estimating the Sonar Influence on Marine Megafauna), that can be used to calculate the numbers of agents (animals) likely to be affected by intense underwater sounds. We illustrate the simulation framework using two species that are likely to be affected by marine renewable energy developments in UK waters: gray seal (Halichoerus grypus) and harbor porpoise (Phocoena phocoena). We investigate three sources of uncertainty: How sound energy is perceived by agents with differing hearing abilities; how agents move in response to noise (i.e., the strength and directionality of their evasive movements); and the way in which these responses may interact with longer term constraints on agent movement. The estimate of received sound exposure level (SEL) is influenced most strongly by the weighting function used to account for the specie's presumed hearing ability. Strongly directional movement away from the sound source can cause modest reductions (~5 dB) in SEL over the short term (periods of less than 10 days). Beyond 10 days, the way in which agents respond to noise exposure has little or no effect on SEL, unless their movements are constrained by natural boundaries. Most experimental studies of noise impacts have been short-term. However, data are needed on long-term effects because uncertainty about predicted SELs accumulates over time. Synthesis and applications. Simulation frameworks offer a powerful way to explore, understand, and estimate effects of cumulative sound exposure on marine mammals and to quantify associated levels of uncertainty. However, they can often require subjective decisions that have important consequences for management recommendations, and the basis for these decisions must be clearly described.
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/103822017-04-01T00:00:00ZDonovan, Carl R.Harris, Catriona M.Milazzo, LorenzoHarwood, JohnMarshall, LauraWilliams, RobIntense underwater sounds caused by military sonar, seismic surveys, and pile driving can harm acoustically sensitive marine mammals. Many jurisdictions require such activities to undergo marine mammal impact assessments to guide mitigation. However, the ability to assess impacts in a rigorous, quantitative way is hindered by large knowledge gaps concerning hearing ability, sensitivity, and behavioral responses to noise exposure. We describe a simulation-based framework, called SAFESIMM (Statistical Algorithms For Estimating the Sonar Influence on Marine Megafauna), that can be used to calculate the numbers of agents (animals) likely to be affected by intense underwater sounds. We illustrate the simulation framework using two species that are likely to be affected by marine renewable energy developments in UK waters: gray seal (Halichoerus grypus) and harbor porpoise (Phocoena phocoena). We investigate three sources of uncertainty: How sound energy is perceived by agents with differing hearing abilities; how agents move in response to noise (i.e., the strength and directionality of their evasive movements); and the way in which these responses may interact with longer term constraints on agent movement. The estimate of received sound exposure level (SEL) is influenced most strongly by the weighting function used to account for the specie's presumed hearing ability. Strongly directional movement away from the sound source can cause modest reductions (~5 dB) in SEL over the short term (periods of less than 10 days). Beyond 10 days, the way in which agents respond to noise exposure has little or no effect on SEL, unless their movements are constrained by natural boundaries. Most experimental studies of noise impacts have been short-term. However, data are needed on long-term effects because uncertainty about predicted SELs accumulates over time. Synthesis and applications. Simulation frameworks offer a powerful way to explore, understand, and estimate effects of cumulative sound exposure on marine mammals and to quantify associated levels of uncertainty. However, they can often require subjective decisions that have important consequences for management recommendations, and the basis for these decisions must be clearly described.A general setting for symmetric distributions and their relationship to general distributions
http://hdl.handle.net/10023/10370
A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/103702016-06-01T00:00:00ZJupp, P.E.Regoli, G.Azzalini, A.A standard method of obtaining non-symmetrical distributions is that of modulating symmetrical distributions by multiplying the densities by a perturbation factor. This has been considered mainly for central symmetry of a Euclidean space in the origin. This paper enlarges the concept of modulation to the general setting of symmetry under the action of a compact topological group on the sample space. The main structural result relates the density of an arbitrary distribution to the density of the corresponding symmetrised distribution. Some general methods for constructing modulating functions are considered. The effect that transformations of the sample space have on symmetry of distributions is investigated. The results are illustrated by general examples, many of them in the setting of directional statistics.Linear response for intermittent maps
http://hdl.handle.net/10023/10334
We consider the one parameter family α↦Tα (α∈[0,1)) of Pomeau-Manneville type interval maps Tα(x)=x(1+2αxα) for x∈[0,1/2) and Tα(x)=2x−1 for x∈[1/2,1], with the associated absolutely continuous invariant probability measure μα. For α∈(0,1), Sarig and Gouëzel proved that the system mixes only polynomially with rate n1−1/α (in particular, there is no spectral gap). We show that for any ψ∈Lq, the map α→∫10ψdμα is differentiable on [0,1−1/q), and we give a (linear response) formula for the value of the derivative. This is the first time that a linear response formula for the SRB measure is obtained in the setting of slowly mixing dynamics. Our argument shows how cone techniques can be used in this context. For α≥1/2 we need the n−1/α decorrelation obtained by Gouëzel under additional conditions.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/103342016-11-01T00:00:00ZBaladi, VivianeTodd, Michael JohnWe consider the one parameter family α↦Tα (α∈[0,1)) of Pomeau-Manneville type interval maps Tα(x)=x(1+2αxα) for x∈[0,1/2) and Tα(x)=2x−1 for x∈[1/2,1], with the associated absolutely continuous invariant probability measure μα. For α∈(0,1), Sarig and Gouëzel proved that the system mixes only polynomially with rate n1−1/α (in particular, there is no spectral gap). We show that for any ψ∈Lq, the map α→∫10ψdμα is differentiable on [0,1−1/q), and we give a (linear response) formula for the value of the derivative. This is the first time that a linear response formula for the SRB measure is obtained in the setting of slowly mixing dynamics. Our argument shows how cone techniques can be used in this context. For α≥1/2 we need the n−1/α decorrelation obtained by Gouëzel under additional conditions.Bayesian P-splines and advanced computing in R for a changepoint analysis on spatio-temporal point processes
http://hdl.handle.net/10023/10323
This work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarize the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a data set of seismic events in Italy over the last 20 years.
As regards authors Linda Altieri and Fedele Greco, the research work underlying this paper was partially funded by an FIRB 2012 [grant number RBFR12URQJ]; title: Statistical modelling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/103232016-01-01T00:00:00ZAltieri, L.Cocchi, D.Greco, F.Illian, J. B.Scott, E. M.This work presents advanced computational aspects of a new method for changepoint detection on spatio-temporal point process data. We summarize the methodology, based on building a Bayesian hierarchical model for the data and declaring prior conjectures on the number and positions of the changepoints, and show how to take decisions regarding the acceptance of potential changepoints. The focus of this work is about choosing an approach that detects the correct changepoint and delivers smooth reliable estimates in a feasible computational time; we propose Bayesian P-splines as a suitable tool for managing spatial variation, both under a computational and a model fitting performance perspective. The main computational challenges are outlined and a solution involving parallel computing in R is proposed and tested on a simulation study. An application is also presented on a data set of seismic events in Italy over the last 20 years.Logarithmic improvement of regularity criteria for the Navier-Stokes equations in terms of pressure
http://hdl.handle.net/10023/10319
In this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible Navier-Stokes equations in terms of pressure. This improves the main result in [S. Benbernou, A note on the regularity criterion in terms of pressure for the Navier-Stokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].
XY is partially supported by a grant from NSERC.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/103192016-08-01T00:00:00ZTran, Chuong VanYu, XinweiIn this article we prove a logarithmic improvement of regularity criteria in the multiplier spaces for the Cauchy problem of the incompressible Navier-Stokes equations in terms of pressure. This improves the main result in [S. Benbernou, A note on the regularity criterion in terms of pressure for the Navier-Stokes equations, Applied Mathematics Letters 22 (2009) 1438–1443].A combined theory for magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/10305
We present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.
Grant numbers: Science and Technology Facilities Council via Doctoral Training Grant [ST/K502327/1], Consolidated Grant [ST/K000950/1] and Consolidated Grant [ST/N000609/1].
Fri, 10 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/103052017-03-10T00:00:00ZHodgson, Jonathan David BrockieNeukirch, ThomasWe present a new approach to the theory of magnetohydrodynamic equilibria with anisotropic pressure, magnetic shear and translational/rotational invariance. This approach involves combining two existing formalisms in order to eliminate their individual weaknesses. The theoretical aspects of the method are explored in detail along with numerical solutions which make use of the method. Eventually, this method could be applied to model various plasma systems, such as planetary magnetospheres.Observations and modelling of the pre-flare period of the 29 March 2014 X1 flare
http://hdl.handle.net/10023/10298
On the 29 March 2014 NOAA active region (AR) 12017 produced an X1 flare which was simultaneously observed by an unprecedented number of observatories. We have investigated the pre-flare period of this flare from 14:00 UT until 19:00 UT using joint observations made by the Interface Region Imaging Spectrometer (IRIS) and the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Spectral lines providing coverage of the solar atmosphere from chromosphere to the corona were analysed to investigate pre-flare activity within the AR. The results of the investigation have revealed evidence of strongly blue-shifted plasma flows, with velocities up to 200 km-1, being observed 40 minutes prior to flaring. These flows are located along the filament present in the active region and are both spatially discrete and transient. In order to constrain the possible explanations for this activity, we undertake non-potential magnetic field modelling of the active region. This modelling indicates the existence of a weakly twisted flux rope along the polarity inversion line in the region where a filament and the strong pre-flare flows are observed. We then discuss how these observations relate to the current models of flare triggering. We conclude that the most likely drivers of the observed activity are internal reconnection in the flux rope, early onset of the flare reconnection, or tether cutting reconnection along the filament.
MMW and SD acknowledge STFC for support via their PhD Studentships. DML is an Early-Career Fellow, funded by the Leverhulme Trust.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/102982017-02-01T00:00:00ZWoods, M. M.Harra, L. K.Matthews, S. A.Mackay, D. H.Dacie, S.Long, D. M.On the 29 March 2014 NOAA active region (AR) 12017 produced an X1 flare which was simultaneously observed by an unprecedented number of observatories. We have investigated the pre-flare period of this flare from 14:00 UT until 19:00 UT using joint observations made by the Interface Region Imaging Spectrometer (IRIS) and the Hinode Extreme Ultraviolet Imaging Spectrometer (EIS). Spectral lines providing coverage of the solar atmosphere from chromosphere to the corona were analysed to investigate pre-flare activity within the AR. The results of the investigation have revealed evidence of strongly blue-shifted plasma flows, with velocities up to 200 km-1, being observed 40 minutes prior to flaring. These flows are located along the filament present in the active region and are both spatially discrete and transient. In order to constrain the possible explanations for this activity, we undertake non-potential magnetic field modelling of the active region. This modelling indicates the existence of a weakly twisted flux rope along the polarity inversion line in the region where a filament and the strong pre-flare flows are observed. We then discuss how these observations relate to the current models of flare triggering. We conclude that the most likely drivers of the observed activity are internal reconnection in the flux rope, early onset of the flare reconnection, or tether cutting reconnection along the filament.Forward modeling of standing slow modes in flaring coronal loops
http://hdl.handle.net/10023/10295
Standing slow-mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow-mode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slow-mode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.
Thu, 02 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/102952015-07-02T00:00:00ZYuan, D.Van Doorsselaere, T.Banerjee, D.Antolin, P.Standing slow-mode waves in hot flaring loops are exclusively observed in spectrometers and are used to diagnose the magnetic field strength and temperature of the loop structure. Owing to the lack of spatial information, the longitudinal mode cannot be effectively identified. In this study, we simulate standing slow-mode waves in flaring loops and compare the synthesized line emission properties with Solar Ultraviolet Measurements of Emitted Radiation spectrographic and Solar Dynamics Observatory/Atmospheric Imaging Assembly imaging observations. We find that the emission intensity and line width oscillations are a quarter period out of phase with Doppler shift velocity in both time and spatial domain, which can be used to identify a standing slow-mode wave from spectroscopic observations. However, the longitudinal overtones could only be measured with the assistance of imagers. We find emission intensity asymmetry in the positive and negative modulations; this is because the contribution function pertaining to the atomic emission process responds differently to positive and negative temperature variations. One may detect half periodicity close to the loop apex, where emission intensity modulation is relatively small. The line-of-sight projection affects the observation of Doppler shift significantly. A more accurate estimate of the amplitude of velocity perturbation is obtained by de-projecting the Doppler shift by a factor of 1–2θ/π rather than the traditionally used cosθ. If a loop is heated to the hotter wing, the intensity modulation could be overwhelmed by background emission, while the Doppler shift velocity could still be detected to a certain extent.Resonant absorption of transverse oscillations and associated heating in a solar prominence. I. Observational aspects
http://hdl.handle.net/10023/10294
Transverse magnetohydrodynamic waves have been shown to be ubiquitous in the solar atmosphere and can, in principle, carry sufficient energy to generate and maintain the Sun's million-degree outer atmosphere or corona. However, direct evidence of the dissipation process of these waves and subsequent heating has not yet been directly observed. Here we report on high spatial, temporal, and spectral resolution observations of a solar prominence that show a compelling signature of so-called resonant absorption, a long hypothesized mechanism to efficiently convert and dissipate transverse wave energy into heat. Aside from coherence in the transverse direction, our observations show telltale phase differences around 180° between transverse motions in the plane-of-sky and line-of-sight velocities of the oscillating fine structures or threads, and also suggest significant heating from chromospheric to higher temperatures. Comparison with advanced numerical simulations support a scenario in which transverse oscillations trigger a Kelvin–Helmholtz instability (KHI) at the boundaries of oscillating threads via resonant absorption. This instability leads to numerous thin current sheets in which wave energy is dissipated and plasma is heated. Our results provide direct evidence for wave-related heating in action, one of the candidate coronal heating mechanisms.
Tue, 11 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/102942015-08-11T00:00:00ZOkamoto, Takenori J.Antolin, PatrickDe Pontieu, BartUitenbroek, HanVan Doorsselaere, TomYokoyama, TakaakiTransverse magnetohydrodynamic waves have been shown to be ubiquitous in the solar atmosphere and can, in principle, carry sufficient energy to generate and maintain the Sun's million-degree outer atmosphere or corona. However, direct evidence of the dissipation process of these waves and subsequent heating has not yet been directly observed. Here we report on high spatial, temporal, and spectral resolution observations of a solar prominence that show a compelling signature of so-called resonant absorption, a long hypothesized mechanism to efficiently convert and dissipate transverse wave energy into heat. Aside from coherence in the transverse direction, our observations show telltale phase differences around 180° between transverse motions in the plane-of-sky and line-of-sight velocities of the oscillating fine structures or threads, and also suggest significant heating from chromospheric to higher temperatures. Comparison with advanced numerical simulations support a scenario in which transverse oscillations trigger a Kelvin–Helmholtz instability (KHI) at the boundaries of oscillating threads via resonant absorption. This instability leads to numerous thin current sheets in which wave energy is dissipated and plasma is heated. Our results provide direct evidence for wave-related heating in action, one of the candidate coronal heating mechanisms.Resonant absorption of transverse oscillations and associated heating in a solar prominence. II. Numerical aspects
http://hdl.handle.net/10023/10293
Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun's million-degree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.
Tue, 11 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/102932015-08-11T00:00:00ZAntolin, P.Okamoto, T. J.De Pontieu, B.Uitenbroek, H.Van Doorsselaere, T.Yokoyama, T.Transverse magnetohydrodynamic (MHD) waves are ubiquitous in the solar atmosphere and may be responsible for generating the Sun's million-degree outer atmosphere. However, direct evidence of the dissipation process and heating from these waves remains elusive. Through advanced numerical simulations combined with appropriate forward modeling of a prominence flux tube, we provide the observational signatures of transverse MHD waves in prominence plasmas. We show that these signatures are characterized by a thread-like substructure, strong transverse dynamical coherence, an out-of-phase difference between plane-of-the-sky motions and line-of-sight velocities, and enhanced line broadening and heating around most of the flux tube. A complex combination between resonant absorption and Kelvin–Helmholtz instabilities (KHIs) takes place in which the KHI extracts the energy from the resonant layer and dissipates it through vortices and current sheets, which rapidly degenerate into turbulence. An inward enlargement of the boundary is produced in which the turbulent flows conserve the characteristic dynamics from the resonance, therefore guaranteeing detectability of the resonance imprints. We show that the features described in the accompanying paper through coordinated Hinode and Interface Region Imaging Spectrograph observations match the numerical results well.Hα and EUV observations of a partial CME
http://hdl.handle.net/10023/10291
We have obtained Hα high spatial and time resolution observations of the upper solar chromosphere and supplemented these with multi-wavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extreme-ultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the Hydrogen-Alpha Rapid Dynamics Camera instrument at the National Solar Observatory's Dunn Solar Telescope. Our Hα observations found large downflows of chromospheric material returning from coronal heights following a failed prominence eruption. We have detected several large condensations ("blobs") returning to the solar surface at velocities of ≈200 km s−1 in both Hα and several SDO Atmospheric Imaging Assembly band passes. The average derived size of these "blobs" in Hα is 500 by 3000 km2 in the directions perpendicular and parallel to the direction of travel, respectively. A comparison of our "blob" widths to those found from coronal rain, indicate that there are additional, smaller, unresolved "blobs" in agreement with previous studies and recent numerical simulations. Our observed velocities and decelerations of the "blobs" in both Hα and SDO bands are less than those expected for gravitational free-fall and imply additional magnetic or gas pressure impeding the flow. We derived a kinetic energy of ≈2 orders of magnitude lower for the main eruption than a typical coronal mass ejection, which may explain its partial nature.
Tue, 12 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/102912015-05-12T00:00:00ZChristian, Damian J.Jess, David B.Antolin, PatrickMathioudakis, MihalisWe have obtained Hα high spatial and time resolution observations of the upper solar chromosphere and supplemented these with multi-wavelength observations from the Solar Dynamics Observatory (SDO) and the Hinode Extreme-ultraviolet Imaging Spectrometer. The Hα observations were conducted on 2012 February 11 with the Hydrogen-Alpha Rapid Dynamics Camera instrument at the National Solar Observatory's Dunn Solar Telescope. Our Hα observations found large downflows of chromospheric material returning from coronal heights following a failed prominence eruption. We have detected several large condensations ("blobs") returning to the solar surface at velocities of ≈200 km s−1 in both Hα and several SDO Atmospheric Imaging Assembly band passes. The average derived size of these "blobs" in Hα is 500 by 3000 km2 in the directions perpendicular and parallel to the direction of travel, respectively. A comparison of our "blob" widths to those found from coronal rain, indicate that there are additional, smaller, unresolved "blobs" in agreement with previous studies and recent numerical simulations. Our observed velocities and decelerations of the "blobs" in both Hα and SDO bands are less than those expected for gravitational free-fall and imply additional magnetic or gas pressure impeding the flow. We derived a kinetic energy of ≈2 orders of magnitude lower for the main eruption than a typical coronal mass ejection, which may explain its partial nature.The multi-thermal and multi-stranded nature of coronal rain
http://hdl.handle.net/10023/10290
We analyze coordinated observations of coronal rain in loops, spanning chromospheric, transition region (TR), and coronal temperatures with sub-arcsecond spatial resolution. Coronal rain is found to be a highly multithermal phenomenon with a high degree of co-spatiality in the multi-wavelength emission. EUV darkening and quasi-periodic intensity variations are found to be strongly correlated with coronal rain showers. Progressive cooling of coronal rain is observed, leading to a height dependence of the emission. A fast-slow two-step catastrophic cooling progression is found, which may reflect the transition to optically thick plasma states. The intermittent and clumpy appearance of coronal rain at coronal heights becomes more continuous and persistent at chromospheric heights just before impact, mainly due to a funnel effect from the observed expansion of the magnetic field. Strong density inhomogeneities of 0.″2-0.″5 are found, in which a transition from temperatures of 105 to 104 K occurs. The 0.″2-0.″8 width of the distribution of coronal rain is found to be independent of temperature. The sharp increase in the number of clumps at the coolest temperatures, especially at higher resolution, suggests that the bulk distribution of the rain remains undetected. Rain clumps appear organized in strands in both chromospheric and TR temperatures. We further find structure reminiscent of the magnetohydrodynamic (MHD) thermal mode (also known as entropy mode), thereby suggesting an important role of thermal instability in shaping the basic loop substructure. Rain core densities are estimated to vary between 2 × 1010 and 2.5 × 1011cm−3, leading to significant downward mass fluxes per loop of 1–5 × 109 g s−1, thus suggesting a major role in the chromosphere-corona mass cycle.
Tue, 09 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/102902015-06-09T00:00:00ZAntolin, P.Vissers, G.Pereira, T. M. D.Rouppe van der Voort, L.Scullion, E.We analyze coordinated observations of coronal rain in loops, spanning chromospheric, transition region (TR), and coronal temperatures with sub-arcsecond spatial resolution. Coronal rain is found to be a highly multithermal phenomenon with a high degree of co-spatiality in the multi-wavelength emission. EUV darkening and quasi-periodic intensity variations are found to be strongly correlated with coronal rain showers. Progressive cooling of coronal rain is observed, leading to a height dependence of the emission. A fast-slow two-step catastrophic cooling progression is found, which may reflect the transition to optically thick plasma states. The intermittent and clumpy appearance of coronal rain at coronal heights becomes more continuous and persistent at chromospheric heights just before impact, mainly due to a funnel effect from the observed expansion of the magnetic field. Strong density inhomogeneities of 0.″2-0.″5 are found, in which a transition from temperatures of 105 to 104 K occurs. The 0.″2-0.″8 width of the distribution of coronal rain is found to be independent of temperature. The sharp increase in the number of clumps at the coolest temperatures, especially at higher resolution, suggests that the bulk distribution of the rain remains undetected. Rain clumps appear organized in strands in both chromospheric and TR temperatures. We further find structure reminiscent of the magnetohydrodynamic (MHD) thermal mode (also known as entropy mode), thereby suggesting an important role of thermal instability in shaping the basic loop substructure. Rain core densities are estimated to vary between 2 × 1010 and 2.5 × 1011cm−3, leading to significant downward mass fluxes per loop of 1–5 × 109 g s−1, thus suggesting a major role in the chromosphere-corona mass cycle.Unresolved fine-scale structure in solar coronal loop-tops
http://hdl.handle.net/10023/10288
New and advanced space-based observing facilities continue to lower the resolution limit and detect solar coronal loops in greater detail. We continue to discover even finer substructures within coronal loop cross-sections, in order to understand the nature of the solar corona. Here, we push this lower limit further to search for the finest coronal loop substructures, through taking advantage of the resolving power of the Swedish 1 m Solar Telescope/CRisp Imaging Spectro-Polarimeter (CRISP), together with co-observations from the Solar Dynamics Observatory/Atmospheric Image Assembly (AIA). High-resolution imaging of the chromospheric Hα 656.28 nm spectral line core and wings can, under certain circumstances, allow one to deduce the topology of the local magnetic environment of the solar atmosphere where its observed. Here, we study post-flare coronal loops, which become filled with evaporated chromosphere that rapidly condenses into chromospheric clumps of plasma (detectable in Hα) known as a coronal rain, to investigate their fine-scale structure. We identify, through analysis of three data sets, large-scale catastrophic cooling in coronal loop-tops and the existence of multi-thermal, multi-stranded substructures. Many cool strands even extend fully intact from loop-top to footpoint. We discover that coronal loop fine-scale strands can appear bunched with as many as eight parallel strands within an AIA coronal loop cross-section. The strand number density versus cross-sectional width distribution, as detected by CRISP within AIA-defined coronal loops, most likely peaks at well below 100 km, and currently, 69% of the substructure strands are statistically unresolved in AIA coronal loops.
Mon, 24 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/102882014-11-24T00:00:00ZScullion, E.Rouppe van der Voort, L.Wedemeyer, S.Antolin, P.New and advanced space-based observing facilities continue to lower the resolution limit and detect solar coronal loops in greater detail. We continue to discover even finer substructures within coronal loop cross-sections, in order to understand the nature of the solar corona. Here, we push this lower limit further to search for the finest coronal loop substructures, through taking advantage of the resolving power of the Swedish 1 m Solar Telescope/CRisp Imaging Spectro-Polarimeter (CRISP), together with co-observations from the Solar Dynamics Observatory/Atmospheric Image Assembly (AIA). High-resolution imaging of the chromospheric Hα 656.28 nm spectral line core and wings can, under certain circumstances, allow one to deduce the topology of the local magnetic environment of the solar atmosphere where its observed. Here, we study post-flare coronal loops, which become filled with evaporated chromosphere that rapidly condenses into chromospheric clumps of plasma (detectable in Hα) known as a coronal rain, to investigate their fine-scale structure. We identify, through analysis of three data sets, large-scale catastrophic cooling in coronal loop-tops and the existence of multi-thermal, multi-stranded substructures. Many cool strands even extend fully intact from loop-top to footpoint. We discover that coronal loop fine-scale strands can appear bunched with as many as eight parallel strands within an AIA coronal loop cross-section. The strand number density versus cross-sectional width distribution, as detected by CRISP within AIA-defined coronal loops, most likely peaks at well below 100 km, and currently, 69% of the substructure strands are statistically unresolved in AIA coronal loops.First high-resolution spectroscopic observations of an erupting prominence within a coronal mass ejection by the Interface Region Imaging Spectrograph (IRIS)
http://hdl.handle.net/10023/10287
Spectroscopic observations of prominence eruptions associated with coronal mass ejections (CMEs), although relatively rare, can provide valuable plasma and three-dimensional geometry diagnostics. We report the first observations by the Interface Region Imaging Spectrograph mission of a spectacular fast CME/prominence eruption associated with an equivalent X1.6 flare on 2014 May 9. The maximum plane-of-sky and Doppler velocities of the eruption are 1200 and 460 km s−1, respectively. There are two eruption components separated by ~200 km s−1 in Doppler velocity: a primary, bright component and a secondary, faint component, suggesting a hollow, rather than solid, cone-shaped distribution of material. The eruption involves a left-handed helical structure undergoing counterclockwise (viewed top-down) unwinding motion. There is a temporal evolution from upward eruption to downward fallback with less-than-free-fall speeds and decreasing nonthermal line widths. We find a wide range of Mg ii k/h line intensity ratios (less than ~2 expected for optically-thin thermal emission): the lowest ever reported median value of 1.17 found in the fallback material, a comparably high value of 1.63 in nearby coronal rain, and intermediate values of 1.53 and 1.41 in the two eruption components. The fallback material exhibits a strong (>5α ) linear correlation between the k/h ratio and the Doppler velocity as well as the line intensity. We demonstrate that Doppler dimming of scattered chromospheric emission by the erupted material can potentially explain such characteristics.
Tue, 21 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/102872015-04-21T00:00:00ZLiu, WeiDe Pontieu, BartVial, Jean-ClaudeTitle, Alan M.Carlsson, MatsUitenbroek, HanOkamoto, Takenori J.Berger, Thomas E.Antolin, PatrickSpectroscopic observations of prominence eruptions associated with coronal mass ejections (CMEs), although relatively rare, can provide valuable plasma and three-dimensional geometry diagnostics. We report the first observations by the Interface Region Imaging Spectrograph mission of a spectacular fast CME/prominence eruption associated with an equivalent X1.6 flare on 2014 May 9. The maximum plane-of-sky and Doppler velocities of the eruption are 1200 and 460 km s−1, respectively. There are two eruption components separated by ~200 km s−1 in Doppler velocity: a primary, bright component and a secondary, faint component, suggesting a hollow, rather than solid, cone-shaped distribution of material. The eruption involves a left-handed helical structure undergoing counterclockwise (viewed top-down) unwinding motion. There is a temporal evolution from upward eruption to downward fallback with less-than-free-fall speeds and decreasing nonthermal line widths. We find a wide range of Mg ii k/h line intensity ratios (less than ~2 expected for optically-thin thermal emission): the lowest ever reported median value of 1.17 found in the fallback material, a comparably high value of 1.63 in nearby coronal rain, and intermediate values of 1.53 and 1.41 in the two eruption components. The fallback material exhibits a strong (>5α ) linear correlation between the k/h ratio and the Doppler velocity as well as the line intensity. We demonstrate that Doppler dimming of scattered chromospheric emission by the erupted material can potentially explain such characteristics.Simulating the in situ condensation process of solar prominences
http://hdl.handle.net/10023/10285
Prominences in the solar corona are a hundredfold cooler and denser than their surroundings, with a total mass of 1013 up to 1015 g. Here, we report on the first comprehensive simulations of three-dimensional, thermally and gravitationally stratified magnetic flux ropes where in situ condensation to a prominence occurs due to radiative losses. After a gradual thermodynamic adjustment, we witness a phase where runaway cooling occurs while counter-streaming shearing flows drain off mass along helical field lines. After this drainage, a prominence-like condensation resides in concave upward field regions, and this prominence retains its overall characteristics for more than two hours. While condensing, the prominence establishes a prominence-corona transition region where magnetic field-aligned thermal conduction is operative during the runaway cooling. The prominence structure represents a force-balanced state in a helical flux rope. The simulated condensation demonstrates a right-bearing barb, as a remnant of the drainage. Synthetic images at extreme ultraviolet wavelengths follow the onset of the condensation, and confirm the appearance of horns and a three-part structure for the stable prominence state, as often seen in erupting prominences. This naturally explains recent Solar Dynamics Observatory views with the Atmospheric Imaging Assembly on prominences in coronal cavities demonstrating horns.
Wed, 27 Aug 2014 00:00:00 GMThttp://hdl.handle.net/10023/102852014-08-27T00:00:00ZXia, C.Keppens, R.Antolin, P.Porth, O.Prominences in the solar corona are a hundredfold cooler and denser than their surroundings, with a total mass of 1013 up to 1015 g. Here, we report on the first comprehensive simulations of three-dimensional, thermally and gravitationally stratified magnetic flux ropes where in situ condensation to a prominence occurs due to radiative losses. After a gradual thermodynamic adjustment, we witness a phase where runaway cooling occurs while counter-streaming shearing flows drain off mass along helical field lines. After this drainage, a prominence-like condensation resides in concave upward field regions, and this prominence retains its overall characteristics for more than two hours. While condensing, the prominence establishes a prominence-corona transition region where magnetic field-aligned thermal conduction is operative during the runaway cooling. The prominence structure represents a force-balanced state in a helical flux rope. The simulated condensation demonstrates a right-bearing barb, as a remnant of the drainage. Synthetic images at extreme ultraviolet wavelengths follow the onset of the condensation, and confirm the appearance of horns and a three-part structure for the stable prominence state, as often seen in erupting prominences. This naturally explains recent Solar Dynamics Observatory views with the Atmospheric Imaging Assembly on prominences in coronal cavities demonstrating horns.Detection of supersonic downflows and associated heating events in the transition region above sunspots
http://hdl.handle.net/10023/10282
Interface Region Imaging Spectrograph data allow us to study the solar transition region (TR) with an unprecedented spatial resolution of 0″33. On 2013 August 30, we observed bursts of high Doppler shifts suggesting strong supersonic downflows of up to 200 km s–1 and weaker, slightly slower upflows in the spectral lines Mg II h and k, C II 1336, Si IV 1394 Å, and 1403 Å, that are correlated with brightenings in the slitjaw images (SJIs). The bursty behavior lasts throughout the 2 hr observation, with average burst durations of about 20 s. The locations of these short-lived events appear to be the umbral and penumbral footpoints of EUV loops. Fast apparent downflows are observed along these loops in the SJIs and in the Atmospheric Imaging Assembly, suggesting that the loops are thermally unstable. We interpret the observations as cool material falling from coronal heights, and especially coronal rain produced along the thermally unstable loops, which leads to an increase of intensity at the loop footpoints, probably indicating an increase of density and temperature in the TR. The rain speeds are on the higher end of previously reported speeds for this phenomenon, and possibly higher than the free-fall velocity along the loops. On other observing days, similar bright dots are sometimes aligned into ribbons, resembling small flare ribbons. These observations provide a first insight into small-scale heating events in sunspots in the TR.
Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/102822014-06-27T00:00:00ZKleint, L.Antolin, P.Tian, H.Judge, P.Testa, P.De Pontieu, B.Martínez-Sykora, J.Reeves, K. K.Wuelser, J. P.McKillop, S.Saar, S.Carlsson, M.Boerner, P.Hurlburt, N.Lemen, J.Tarbell, T. D.Title, A.Golub, L.Hansteen, V.Jaeggli, S.Kankelborg, C.Interface Region Imaging Spectrograph data allow us to study the solar transition region (TR) with an unprecedented spatial resolution of 0″33. On 2013 August 30, we observed bursts of high Doppler shifts suggesting strong supersonic downflows of up to 200 km s–1 and weaker, slightly slower upflows in the spectral lines Mg II h and k, C II 1336, Si IV 1394 Å, and 1403 Å, that are correlated with brightenings in the slitjaw images (SJIs). The bursty behavior lasts throughout the 2 hr observation, with average burst durations of about 20 s. The locations of these short-lived events appear to be the umbral and penumbral footpoints of EUV loops. Fast apparent downflows are observed along these loops in the SJIs and in the Atmospheric Imaging Assembly, suggesting that the loops are thermally unstable. We interpret the observations as cool material falling from coronal heights, and especially coronal rain produced along the thermally unstable loops, which leads to an increase of intensity at the loop footpoints, probably indicating an increase of density and temperature in the TR. The rain speeds are on the higher end of previously reported speeds for this phenomenon, and possibly higher than the free-fall velocity along the loops. On other observing days, similar bright dots are sometimes aligned into ribbons, resembling small flare ribbons. These observations provide a first insight into small-scale heating events in sunspots in the TR.Forward modeling of gyrosynchrotron intensity perturbations by sausage modes
http://hdl.handle.net/10023/10280
To determine the observable radio signatures of the fast sausagestanding wave, we examine gyrosynchrotron (GS) emission modulation usinga linear three-dimensional magnetohydrodynamic model of a plasmacylinder. Effects of the line-of-sight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a low-density model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an in-phase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the low-density model and ananti-phase variation for the base model in the case of a viewing angleof 45°. The spatially inhomogeneous character of the oscillatingemission source and the spatial resolution of the model are found tohave a significant effect on the resulting intensity.
Fri, 28 Mar 2014 00:00:00 GMThttp://hdl.handle.net/10023/102802014-03-28T00:00:00ZReznikova, V. E.Antolin, P.Van Doorsselaere, T.To determine the observable radio signatures of the fast sausagestanding wave, we examine gyrosynchrotron (GS) emission modulation usinga linear three-dimensional magnetohydrodynamic model of a plasmacylinder. Effects of the line-of-sight angle and instrumental resolutionon perturbations of the GS intensity are analyzed for two models: a basemodel with strong Razin suppression and a low-density model in which theRazin effect was unimportant. Our finding contradicts previouspredictions made with simpler models: an in-phase variation of intensitybetween low (f <fpeak) and high (f > fpeak) frequencies is found for the low-density model and ananti-phase variation for the base model in the case of a viewing angleof 45°. The spatially inhomogeneous character of the oscillatingemission source and the spatial resolution of the model are found tohave a significant effect on the resulting intensity.Fine strand-like structure in the solar corona from magnetohydrodynamic transverse oscillations
http://hdl.handle.net/10023/10279
Current analytical and numerical modeling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organize itself in fine strand-like structures of few hundred kilometers widths. The link between small structure in models and the observed widths of strand-like structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modeling of three-dimensional MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strand-like structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to Kelvin-Helmholtz instabilities that deform the cross-sectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the line-of-sight angle, last for timescales of a period, and can be observed for spatial resolutions of a tenth of loop radius.
Tue, 13 May 2014 00:00:00 GMThttp://hdl.handle.net/10023/102792014-05-13T00:00:00ZAntolin, P.Yokoyama, T.Van Doorsselaere, T.Current analytical and numerical modeling suggest the existence of ubiquitous thin current sheets in the corona that could explain the observed heating requirements. On the other hand, new high resolution observations of the corona indicate that its magnetic field may tend to organize itself in fine strand-like structures of few hundred kilometers widths. The link between small structure in models and the observed widths of strand-like structure several orders of magnitude larger is still not clear. A popular theoretical scenario is the nanoflare model, in which each strand is the product of an ensemble of heating events. Here, we suggest an alternative mechanism for strand generation. Through forward modeling of three-dimensional MHD simulations we show that small amplitude transverse MHD waves can lead in a few periods time to strand-like structure in loops in EUV intensity images. Our model is based on previous numerical work showing that transverse MHD oscillations can lead to Kelvin-Helmholtz instabilities that deform the cross-sectional area of loops. While previous work has focused on large amplitude oscillations, here we show that the instability can occur even for low wave amplitudes for long and thin loops, matching those presently observed in the corona. We show that the vortices generated from the instability are velocity sheared regions with enhanced emissivity hosting current sheets. Strands result as a complex combination of the vortices and the line-of-sight angle, last for timescales of a period, and can be observed for spatial resolutions of a tenth of loop radius.Forward modeling of EUV and gyrosynchrotron emission from coronal plasmas with FoMo
http://hdl.handle.net/10023/10275
The FOMO code was developed to calculate the EUV and UV emission from optically thin coronal plasmas. The input data for FOMO consists of the plasma density, temperature and velocity on a 3D grid. This is translated to emissivity on the 3D grid, using CHIANTI data. Then, the emissivity is integrated along the line-of-sight (LOS) to calculate the emergent spectral line for synthetic spectrometer observations. The code also generates the emission channels for synthetic AIA imaging observations. Moreover, the code has been extended to model also the gyrosynchrotron emission from plasmas with a population of non-thermal particles. In this case, also optically thick plasmas may be modeled. The radio spectrum is calculated over a large wavelength range, allowing for the comparison with data from a wide range of radio telescopes.
Odysseus funding (FWO-Vlaanderen), IAPP7/08CHARM (Belspo), GOA-2015-014 (KULeuven), NAOJ Visiting Fellows Program. N Misa PhD student of the FWO-Vlaanderen.
Fri, 26 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/102752016-02-26T00:00:00ZVan Doorsselaere, TomAntolin, PatrickYuan, DingReznikova, VeronikaMagyar, NorbertThe FOMO code was developed to calculate the EUV and UV emission from optically thin coronal plasmas. The input data for FOMO consists of the plasma density, temperature and velocity on a 3D grid. This is translated to emissivity on the 3D grid, using CHIANTI data. Then, the emissivity is integrated along the line-of-sight (LOS) to calculate the emergent spectral line for synthetic spectrometer observations. The code also generates the emission channels for synthetic AIA imaging observations. Moreover, the code has been extended to model also the gyrosynchrotron emission from plasmas with a population of non-thermal particles. In this case, also optically thick plasmas may be modeled. The radio spectrum is calculated over a large wavelength range, allowing for the comparison with data from a wide range of radio telescopes.Randomized low-rank Dynamic Mode Decomposition for motion detection
http://hdl.handle.net/10023/10273
This paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static video source. DMD was originally introduced in the fluid mechanics community, but is also suitable for motion detection in video streams and its use for background subtraction has received little previous investigation. In this study we present a comprehensive evaluation of background subtraction, using the randomized DMD and compare the results with leading robust principal component analysis algorithms. The results are convincing and show the random DMD is an efficient and powerful approach for background modeling, allowing processing of high resolution videos in real-time. Supplementary materials include implementations of the algorithms in Python.
N. Benjamin Erichson acknowledges support from the UK Engineering and Physical Sciences Research Council (EPSRC).
Fri, 12 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/102732016-02-12T00:00:00ZErichson, Nils BenjaminDonovan, Carl RobertThis paper introduces a fast algorithm for randomized computation of a low-rank Dynamic Mode Decomposition (DMD) of a matrix. Here we consider this matrix to represent the development of a spatial grid through time e.g. data from a static video source. DMD was originally introduced in the fluid mechanics community, but is also suitable for motion detection in video streams and its use for background subtraction has received little previous investigation. In this study we present a comprehensive evaluation of background subtraction, using the randomized DMD and compare the results with leading robust principal component analysis algorithms. The results are convincing and show the random DMD is an efficient and powerful approach for background modeling, allowing processing of high resolution videos in real-time. Supplementary materials include implementations of the algorithms in Python.Observational signatures of transverse magnetohydrodynamic waves and associated dynamic instabilities in coronal flux tubes
http://hdl.handle.net/10023/10256
MHD waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints, but also by wave processes that localise the wave power in undetectable spatial scales. In this study we conduct 3D MHD simulations and forward modelling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin-Helmholtz instability (KHI), resonant absorption and phase mixing. In the presence of a cross-loop temperature gradient we find that emission lines sensitive to the loop core catch different signatures than those more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity modulation produced by the KHI mixing. Common signatures to all considered models include an intensity and loop width modulation at half the kink period, fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.33″ and spectral resolution of 25 km s-1, although severe over-estimation of the line width is obtained. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and the KHI motions. We estimate this hidden wave energy to be a factor of 5-10 of the observed value.
This research has received funding from the UK Science and Technology Facilities Council and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214), and also from JSPS KAKENHI Grant Numbers 25220703 (PI: S. Tsuneta) and 15H03640 (PI: T. Yokoyama). T.V.D. was supported by FWO Vlaanderen’s Odysseus programme, GOA-2015-014 (KU Leuven) and the IAP P7/08 CHARM (Belspo).
Wed, 22 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/102562017-02-22T00:00:00ZAntolin, PatrickMoortel, Ineke DeDoorsselaere, Tom VanYokoyama, TakaakiMHD waves permeate the solar atmosphere and constitute potential coronal heating agents. Yet, the waves detected so far may be but a small subset of the true existing wave power. Detection is limited by instrumental constraints, but also by wave processes that localise the wave power in undetectable spatial scales. In this study we conduct 3D MHD simulations and forward modelling of standing transverse MHD waves in coronal loops with uniform and non-uniform temperature variation in the perpendicular cross-section. The observed signatures are largely dominated by the combination of the Kelvin-Helmholtz instability (KHI), resonant absorption and phase mixing. In the presence of a cross-loop temperature gradient we find that emission lines sensitive to the loop core catch different signatures than those more sensitive to the loop boundary and the surrounding corona, leading to an out-of-phase intensity modulation produced by the KHI mixing. Common signatures to all considered models include an intensity and loop width modulation at half the kink period, fine strand-like structure, a characteristic arrow-shaped structure in the Doppler maps, overall line broadening in time but particularly at the loop edges. For our model, most of these features can be captured with a spatial resolution of 0.33″ and spectral resolution of 25 km s-1, although severe over-estimation of the line width is obtained. Resonant absorption leads to a significant decrease of the observed kinetic energy from Doppler motions over time, which is not recovered by a corresponding increase in the line width from phase mixing and the KHI motions. We estimate this hidden wave energy to be a factor of 5-10 of the observed value.Going off grid : computationally efficient inference for log-Gaussian Cox processes
http://hdl.handle.net/10023/10232
This paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, whereas an approximation based on a counting process on a partition of the domain achieves only first-order convergence. The results improve upon the general theory of convergence for stochastic partial differential equation models introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern dataset, and two interesting extensions to the classical log-Gaussian Cox process framework are discussed. The first extension considers variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (2011). The second extension constructs a log-Gaussian Cox process on the world's oceans. The analysis is performed using integrated nested Laplace approximation for fast approximate inference.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/102322016-03-01T00:00:00ZSimpson, DanielIllian, Janine BaerbelLindgren, FinnSørbye, Sigrunn H.Rue, HaavardThis paper introduces a new method for performing computational inference on log-Gaussian Cox processes. The likelihood is approximated directly by making use of a continuously specified Gaussian random field. We show that for sufficiently smooth Gaussian random field prior distributions, the approximation can converge with arbitrarily high order, whereas an approximation based on a counting process on a partition of the domain achieves only first-order convergence. The results improve upon the general theory of convergence for stochastic partial differential equation models introduced by Lindgren et al. (2011). The new method is demonstrated on a standard point pattern dataset, and two interesting extensions to the classical log-Gaussian Cox process framework are discussed. The first extension considers variable sampling effort throughout the observation window and implements the method of Chakraborty et al. (2011). The second extension constructs a log-Gaussian Cox process on the world's oceans. The analysis is performed using integrated nested Laplace approximation for fast approximate inference.The classification of partition homogeneous groups with applications to semigroup theory
http://hdl.handle.net/10023/10228
Let λ=(λ1,λ2,...) be a partition of n, a sequence of positive integers in non-increasing order with sum n. Let Ω:={1,...,n}. An ordered partition P=(A1,A2,...) of Ω has type λ if |Ai|=λi.Following Martin and Sagan, we say that G is λ-transitive if, for any two ordered partitions P=(A1,A2,...) and Q=(B1,B2,...) of Ω of type λ, there exists g ∈ G with Aig=Bi for all i. A group G is said to be λ-homogeneous if, given two ordered partitions P and Q as above, inducing the sets P'={A1,A2,...} and Q'={B1,B2,...}, there exists g ∈ G such that P'g=Q'. Clearly a λ-transitive group is λ-homogeneous.The first goal of this paper is to classify the λ-homogeneous groups (Theorems 1.1 and 1.2). The second goal is to apply this classification to a problem in semigroup theory.Let Tn and Sn denote the transformation monoid and the symmetric group on Ω, respectively. Fix a group H<=Sn. Given a non-invertible transformation a in Tn-Sn and a group G<=Sn, we say that (a,G) is an H-pair if the semigroups generated by {a} ∪ H and {a} ∪ G contain the same non-units, that is, {a,G}\G= {a,H}\H. Using the classification of the λ-homogeneous groups we classify all the Sn-pairs (Theorem 1.8). For a multitude of transformation semigroups this theorem immediately implies a description of their automorphisms, congruences, generators and other relevant properties (Theorem 8.5). This topic involves both group theory and semigroup theory; we have attempted to include enough exposition to make the paper self-contained for researchers in both areas. The paper finishes with a number of open problems on permutation and linear groups.
Fri, 15 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/102282016-04-15T00:00:00ZAndré, JorgeAraúo, JoāoCameron, Peter JephsonLet λ=(λ1,λ2,...) be a partition of n, a sequence of positive integers in non-increasing order with sum n. Let Ω:={1,...,n}. An ordered partition P=(A1,A2,...) of Ω has type λ if |Ai|=λi.Following Martin and Sagan, we say that G is λ-transitive if, for any two ordered partitions P=(A1,A2,...) and Q=(B1,B2,...) of Ω of type λ, there exists g ∈ G with Aig=Bi for all i. A group G is said to be λ-homogeneous if, given two ordered partitions P and Q as above, inducing the sets P'={A1,A2,...} and Q'={B1,B2,...}, there exists g ∈ G such that P'g=Q'. Clearly a λ-transitive group is λ-homogeneous.The first goal of this paper is to classify the λ-homogeneous groups (Theorems 1.1 and 1.2). The second goal is to apply this classification to a problem in semigroup theory.Let Tn and Sn denote the transformation monoid and the symmetric group on Ω, respectively. Fix a group H<=Sn. Given a non-invertible transformation a in Tn-Sn and a group G<=Sn, we say that (a,G) is an H-pair if the semigroups generated by {a} ∪ H and {a} ∪ G contain the same non-units, that is, {a,G}\G= {a,H}\H. Using the classification of the λ-homogeneous groups we classify all the Sn-pairs (Theorem 1.8). For a multitude of transformation semigroups this theorem immediately implies a description of their automorphisms, congruences, generators and other relevant properties (Theorem 8.5). This topic involves both group theory and semigroup theory; we have attempted to include enough exposition to make the paper self-contained for researchers in both areas. The paper finishes with a number of open problems on permutation and linear groups.Balanced solutions for an ellipsoidal vortex in a rotating stratified flow
http://hdl.handle.net/10023/10227
We consider the motion of a single ellipsoidal vortex with uniform potential vorticity in a rotating stratified fluid at finite Rossby number . Building on previous solutions obtained under the quasi-geostrophic approximation (at first order in ), we obtain analytical solutions for the balanced part of the flow at . These solutions capture important ageostrophic effects giving rise to an asymmetry in the evolution of cyclonic and anticyclonic vortices. Previous work has shown that, if the velocity field induced by an ellipsoidal vortex only depends linearly on spatial coordinates inside the vortex, i.e. , then the dynamics reduces markedly to a simple matrix equation. The instantaneous vortex shape and orientation are encapsulated in a symmetric matrix , which is acted upon by the flow matrix to provide the vortex evolution. Under the quasi-geostrophic approximation, the flow matrix is determined by inverting the potential vorticity to obtain the streamfunction via Poisson's equation, which has a known analytical solution depending on elliptic integrals. Here we show that higher-order balanced solutions, up to second order in the Rossby number, can also be calculated analytically. However, in this case there is a vector potential that requires the solution of three Poisson equations for each of its components. The source terms for these equations are independent of spatial coordinates within the ellipsoid, depending only on the elliptic integrals solved at the leading, quasi-geostrophic order. Unlike the quasi-geostrophic case, these source terms do not in general vanish outside the ellipsoid and have an inordinately complicated dependence on spatial coordinates. In the special case of an ellipsoid whose axes are aligned with the coordinate axes, we are able to derive these source terms and obtain the full analytical solution to the three Poisson equations. However, if one considers the homogeneous case, whereby the outer source terms are neglected, one can obtain an approximate solution having a compact matrix form analogous to the leading-order quasi-geostrophic case. This approximate solution proves to be highly accurate for the general case of an arbitrarily oriented ellipsoid, as verified through comparisons of the solutions with solutions obtained from numerical simulations of an ellipsoid using an accurate nonlinear balance model, even at moderate Rossby numbers.
Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant number EP/H001794/1).
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/102272016-09-01T00:00:00ZMckiver, William J.Dritschel, David G.We consider the motion of a single ellipsoidal vortex with uniform potential vorticity in a rotating stratified fluid at finite Rossby number . Building on previous solutions obtained under the quasi-geostrophic approximation (at first order in ), we obtain analytical solutions for the balanced part of the flow at . These solutions capture important ageostrophic effects giving rise to an asymmetry in the evolution of cyclonic and anticyclonic vortices. Previous work has shown that, if the velocity field induced by an ellipsoidal vortex only depends linearly on spatial coordinates inside the vortex, i.e. , then the dynamics reduces markedly to a simple matrix equation. The instantaneous vortex shape and orientation are encapsulated in a symmetric matrix , which is acted upon by the flow matrix to provide the vortex evolution. Under the quasi-geostrophic approximation, the flow matrix is determined by inverting the potential vorticity to obtain the streamfunction via Poisson's equation, which has a known analytical solution depending on elliptic integrals. Here we show that higher-order balanced solutions, up to second order in the Rossby number, can also be calculated analytically. However, in this case there is a vector potential that requires the solution of three Poisson equations for each of its components. The source terms for these equations are independent of spatial coordinates within the ellipsoid, depending only on the elliptic integrals solved at the leading, quasi-geostrophic order. Unlike the quasi-geostrophic case, these source terms do not in general vanish outside the ellipsoid and have an inordinately complicated dependence on spatial coordinates. In the special case of an ellipsoid whose axes are aligned with the coordinate axes, we are able to derive these source terms and obtain the full analytical solution to the three Poisson equations. However, if one considers the homogeneous case, whereby the outer source terms are neglected, one can obtain an approximate solution having a compact matrix form analogous to the leading-order quasi-geostrophic case. This approximate solution proves to be highly accurate for the general case of an arbitrarily oriented ellipsoid, as verified through comparisons of the solutions with solutions obtained from numerical simulations of an ellipsoid using an accurate nonlinear balance model, even at moderate Rossby numbers.High Gaussicity feedhorns for sub-/ millimeter wave applications
http://hdl.handle.net/10023/10171
In feedhorn design, the power coupling to the fundamental free-space LG00 mode, or Gaussicity, is a good proxy for high performance, particularly the sidelobe and cross-polar levels and the near-field behavior. Gaussicity can be maximized by ensuring that the first few horn modes reach the aperture with the appropriate phase and amplitude relationship. We present two feedhorn designs for which the Gaussicity was maximized in order to achieve high performance. The first is a 94 GHz corrugated horn with a tanh-linear profile, manufactured by electroforming, which achieves a Gaussicity of 99.92% at band center and sidelobes at the -60 dB level. The second is a 340 GHz smooth-walled spline horn which achieves a Gaussicity of >99.2% over a 10% bandwidth, sidelobes below -30 dB and excellent near-field behavior. This design has been successfully fabricated in E-plane split block suitable for low volume manufacture, for example for imaging arrays.
Mon, 28 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/101712016-11-28T00:00:00ZRobertson, Duncan A.McKay, Johannes E.Hunter, Robert I.Speirs, Peter J.Smith, Graham M.In feedhorn design, the power coupling to the fundamental free-space LG00 mode, or Gaussicity, is a good proxy for high performance, particularly the sidelobe and cross-polar levels and the near-field behavior. Gaussicity can be maximized by ensuring that the first few horn modes reach the aperture with the appropriate phase and amplitude relationship. We present two feedhorn designs for which the Gaussicity was maximized in order to achieve high performance. The first is a 94 GHz corrugated horn with a tanh-linear profile, manufactured by electroforming, which achieves a Gaussicity of 99.92% at band center and sidelobes at the -60 dB level. The second is a 340 GHz smooth-walled spline horn which achieves a Gaussicity of >99.2% over a 10% bandwidth, sidelobes below -30 dB and excellent near-field behavior. This design has been successfully fabricated in E-plane split block suitable for low volume manufacture, for example for imaging arrays.On The Lq dimensions of measures on Heuter-Lalley type self-affine sets
http://hdl.handle.net/10023/10165
We study the Lq-dimensions of self-affine measures and the Käenmäki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, checkable conditions under which the Lq-dimensions are equal to the value predicted by Falconer for a range of q. As a corollary this gives a wider class of self-affine sets for which the Hausdorff dimension can be explicitly calculated. Our proof combines the potential theoretic approach developed by Hunt and Kaloshin with recent advances in the dynamics of self-affine sets.
JMF acknowledges financial support from a Leverhulme Trust Research Fellowship (RF-2016-500).
Sat, 21 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/101652017-01-21T00:00:00ZFraser, Jonathan MacDonaldKempton, TomWe study the Lq-dimensions of self-affine measures and the Käenmäki measure on a class of self-affine sets similar to the class considered by Hueter and Lalley. We give simple, checkable conditions under which the Lq-dimensions are equal to the value predicted by Falconer for a range of q. As a corollary this gives a wider class of self-affine sets for which the Hausdorff dimension can be explicitly calculated. Our proof combines the potential theoretic approach developed by Hunt and Kaloshin with recent advances in the dynamics of self-affine sets.An experiment of the impact of a neonicotinoid pesticide on honeybees : the value of a formal analysis of the data
http://hdl.handle.net/10023/10159
Background: We assess the analysis of the data resulting from a field experiment conducted by Pilling et al. (2013) on the potential effects of thiamethoxam on honey bees. The experiment had low levels of replication, so Pilling et al. concluded that formal statistical analysis would be misleading. This would be true if such an analysis merely comprised tests of statistical significance and if the investigators concluded that lack of significance meant little or no effect. However, an analysis that includes estimation of the size of any effects—with confidence limits—allows one to reach conclusions that are not misleading and that produce useful insights. Main Body: For the data of Pilling et al. we use straightforward statistical analysis to show that the confidence limits are generally so wide that any effects of thiamethoxam could have been large without being statistically significant. Instead of formal analysis, Pilling et al. simply inspected the data and concluded that they provided no evidence of detrimental effects and from this that thiamethoxam poses a “low risk” to bees. Conclusions: Conclusions derived from inspection of the data were not just misleading in this case but are unacceptable in principle, for if data are inadequate for a formal analysis (or only good enough to provide estimates with wide confidence intervals) then they are bound to be inadequate as a basis for reaching any sound conclusions. Given that the data in this case are largely uninformative with respect to the treatment effect, any conclusions reached from such informal approaches can do little more than reflect the prior beliefs of those involved.
This work received funding from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) and their support is gratefully acknowledged. MASTS is funded by the Scottish Funding Council (Grant reference HR09011) and contributing institutions.
Mon, 23 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/101592017-01-23T00:00:00ZSchick, Robert S.Greenwood, Jeremy J. D.Buckland, Stephen T.Background: We assess the analysis of the data resulting from a field experiment conducted by Pilling et al. (2013) on the potential effects of thiamethoxam on honey bees. The experiment had low levels of replication, so Pilling et al. concluded that formal statistical analysis would be misleading. This would be true if such an analysis merely comprised tests of statistical significance and if the investigators concluded that lack of significance meant little or no effect. However, an analysis that includes estimation of the size of any effects—with confidence limits—allows one to reach conclusions that are not misleading and that produce useful insights. Main Body: For the data of Pilling et al. we use straightforward statistical analysis to show that the confidence limits are generally so wide that any effects of thiamethoxam could have been large without being statistically significant. Instead of formal analysis, Pilling et al. simply inspected the data and concluded that they provided no evidence of detrimental effects and from this that thiamethoxam poses a “low risk” to bees. Conclusions: Conclusions derived from inspection of the data were not just misleading in this case but are unacceptable in principle, for if data are inadequate for a formal analysis (or only good enough to provide estimates with wide confidence intervals) then they are bound to be inadequate as a basis for reaching any sound conclusions. Given that the data in this case are largely uninformative with respect to the treatment effect, any conclusions reached from such informal approaches can do little more than reflect the prior beliefs of those involved.Solar science with the Atacama Large Millimeter/Submillimeter Array — a new view of our sun
http://hdl.handle.net/10023/10156
The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere—a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.
Fri, 01 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/101562016-04-01T00:00:00ZWedemeyer, S.Bastian, T.Brajša, R.Hudson, H.Fleishman, G.Loukitcheva, M.Fleck, B.Kontar, E. P.De Pontieu, B.Yagoubov, P.Tiwari, S. K.Soler, R.Black, J. H.Antolin, P.Scullion, E.Gunár, S.Labrosse, N.Ludwig, H.-G.Benz, A. O.White, S. M.Hauschildt, P.Doyle, J. G.Nakariakov, V. M.Ayres, T.Heinzel, P.Karlicky, M.Van Doorsselaere, T.Gary, D.Alissandrakis, C. E.Nindos, A.Solanki, S. K.Rouppe van der Voort, L.Shimojo, M.Kato, Y.Zaqarashvili, T.Perez, E.Selhorst, C. L.Barta, M.The Atacama Large Millimeter/submillimeter Array (ALMA) is a new powerful tool for observing the Sun at high spatial, temporal, and spectral resolution. These capabilities can address a broad range of fundamental scientific questions in solar physics. The radiation observed by ALMA originates mostly from the chromosphere—a complex and dynamic region between the photosphere and corona, which plays a crucial role in the transport of energy and matter and, ultimately, the heating of the outer layers of the solar atmosphere. Based on first solar test observations, strategies for regular solar campaigns are currently being developed. State-of-the-art numerical simulations of the solar atmosphere and modeling of instrumental effects can help constrain and optimize future observing modes for ALMA. Here we present a short technical description of ALMA and an overview of past efforts and future possibilities for solar observations at submillimeter and millimeter wavelengths. In addition, selected numerical simulations and observations at other wavelengths demonstrate ALMA's scientific potential for studying the Sun for a large range of science cases.A dynamical definition of f.g. virtually free groups
http://hdl.handle.net/10023/10148
We show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson's group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0,1}ω. There are also connections with formal language theory, as the class of groups with context-free word problem is also the class of finitely generated virtually free groups, while R. Thompson's group V is a candidate as a universal coCF group by Lehnert's conjecture, corresponding to the class of groups with context free co-word problem (as introduced by Holt, Rees, Röver, and Thomas). Our main results answers a question of Berns-Zieze, Fry, Gillings, Hoganson, and Matthews, and separately of Bleak and Salazar-Días, and fits into the larger exploration of the class of coCF groups as it shows that all four of the known properties of the class of coCF groups hold for the set of finitely generation subgroups of V .
Mon, 01 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/101482016-02-01T00:00:00ZBennett, DanielBleak, CollinWe show that the class of finitely generated virtually free groups is precisely the class of demonstrable subgroups for R. Thompson's group V . The class of demonstrable groups for V consists of all groups which can embed into V with a natural dynamical behaviour in their induced actions on the Cantor space C2 := {0,1}ω. There are also connections with formal language theory, as the class of groups with context-free word problem is also the class of finitely generated virtually free groups, while R. Thompson's group V is a candidate as a universal coCF group by Lehnert's conjecture, corresponding to the class of groups with context free co-word problem (as introduced by Holt, Rees, Röver, and Thomas). Our main results answers a question of Berns-Zieze, Fry, Gillings, Hoganson, and Matthews, and separately of Bleak and Salazar-Días, and fits into the larger exploration of the class of coCF groups as it shows that all four of the known properties of the class of coCF groups hold for the set of finitely generation subgroups of V .Global sausage oscillation of solar flare loops detected by the Interface Region Imaging Spectrograph
http://hdl.handle.net/10023/10140
An observation from the Interface Region Imaging Spectrograph reveals coherent oscillations in the loops of an M1.6 flare on 2015 March 12. Both the intensity and Doppler shift of Fe xxi 1354.08 Å show clear oscillations with a period of ˜25 s. Remarkably similar oscillations were also detected in the soft X-ray flux recorded by the Geostationary Operational Environmental Satellites (GOES). With an estimated phase speed of ˜2420 km s-1 and a derived electron density of at least 5.4 × 1010cm-3, the observed short-period oscillation is most likely the global fast sausage mode of a hot flare loop. We find a phase shift of ˜π/2 (1/4 period) between the Doppler shift oscillation and the intensity/GOES oscillations, which is consistent with a recent forward modeling study of the sausage mode. The observed oscillation requires a density contrast between the flare loop and coronal background of a factor ≥42. The estimated phase speed of the global mode provides a lower limit of the Alfvén speed outside the flare loop. We also find an increase of the oscillation period,which might be caused by the separation of the loop footpoints with time.
Fri, 20 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/101402016-05-20T00:00:00ZTian, HuiYoung, Peter R.Reeves, Katharine K.Wang, TongjiangAntolin, PatrickChen, BinHe, JiansenAn observation from the Interface Region Imaging Spectrograph reveals coherent oscillations in the loops of an M1.6 flare on 2015 March 12. Both the intensity and Doppler shift of Fe xxi 1354.08 Å show clear oscillations with a period of ˜25 s. Remarkably similar oscillations were also detected in the soft X-ray flux recorded by the Geostationary Operational Environmental Satellites (GOES). With an estimated phase speed of ˜2420 km s-1 and a derived electron density of at least 5.4 × 1010cm-3, the observed short-period oscillation is most likely the global fast sausage mode of a hot flare loop. We find a phase shift of ˜π/2 (1/4 period) between the Doppler shift oscillation and the intensity/GOES oscillations, which is consistent with a recent forward modeling study of the sausage mode. The observed oscillation requires a density contrast between the flare loop and coronal background of a factor ≥42. The estimated phase speed of the global mode provides a lower limit of the Alfvén speed outside the flare loop. We also find an increase of the oscillation period,which might be caused by the separation of the loop footpoints with time.Numerical simulations of sunspot rotation driven by magnetic flux emergence
http://hdl.handle.net/10023/10129
Magnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the sub-photospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length
equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by sub-photospheric velocities twisting the
footpoints of flux tubes.
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/101292017-06-23T00:00:00ZSturrock, ZoeMagnetic flux continually emerges from the Sun, rising through the solar interior, emerging at the photosphere in the form of sunspots and expanding into the atmosphere. Observations of sunspot rotations have been reported for over a century and are often accompanied by solar eruptions and flaring activity. In this thesis, we present 3D numerical simulations of the emergence of twisted flux tubes from the uppermost layers of the solar interior, examining the rotational movements of sunspots in the photospheric plane. The basic experiment introduces the mechanism and characteristics of sunspot rotation by a clear calculation of rotation angle, vorticity, magnetic helicity and energy, whereby we find an untwisting of the interior portion of the field, accompanied by an injection of twist into the atmospheric field. We extend this model by altering the initial field strength and twist of the sub-photospheric tube. This comparison reveals the rotation angle, helicity and current show a direct dependence on field strength. An increase in field strength increases the rotation angle, the length of fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. The fieldline length is crucial as we predict the twist per unit length
equilibrates to a lower value on longer fieldlines, and hence possesses a larger rotation angle. No such direct dependence is found when varying the twist but there is a clear ordering in rotation angle, helicity, and energy, with more highly twisted tubes undergoing larger rotation angles. We believe the final angle of rotation is reached when the system achieves a constant degree of twist along the length of fieldlines. By extrapolating the size of the modelled active region, we find rotation angles and rates comparable with those observed. In addition, we explore sunspot rotation caused by sub-photospheric velocities twisting the
footpoints of flux tubes.From distance sampling to spatial capture-recapture
http://hdl.handle.net/10023/10116
Distance sampling and capture–recapture are the two most widely used wildlife abundance estimation methods. capture–recapture methods have only recently incorporated models for spatial distribution and there is an increasing tendency for distance sampling methods to incorporated spatial models rather than to rely on partly design-based spatial inference. In this overview we show how spatial models are central to modern distance sampling and that spatial capture–recapture models arise as an extension of distance sampling methods. Depending on the type of data recorded, they can be viewed as particular kinds of hierarchical binary regression, Poisson regression, survival or time-to-event models, with individuals’ locations as latent variables and a spatial model as the latent variable distribution. Incorporation of spatial models in these two methods provides new opportunities for drawing explicitly spatial inferences. Areas of likely future development include more sophisticated spatial and spatio-temporal modelling of individuals’ locations and movements, new methods for integrating spatial capture–recapture and other kinds of ecological survey data, and methods for dealing with the recapture uncertainty that often arise when “capture” consists of detection by a remote device like a camera trap or microphone.
TAM thanks support by CEAUL (funded by FCT—Fundação para a Ciência e a Tecnologia, Portugal, through the Project UID/MAT/00006/2013).
Tue, 10 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/101162017-01-10T00:00:00ZBorchers, David L.Marques, Tiago A.Distance sampling and capture–recapture are the two most widely used wildlife abundance estimation methods. capture–recapture methods have only recently incorporated models for spatial distribution and there is an increasing tendency for distance sampling methods to incorporated spatial models rather than to rely on partly design-based spatial inference. In this overview we show how spatial models are central to modern distance sampling and that spatial capture–recapture models arise as an extension of distance sampling methods. Depending on the type of data recorded, they can be viewed as particular kinds of hierarchical binary regression, Poisson regression, survival or time-to-event models, with individuals’ locations as latent variables and a spatial model as the latent variable distribution. Incorporation of spatial models in these two methods provides new opportunities for drawing explicitly spatial inferences. Areas of likely future development include more sophisticated spatial and spatio-temporal modelling of individuals’ locations and movements, new methods for integrating spatial capture–recapture and other kinds of ecological survey data, and methods for dealing with the recapture uncertainty that often arise when “capture” consists of detection by a remote device like a camera trap or microphone.Flux-rope twist in eruptive flares and CMEs : due to zipper and main-phase reconnection
http://hdl.handle.net/10023/10114
The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.
Funding: UK Science and Technology Facilities Council
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/101142017-01-01T00:00:00ZPriest, Eric RonaldLongcope, D.W.The nature of three-dimensional reconnection when a twisted flux tube erupts during an eruptive flare or coronal mass ejection is considered. The reconnection has two phases: first of all, 3D “zipper reconnection” propagates along the initial coronal arcade, parallel to the polarity inversion line (PIL); then subsequent quasi-2D “main phase reconnection” in the low corona around a flux rope during its eruption produces coronal loops and chromospheric ribbons that propagate away from the PIL in a direction normal to it. One scenario starts with a sheared arcade: the zipper reconnection creates a twisted flux rope of roughly one turn (2π radians of twist), and then main phase reconnection builds up the bulk of the erupting flux rope with a relatively uniform twist of a few turns. A second scenario starts with a pre-existing flux rope under the arcade. Here the zipper phase can create a core with many turns that depend on the ratio of the magnetic fluxes in the newly formed flare ribbons and the new flux rope. Main phase reconnection then adds a layer of roughly uniform twist to the twisted central core. Both phases and scenarios are modeled in a simple way that assumes the initial magnetic flux is fragmented along the PIL. The model uses conservation of magnetic helicity and flux, together with equipartition of magnetic helicity, to deduce the twist of the erupting flux rope in terms the geometry of the initial configuration. Interplanetary observations show some flux ropes have a fairly uniform twist, which could be produced when the zipper phase and any pre-existing flux rope possess small or moderate twist (up to one or two turns). Other interplanetary flux ropes have highly twisted cores (up to five turns), which could be produced when there is a pre-existing flux rope and an active zipper phase that creates substantial extra twist.An assessment of the population of cotton-top tamarins (Saguinus oedipus) and their habitat in Colombia
http://hdl.handle.net/10023/10100
Numerous animals have declining populations due to habitat loss, illegal wildlife trade, and climate change. The cotton-top tamarin (Saguinus oedipus) is a Critically Endangered primate species, endemic to northwest Colombia, threatened by deforestation and illegal trade. In order to assess the current state of this species, we analyzed changes in the population of cotton-top tamarins and its habitat from 2005 to 2012. We used a tailor-made "lure strip transect" method to survey 43 accessible forest parcels that represent 30% of the species' range. Estimated population size in the surveyed region was approximately 2,050 in 2005 and 1,900 in 2012, with a coefficient of variation of approximately 10%. The estimated population change between surveys was -7% (a decline of approximately 1.3% per year) suggesting a relatively stable population. If densities of inaccessible forest parcels are similar to those of surveyed samples, the estimated population of cotton-top tamarins in the wild in 2012 was 6,946 individuals. We also recorded little change in the amount of suitable habitat for cotton-top tamarins between sample periods: in 2005, 18% of surveyed forest was preferred habitat for cotton-top tamarins, while in 2012, 17% percent was preferred. We attribute the relatively stable population of this Critically Endangered species to increased conservation efforts of Proyecto Tití, conservation NGOs, and the Colombian government. Due to continued threats to cotton-top tamarins and their habitat such as agriculture and urban expansion, ongoing conservation efforts are needed to ensure the long-term survival of cotton-top tamarins in Colombia.
Wed, 28 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/101002016-12-28T00:00:00ZSavage, AnneThomas, LenFeilen, Katie L.Kidney, DarrenSoto, Luis H.Pearson, MackenzieMedina, Felix S.Emeris, GermanGuillen, Rosamira R.Numerous animals have declining populations due to habitat loss, illegal wildlife trade, and climate change. The cotton-top tamarin (Saguinus oedipus) is a Critically Endangered primate species, endemic to northwest Colombia, threatened by deforestation and illegal trade. In order to assess the current state of this species, we analyzed changes in the population of cotton-top tamarins and its habitat from 2005 to 2012. We used a tailor-made "lure strip transect" method to survey 43 accessible forest parcels that represent 30% of the species' range. Estimated population size in the surveyed region was approximately 2,050 in 2005 and 1,900 in 2012, with a coefficient of variation of approximately 10%. The estimated population change between surveys was -7% (a decline of approximately 1.3% per year) suggesting a relatively stable population. If densities of inaccessible forest parcels are similar to those of surveyed samples, the estimated population of cotton-top tamarins in the wild in 2012 was 6,946 individuals. We also recorded little change in the amount of suitable habitat for cotton-top tamarins between sample periods: in 2005, 18% of surveyed forest was preferred habitat for cotton-top tamarins, while in 2012, 17% percent was preferred. We attribute the relatively stable population of this Critically Endangered species to increased conservation efforts of Proyecto Tití, conservation NGOs, and the Colombian government. Due to continued threats to cotton-top tamarins and their habitat such as agriculture and urban expansion, ongoing conservation efforts are needed to ensure the long-term survival of cotton-top tamarins in Colombia.Inference of heating properties from "hot" non-flaring plasmas in active region cores. II. Nanoflare trains
http://hdl.handle.net/10023/10097
Despite its prediction over two decades ago, the detection of faint, high-temperature ("hot") emission due to nanoflare heating in non-flaring active region cores has proved challenging. Using an efficient two-fluid hydrodynamic model, this paper investigates the properties of the emission expected from repeating nanoflares (a nanoflare train) of varying frequency as well as the separate heating of electrons and ions. If the emission measure distribution (EM(T)) peaks at T = Tm, we find that EM(Tm) is independent of details of the nanoflare train, and EM(T) above and below Tm reflects different aspects of the heating. Below Tm, the main influence is the relationship of the waiting time between successive nanoflares to the nanoflare energy. Above Tm, power-law nanoflare distributions lead to an extensive plasma population not present in a mono-energetic train. Furthermore, in some cases, characteristic features are present in EM(T). Such details may be detectable given adequate spectral resolution and a good knowledge of the relevant atomic physics. In the absence of such resolution we propose some metrics that can be used to infer the presence of "hot" plasma.
This work was supported in part by the Big-Data Private-Cloud Research Cyberinfrastructure MRI-award funded by NSF under grant CNS-1338099 and by Rice University.
Tue, 20 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/100972016-12-20T00:00:00ZBarnes, W. T.Cargill, P. J.Bradshaw, S. J.Despite its prediction over two decades ago, the detection of faint, high-temperature ("hot") emission due to nanoflare heating in non-flaring active region cores has proved challenging. Using an efficient two-fluid hydrodynamic model, this paper investigates the properties of the emission expected from repeating nanoflares (a nanoflare train) of varying frequency as well as the separate heating of electrons and ions. If the emission measure distribution (EM(T)) peaks at T = Tm, we find that EM(Tm) is independent of details of the nanoflare train, and EM(T) above and below Tm reflects different aspects of the heating. Below Tm, the main influence is the relationship of the waiting time between successive nanoflares to the nanoflare energy. Above Tm, power-law nanoflare distributions lead to an extensive plasma population not present in a mono-energetic train. Furthermore, in some cases, characteristic features are present in EM(T). Such details may be detectable given adequate spectral resolution and a good knowledge of the relevant atomic physics. In the absence of such resolution we propose some metrics that can be used to infer the presence of "hot" plasma.On optimality and construction of circular repeated-measurements designs
http://hdl.handle.net/10023/10092
The aim of this paper is to characterize and construct universally optimal designs among the class of circular repeated-measurements designs when the parameters do not permit balance for carry-over effects. It is shown that some circular weakly neighbour balanced designs defined by Filipiak and Markiewicz (2012) are universally optimal repeated-measurements designs. These results extend the work of Magda (1980), Kunert (1984b) and Filipiak and Markiewicz (2012).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/100922017-01-01T00:00:00ZBailey, Rosemary AnneCameron, Peter JephsonFilipiak, KatarzynaKunert, JoachimMarkiewicz, AugustynThe aim of this paper is to characterize and construct universally optimal designs among the class of circular repeated-measurements designs when the parameters do not permit balance for carry-over effects. It is shown that some circular weakly neighbour balanced designs defined by Filipiak and Markiewicz (2012) are universally optimal repeated-measurements designs. These results extend the work of Magda (1980), Kunert (1984b) and Filipiak and Markiewicz (2012).On the stability of homogeneous steady states of a chemotaxis system with logistic growth term
http://hdl.handle.net/10023/10087
We consider a nonlinear PDEs system of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a population “n” towards a higher concentration of a chemical “c” in a bounded domain Ω. We consider constant chemotactic sensitivity χ and an elliptic equation to describe the distribution of the chemicalnt − dnΔn = −χdiv(n∇c) + μn(1−n), −dcΔc + c = h(n) for a monotone increasing and lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2χ∣h′∣ < μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.
Fri, 01 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/100872016-07-01T00:00:00ZChaplain, Mark Andrew JosephTello, J. I.We consider a nonlinear PDEs system of Parabolic-Elliptic type with chemotactic terms. The system models the movement of a population “n” towards a higher concentration of a chemical “c” in a bounded domain Ω. We consider constant chemotactic sensitivity χ and an elliptic equation to describe the distribution of the chemicalnt − dnΔn = −χdiv(n∇c) + μn(1−n), −dcΔc + c = h(n) for a monotone increasing and lipschitz function h. We study the asymptotic behavior of solutions under the assumption of 2χ∣h′∣ < μ. As a result of the asymptotic stability we obtain the uniqueness of the strictly positive steady states.Transience and multifractal analysis
http://hdl.handle.net/10023/10086
We study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole system is considered (and not just its recurrent part) the conditional variational principle does not necessarily hold. Moreover, we exhibit an example of a topologically transitive map having discontinuous Lyapunov spectrum. The mechanism producing all these pathological features on the multifractal spectra is transience, that is, the non-recurrent part of the dynamics.
G.I. was partially supported by the Center of Dynamical Systems and Related Fields código ACT1103 and by Proyecto Fondecyt 1150058. T.J. wishes to thank Proyecto Mecesup-0711 for funding his visit to PUC-Chile. M.T. is grateful for the support of Proyecto Fondecyt 1110040 for funding his visit to PUC-Chile and for partial support from NSF grant DMS 1109587.
Mon, 11 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/100862016-01-11T00:00:00ZIommi, GodofredoJordan, ThomasTodd, Michael JohnWe study dimension theory for dissipative dynamical systems, proving a conditional variational principle for the quotients of Birkhoff averages restricted to the recurrent part of the system. On the other hand, we show that when the whole system is considered (and not just its recurrent part) the conditional variational principle does not necessarily hold. Moreover, we exhibit an example of a topologically transitive map having discontinuous Lyapunov spectrum. The mechanism producing all these pathological features on the multifractal spectra is transience, that is, the non-recurrent part of the dynamics.Magneto-static modeling from SUNRISE/IMaX : application to an active region observed with SUNRISE II
http://hdl.handle.net/10023/10083
Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the \sunrise{} balloon-borne solar observatory in June 2013 as boundary condition for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magneto-static extrapolation approach, which has been applied earlier ({\it Paper I}) to a quiet Sun region observed with \sunrise{} I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110-130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents.
Wed, 22 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/100832017-03-22T00:00:00ZWiegelmann, T.Neukirch, ThomasNickeler, D. H.Solanki, S. K.Barthol, P.Gandorfer, A.Gizon, L.Hirzberger, J.Riethmüller, T. L.Noort, M. vanRodríguez, J. BlancoDel Toro Iniesta, J. C.Suárez, D. OrozcoSchmidt, W.Pillet, V. MartínezKnölker, M.Magneto-static models may overcome some of the issues facing force-free magnetic field extrapolations. So far they have seen limited use and have faced problems when applied to quiet-Sun data. Here we present a first application to an active region. We use solar vector magnetic field measurements gathered by the IMaX polarimeter during the flight of the \sunrise{} balloon-borne solar observatory in June 2013 as boundary condition for a magneto-static model of the higher solar atmosphere above an active region. The IMaX data are embedded in active region vector magnetograms observed with SDO/HMI. This work continues our magneto-static extrapolation approach, which has been applied earlier ({\it Paper I}) to a quiet Sun region observed with \sunrise{} I. In an active region the signal-to-noise-ratio in the measured Stokes parameters is considerably higher than in the quiet Sun and consequently the IMaX measurements of the horizontal photospheric magnetic field allow us to specify the free parameters of the model in a special class of linear magneto-static equilibria. The high spatial resolution of IMaX (110-130 km, pixel size 40 km) enables us to model the non-force-free layer between the photosphere and the mid chromosphere vertically by about 50 grid points. In our approach we can incorporate some aspects of the mixed beta layer of photosphere and chromosphere, e.g., taking a finite Lorentz force into account, which was not possible with lower resolution photospheric measurements in the past. The linear model does not, however, permit to model intrinsic nonlinear structures like strongly localized electric currents.Multifractal spectra and multifractal zeta-functions
http://hdl.handle.net/10023/10071
We introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. More precisely, we prove that these and more general multifractal spectra equal the abscissae of convergence of the associated zeta-functions.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/100712017-02-01T00:00:00ZMijovic, VuksanOlsen, Lars Ole RonnowWe introduce multifractal zetafunctions providing precise information of a very general class of multifractal spectra, including, for example, the multifractal spectra of self-conformal measures and the multifractal spectra of ergodic Birkhoff averages of continuous functions. More precisely, we prove that these and more general multifractal spectra equal the abscissae of convergence of the associated zeta-functions.A relaxation model of coronal heating in multiple interacting flux ropes
http://hdl.handle.net/10023/10070
Context: Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events. Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles. Methods: The final state is calculated by assuming a helicity-conserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kink-unstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state. Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multi-thread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope. Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kink-unstable.
The authors wish to recognise funding from EPSRC through the Fusion Centre for Doctoral Training (Fusion-CDT - grant code: EP/K504178/1) through which this project is possible. Support from STFC for PKB and AWH is also acknowledged (grant numbers ST/L000768/1 and ST/N000609/1).
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/100702017-04-01T00:00:00ZHussain, A. S.Browning, P. K.Hood, A. W.Context: Heating the solar corona requires dissipation of stored magnetic energy, which may occur in twisted magnetic fields. Recently published numerical simulations show that the ideal kink instability in a twisted magnetic thread may trigger energy release in stable twisted neighbours, and demonstrate an avalanche of heating events. Aims: We aim to construct a Taylor relaxation model for the energy release from two flux ropes and compare this with the outcomes of the simulations. We then aim to extend the model to large numbers of flux ropes, allowing the possibility of modelling a heating avalanche, and calculation of the energy release for ensembles of twisted threads with varying twist profiles. Methods: The final state is calculated by assuming a helicity-conserving relaxation to a minimum energy state. Multiple scenarios are examined, which include kink-unstable flux ropes relaxing on their own, as well as stable and unstable flux ropes merging into a single rope as a result of magnetic reconnection. We consider alternative constraints that determine the spatial extent of the final relaxed state. Results: Good agreement is found between the relaxation model and the magnetohydrodynamic simulations, both for interactions of two twisted threads and for a multi-thread avalanche. The model can predict the energy release for flux ropes of varying degrees of twist, which relax individually or which merge through reconnection into a single flux rope. It is found that the energy output of merging flux ropes is dominated by the energy of the most strongly twisted rope. Conclusions: The relaxation approach provides a very good estimate of the energy release in an ensemble of twisted threads of which one is kink-unstable.Average distances on self-similar sets and higher order average distances of self-similar measures
http://hdl.handle.net/10023/10069
The purpose of this paper is twofold: (1) We study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of in ℝ.
Thu, 29 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/100692016-12-29T00:00:00ZAllen, D.Edwards, H.Harper, S.Olsen, Lars Ole RonnowThe purpose of this paper is twofold: (1) We study different notions of the average distance between two points of a self-similar subset of ℝ, and (2) we investigate the asymptotic behaviour of higher order average moments of self-similar measures on self-similar subsets of in ℝ.A new approach for modelling chromospheric evaporation in response to enhanced coronal heating. I. The method
http://hdl.handle.net/10023/10063
We present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation).However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux ‘jumps’ across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed.
C.D.J. acknowledges the financial support of the Carnegie Trust for the Universities of Scotland. This project has received funding from the Science and Technology Facilities Council (UK) through the consolidated grant ST/N000609/1 and the European Research Council (ERC) under the European Union’s Horizon 2020 research and innovation program (grant agreement No 647214).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/100632017-01-01T00:00:00ZJohnston, Craig DavidHood, Alan WilliamCargill, PeterDe Moortel, InekeWe present a new computational approach that addresses the difficulty of obtaining the correct interaction between the solar corona and the transition region in response to rapid heating events. In the coupled corona, transition region and chromosphere system, an enhanced downward conductive flux results in an upflow (chromospheric evaporation).However, obtaining the correct upflow generally requires high spatial resolution in order to resolve the transition region. With an unresolved transition region, artificially low coronal densities are obtained because the downward heat flux ‘jumps’ across the unresolved region to the chromosphere, underestimating the upflows. Here, we treat the lower transition region as a discontinuity that responds to changing coronal conditions through the imposition of a jump condition that is derived from an integrated form of energy conservation. To illustrate and benchmark this approach against a fully resolved one-dimensional model, we present field-aligned simulations of coronal loops in response to a range of impulsive (spatially uniform) heating events. We show that our approach leads to a significant improvement in the coronal density evolution than just when using coarse spatial resolutions insufficient to resolve the lower transition region. Our approach compensates for the jumping of the heat flux by imposing a velocity correction that ensures that the energy from the heat flux goes into driving the transition region dynamics, rather than being lost through radiation. Hence, it is possible to obtain improved coronal densities. The advantages of using this approach in both one-dimensional hydrodynamic and three-dimensional magnetohydrodynamic simulations are discussed.Spectral non-locality, absolute equilibria and Kraichnan-Leith-Batchelor phenomenology in two-dimensional turbulent energy cascades
http://hdl.handle.net/10023/10062
We study the degree to which Kraichnan-Leith-Batchelor (KLB) phenomenology describes two-dimensional energy cascades in alpha turbulence, governed by δθ/δt + J(ψ, θ) = ν ∇2θ + f, where θ = (-Δ)α/2ψ is generalized vorticity, and ψ over bar (k)= k-α θ over bar (k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (alpha = 1), regular two-dimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5 <α <10. At α = 2.5 and α = 10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α <4. However, downscale energy flux in the EDQNM self-similar inertial range for α > 2.5 leads us to predict that any inverse cascade for α ≥ 2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α ≥ 2.5 is significantly steeper than the KLB prediction, while for α <2.5 we obtain the KLB spectrum.
Sat, 01 Jun 2013 00:00:00 GMThttp://hdl.handle.net/10023/100622013-06-01T00:00:00ZBurgess, B. H.Shepherd, T. G.We study the degree to which Kraichnan-Leith-Batchelor (KLB) phenomenology describes two-dimensional energy cascades in alpha turbulence, governed by δθ/δt + J(ψ, θ) = ν ∇2θ + f, where θ = (-Δ)α/2ψ is generalized vorticity, and ψ over bar (k)= k-α θ over bar (k) in Fourier space. These models differ in spectral non-locality, and include surface quasigeostrophic flow (alpha = 1), regular two-dimensional flow (α = 2) and rotating shallow flow (α = 3), which is the isotropic limit of a mantle convection model. We re-examine arguments for dual inverse energy and direct enstrophy cascades, including Fjørtoft analysis, which we extend to general α, and point out their limitations. Using an α-dependent eddy-damped quasinormal Markovian (EDQNM) closure, we seek self-similar inertial range solutions and study their characteristics. Our present focus is not on coherent structures, which the EDQNM filters out, but on any self-similar and approximately Gaussian turbulent component that may exist in the flow and be described by KLB phenomenology. For this, the EDQNM is an appropriate tool. Non-local triads contribute increasingly to the energy flux as α increases. More importantly, the energy cascade is downscale in the self-similar inertial range for 2.5 <α <10. At α = 2.5 and α = 10, the KLB spectra correspond, respectively, to enstrophy and energy equipartition, and the triad energy transfers and flux vanish identically. Eddy turnover time and strain rate arguments suggest the inverse energy cascade should obey KLB phenomenology and be self-similar for α <4. However, downscale energy flux in the EDQNM self-similar inertial range for α > 2.5 leads us to predict that any inverse cascade for α ≥ 2.5 will not exhibit KLB phenomenology, and specifically the KLB energy spectrum. Numerical simulations confirm this: the inverse cascade energy spectrum for α ≥ 2.5 is significantly steeper than the KLB prediction, while for α <2.5 we obtain the KLB spectrum.The Assouad dimension of self-affine carpets with no grid structure
http://hdl.handle.net/10023/10061
Previous study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urbański sets to the lower local dimensions of Bernoulli convolutions.
JMF is financially supported by a Leverhulme Trust Research Fellowship.
Wed, 21 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/100612016-12-21T00:00:00ZFraser, Jonathan MacDonaldJordan, ThomasPrevious study of the Assouad dimension of planar self-affine sets has relied heavily on the underlying IFS having a `grid structure', thus allowing for the use of approximate squares. We study the Assouad dimension of a class of self-affine carpets which do not have an associated grid structure. We find that the Assouad dimension is related to the box and Assouad dimensions of the (self-similar) projection of the self-affine set onto the first coordinate and to the local dimensions of the projection of a natural Bernoulli measure onto the first coordinate. In a special case we relate the Assouad dimension of the Przytycki-Urbański sets to the lower local dimensions of Bernoulli convolutions.Strong Marstrand theorems and dimensions of sets formed by subsets of hyperplanes
http://hdl.handle.net/10023/10058
We present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional measure, has Hausdorff dimension min(1,s), i.e. the set of exceptional directions is independent of F. Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/100582016-01-01T00:00:00ZFalconer, KennethMattila, PerttiWe present strong versions of Marstrand's projection theorems and other related theorems. For example, if E is a plane set of positive and finite s-dimensional Hausdorff measure, there is a set X of directions of Lebesgue measure 0, such that the projection onto any line with direction outside X, of any subset F of E of positive s-dimensional measure, has Hausdorff dimension min(1,s), i.e. the set of exceptional directions is independent of F. Using duality this leads to results on the dimension of sets that intersect families of lines or hyperplanes in positive Lebesgue measure.Note on Prodi-Serrin-Ladyzhenskaya type regularity criteria for the Navier-Stokes equations
http://hdl.handle.net/10023/10048
In this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional Navier-Stokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norm ||u||L3 and ||u||H1/2.
X.Y. is partially supported by the Discovery Grant No. RES0020476 from NSERC.
Wed, 18 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/100482017-01-18T00:00:00ZTran, Chuong VanYu, XinweiIn this article we prove new regularity criteria of the Prodi-Serrin-Ladyzhenskaya type for the Cauchy problem of the three-dimensional Navier-Stokes equations. Our results improve the classical Lr(0,T;Ls) regularity criteria for both velocity and pressure by factors of certain nagative powers of the scaling invariant norm ||u||L3 and ||u||H1/2.Using hierarchical centering to facilitate a reversible jump MCMC algorithm for random effects models
http://hdl.handle.net/10023/10035
Hierarchical centering has been described as a reparameterisation method applicable to random effects models. It has been shown to improve mixing of models in the context of Markov chain Monte Carlo (MCMC) methods. A hierarchical centering approach is proposed for reversible jump MCMC (RJMCMC) chains which builds upon the hierarchical centering methods for MCMC chains and uses them to reparameterize models in an RJMCMC algorithm. Although these methods may be applicable to models with other error distributions, the case is described for a log-linear Poisson model where the expected value λλ includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modelling the mean of the random effect coefficients as a function of the intercept of the λλ model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups. This has an effect on the dynamics of the RJMCMC algorithm and improves model mixing. The methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the starting model. With hierarchical centering on the other hand, the chain moved freely over model and parameter space. These results are confirmed with a simulation study. Hence, the proposed methods should be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference on model parameters.
The first author was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC grant EP/C522702/1), with subsequent funding from EPSRC/NERC grant EP/I000917/1.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/100352016-06-01T00:00:00ZOedekoven, Cornelia SabrinaKing, R.Buckland, Stephen TerrenceMacKenzie, Monique LeaEvans, K. O.Burger Jr., L. WHierarchical centering has been described as a reparameterisation method applicable to random effects models. It has been shown to improve mixing of models in the context of Markov chain Monte Carlo (MCMC) methods. A hierarchical centering approach is proposed for reversible jump MCMC (RJMCMC) chains which builds upon the hierarchical centering methods for MCMC chains and uses them to reparameterize models in an RJMCMC algorithm. Although these methods may be applicable to models with other error distributions, the case is described for a log-linear Poisson model where the expected value λλ includes fixed effect covariates and a random effect for which normality is assumed with a zero-mean and unknown standard deviation. For the proposed RJMCMC algorithm including hierarchical centering, the models are reparameterized by modelling the mean of the random effect coefficients as a function of the intercept of the λλ model and one or more of the available fixed effect covariates depending on the model. The method is appropriate when fixed-effect covariates are constant within random effect groups. This has an effect on the dynamics of the RJMCMC algorithm and improves model mixing. The methods are applied to a case study of point transects of indigo buntings where, without hierarchical centering, the RJMCMC algorithm had poor mixing and the estimated posterior distribution depended on the starting model. With hierarchical centering on the other hand, the chain moved freely over model and parameter space. These results are confirmed with a simulation study. Hence, the proposed methods should be considered as a regular strategy for implementing models with random effects in RJMCMC algorithms; they facilitate convergence of these algorithms and help avoid false inference on model parameters.Vortex merger in surface quasi-geostrophy
http://hdl.handle.net/10023/10016
The merger of two identical surface temperature vortices is studied in the surface quasi- geostrophic model. The motivation for this study is the observation of the merger of sub- mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incom- pressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and sym- metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor- tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/100162016-01-01T00:00:00ZCarton, XavierCiani, DanieleVerron, JacquesReinaud, Jean NoelSokolovskiy, MikhailThe merger of two identical surface temperature vortices is studied in the surface quasi- geostrophic model. The motivation for this study is the observation of the merger of sub- mesoscale vortices in the ocean. Firstly, the interaction between two point vortices, in the absence or in the presence of an external deformation field, is investigated. The rotation rate of the vortices, their stationary positions and the stability of these positions are determined. Then, a numerical model provides the steady states of two finite-area, constant-temperature, vortices. Such states are less deformed than their counterparts in two-dimensional incom- pressible flows. Finally, numerical simulations of the nonlinear surface quasi-geostrophic equations are used to investigate the finite-time evolution of initially identical and sym- metric, constant temperature vortices. The critical merger distance is obtained and the deformation of the vortices before or after merger is determined. The addition of external deformation is shown to favor or to oppose merger depending on the orientation of the vor- tex pair with respect to the strain axes. An explanation for this observation is proposed. Conclusions are drawn towards an application of this study to oceanic vortices.Observing the formation of flare-driven coronal rain
http://hdl.handle.net/10023/10001
Flare-driven coronal rain can manifest from rapidly cooled plasma condensations near coronal loop-tops in thermally unstable post-flare arcades. We detect 5 phases that characterise the post-flare decay:heating, evaporation, conductive cooling dominance for ~120 s, radiative/ enthalpy cooling dominance for ~4700 s and finally catastrophic cooling occurring within 35-124 s leading to rain strands with s periodicity of 55-70 s. We find an excellent agreement between the observations and model predictions of the dominant cooling timescales and the onset of catastrophic cooling. At the rain formation site we detect co-moving, multi-thermal rain clumps that undergo catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the plasma cools at a maximum rate of 22700 K s-1 in multiple loop-top sources. We calculated the density of the EUV plasma from the DEM of the multi-thermal source employing regularised inversion. Assuming a pressure balance, we estimate the density of the chromospheric component of rain to be 9.21x1011 ±1.76x1011 cm-3 which is comparable with quiescent coronal rain densities. With up to 8 parallel strands in the EUV loop cross section, we calculate the mass loss rate from the post-flare arcade to be as much as 1.98x1012 ± 4.95x1011 g s-1. Finally, we reveal a close proximity between the model predictions of 105.8 K and the observed properties between 105.9 K and 106.2 K, that defines the temperature onset of catastrophic cooling. The close correspondence between the observations and numerical models suggests that indeed acoustic waves (with a sound travel time of 68 s) could play an important role in redistributing energy and sustaining the enthalpy-based radiative cooling.
PA. GV are funded by the European Research Council under the European Union Seventh Framework Programme (FP7/2007-2013) / ERC grant agreement nr. 291058
Tue, 20 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/100012016-12-20T00:00:00ZScullion, E.Rouppe Van Der Voort, L.Antolin, P.Wedemeyer, S.Vissers, G.Kontar, E. P.Gallagher, P.Flare-driven coronal rain can manifest from rapidly cooled plasma condensations near coronal loop-tops in thermally unstable post-flare arcades. We detect 5 phases that characterise the post-flare decay:heating, evaporation, conductive cooling dominance for ~120 s, radiative/ enthalpy cooling dominance for ~4700 s and finally catastrophic cooling occurring within 35-124 s leading to rain strands with s periodicity of 55-70 s. We find an excellent agreement between the observations and model predictions of the dominant cooling timescales and the onset of catastrophic cooling. At the rain formation site we detect co-moving, multi-thermal rain clumps that undergo catastrophic cooling from ~1 MK to ~22000 K. During catastrophic cooling the plasma cools at a maximum rate of 22700 K s-1 in multiple loop-top sources. We calculated the density of the EUV plasma from the DEM of the multi-thermal source employing regularised inversion. Assuming a pressure balance, we estimate the density of the chromospheric component of rain to be 9.21x1011 ±1.76x1011 cm-3 which is comparable with quiescent coronal rain densities. With up to 8 parallel strands in the EUV loop cross section, we calculate the mass loss rate from the post-flare arcade to be as much as 1.98x1012 ± 4.95x1011 g s-1. Finally, we reveal a close proximity between the model predictions of 105.8 K and the observed properties between 105.9 K and 106.2 K, that defines the temperature onset of catastrophic cooling. The close correspondence between the observations and numerical models suggests that indeed acoustic waves (with a sound travel time of 68 s) could play an important role in redistributing energy and sustaining the enthalpy-based radiative cooling.Estimability of variance components when all model matrices commute
http://hdl.handle.net/10023/9983
This paper deals with estimability of variance components in mixed models when all model matrices commute. In this situation, it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators. If, in addition, the family of possible variance-covariance matrices forms an orthogonal block structure, then there are the same number of variance components as strata, and the variance components are all estimable if and only if there are non-zero residual degrees of freedom in each stratum. We investigate the case where the family of possible variance-covariance matrices, while still commutative, no longer forms an orthogonal block structure. Now the variance components may or may not all be estimable, but there is no clear link with residual degrees of freedom. Whether or not they are all estimable, there may or may not be uniformly best unbiased quadratic estimators of those that are estimable. Examples are given to demonstrate all four possibilities.
This work was partially supported by national funds of FCT - Foundation for Science and Technology under UID/MAT/00212/2013.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/99832016-03-01T00:00:00ZBailey, Rosemary AnneFerreira, Sandra S.Ferreira, DarioNunes, CeliaThis paper deals with estimability of variance components in mixed models when all model matrices commute. In this situation, it is well known that the best linear unbiased estimators of fixed effects are the ordinary least squares estimators. If, in addition, the family of possible variance-covariance matrices forms an orthogonal block structure, then there are the same number of variance components as strata, and the variance components are all estimable if and only if there are non-zero residual degrees of freedom in each stratum. We investigate the case where the family of possible variance-covariance matrices, while still commutative, no longer forms an orthogonal block structure. Now the variance components may or may not all be estimable, but there is no clear link with residual degrees of freedom. Whether or not they are all estimable, there may or may not be uniformly best unbiased quadratic estimators of those that are estimable. Examples are given to demonstrate all four possibilities.Compressed dynamic mode decomposition for background modeling
http://hdl.handle.net/10023/9981
We introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition is a regression technique that integrates two of the leading data analysis methods in use today: Fourier transforms and singular value decomposition. Borrowing ideas from compressed sensing and matrix sketching, cDMD eases the computational workload of high-resolution video processing. The key principal of cDMD is to obtain the decomposition on a (small) compressed matrix representation of the video feed. Hence, the cDMD algorithm scales with the intrinsic rank of the matrix, rather than the size of the actual video (data) matrix. Selection of the optimal modes characterizing the background is formulated as a sparsity-constrained sparse coding problem. Our results show that the quality of the resulting background model is competitive, quantified by the F-measure, recall and precision. A graphics processing unit accelerated implementation is also presented which further boosts the computational performance of the algorithm.
JNK acknowledges support from Air Force Office of Scientific Research (FA9500-15-C-0039). SLB acknowledges support from the Department of Energy under award DE-EE0006785. NBE acknowledges support from the UK Engineering and Physical Sciences Research Council (EP/L505079/1).
Tue, 29 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/99812016-11-29T00:00:00ZErichson, N. BenjaminBrunton, Steven L.Kutz, J. NathanWe introduce the method of compressed dynamic mode decomposition (cDMD) for background modeling. The dynamic mode decomposition is a regression technique that integrates two of the leading data analysis methods in use today: Fourier transforms and singular value decomposition. Borrowing ideas from compressed sensing and matrix sketching, cDMD eases the computational workload of high-resolution video processing. The key principal of cDMD is to obtain the decomposition on a (small) compressed matrix representation of the video feed. Hence, the cDMD algorithm scales with the intrinsic rank of the matrix, rather than the size of the actual video (data) matrix. Selection of the optimal modes characterizing the background is formulated as a sparsity-constrained sparse coding problem. Our results show that the quality of the resulting background model is competitive, quantified by the F-measure, recall and precision. A graphics processing unit accelerated implementation is also presented which further boosts the computational performance of the algorithm.Free monoids are coherent
http://hdl.handle.net/10023/9979
A monoid S is said to be right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left coherent. These notions are analogous to those for a ring R (where, of course, S-acts are replaced by R-modules). Choo, Lam and Luft have shown that free rings are coherent. In this note we prove that, correspondingly, any free monoid is coherent, thus answering a question posed by the first author in 1992.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/99792017-02-01T00:00:00ZGould, VHartmann, MRuskuc, NikA monoid S is said to be right coherent if every finitely generated subact of every finitely presented right S-act is finitely presented. Left coherency is defined dually and S is coherent if it is both right and left coherent. These notions are analogous to those for a ring R (where, of course, S-acts are replaced by R-modules). Choo, Lam and Luft have shown that free rings are coherent. In this note we prove that, correspondingly, any free monoid is coherent, thus answering a question posed by the first author in 1992.Toward a PV-based algorithm for the dynamical core of hydrostatic global models
http://hdl.handle.net/10023/9957
The diabatic contour-advective semi-Lagrangian (DCASL) algorithms previously constructed for the shallow-water and multilayer Boussinesq primitive equations are extended to multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following-isentropic (sigma-) vertical coordinate. It is shown that the DCASL algorithms face challenges beyond more conventional algorithms in that various types of damping, filtering, and regularization are required for computational stability, and the nonlinearity of the hydrostatic equation in the sigma- coordinate causes convergence problems with setting up a semi-implicit time-stepping scheme to reduce computational cost. The prognostic variables are an approximation to the Rossby-Ertel potential vorticity Q, a scaled pressure thickness, the horizontal divergence, and the surface potential temperature. Results from the DCASL algorithm in two formulations of the sigma- coordinate, differing only in the rate at which the vertical coordinate tends to with increasing height, are assessed using the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. The assessment is based on comparisons with available reference solutions as well as results from two other algorithms derived from the DCASL algorithm: one with a semi-Lagrangian solution for Q and another with an Eulerian grid-based solution procedure with relative vorticity replacing Q as the prognostic variable. It is shown that at intermediate resolutions, results comparable to the reference solutions can be obtained.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/99572016-06-01T00:00:00ZMohebalhojeh, Ali R.Joghataei, MohammadDritschel, David G.The diabatic contour-advective semi-Lagrangian (DCASL) algorithms previously constructed for the shallow-water and multilayer Boussinesq primitive equations are extended to multilayer non-Boussinesq equations on the sphere using a hybrid terrain-following-isentropic (sigma-) vertical coordinate. It is shown that the DCASL algorithms face challenges beyond more conventional algorithms in that various types of damping, filtering, and regularization are required for computational stability, and the nonlinearity of the hydrostatic equation in the sigma- coordinate causes convergence problems with setting up a semi-implicit time-stepping scheme to reduce computational cost. The prognostic variables are an approximation to the Rossby-Ertel potential vorticity Q, a scaled pressure thickness, the horizontal divergence, and the surface potential temperature. Results from the DCASL algorithm in two formulations of the sigma- coordinate, differing only in the rate at which the vertical coordinate tends to with increasing height, are assessed using the baroclinic instability test case introduced by Jablonowski and Williamson in 2006. The assessment is based on comparisons with available reference solutions as well as results from two other algorithms derived from the DCASL algorithm: one with a semi-Lagrangian solution for Q and another with an Eulerian grid-based solution procedure with relative vorticity replacing Q as the prognostic variable. It is shown that at intermediate resolutions, results comparable to the reference solutions can be obtained.Extinction is imminent for Mexico’s endemic porpoise unless fishery bycatch is eliminated
http://hdl.handle.net/10023/9938
The number of Mexico’s endemic porpoise, the vaquita (Phocoena sinus), is collapsing primarily due to bycatch in illegal gillnets set for totoaba (Totoaba macdonaldi), an endangered fish whose swim bladders are exported to China. Previous research estimated that vaquitas declined from about 567 to 245 individuals between 1997 and 2008. Acoustic monitoring between 2011 and 2015 showed a decline of 34%/year. Here, we combine visual line transect and passive acoustic data collected simultaneously in a robust spatial analysis to estimate that only 59 (95% Bayesian Credible Interval [CRI] 22 – 145) vaquita remained as of autumn 2015, a decrease since 1997 of 92% (95% CRI 80%-97%). Risk analysis suggests that if the current, temporary gillnet ban is maintained and effectively enforced, vaquitas could recover to 2008 population levels by 2050. Otherwise, the species is likely to be extinct within a decade.
Primary funding was by Secretaria del Medio Ambiente y Recursos Naturales (Secretario R. Pacchiano). Mexican support was from SEMARNAT, CONABIO, CONANP, PROFEPA, SEMAR, and WWF-Mexico. US support from NOAA-Fisheries-SWFSC and The Marine Mammal Center.
Mon, 05 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/99382016-12-05T00:00:00ZTaylor, Barbara L.Rojas-Bracho, LorenzoMoore, JeffreyJaramillo-Legorreta, ArmandoVer Hoef, Jay M.Cardenas-Hinojosa, GustavoNieto-Garcia, EdwynaBarlow, JayGerrodette, TimTregenza, NicholasThomas, LenHammond, Philip S.The number of Mexico’s endemic porpoise, the vaquita (Phocoena sinus), is collapsing primarily due to bycatch in illegal gillnets set for totoaba (Totoaba macdonaldi), an endangered fish whose swim bladders are exported to China. Previous research estimated that vaquitas declined from about 567 to 245 individuals between 1997 and 2008. Acoustic monitoring between 2011 and 2015 showed a decline of 34%/year. Here, we combine visual line transect and passive acoustic data collected simultaneously in a robust spatial analysis to estimate that only 59 (95% Bayesian Credible Interval [CRI] 22 – 145) vaquita remained as of autumn 2015, a decrease since 1997 of 92% (95% CRI 80%-97%). Risk analysis suggests that if the current, temporary gillnet ban is maintained and effectively enforced, vaquitas could recover to 2008 population levels by 2050. Otherwise, the species is likely to be extinct within a decade.Passive acoustic monitoring of the decline of Mexico's critically endangered vaquita
http://hdl.handle.net/10023/9937
The vaquita (Phocoena sinus) is the world's most endangered marine mammal with ≈245 individuals remaining in 2008. This species of porpoise is endemic to the northern Gulf of California, Mexico, and has historically suffered population declines from unsustainable bycatch in gillnets. An illegal gillnet fishery for an endangered fish, the totoaba (Totoaba macdonaldi), has recently resurged throughout the vaquita's range. The secretive but lucrative wildlife trade with China for totoaba swim bladders has probably increased vaquita bycatch mortality, but by an unknown amount. Precise population monitoring by visual surveys is difficult because vaquitas are inherently hard to see and have now become so rare that sighting rates are very low. However, their echolocation clicks can be identified readily on specialized acoustic detectors. Acoustic detections on an array of 46 moored detectors indicate that vaquita acoustic activity declined by 80% between 2011 and 2015 in the central part of the species’ range. Statistical models estimate an annual rate of decline of 34% (95% Bayesian Credible Interval -48% to -21%). Based on preliminary acoustic monitoring results from 2011–2014 the Government of Mexico enacted and is enforcing an emergency 2-year ban of gillnets throughout the species’ range to prevent extinction, at a cost of $74 million USD to compensate fishers. Developing precise acoustic monitoring methods proved critical to exposing the severity of vaquitas’ decline and emphasizes the need for continual monitoring to effectively manage critically endangered species.
Different institutions and agencies have provided funding during the development and implementation of the acoustic monitoring program.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/99372017-02-01T00:00:00ZJaramillo-Legorreta, ArmandoCardenas-Hinojosa, GustavoNieto-Garcia, EdwynaRojas-Bracho, LorenzoHoef, Jay VerMoore, JeffreyTregenza, NicholasBarlow, JayGerrodette, TimThomas, LenTaylor, BarbaraThe vaquita (Phocoena sinus) is the world's most endangered marine mammal with ≈245 individuals remaining in 2008. This species of porpoise is endemic to the northern Gulf of California, Mexico, and has historically suffered population declines from unsustainable bycatch in gillnets. An illegal gillnet fishery for an endangered fish, the totoaba (Totoaba macdonaldi), has recently resurged throughout the vaquita's range. The secretive but lucrative wildlife trade with China for totoaba swim bladders has probably increased vaquita bycatch mortality, but by an unknown amount. Precise population monitoring by visual surveys is difficult because vaquitas are inherently hard to see and have now become so rare that sighting rates are very low. However, their echolocation clicks can be identified readily on specialized acoustic detectors. Acoustic detections on an array of 46 moored detectors indicate that vaquita acoustic activity declined by 80% between 2011 and 2015 in the central part of the species’ range. Statistical models estimate an annual rate of decline of 34% (95% Bayesian Credible Interval -48% to -21%). Based on preliminary acoustic monitoring results from 2011–2014 the Government of Mexico enacted and is enforcing an emergency 2-year ban of gillnets throughout the species’ range to prevent extinction, at a cost of $74 million USD to compensate fishers. Developing precise acoustic monitoring methods proved critical to exposing the severity of vaquitas’ decline and emphasizes the need for continual monitoring to effectively manage critically endangered species.The challenges of analyzing behavioral response study data : an overview of the MOCHA (Multi-study OCean acoustics Human effects Analysis) project
http://hdl.handle.net/10023/9923
This paper describes the MOCHA project which aims to develop novel approaches for the analysis of data collected during Behavioral Response Studies (BRSs). BRSs are experiments aimed at directly quantifying the effects of controlled dosages of natural or anthropogenic stimuli (typically sound) on marine mammal behavior. These experiments typically result in low sample size, relative to variability, and so we are looking at a number of studies in combination to maximize the gain from each one. We describe a suite of analytical tools applied to BRS data on beaked whales, including a simulation study aimed at informing future experimental design.
Date of Acceptance:
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/99232016-01-01T00:00:00ZHarris, Catriona MThomas, LenSadykova, DinaraDe Ruiter, Stacy LynnTyack, Peter LloydSouthall, Brandon L.Read, Andrew J.Miller, PatrickThis paper describes the MOCHA project which aims to develop novel approaches for the analysis of data collected during Behavioral Response Studies (BRSs). BRSs are experiments aimed at directly quantifying the effects of controlled dosages of natural or anthropogenic stimuli (typically sound) on marine mammal behavior. These experiments typically result in low sample size, relative to variability, and so we are looking at a number of studies in combination to maximize the gain from each one. We describe a suite of analytical tools applied to BRS data on beaked whales, including a simulation study aimed at informing future experimental design.Counting chirps : acoustic monitoring of cryptic frogs
http://hdl.handle.net/10023/9921
1 . Global amphibian declines have resulted in a vital need for monitoring programmes that follow population trends. Monitoring using advertisement calls is ideal as choruses are undisturbed during data collection. However, methods currently employed by managers frequently rely on trained observers, and/or do not provide density data on which to base trends. 2 . This study explores the utility of monitoring using acoustic spatially explicit capture-recapture (aSECR) with time of arrival (ToA) and signal strength (SS) as a quantitative monitoring technique to measure call density of a threatened but visually cryptic anuran, the Cape peninsula moss frog Arthroleptella lightfooti. 3 . The relationships between temporal and environmental variables (date, rainfall, temperature) and A. lightfooti call density at three study sites on the Cape peninsula, South Africa were examined. Acoustic data, collected from an array of six microphones over four months during the winter breeding season, provided a time series of call density estimates. 4 . Model selection indicated that call density was primarily associated with seasonality fitted as a quadratic function. Call density peaked mid-breeding season. At the main study site, the lowest recorded mean call density (0·160 calls m-2 min-1) occurred in May and reached its peak mid-July (1·259 calls m-2 min-1). The sites differed in call density, but also the effective sampling area. 5 . Synthesis and applications.The monitoring technique, acoustic spatially explicit capture–recapture (aSCR), quantitatively estimates call density without disturbing the calling animals or their environment, while time of arrival (ToA) and signal strength (SS) significantly add to the accuracy of call localisation, which in turn increases precision of call density estimates without the need for specialist field staff. This technique appears ideally suited to aid the monitoring of visually cryptic, acoustically active species.
Funding for the frog survey was received from the National Geographic Society/Waitt Grants Program (No. W184-11). The EPSRC and NERC helped to fund this research through a PhD grant (No. EP/1000917/1) to D.L.B. R.A. and G.J.M. acknowledge initiative funding from the National Research Foundation of South Africa.
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/99212017-06-01T00:00:00ZMeasey, G. JohnStevenson, Ben C.Scott, TanyaAltwegg, ResBorchers, David L.1 . Global amphibian declines have resulted in a vital need for monitoring programmes that follow population trends. Monitoring using advertisement calls is ideal as choruses are undisturbed during data collection. However, methods currently employed by managers frequently rely on trained observers, and/or do not provide density data on which to base trends. 2 . This study explores the utility of monitoring using acoustic spatially explicit capture-recapture (aSECR) with time of arrival (ToA) and signal strength (SS) as a quantitative monitoring technique to measure call density of a threatened but visually cryptic anuran, the Cape peninsula moss frog Arthroleptella lightfooti. 3 . The relationships between temporal and environmental variables (date, rainfall, temperature) and A. lightfooti call density at three study sites on the Cape peninsula, South Africa were examined. Acoustic data, collected from an array of six microphones over four months during the winter breeding season, provided a time series of call density estimates. 4 . Model selection indicated that call density was primarily associated with seasonality fitted as a quadratic function. Call density peaked mid-breeding season. At the main study site, the lowest recorded mean call density (0·160 calls m-2 min-1) occurred in May and reached its peak mid-July (1·259 calls m-2 min-1). The sites differed in call density, but also the effective sampling area. 5 . Synthesis and applications.The monitoring technique, acoustic spatially explicit capture–recapture (aSCR), quantitatively estimates call density without disturbing the calling animals or their environment, while time of arrival (ToA) and signal strength (SS) significantly add to the accuracy of call localisation, which in turn increases precision of call density estimates without the need for specialist field staff. This technique appears ideally suited to aid the monitoring of visually cryptic, acoustically active species.Generating "large" subgroups and subsemigroups
http://hdl.handle.net/10023/9913
In this thesis we will be exclusively considering uncountable groups and semigroups.
Roughly speaking the underlying problem is to find “large” subgroups
(or subsemigroups) of the object in question, where we consider three different
notions of “largeness”:
(i) We classify all the subsemigroups of the set of all mapping from a countable
set back to itself which contains a specific uncountable subsemigroup;
(ii) We investigate topological “largeness”, in particular subgroups which are
finitely generated and dense;
(iii) We investigate if it is possible to find an integer r such that any countable
collection of elements belongs to some r-generated subsemigroup, and more
precisely can these elements be obtained by multiplying the generators in a
prescribed fashion.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/99132016-01-01T00:00:00ZJonušas, JuliusIn this thesis we will be exclusively considering uncountable groups and semigroups.
Roughly speaking the underlying problem is to find “large” subgroups
(or subsemigroups) of the object in question, where we consider three different
notions of “largeness”:
(i) We classify all the subsemigroups of the set of all mapping from a countable
set back to itself which contains a specific uncountable subsemigroup;
(ii) We investigate topological “largeness”, in particular subgroups which are
finitely generated and dense;
(iii) We investigate if it is possible to find an integer r such that any countable
collection of elements belongs to some r-generated subsemigroup, and more
precisely can these elements be obtained by multiplying the generators in a
prescribed fashion.Synchronizing permutation groups and graph endomorphisms
http://hdl.handle.net/10023/9912
The current thesis is focused on synchronizing permutation groups and on graph endo-
morphisms. Applying the implicit classification of rank 3 groups, we provide a bound
on synchronizing ranks of rank 3 groups, at first. Then, we determine the singular graph
endomorphisms of the Hamming graph and related graphs, count Latin hypercuboids of
class r, establish their relation to mixed MDS codes, investigate G-decompositions of
(non)-synchronizing semigroups, and analyse the kernel graph construction used in the
theorem of Cameron and Kazanidis which identifies non-synchronizing transformations
with graph endomorphisms [20].
The contribution lies in the following points:
1. A bound on synchronizing ranks of groups of permutation rank 3 is given, and a
complete list of small non-synchronizing groups of permutation rank 3 is provided
(see Chapter 3).
2. The singular endomorphisms of the Hamming graph and some related graphs are
characterised (see Chapter 5).
3. A theorem on the extension of partial Latin hypercuboids is given, Latin hyper-
cuboids for small values are counted, and their correspondence to mixed MDS
codes is unveiled (see Chapter 6).
4. The research on normalizing groups from [3] is extended to semigroups of the
form <G, T>, and decomposition properties of non-synchronizing semigroups are described which are then applied to semigroups induced by combinatorial tiling
problems (see Chapter 7).
5. At last, it is shown that all rank 3 graphs admitting singular endomorphisms are
hulls and it is conjectured that a hull on n vertices has minimal generating set of at
most n generators (see Chapter 8).
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/99122016-01-01T00:00:00ZSchaefer, ArturThe current thesis is focused on synchronizing permutation groups and on graph endo-
morphisms. Applying the implicit classification of rank 3 groups, we provide a bound
on synchronizing ranks of rank 3 groups, at first. Then, we determine the singular graph
endomorphisms of the Hamming graph and related graphs, count Latin hypercuboids of
class r, establish their relation to mixed MDS codes, investigate G-decompositions of
(non)-synchronizing semigroups, and analyse the kernel graph construction used in the
theorem of Cameron and Kazanidis which identifies non-synchronizing transformations
with graph endomorphisms [20].
The contribution lies in the following points:
1. A bound on synchronizing ranks of groups of permutation rank 3 is given, and a
complete list of small non-synchronizing groups of permutation rank 3 is provided
(see Chapter 3).
2. The singular endomorphisms of the Hamming graph and some related graphs are
characterised (see Chapter 5).
3. A theorem on the extension of partial Latin hypercuboids is given, Latin hyper-
cuboids for small values are counted, and their correspondence to mixed MDS
codes is unveiled (see Chapter 6).
4. The research on normalizing groups from [3] is extended to semigroups of the
form <G, T>, and decomposition properties of non-synchronizing semigroups are described which are then applied to semigroups induced by combinatorial tiling
problems (see Chapter 7).
5. At last, it is shown that all rank 3 graphs admitting singular endomorphisms are
hulls and it is conjectured that a hull on n vertices has minimal generating set of at
most n generators (see Chapter 8).On the theory of symmetric MHD equilibria with anisotropic pressure
http://hdl.handle.net/10023/9908
In this thesis we discuss the theory of symmetric MHD equilibria with anisotropic pressure. More
specifically, we focus on gyrotropic pressures, where the pressure tensor can be split into components along
and across the magnetic field. We first explore 2D solutions, which can be found using total field type
formalisms. These formalisms rely on treating quantities as functions of both the magnetic flux function
and the magnetic field strength, and reduce the equilibrium equations to a single Grad-Shafranov equation
that can be solved to find the magnetic flux function. However, these formalisms are not appropriate
when one includes a shear field component of magnetic flux, since they lead to a set of equations which
are implicitly coupled. Therefore, in order to solve the equilibrium problem with a magnetic shear field
component, we introduce the poloidal formalism. This new formalism considers quantities as functions
of the poloidal magnetic field strength (instead of the total magnetic field strength), and yields a set
of two equations which are not coupled, and can be solved to find the magnetic flux function and the
shear field. There are some situations where the poloidal formalism is difficult to use, however, such as
in rotationally symmetric systems. Thus we require a further formalism, which we call the combined
approach, which allows a more general use of the poloidal formalism. One finds that the combined
formalism leads to multi-valued functions, which must be dealt with appropriately. Finally, we present
some numerical examples of MHD equilibria, which have been found using each of the three formalisms
mentioned above.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/99082016-01-01T00:00:00ZHodgson, Jonathan David BrockieIn this thesis we discuss the theory of symmetric MHD equilibria with anisotropic pressure. More
specifically, we focus on gyrotropic pressures, where the pressure tensor can be split into components along
and across the magnetic field. We first explore 2D solutions, which can be found using total field type
formalisms. These formalisms rely on treating quantities as functions of both the magnetic flux function
and the magnetic field strength, and reduce the equilibrium equations to a single Grad-Shafranov equation
that can be solved to find the magnetic flux function. However, these formalisms are not appropriate
when one includes a shear field component of magnetic flux, since they lead to a set of equations which
are implicitly coupled. Therefore, in order to solve the equilibrium problem with a magnetic shear field
component, we introduce the poloidal formalism. This new formalism considers quantities as functions
of the poloidal magnetic field strength (instead of the total magnetic field strength), and yields a set
of two equations which are not coupled, and can be solved to find the magnetic flux function and the
shear field. There are some situations where the poloidal formalism is difficult to use, however, such as
in rotationally symmetric systems. Thus we require a further formalism, which we call the combined
approach, which allows a more general use of the poloidal formalism. One finds that the combined
formalism leads to multi-valued functions, which must be dealt with appropriately. Finally, we present
some numerical examples of MHD equilibria, which have been found using each of the three formalisms
mentioned above.Re-evaluation of individual diameter : height allometric models to improve biomass estimation of tropical trees
http://hdl.handle.net/10023/9898
Accurate estimation of tree biomass is necessary to provide realistic values of the carbon stored in the terrestrial biosphere. A recognized source of errors in tree above-ground biomass (AGB) estimation is introduced when individual tree height values (H) are not directly measured but estimated from diameter at breast height (DBH) using allometric equations. In this paper we evaluate the performance of 12 alternative DBH : H equations and compare their effects on AGB estimation for three tropical forests that occur in contrasting climatic and altitudinal zones. We found that fitting a 3-parameter Weibull function using data collected locally generated the lowest errors and bias in H estimation, and that equations fitted to these data were more accurate than equations with parameters derived from the literature. For computing AGB, the introduced error values differed notably among DBH : H allometric equations, and in most cases showed a clear bias that resulted in either over- or under-estimation of AGB. Fitting the three-parameter Weibull function minimized errors in AGB estimates in our study and we recommend its widespread adoption for carbon stock estimation. We conclude that many previous studies are likely to present biased estimates of AGB due to the method of H estimation.
The first author was supported by the European Union under a IEF Marie-Curie Action.
Thu, 01 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/98982016-12-01T00:00:00ZLedo, AliciaCornulier, ThomasIllian, Janine B.Iida, YoshikoKassim, Abdul RahmanBurslem, David F. R. P.Accurate estimation of tree biomass is necessary to provide realistic values of the carbon stored in the terrestrial biosphere. A recognized source of errors in tree above-ground biomass (AGB) estimation is introduced when individual tree height values (H) are not directly measured but estimated from diameter at breast height (DBH) using allometric equations. In this paper we evaluate the performance of 12 alternative DBH : H equations and compare their effects on AGB estimation for three tropical forests that occur in contrasting climatic and altitudinal zones. We found that fitting a 3-parameter Weibull function using data collected locally generated the lowest errors and bias in H estimation, and that equations fitted to these data were more accurate than equations with parameters derived from the literature. For computing AGB, the introduced error values differed notably among DBH : H allometric equations, and in most cases showed a clear bias that resulted in either over- or under-estimation of AGB. Fitting the three-parameter Weibull function minimized errors in AGB estimates in our study and we recommend its widespread adoption for carbon stock estimation. We conclude that many previous studies are likely to present biased estimates of AGB due to the method of H estimation.Distance sampling detection functions : 2D or not 2D?
http://hdl.handle.net/10023/9885
Conventional distance sampling (CDS) methods assume that animals are uniformly distributed in the vicinity of lines or points. But when animals move in response to observers before detection, or when lines or points are not located randomly, this assumption may fail. By formulating distance sampling models as survival models, we show that using time to first detection in addition to perpendicular distance (line transect surveys) or radial distance (point transect surveys) allows estimation of detection probability, and hence density, when animal distribution in the vicinity of lines or points is not uniform and is unknown. We also show that times to detection can provide information about failure of the CDS assumption that detection probability is 1 at distance zero. We obtain a maximum likelihood estimator of line transect survey detection probability and effective strip half-width using times to detection, and we investigate its properties by simulation in situations where animals are nonuniformly distributed and their distribution is unknown. The estimator is found to perform well when detection probability at distance zero is 1. It allows unbiased estimates of density to be obtained in this case from surveys in which there has been responsive movement prior to animals coming within detectable range. When responsive movement continues within detectable range, estimates may be biased but are likely less biased than estimates from methods that assuming no responsive movement. We illustrate by estimating primate density from a line transect survey in which animals are known to avoid the transect line, and a shipboard survey of dolphins that are attracted to it.
MJC was funded by Australian Research Council grant FS110200057.
Mon, 17 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/98852016-10-17T00:00:00ZBorchers, David LouisCox, Martin JamesConventional distance sampling (CDS) methods assume that animals are uniformly distributed in the vicinity of lines or points. But when animals move in response to observers before detection, or when lines or points are not located randomly, this assumption may fail. By formulating distance sampling models as survival models, we show that using time to first detection in addition to perpendicular distance (line transect surveys) or radial distance (point transect surveys) allows estimation of detection probability, and hence density, when animal distribution in the vicinity of lines or points is not uniform and is unknown. We also show that times to detection can provide information about failure of the CDS assumption that detection probability is 1 at distance zero. We obtain a maximum likelihood estimator of line transect survey detection probability and effective strip half-width using times to detection, and we investigate its properties by simulation in situations where animals are nonuniformly distributed and their distribution is unknown. The estimator is found to perform well when detection probability at distance zero is 1. It allows unbiased estimates of density to be obtained in this case from surveys in which there has been responsive movement prior to animals coming within detectable range. When responsive movement continues within detectable range, estimates may be biased but are likely less biased than estimates from methods that assuming no responsive movement. We illustrate by estimating primate density from a line transect survey in which animals are known to avoid the transect line, and a shipboard survey of dolphins that are attracted to it.A comparison of global magnetic field skeletons and active-region upflows
http://hdl.handle.net/10023/9875
Plasma upflows have been detected in active regions using Doppler velocity maps. The origin and nature of these upflows is not well known with many of their characteristics determined from the examination of single events. In particular, some studies suggest these upflows occur along open field lines and, hence, are linked to sources of the solar wind. To investigate the relationship these upflows may have with the solar wind, and to probe what may be driving them, this paper considers seven active regions observed on the solar disc using the Extreme ultraviolet Imaging Spectrometer aboard Hinode between August 2011 and September 2012. Plasma upflows are observed in all these active regions. The locations of these upflows are compared to the global potential magnetic field extrapolated from the Solar Dynamics Observatory, Helioseismic and Magnetic Imager daily synoptic magnetogram taken on the day the upflows were observed. The structure of the magnetic field is determined by constructing its magnetic skeleton in order to help identify open-field regions and also sites where magnetic reconnection at global features is likely to occur. As a further comparison, measurements of the temperature, density and composition of the plasma are taken from regions with active-region upflows. In most cases the locations of the upflows in the active regions do not correspond to areas of open field, as predicted by a global coronal potential-field model, and therefore these upflows are not always sources of the slow solar wind. The locations of the upflows are, in general, intersected by separatrix surfaces associated with null points located high in the corona; these could be important sites of reconnection with global consequences.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/98752016-01-01T00:00:00ZEdwards, S. J.Parnell, C. E.Harra, L. K.Culhane, J. L.Brooks, D. H.Plasma upflows have been detected in active regions using Doppler velocity maps. The origin and nature of these upflows is not well known with many of their characteristics determined from the examination of single events. In particular, some studies suggest these upflows occur along open field lines and, hence, are linked to sources of the solar wind. To investigate the relationship these upflows may have with the solar wind, and to probe what may be driving them, this paper considers seven active regions observed on the solar disc using the Extreme ultraviolet Imaging Spectrometer aboard Hinode between August 2011 and September 2012. Plasma upflows are observed in all these active regions. The locations of these upflows are compared to the global potential magnetic field extrapolated from the Solar Dynamics Observatory, Helioseismic and Magnetic Imager daily synoptic magnetogram taken on the day the upflows were observed. The structure of the magnetic field is determined by constructing its magnetic skeleton in order to help identify open-field regions and also sites where magnetic reconnection at global features is likely to occur. As a further comparison, measurements of the temperature, density and composition of the plasma are taken from regions with active-region upflows. In most cases the locations of the upflows in the active regions do not correspond to areas of open field, as predicted by a global coronal potential-field model, and therefore these upflows are not always sources of the slow solar wind. The locations of the upflows are, in general, intersected by separatrix surfaces associated with null points located high in the corona; these could be important sites of reconnection with global consequences.MapMySmoke–a context aware mobile phone application targeted at smoking cessation
http://hdl.handle.net/10023/9872
Tue, 22 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/98722016-11-22T00:00:00ZSchick, Robert SchillingHumphris, Gerald MichaelKelsey, Thomas WilliamMarston, JohnSampson, KayThe energy budget of stellar magnetic fields : comparing non-potential simulations and observations
http://hdl.handle.net/10023/9869
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic fieldt opology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the high-resolution non-potential magnetofrictional simulations and the relatively low-resolution observations, we filter out the small-scale field in the simulations using a spherical harmonics decomposition. We show that the large-scalefield topologies of the solar-based simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global non-potential evolution model simulations capture key magnetic features of the observed solar-like stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of M-dwarfs or stars with dominantly toroidal field.Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.
LTL acknowledges support from the Scottish Universities Physics Alliance (SUPA) prize studentship and the University of St Andrews Higgs studentship. MMJ and VS acknowledge a Science & Technology Facilities Council (STFC) postdoctoral fellowship.
Thu, 27 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/98692016-10-27T00:00:00ZLehmann, L. T.Jardine, M. M.Vidotto, A. A.Mackay, D. H.See, V.Donati, J.-F.Folsom, C. P.Jeffers, S. V.Marsden, S. C.Morin, J.Petit, P.The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic fieldt opology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the high-resolution non-potential magnetofrictional simulations and the relatively low-resolution observations, we filter out the small-scale field in the simulations using a spherical harmonics decomposition. We show that the large-scalefield topologies of the solar-based simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global non-potential evolution model simulations capture key magnetic features of the observed solar-like stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of M-dwarfs or stars with dominantly toroidal field.Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.Theoretical foundation of 3D Alfvén resonances : normal modes
http://hdl.handle.net/10023/9847
We consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (∝ exp(−iωt)) are presented along with a theoretical framework to interpret them. The solutions we find are fundamentally different to those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a “Resonant Zone", and we show how boundary conditions and locally 2D regions can favour particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation we develop relies upon recognising that in 3D the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.
Tue, 20 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/98472016-12-20T00:00:00ZWright, Andrew NicholasElsden, Thomas WilliamWe consider the resonant coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a 3D equilibrium. Numerical solutions to normal modes (∝ exp(−iωt)) are presented along with a theoretical framework to interpret them. The solutions we find are fundamentally different to those in 1D and 2D. In 3D there exists an infinite number of possible resonant solutions within a “Resonant Zone", and we show how boundary conditions and locally 2D regions can favour particular solutions. A unique feature of the resonance in 3D is switching between different permissible solutions when the boundary of the Resonant Zone is encountered. The theoretical foundation we develop relies upon recognising that in 3D the orientation of the resonant surface will not align in a simple fashion with an equilibrium coordinate. We present a method for generating the Alfvén wave natural frequencies for an arbitrarily oriented Alfvén wave, which requires a careful treatment of scale factors describing the background magnetic field geometry.On the dimensions of a family of overlapping self-affine carpets
http://hdl.handle.net/10023/9835
We consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman's recent work on the dimensions of self-similar sets and measures.
The work of J.M.F. was supported by the EPSRC grant EP/J013560/1 whilst at Warwick and an EPSRC doctoral training grant whilst at St Andrews.
Thu, 01 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/98352016-12-01T00:00:00ZFraser, Jonathan MacDonaldShmerkin, PabloWe consider the dimensions of a family of self-affine sets related to the Bedford-McMullen carpets. In particular, we fix a Bedford-McMullen system and then randomise the translation vectors with the stipulation that the column structure is preserved. As such, we maintain one of the key features in the Bedford-McMullen set up in that alignment causes the dimensions to drop from the affinity dimension. We compute the Hausdorff, packing and box dimensions outside of a small set of exceptional translations, and also for some explicit translations even in the presence of overlapping. Our results rely on, and can be seen as a partial extension of, M. Hochman's recent work on the dimensions of self-similar sets and measures.String C-groups as transitive subgroups of Sn
http://hdl.handle.net/10023/9794
If Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded.
Mon, 01 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/97942016-02-01T00:00:00ZCameron, Peter JephsonFernandes, Maria ElisaLeemans, DimitriMixer, MarkIf Γ is a string C-group which is isomorphic to a transitive subgroup of the symmetric group Sn (other than Sn and the alternating group An), then the rank of Γ is at most n/2+1, with finitely many exceptions (which are classified). It is conjectured that only the symmetric group has to be excluded.Coupled bulk-surface free boundary problems arising from a mathematical model of receptor-ligand dynamics
http://hdl.handle.net/10023/9779
We consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extra-cellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatio-temporal distributions of the receptors and ligands in a realistic geometry.
This work was started whilst the authors were participants in the Isaac Newton Institute programme: “Free Boundary Problems and Related Topics” and finalised whilst the authors were participants in the Isaac Newton Institute programme: “Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation” supported by EPSRC Grant Number EP/K032208/1. The work of CV received support from the Leverhulme Trust Research Project Grant (RPG-2014-149).
Wed, 08 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/97792017-02-08T00:00:00ZElliot, Charles M.Ranner, ThomasVenkataraman, ChandrasekharWe consider a coupled bulk-surface system of partial differential equations with nonlinear coupling modelling receptor-ligand dynamics. The model arises as a simplification of a mathematical model for the reaction between cell surface resident receptors and ligands present in the extra-cellular medium. We prove the existence and uniqueness of solutions. We also consider a number of biologically relevant asymptotic limits of the model. We prove convergence to limiting problems which take the form of free boundary problems posed on the cell surface. We also report on numerical simulations illustrating convergence to one of the limiting problems as well as the spatio-temporal distributions of the receptors and ligands in a realistic geometry.Kinematics of coronal rain in a transversely oscillating loop : ponderomotive force and rain-excited oscillations
http://hdl.handle.net/10023/9777
Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at sub-ballistic speeds, which is not well-understood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed sub-ballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a one dimensional shear Alfvén wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one in-depth comparison with an observation that shows rain with up-and down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured sub-ballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding sub-ballistic motion, but it plays a role in cases of large loop oscillations.The appearance of rain causes the excitation of small-amplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.
E.V. acknowledges support from the Warwick STFC Consolidated Grant ST/L000733/I. P.A. acknowledges support from the EU Horizon 2020 Research and Innovation programme (grant agreement No. 647214). P.K. acknowledges support from a UK STFC PhD studentship. T.N. acknowledges support from the St Andrews STFC Consolidated Grant SN/N000609/1.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/97772017-02-01T00:00:00ZVerwichte, E.Antolin, P.Rowlands, G.Kohutova, P.Neukirch, T.Context. Coronal rain are cool dense blobs that form in solar coronal loops and are a manifestation of catastrophic cooling linked to thermal instability. Once formed, rain falls towards the solar surface at sub-ballistic speeds, which is not well-understood. Pressure forces seem to be the prime candidate to explain this. In many observations rain is accompanied by transverse oscillations and the interaction between the two needs to be explored. Aims. Therefore, an alternative kinematic model for coronal rain kinematics in transversely oscillating loops is developed to understand the physical nature of the observed sub-ballistic falling motion of rain. It explicitly explores the role of the ponderomotive force arising from the transverse oscillation on the rain motion as well as the capacity of rain to excite wave motion. Methods. An analytical model is presented that describes a rain blob guided by the coronal magnetic field supporting a one dimensional shear Alfvén wave as a point mass on an oscillating string. The model includes gravity and the ponderomotive force from the oscillation acting on the mass, as well as the inertia of the mass acting on the oscillation. Results. The kinematics of rain in the limit of negligible rain mass are explored and falling and trapped regimes are found, depending on wave amplitude. In the trapped regime for the fundamental mode, the rain blob bounces back and forth around the loop top at a long period inversely proportional to the oscillation amplitude. The model is compared with several observational rain studies, including one in-depth comparison with an observation that shows rain with up-and down bobbing motion. The role of rain inertia in exciting transverse oscillations is explored in inclined loops. Conclusions. It is found that the model requires displacement amplitudes of the transverse oscillation that are typically an order of magnitude larger than observed to explain the measured sub-ballistic motion of the rain. Therefore, it is concluded that the ponderomotive force is not the primary reason for understanding sub-ballistic motion, but it plays a role in cases of large loop oscillations.The appearance of rain causes the excitation of small-amplitude transverse oscillations that may explain observed events and provide a seismological tool to measure rain mass.Identifying multispecies synchrony in response to environmental covariates
http://hdl.handle.net/10023/9775
The importance of multi-species models for understanding complex ecological processes and interactions is beginning to be realised. Recent developments, such as those by Lahoz-Monfort et al. (2011), have enabled synchrony in demographic parameters across multiple species to be explored. Species in a similar environment would be expected to be subject to similar exogenous factors, although their response to each of these factors may be quite different. The ability to group species together according to how they respond to a particular measured covariate may be of particular interest to ecologists. We fit a multi-species model to two sets of similar species of garden bird monitored under the British Trust for Ornithology’s Garden Bird Feeding Survey. Posterior model probabilities were estimated using the reversible jump algorithm to compare posterior support for competing models with different species sharing different subsets of regression coefficients.There was frequently good agreement between species with small asynchronous random effect components and those with posterior support for models with shared regression coefficients; however, this was not always the case. When groups of species were less correlated, greater uncertainty was found in whether regression coefficients should be shared or not.The methods outlined in this paper can test additional hypotheses about the similarities or synchrony across multiple species that share the same environment. Through the use of posterior model probabilities, estimated using the reversible jump algorithm, we can detect multi-species responses in relation to measured covariates across any combination of species and covariates under consideration. The method can account for synchrony across species in relation to measured covariates, as well as unexplained variation accounted for using random effects. For more flexible, multi-parameter distributions, the support for species-specific parameters can also be measured.
BTS was part funded by EPSRC/NERC grant EP/10009171/1.
Thu, 01 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/97752016-12-01T00:00:00ZSwallow, Benjamin ThomasKing, RuthBuckland, Stephen TerrenceToms, Mike P.The importance of multi-species models for understanding complex ecological processes and interactions is beginning to be realised. Recent developments, such as those by Lahoz-Monfort et al. (2011), have enabled synchrony in demographic parameters across multiple species to be explored. Species in a similar environment would be expected to be subject to similar exogenous factors, although their response to each of these factors may be quite different. The ability to group species together according to how they respond to a particular measured covariate may be of particular interest to ecologists. We fit a multi-species model to two sets of similar species of garden bird monitored under the British Trust for Ornithology’s Garden Bird Feeding Survey. Posterior model probabilities were estimated using the reversible jump algorithm to compare posterior support for competing models with different species sharing different subsets of regression coefficients.There was frequently good agreement between species with small asynchronous random effect components and those with posterior support for models with shared regression coefficients; however, this was not always the case. When groups of species were less correlated, greater uncertainty was found in whether regression coefficients should be shared or not.The methods outlined in this paper can test additional hypotheses about the similarities or synchrony across multiple species that share the same environment. Through the use of posterior model probabilities, estimated using the reversible jump algorithm, we can detect multi-species responses in relation to measured covariates across any combination of species and covariates under consideration. The method can account for synchrony across species in relation to measured covariates, as well as unexplained variation accounted for using random effects. For more flexible, multi-parameter distributions, the support for species-specific parameters can also be measured.Purse-seine vessels as platforms for monitoring the population status of dolphin species in the eastern tropical Pacific Ocean : the use of fishing vessels as scientific platforms
http://hdl.handle.net/10023/9773
In the eastern tropical Pacific Ocean, yellowfin tuna (Thunnus albacares) are often found in association with spotted (Stenella attenuata) and spinner (Stenella longirostris) dolphins. Purse-seine vessels use this co-occurrence to locate the tuna by searching for dolphins and associated birds. Data collected by onboard observers since the late 1970s were used to develop indices of relative abundance for dolphins, based on line-transect methodology, when the primary method of detection of dolphin herds was with binoculars. However, trend estimation was subsequently discontinued in 2000 due to concerns about changes in reporting rates of dolphin herd detections with increased use of helicopter and radar search. At present, as a result of a hiatus in fishery-independent surveys since 2006, fisheries observer data are the only source of information with which to monitor the status of eastern tropical Pacific Ocean dolphin populations. In this paper, trend estimation with the onboard observer data is revisited using a sightings-per-unit-effort approach. Despite different assumptions and model structure, the results indicate a lack of independence between the distribution of search effort and the search methods used, and the abundance of dolphin herds associated with tunas, on several spatial and temporal scales. This lack of independence poses a considerable challenge to the development of a reliable index of relative abundance for dolphins with these data. Given these results, alternatives for dolphin abundance estimation are discussed. One alternative is the use of purse-seine vessels for line-transect surveys during fishery closure periods. Another alternative is the use of purse-seine vessels during normal fishing operations as platforms for the collection of mark-recapture data (e.g., passive integrated transponder tags or genetics sampling). Life-history data collection, as a supplement to the collection of other data types, is also discussed. Further research and development is needed to assess whether these alternative methods will be useful.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/97732016-06-01T00:00:00ZLennert-Cody, Cleridy E.Maunder, Mark N.Fiedler, Paul C.Minami, MihokoGerrodette, TimRusin, JeremyMinte-Vera, Carolina V.Scott, MichaelBuckland, Stephen TerrenceIn the eastern tropical Pacific Ocean, yellowfin tuna (Thunnus albacares) are often found in association with spotted (Stenella attenuata) and spinner (Stenella longirostris) dolphins. Purse-seine vessels use this co-occurrence to locate the tuna by searching for dolphins and associated birds. Data collected by onboard observers since the late 1970s were used to develop indices of relative abundance for dolphins, based on line-transect methodology, when the primary method of detection of dolphin herds was with binoculars. However, trend estimation was subsequently discontinued in 2000 due to concerns about changes in reporting rates of dolphin herd detections with increased use of helicopter and radar search. At present, as a result of a hiatus in fishery-independent surveys since 2006, fisheries observer data are the only source of information with which to monitor the status of eastern tropical Pacific Ocean dolphin populations. In this paper, trend estimation with the onboard observer data is revisited using a sightings-per-unit-effort approach. Despite different assumptions and model structure, the results indicate a lack of independence between the distribution of search effort and the search methods used, and the abundance of dolphin herds associated with tunas, on several spatial and temporal scales. This lack of independence poses a considerable challenge to the development of a reliable index of relative abundance for dolphins with these data. Given these results, alternatives for dolphin abundance estimation are discussed. One alternative is the use of purse-seine vessels for line-transect surveys during fishery closure periods. Another alternative is the use of purse-seine vessels during normal fishing operations as platforms for the collection of mark-recapture data (e.g., passive integrated transponder tags or genetics sampling). Life-history data collection, as a supplement to the collection of other data types, is also discussed. Further research and development is needed to assess whether these alternative methods will be useful.A test case for the inviscid shallow-water equations on the sphere
http://hdl.handle.net/10023/9761
A numerically converged solution to the inviscid global shallow-water equations for a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics and the other a finite-volume scheme on a cubed-sphere grid. Flow fields and various integral norms are documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.
Partial support for this work was provided through the National Science Foundation award AGS-1333029.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/97612016-01-01T00:00:00ZScott, R. K.Harris, L. M.Polvani, L. M.A numerically converged solution to the inviscid global shallow-water equations for a predefined time interval is documented to provide a convenient benchmark for model validation. The solution is based on the same initial conditions as a previously documented solution for the viscous equations. The solution is computed using two independent numerical schemes, one a pseudospectral scheme based on an expansion in spherical harmonics and the other a finite-volume scheme on a cubed-sphere grid. Flow fields and various integral norms are documented to facilitate model comparison and validation. Attention is drawn to the utility of the potential vorticity supremum as a convenient and sensitive test of numerical convergence, in which the exact value is known a priori over the entire time interval.Inference of heating properties from "hot" non-flaring plasmas in active region cores. I. Single nanoflares
http://hdl.handle.net/10023/9753
The properties that are expected of “hot” non-flaring plasmas due to nanoflare heating in active regions are investigated using hydrodynamic modeling tools, including a two-fluid development of the Enthalpy Based Thermal Evolution of Loops code. Here we study a single nanoflare and show that while simple models predict an emission measure distribution extending well above 10 MK, which is consistent with cooling by thermal conduction, many other effects are likely to limit the existence and detectability of such plasmas. These include: differential heating between electrons and ions, ionization non-equilibrium, and for short nanoflares, the time taken for the coronal density to increase. The most useful temperature range to look for this plasma, often called the “smoking gun” of nanoflare heating, lies between 10 6.6 and 10 7 K. Signatures of the actual heating may be detectable in some instances.
Tue, 20 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/97532016-09-20T00:00:00ZBarnes, W. T.Cargill, P. J.Bradshaw, S. J.The properties that are expected of “hot” non-flaring plasmas due to nanoflare heating in active regions are investigated using hydrodynamic modeling tools, including a two-fluid development of the Enthalpy Based Thermal Evolution of Loops code. Here we study a single nanoflare and show that while simple models predict an emission measure distribution extending well above 10 MK, which is consistent with cooling by thermal conduction, many other effects are likely to limit the existence and detectability of such plasmas. These include: differential heating between electrons and ions, ionization non-equilibrium, and for short nanoflares, the time taken for the coronal density to increase. The most useful temperature range to look for this plasma, often called the “smoking gun” of nanoflare heating, lies between 10 6.6 and 10 7 K. Signatures of the actual heating may be detectable in some instances.Habitat complexity in aquatic microcosms affects processes driven by detrivores
http://hdl.handle.net/10023/9749
Habitat complexity can influence predation rates (e.g. by providing refuge) but other ecosystem processes and species interactions might also be modulated by the properties of habitat structure. Here, we focussed on how complexity of artificial habitat (plastic plants), in microcosms, influenced short-term processes driven by three aquatic detritivores. The effects of habitat complexity on leaf decomposition, production of fine organic matter and pH levels were explored by measuring complexity in three ways: 1. as the presence vs. absence of habitat structure; 2. as the amount of structure (3 or 4.5 g of plastic plants); and 3. as the spatial configuration of structures (measured as fractal dimension). The experiment also addressed potential interactions among the consumers by running all possible species combinations. In the experimental microcosms, habitat complexity influenced how species performed, especially when comparing structure present vs. structure absent. Treatments with structure showed higher fine particulate matter production and lower pH compared to treatments without structures and this was probably due to higher digestion and respiration when structures were present. When we explored the effects of the different complexity levels, we found that the amount of structure added explained more than the fractal dimension of the structures. We give a detailed overview of the experimental design, statistical models and R codes, because our statistical analysis can be applied to other study systems (and disciplines such as restoration ecology). We further make suggestions of how to optimise statistical power when artificially assembling, and analysing, ‘habitat complexity’ by not confounding complexity with the amount of structure added. In summary, this study highlights the importance of habitat complexity for energy flow and the maintenance of ecosystem processes in aquatic ecosystems.
LF was supported in part by the Spanish Ministry of Economy and Competitiveness through the project SCARCE Consolider-Ingenio CSD2009-00065.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/97492016-11-01T00:00:00ZFlores, LoreaBailey, R. A.Elosegi, ArturoLarrañaga, AitorReiss, JuliaHabitat complexity can influence predation rates (e.g. by providing refuge) but other ecosystem processes and species interactions might also be modulated by the properties of habitat structure. Here, we focussed on how complexity of artificial habitat (plastic plants), in microcosms, influenced short-term processes driven by three aquatic detritivores. The effects of habitat complexity on leaf decomposition, production of fine organic matter and pH levels were explored by measuring complexity in three ways: 1. as the presence vs. absence of habitat structure; 2. as the amount of structure (3 or 4.5 g of plastic plants); and 3. as the spatial configuration of structures (measured as fractal dimension). The experiment also addressed potential interactions among the consumers by running all possible species combinations. In the experimental microcosms, habitat complexity influenced how species performed, especially when comparing structure present vs. structure absent. Treatments with structure showed higher fine particulate matter production and lower pH compared to treatments without structures and this was probably due to higher digestion and respiration when structures were present. When we explored the effects of the different complexity levels, we found that the amount of structure added explained more than the fractal dimension of the structures. We give a detailed overview of the experimental design, statistical models and R codes, because our statistical analysis can be applied to other study systems (and disciplines such as restoration ecology). We further make suggestions of how to optimise statistical power when artificially assembling, and analysing, ‘habitat complexity’ by not confounding complexity with the amount of structure added. In summary, this study highlights the importance of habitat complexity for energy flow and the maintenance of ecosystem processes in aquatic ecosystems.Models of interacting pairs of thin, quasi-geostrophic vortices: steady-state solutions and nonlinear stability
http://hdl.handle.net/10023/9744
We study pairwise interactions of elliptical quasi-geostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting non-elliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasi-geostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions.
This work was supported by the Office of Naval Research under Grant N00014-11- 1-0087; the National Science Foundation under Grant 1107307; and the UK Engineering and Physical Sciences Research Council under grant EP/H001794/1.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/97442016-01-01T00:00:00ZBersanelli, MatteoDritschel, David G.Lancellotti, CarloPoje, Andrew C.We study pairwise interactions of elliptical quasi-geostrophic vortices as the limiting case of vanishingly thin uniform potential vorticity ellipsoids. In this limit, the product of the vertical extent of the ellipsoid and the potential vorticity within it is held fixed to a finite non-zero constant. Such elliptical 'lenses' inherit the property that, in isolation, they steadily rotate without changing shape. Here, we use this property to extend both standard moment models and Hamiltonian ellipsoidal models to approximate the dynamical interaction of such elliptical lenses. By neglecting non-elliptical deformations, the simplified models reduce the dynamics to just four degrees of freedom per vortex. For simplicity, we focus on pairwise interactions between identical elliptical vortices initially separated in both the horizontal and vertical directions. The dynamics of the simplified models are compared with the full quasi-geostrophic (QG) dynamics of the system, and show good agreement as expected for sufficiently distant lenses. The results reveal the existence of families of steadily rotating equilibria in the initial horizontal and vertical separation parameter space. For sufficiently large vertical separations, equilibria with varying shape exist for all horizontal separations. Below a critical vertical separation (stretched by the constant ratio of buoyancy to Coriolis frequencies N/f), comparable to the mean radius of either vortex, a gap opens in horizontal separation where no equilibria are possible. Solutions near the edge of this gap are unstable. In the full QG system, equilibria at the edge of the gap exhibit corners (infinite curvature) along their boundaries. Comparisons of the model results with the full nonlinear QG evolution show that the early stages of the instability are captured by the Hamiltonian elliptical model but not by the moment model that inaccurately estimates shorter-range interactions.The energy budget of stellar magnetic fields : comparing non-potential simulations and observations
http://hdl.handle.net/10023/9742
The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the high-resolution non-potential magnetofrictional simulations and the relatively low-resolution observations, we filter out the small-scale field in the simulations using a spherical harmonics decomposition. We show that the large-scale field topologies of the solar-based simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global non-potential evolution model simulations capture key magnetic features of the observed solar-like stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of M-dwarfs or stars with dominantly toroidal field. Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.
LTL acknowledges support from the Scottish Universities Physics Alliance (SUPA) prize studentship and the University of St Andrews Higgs studentship. MMJ and VS acknowledge a Science & Technology Facilities Council (STFC) postdoctoral fellowship.
Tue, 21 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/97422017-03-21T00:00:00ZLehmann, L. T.Jardine, M. M.Vidotto, A. A.Mackay, D. H.See, Wyke Chun VictorDonati, J. -F.Folsom, C. P.Jeffers, S. V.Marsden, SteveMorin, J.Petit, P.The magnetic geometry of the surface magnetic fields of more than 55 cool stars have now been mapped using spectropolarimetry. In order to better understand these observations, we compare the magnetic field topology at different surface scale sizes of observed and simulated cool stars. For ease of comparison between the high-resolution non-potential magnetofrictional simulations and the relatively low-resolution observations, we filter out the small-scale field in the simulations using a spherical harmonics decomposition. We show that the large-scale field topologies of the solar-based simulations produce values of poloidal/toroidal fields and fractions of energy in axisymmetric modes that are similar to the observations. These global non-potential evolution model simulations capture key magnetic features of the observed solar-like stars through the processes of surface flux transport and magnetic flux emergence. They do not, however, reproduce the magnetic field of M-dwarfs or stars with dominantly toroidal field. Furthermore, we analyse the magnetic field topologies of individual spherical harmonics for the simulations and discover that the dipole is predominately poloidal, while the quadrupole shows the highest fraction of toroidal fields. Magnetic field structures smaller than a quadrupole display a fixed ratio between the poloidal and toroidal magnetic energies.Spatial models of abundance and habitat preferences of Commerson’s and Peale’s dolphin in southern Patagonian waters
http://hdl.handle.net/10023/9740
Commerson’s dolphins (Cephalorhynchus c. commersonii) and Peale’s dolphins (Lagenorhynchus australis) are two of the most common species of cetaceans in the coastal waters of southwest South Atlantic Ocean. Both species are listed as Data Deficient by the IUCN, mainly due to the lack of information about population sizes and trends. The goal of this study was to build spatially explicit models for the abundance of both species in relation to environmental variables using data collected during eight scientific cruises along the Patagonian shelf. Spatial models were constructed using generalized additive models. In total, 88 schools (212 individuals) of Commerson’s dolphin and 134 schools (465 individuals) of Peale’s dolphin were recorded in 8,535 km surveyed. Commerson’s dolphin was found less than 60 km from shore; whereas Peale’s dolphins occurred over a wider range of distances from the coast, the number of animals sighted usually being larger near or far from the coast. Fitted models indicate overall abundances of approximately 22,000 Commerson’s dolphins and 20,000 Peale’s dolphins in the total area studied. This work provides the first large-scale abundance estimate for Peale’s dolphin in the Atlantic Ocean and an update of population size for Commerson’s dolphin. Additionally, our results contribute to baseline data on suitable habitat conditions for both species in southern Patagonia, which is essential for the implementation of adequate conservation measures.
This research was possible with the support of the Consejo Nacional de Investigaciones Científicas y Técnicas (CONICET). Funding for travel to and accommodation for NAD in Aberdeen, Scotland was provided by CONICET and Cetacean Society International. The work of NAD was part of a postdoctoral fellowship funded by CONICET.
Wed, 26 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/97402016-10-26T00:00:00ZDellabianca, Natalia A.Pierce, Graham J.Rey, Andrea RayaScioscia, GabrielaMiller, David L.Torres, Mónica A.Viola, M. Natalia PasoGoodall, R. Natalie PSchiavini, Adrián C MCommerson’s dolphins (Cephalorhynchus c. commersonii) and Peale’s dolphins (Lagenorhynchus australis) are two of the most common species of cetaceans in the coastal waters of southwest South Atlantic Ocean. Both species are listed as Data Deficient by the IUCN, mainly due to the lack of information about population sizes and trends. The goal of this study was to build spatially explicit models for the abundance of both species in relation to environmental variables using data collected during eight scientific cruises along the Patagonian shelf. Spatial models were constructed using generalized additive models. In total, 88 schools (212 individuals) of Commerson’s dolphin and 134 schools (465 individuals) of Peale’s dolphin were recorded in 8,535 km surveyed. Commerson’s dolphin was found less than 60 km from shore; whereas Peale’s dolphins occurred over a wider range of distances from the coast, the number of animals sighted usually being larger near or far from the coast. Fitted models indicate overall abundances of approximately 22,000 Commerson’s dolphins and 20,000 Peale’s dolphins in the total area studied. This work provides the first large-scale abundance estimate for Peale’s dolphin in the Atlantic Ocean and an update of population size for Commerson’s dolphin. Additionally, our results contribute to baseline data on suitable habitat conditions for both species in southern Patagonia, which is essential for the implementation of adequate conservation measures.Predicting the effects of human developments on individual dolphins to understand potential long-term population consequences
http://hdl.handle.net/10023/9731
Human activities that impact wildlife do not necessarily remove individuals from populations. They may also change individual behaviour in ways that have sublethal effects. This has driven interest in developing analytical tools that predict the population consequences of short-term behavioural responses. In this study, we incorporate empirical information on the ecology of a population of bottlenose dolphins into an individual-based model that predicts how individuals' behavioural dynamics arise from their underlying motivational states, as well as their interaction with boat traffic and dredging activities. We simulate the potential effects of proposed coastal developments on this population and predict that the operational phase may affect animals' motivational states. For such results to be relevant for management, the effects on individuals' vital rates also need to be quantified. We investigate whether the relationship between an individual's exposure and the survival of its calves can be directly estimated using a Bayesian multi-stage model for calf survival. The results suggest that any effect on calf survival is probably small and that a significant relationship could only be detected in large, closely studied populations. Our work can be used to guide management decisions, accelerate the consenting process for coastal and offshore developments and design targeted monitoring
This work received funding from the Marine Alliance for Science and Technology for Scotland (MASTS pooling initiative).
Sun, 01 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/97312015-11-01T00:00:00ZPirotta, EnricoHarwood, JohnThompson, PaulNew, LeslieCheney, BarbaraArso Civil, MonicaHammond, Philip StevenDonovan, Carl RobertLusseau, DavidHuman activities that impact wildlife do not necessarily remove individuals from populations. They may also change individual behaviour in ways that have sublethal effects. This has driven interest in developing analytical tools that predict the population consequences of short-term behavioural responses. In this study, we incorporate empirical information on the ecology of a population of bottlenose dolphins into an individual-based model that predicts how individuals' behavioural dynamics arise from their underlying motivational states, as well as their interaction with boat traffic and dredging activities. We simulate the potential effects of proposed coastal developments on this population and predict that the operational phase may affect animals' motivational states. For such results to be relevant for management, the effects on individuals' vital rates also need to be quantified. We investigate whether the relationship between an individual's exposure and the survival of its calves can be directly estimated using a Bayesian multi-stage model for calf survival. The results suggest that any effect on calf survival is probably small and that a significant relationship could only be detected in large, closely studied populations. Our work can be used to guide management decisions, accelerate the consenting process for coastal and offshore developments and design targeted monitoringInfluence of non-potential coronal magnetic topology on solar wind models
http://hdl.handle.net/10023/9729
By comparing a magneto-frictional model of the low coronal magnetic field to a potential field source surface model, we investigate the possible impact of non-potential magnetic structure on empirical solar wind models. These empirical models (such as Wang-Sheeley-Arge) estimate the distribution of solar wind speed solely from the magnetic field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and are extended to 0.1 AU using a Schatten current sheet model. The non-potential field has a more complex magnetic skeleton and quasi-separatrix structures than the potential field, leading to different sub-structure in the solar wind speed proxies. It contains twisted magnetic structures which can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the non-potential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic flux tubes expand less rapidly with height, but more importantly because more open field lines are further from coronal hole boundaries.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/97292015-10-01T00:00:00ZEdwards, Sarah JaneYeates, Anthony RobinsonBocquet, FrancoisMackay, Duncan HendryBy comparing a magneto-frictional model of the low coronal magnetic field to a potential field source surface model, we investigate the possible impact of non-potential magnetic structure on empirical solar wind models. These empirical models (such as Wang-Sheeley-Arge) estimate the distribution of solar wind speed solely from the magnetic field structure in the low corona. Our models are computed in a domain between the solar surface and 2.5 solar radii, and are extended to 0.1 AU using a Schatten current sheet model. The non-potential field has a more complex magnetic skeleton and quasi-separatrix structures than the potential field, leading to different sub-structure in the solar wind speed proxies. It contains twisted magnetic structures which can perturb the separatrix surfaces traced down from the base of the heliospheric current sheet. A significant difference between the models is the greater amount of open magnetic flux in the non-potential model. Using existing empirical formulae this leads to higher predicted wind speeds for two reasons: partly because magnetic flux tubes expand less rapidly with height, but more importantly because more open field lines are further from coronal hole boundaries.The Assouad dimensions of projections of planar sets
http://hdl.handle.net/10023/9725
We consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and self-similar sets. For general sets, the main result is the following: if a set in the plane has Assouad dimension s ∈ [0, 2], then the projections have Assouad dimension at least min{1, s} almost surely. Compared to the famous analogue for Hausdorff dimension – namely Marstrand’s Projection Theorem – a striking difference is that the words ‘at least’cannot be dispensed with: in fact, for many planar self-similar sets of dimension s < 1, we prove that the Assouad dimension of projections can attain both values sand 1 for a set of directions of positive measure. For self-similar sets, our investigation splits naturally into two cases: when the group of rotations is discrete, and when it is dense. In the ‘discrete rotations’ case we prove the following dichotomy for any given projection: either the Hausdorff measure is positive in the Hausdorff dimension, in which case the Hausdorff and Assouad dimensions coincide; or the Hausdorff measure is zero in the Hausdorff dimension,in which case the Assouad dimension is equal to 1. In the ‘dense rotations’ case we prove that every projection has Assouad dimension equal to one, assuming that the planar set is not a singleton. As another application of our results, we show that there is no Falconer’s Theorem for Assouad dimension. More precisely, the Assouad dimension of a self-similar (or self-affine) set is not in general almost surely constant when one randomises the translation vectors.
The first named author is supported by a Leverhulme Trust Research Fellowship and the second named author is supported by the Academy of Finland through the grant Restricted families of projections and connections to Kakeya type problems, grant number 274512.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/97252017-02-01T00:00:00ZFraser, Jonathan M.Orponen, TuomasWe consider the Assouad dimensions of orthogonal projections of planar sets onto lines. Our investigation covers both general and self-similar sets. For general sets, the main result is the following: if a set in the plane has Assouad dimension s ∈ [0, 2], then the projections have Assouad dimension at least min{1, s} almost surely. Compared to the famous analogue for Hausdorff dimension – namely Marstrand’s Projection Theorem – a striking difference is that the words ‘at least’cannot be dispensed with: in fact, for many planar self-similar sets of dimension s < 1, we prove that the Assouad dimension of projections can attain both values sand 1 for a set of directions of positive measure. For self-similar sets, our investigation splits naturally into two cases: when the group of rotations is discrete, and when it is dense. In the ‘discrete rotations’ case we prove the following dichotomy for any given projection: either the Hausdorff measure is positive in the Hausdorff dimension, in which case the Hausdorff and Assouad dimensions coincide; or the Hausdorff measure is zero in the Hausdorff dimension,in which case the Assouad dimension is equal to 1. In the ‘dense rotations’ case we prove that every projection has Assouad dimension equal to one, assuming that the planar set is not a singleton. As another application of our results, we show that there is no Falconer’s Theorem for Assouad dimension. More precisely, the Assouad dimension of a self-similar (or self-affine) set is not in general almost surely constant when one randomises the translation vectors.On the Lq -spectrum of planar self-affine measures
http://hdl.handle.net/10023/9724
We study the dimension theory of a class of planar self-affine multifractal measures. These measures are the Bernoulli measures supported on box-like self-affine sets, introduced by the author, which are the attractors of iterated function systems consisting of contracting affine maps which take the unit square to rectangles with sides parallel to the axes. This class contains the self-affine measures recently considered by Feng and Wang as well as many other measures. In particular, we allow the defining maps to have non-trivial rotational and reflectional components. Assuming the rectangular open set condition, we compute the Lq-spectrum by means of a q-modified singular value function. A key application of our results is a closed form expression for the Lq-spectrum in the case where there are no mappings that switch the coordinate axes. This is useful for computational purposes and also allows us to prove differentiability of the Lq-spectrum at q=1 in the more difficult `non-multiplicative' situation. This has applications concerning the Hausdorff, packing and entropy dimension of the measure as well as the Hausdorff and packing dimension of the support. Due to the possible inclusion of axis reversing maps, we are led to extend some results of Peres and Solomyak on the existence of the Lq-spectrum of self-similar measures to the graph-directed case.
The author was supported by the EPSRC grant EP/J013560/1. This work was started whilst the author was an EPSRC funded PhD student at the University of St Andrews, and he expresses his gratitude for the support he found there.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/97242016-01-01T00:00:00ZFraser, Jonathan M.We study the dimension theory of a class of planar self-affine multifractal measures. These measures are the Bernoulli measures supported on box-like self-affine sets, introduced by the author, which are the attractors of iterated function systems consisting of contracting affine maps which take the unit square to rectangles with sides parallel to the axes. This class contains the self-affine measures recently considered by Feng and Wang as well as many other measures. In particular, we allow the defining maps to have non-trivial rotational and reflectional components. Assuming the rectangular open set condition, we compute the Lq-spectrum by means of a q-modified singular value function. A key application of our results is a closed form expression for the Lq-spectrum in the case where there are no mappings that switch the coordinate axes. This is useful for computational purposes and also allows us to prove differentiability of the Lq-spectrum at q=1 in the more difficult `non-multiplicative' situation. This has applications concerning the Hausdorff, packing and entropy dimension of the measure as well as the Hausdorff and packing dimension of the support. Due to the possible inclusion of axis reversing maps, we are led to extend some results of Peres and Solomyak on the existence of the Lq-spectrum of self-similar measures to the graph-directed case.Finite presentability and isomorphism of Cayley graphs of monoids
http://hdl.handle.net/10023/9711
Two finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.
Wed, 26 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/97112016-10-26T00:00:00ZAwang, Jennifer SylviaPfeiffer, Markus JohannesRuskuc, NikolaTwo finitely generated monoids are constructed, one finitely presented the other not, whose (directed, unlabelled) Cayley graphs are isomorphic.Quiescent prominences in the era of ALMA : simulated observations using 3D whole-prominence fine structure model
http://hdl.handle.net/10023/9710
We use the detailed 3D whole-prominence fine structure model to produce the first simulated high-resolution ALMA observations of a modeled quiescent solar prominence. The synthetic brightness temperature and optical thickness maps shown in the present paper are produced using a visualization method for the sub-millimeter/millimeter radio continua synthesis. We have obtained the simulated observations of both the prominence at the limb and the filament on the disk at wavelengths covering a broad range which encompasses the full potential of ALMA.We demonstrate here to what extent the small-scale and large-scale prominence and filament structures will be visible in the ALMA observations spanning both the optically thin and thick regimes. We analyze the relationship between the brightness and kinetic temperature of the prominence plasma. We also illustrate the opportunities ALMA will provide for studying the thermal structure of the prominence plasma from the cool prominence fine structure cores to the prominence-corona transition region. In addition, we show that the detailed 3D modeling of entire prominences with their numerous fine structures will be important for the correct interpretation of future ALMA prominence observations.
Tue, 20 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/97102016-12-20T00:00:00ZGunar, StanislavHeinzel, PetrMackay, Duncan HendryAnzer, UlrichWe use the detailed 3D whole-prominence fine structure model to produce the first simulated high-resolution ALMA observations of a modeled quiescent solar prominence. The synthetic brightness temperature and optical thickness maps shown in the present paper are produced using a visualization method for the sub-millimeter/millimeter radio continua synthesis. We have obtained the simulated observations of both the prominence at the limb and the filament on the disk at wavelengths covering a broad range which encompasses the full potential of ALMA.We demonstrate here to what extent the small-scale and large-scale prominence and filament structures will be visible in the ALMA observations spanning both the optically thin and thick regimes. We analyze the relationship between the brightness and kinetic temperature of the prominence plasma. We also illustrate the opportunities ALMA will provide for studying the thermal structure of the prominence plasma from the cool prominence fine structure cores to the prominence-corona transition region. In addition, we show that the detailed 3D modeling of entire prominences with their numerous fine structures will be important for the correct interpretation of future ALMA prominence observations.Population scaling in 5 km x 5 km grey and harbour seal usage maps. Note to Scottish Government MMSS/002/15
http://hdl.handle.net/10023/9704
Fri, 14 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/97042016-10-14T00:00:00ZJones, Esther LaneMorris, ChristopherSmout, Sophie CarolineMcConnell, Bernie JDeciphering satellite observations of compressional ULF waveguide modes
http://hdl.handle.net/10023/9702
We present an analytical method for determining incident and reflection co- efficients for flank ULF compressional waveguide modes in Earth’s magnetosphere. In the flank magnetosphere, compressional waves propagate azimuthally, but exhibit a mixed standing/propagating nature radially. Understanding this radial dependence will yield information on the energy absorption and transport of these waves. We provide a step by step method that can be applied to observations of flank ULF waves, which separates these fluctuations into incident and reflected parts. As a means of testing, we apply the method to data from a numerical waveguide simulation, which shows the effect on the reflection coefficient when energy is absorbed at a field line resonance.
T. Elsden would like to thank STFC for financial support for a doctoral training grant, number AMC3 STFC12. A.N. Wright was supported by STFC grant ST/N000609/1.
Fri, 01 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/97022016-04-01T00:00:00ZElsden, TomWright, Andrew NicholasHartinger, MichaelWe present an analytical method for determining incident and reflection co- efficients for flank ULF compressional waveguide modes in Earth’s magnetosphere. In the flank magnetosphere, compressional waves propagate azimuthally, but exhibit a mixed standing/propagating nature radially. Understanding this radial dependence will yield information on the energy absorption and transport of these waves. We provide a step by step method that can be applied to observations of flank ULF waves, which separates these fluctuations into incident and reflected parts. As a means of testing, we apply the method to data from a numerical waveguide simulation, which shows the effect on the reflection coefficient when energy is absorbed at a field line resonance.Transverse, propagating velocity perturbations in solar coronal loops
http://hdl.handle.net/10023/9684
As waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms. This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfven) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvenic) turbulence.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/96842016-01-01T00:00:00ZDe Moortel, InekePascoe, David JamesWright, Andrew NicholasHood, Alan WilliamAs waves and oscillations carry both energy and information, they have enormous potential as a plasma heating mechanism and, through seismology, to provide estimates of local plasma properties which are hard to obtain from direct measurements. Being sufficiently near to allow high-resolution observations, the atmosphere of the Sun forms a natural plasma laboratory. Recent observations have revealed that an abundance of waves and oscillations is present in the solar atmosphere, leading to a renewed interest in wave heating mechanisms. This short review paper gives an overview of recently observed transverse, propagating velocity perturbations in coronal loops. These ubiquitous perturbations are observed to undergo strong damping as they propagate. Using 3D numerical simulations of footpoint-driven transverse waves propagating in a coronal plasma with a cylindrical density structure, in combination with analytical modelling, it is demonstrated that the observed velocity perturbations can be understood in terms of coupling of different wave modes in the inhomogeneous boundaries of the loops. Mode coupling in the inhomogeneous boundary layers of the loops leads to the coupling of the transversal (kink) mode to the azimuthal (Alfven) mode, observed as the decay of the transverse kink oscillations. Both the numerical and analytical results show the spatial profile of the damped wave has a Gaussian shape to begin with, before switching to exponential decay at large heights. In addition, recent analysis of CoMP (Coronal Multi-channel Polarimeter) Doppler shift observations of large, off-limb, trans-equatorial loops shows that Fourier power at the apex appears to be higher in the high-frequency part of the spectrum than expected from theoretical models. This excess high-frequency FFT power could be tentative evidence for the onset of a cascade of the low-to-mid frequency waves into (Alfvenic) turbulence.Primitive groups, graph endomorphisms and synchronization
http://hdl.handle.net/10023/9648
Let Ω be a set of cardinality n, G be a permutation group on Ω and f:Ω→Ω be a map that is not a permutation. We say that G synchronizes f if the transformation semigroup ⟨G,f⟩ contains a constant map, and that G is a synchronizing group if G synchronizes every non-permutation. A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every non-synchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has parts of equal size), and it had previously been conjectured that this was essentially the only way in which a primitive group could fail to be synchronizing, in other words, that a primitive group synchronizes every non-uniform transformation. The first goal of this paper is to prove that this conjecture is false, by exhibiting primitive groups that fail to synchronize specific non-uniform transformations of ranks 5 and 6. As it has previously been shown that primitive groups synchronize every non-uniform transformation of rank at most 4, these examples are of the lowest possible rank. In addition, we produce graphs with primitive automorphism groups that have approximately √n non-synchronizing ranks, thus refuting another conjecture on the number of non-synchronizing ranks of a primitive group. The second goal of this paper is to extend the spectrum of ranks for which it is known that primitive groups synchronize every non-uniform transformation of that rank. It has previously been shown that a primitive group of degree n synchronizes every non-uniform transformation of rank n−1 and n−2, and here this is extended to n−3 and n−4. In the process, we will obtain a purely graph-theoretical result showing that, with limited exceptions, in a vertex-primitive graph the union of neighbourhoods of a set of vertices A is bounded below by a function that is asymptotically √|A|. Determining the exact spectrum of ranks for which there exist non-uniform transformations not synchronized by some primitive group is just one of several natural, but possibly difficult, problems on automata, primitive groups, graphs and computational algebra arising from this work; these are outlined in the final section.
The third author has been partially supported by the Fundação para a Ciência e a Tecnologia through the project CEMAT-CIÊNCIAS UID/Multi/04621/2013.
Thu, 01 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/96482016-12-01T00:00:00ZAraújo, JoãoBentz, WolframCameron, Peter JephsonRoyle, GordonSchaefer, ArturLet Ω be a set of cardinality n, G be a permutation group on Ω and f:Ω→Ω be a map that is not a permutation. We say that G synchronizes f if the transformation semigroup ⟨G,f⟩ contains a constant map, and that G is a synchronizing group if G synchronizes every non-permutation. A synchronizing group is necessarily primitive, but there are primitive groups that are not synchronizing. Every non-synchronizing primitive group fails to synchronize at least one uniform transformation (that is, transformation whose kernel has parts of equal size), and it had previously been conjectured that this was essentially the only way in which a primitive group could fail to be synchronizing, in other words, that a primitive group synchronizes every non-uniform transformation. The first goal of this paper is to prove that this conjecture is false, by exhibiting primitive groups that fail to synchronize specific non-uniform transformations of ranks 5 and 6. As it has previously been shown that primitive groups synchronize every non-uniform transformation of rank at most 4, these examples are of the lowest possible rank. In addition, we produce graphs with primitive automorphism groups that have approximately √n non-synchronizing ranks, thus refuting another conjecture on the number of non-synchronizing ranks of a primitive group. The second goal of this paper is to extend the spectrum of ranks for which it is known that primitive groups synchronize every non-uniform transformation of that rank. It has previously been shown that a primitive group of degree n synchronizes every non-uniform transformation of rank n−1 and n−2, and here this is extended to n−3 and n−4. In the process, we will obtain a purely graph-theoretical result showing that, with limited exceptions, in a vertex-primitive graph the union of neighbourhoods of a set of vertices A is bounded below by a function that is asymptotically √|A|. Determining the exact spectrum of ranks for which there exist non-uniform transformations not synchronized by some primitive group is just one of several natural, but possibly difficult, problems on automata, primitive groups, graphs and computational algebra arising from this work; these are outlined in the final section.Bernoulli convolutions and 1D dynamics
http://hdl.handle.net/10023/9629
We describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.
Thu, 08 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/96292015-10-08T00:00:00ZKempton, Thomas Michael WilliamPersson, TomasWe describe a family φλ of dynamical systems on the unit interval which preserve Bernoulli convolutions. We show that if there are parameter ranges for which these systems are piecewise convex, then the corresponding Bernoulli convolution will be absolutely continuous with bounded density. We study the systems φλ and give some numerical evidence to suggest values of λ for which φλ may be piecewise convex.Bayesian multi-species modelling of non-negative continuous ecological data with a discrete mass at zero
http://hdl.handle.net/10023/9626
Severe declines in the number of some songbirds over the last 40 years
have caused heated debate amongst interested parties. Many factors
have been suggested as possible causes for these declines, including
an increase in the abundance and distribution of an avian predator,
the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a
predator effect on the abundance of its prey, we analyse data on 10
species visiting garden bird feeding stations monitored by the British
Trust for Ornithology in relation to the abundance of sparrowhawks.
We apply Bayesian hierarchical models to data relating to averaged
maximum weekly counts from a garden bird monitoring survey. These
data are essentially continuous, bounded below by zero, but for many
species show a marked spike at zero that many standard distributions
would not be able to account for. We use the Tweedie distributions,
which for certain areas of parameter space relate to continuous nonnegative
distributions with a discrete probability mass at zero, and
are hence able to deal with the shape of the empirical distributions of
the data.
The methods developed in this thesis begin by modelling single prey
species independently with an avian predator as a covariate, using
MCMC methods to explore parameter and model spaces. This model
is then extended to a multiple-prey species model, testing for interactions
between species as well as synchrony in their response to environmental
factors and unobserved variation.
Finally we use a relatively new methodological framework, namely
the SPDE approach in the INLA framework, to fit a multi-species
spatio-temporal model to the ecological data.
The results from the analyses are consistent with the hypothesis that
sparrowhawks are suppressing the numbers of some species of birds
visiting garden feeding stations. Only the species most susceptible to
sparrowhawk predation seem to be affected.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/96262015-01-01T00:00:00ZSwallow, BenSevere declines in the number of some songbirds over the last 40 years
have caused heated debate amongst interested parties. Many factors
have been suggested as possible causes for these declines, including
an increase in the abundance and distribution of an avian predator,
the Eurasian sparrowhawk Accipiter nisus. To test for evidence for a
predator effect on the abundance of its prey, we analyse data on 10
species visiting garden bird feeding stations monitored by the British
Trust for Ornithology in relation to the abundance of sparrowhawks.
We apply Bayesian hierarchical models to data relating to averaged
maximum weekly counts from a garden bird monitoring survey. These
data are essentially continuous, bounded below by zero, but for many
species show a marked spike at zero that many standard distributions
would not be able to account for. We use the Tweedie distributions,
which for certain areas of parameter space relate to continuous nonnegative
distributions with a discrete probability mass at zero, and
are hence able to deal with the shape of the empirical distributions of
the data.
The methods developed in this thesis begin by modelling single prey
species independently with an avian predator as a covariate, using
MCMC methods to explore parameter and model spaces. This model
is then extended to a multiple-prey species model, testing for interactions
between species as well as synchrony in their response to environmental
factors and unobserved variation.
Finally we use a relatively new methodological framework, namely
the SPDE approach in the INLA framework, to fit a multi-species
spatio-temporal model to the ecological data.
The results from the analyses are consistent with the hypothesis that
sparrowhawks are suppressing the numbers of some species of birds
visiting garden feeding stations. Only the species most susceptible to
sparrowhawk predation seem to be affected.Dynamical patterns of coexisting strategies in a hybrid discrete-continuum spatial evolutionary game model
http://hdl.handle.net/10023/9625
We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individual-based model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reaction-diffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxis-diffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a two-player game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the Hawk-Dove game. Numerical simulations illustrate how random motion and chemotactic response can bring about self-generated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatially-structured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.
Wed, 07 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/96252016-12-07T00:00:00ZBurgess, A. E. FSchofield, P. G.Hubbard, S. F.Chaplain, Mark A. J.Lorenzi, T.We present a novel hybrid modelling framework that takes into account two aspects which have been largely neglected in previous models of spatial evolutionary games: random motion and chemotaxis. A stochastic individual-based model is used to describe the player dynamics,whereas the evolution of the chemoattractant is governed by a reaction-diffusion equation. The two models are coupled by deriving individual movement rules via the discretisation of a taxis-diffusion equation which describes the evolution of the local number of players. In this framework, individuals occupying the same position can engage in a two-player game, and are awarded a payoff, interms of reproductive fitness, according to their strategy. As an example, we let individuals play the Hawk-Dove game. Numerical simulations illustrate how random motion and chemotactic response can bring about self-generated dynamical patterns that create favourable conditions for the coexistence of hawks and doves in situations in which the two strategies cannot coexist otherwise.In this sense, our work offers a new perspective of research on spatial evolutionary games, and provides a general formalism to study the dynamics of spatially-structured populations in biological and social contexts where individual motion is likely to affect natural selection of behavioural traits.The usage of a three-compartment model to investigate the metabolic differences between hepatic reductase null and wild-type mice
http://hdl.handle.net/10023/9611
The Cytochrome P450 (CYP) system is involved in 90% of the human body’s interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a three-compartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. 278, 13480–13486). The model is compared with a two-compartment model using experimental data from studies using wild-type and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism.
L.H. is currently funded by the Research Foundation Flanders (FWO) and the Belgian Science Policy Office under Grant No. IAP-VI/10.
Mon, 05 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/96112015-10-05T00:00:00ZHill, LydiaChaplain, Mark Andrew JosephWolf, RolandKapelyukh, YuryThe Cytochrome P450 (CYP) system is involved in 90% of the human body’s interactions with xenobiotics and due to this, it has become an area of avid research including the creation of transgenic mice. This paper proposes a three-compartment model which is used to explain the drug metabolism in the Hepatic Reductase Null (HRN) mouse developed by the University of Dundee (Henderson, C. J., Otto, D. M. E., Carrie, D., Magnuson, M. A., McLaren, A. W., Rosewell, I. and Wolf, C. R. (2003) Inactivation of the hepatic cytochrome p450 system by conditional deletion of hepatic cytochrome p450 reductase. J. Biol. Chem. 278, 13480–13486). The model is compared with a two-compartment model using experimental data from studies using wild-type and HRN mice. This comparison allowed for metabolic differences between the two types of mice to be isolated. The three sets of drug data (Gefitinib, Midazolam and Thalidomide) showed that the transgenic mouse has a decreased rate of metabolism.On the connection between propagating solar coronal disturbances and chromospheric footpoints
http://hdl.handle.net/10023/9600
The Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—“propagating coronal disturbances” (PCDs) with apparent speeds of the order of 100–120 km/s-1. That signal has a clear signature in the slit-jaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg IIh (2803 Å) line. In analyzing the Mg IIh line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg IIh, the evolution of the Si IV line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jet-like features in the IRIS Si IV slit-jaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/96002016-09-01T00:00:00ZBryans, PaulMcIntosh, Scott W.De Moortel, InekeDe Pontieu, BartThe Interface Region Imaging Spectrograph (IRIS) provides an unparalleled opportunity to explore the (thermal) interface between the chromosphere, transition region, and the coronal plasma observed by the Atmospheric Imaging Assembly (AIA) of the Solar Dynamics Observatory (SDO). The SDO/AIA observations of coronal loop footpoints show strong recurring upward propagating signals—“propagating coronal disturbances” (PCDs) with apparent speeds of the order of 100–120 km/s-1. That signal has a clear signature in the slit-jaw images of IRIS in addition to identifiable spectral signatures and diagnostics in the Mg IIh (2803 Å) line. In analyzing the Mg IIh line, we are able to observe the presence of magnetoacoustic shock waves that are also present in the vicinity of the coronal loop footpoints. We see there is enough of a correspondence between the shock propagation in Mg IIh, the evolution of the Si IV line profiles, and the PCD evolution to indicate that these waves are an important ingredient for PCDs. In addition, the strong flows in the jet-like features in the IRIS Si IV slit-jaw images are also associated with PCDs, such that waves and flows both appear to be contributing to the signals observed at the footpoints of PCDs.The interaction between two oppositely travelling, horizontally offset, antisymmetric quasi-geostrophic hetons
http://hdl.handle.net/10023/9593
We investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a meta-stable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/95932016-05-01T00:00:00ZReinaud, Jean NoelCarton, XavierWe investigate numerically the nonlinear interactions between hetons. Hetons are baroclinic structures consisting of two vortices of opposite sign lying at different depths. Hetons are long-lived. They most often translate (they can sometimes rotate) and therefore they can noticeably contribute to the transport of scalar properties in the oceans. Heton interactions can interrupt this translation and thus this transport, by inducing a reconfiguration of interacting hetons into more complex baroclinic multipoles. More specifically, we study here the general case of two hetons, which collide with an offset between their translation axes. For this purpose, we use the point vortex theory, the ellipsoidal vortex model and direct simulations in the three-dimensional quasi-geostrophic, contour surgery model. More specifically, this paper shows that there are in general three regimes for the interaction. For small horizontal offsets between the hetons, their vortices recombine as same-depth dipoles which escape at an angle. The angle depends in particular on the horizontal offset. It is a right angle for no offset, and the angle is shallower for small but finite offsets. The second limiting regime is for large horizontal offsets where the two hetons remain the same hetonic structures but are deflected by the weaker mutual interaction. Finally the intermediate regime is for moderate offsets. This is the regime where the formation of a meta-stable quadrupole is possible. The formation of this quadrupole greatly restrains transport. Indeed, it constrains the vortices to reside in a closed area. It is shown that the formation of such structures is enhanced by the quasi periodic deformation of the vortices. Indeed, these structures are nearly unobtainable for singular vortices (point vortices) but may be obtained using deformable, finite-core vortices.Modeling observed decay-less oscillations as resonantly enhanced Kelvin-Helmholtz vortices from transverse MHD waves and their seismological application
http://hdl.handle.net/10023/9577
In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.
Wed, 12 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/95772016-10-12T00:00:00ZAntolin, P.De Moortel, InekeVan Doorsselaere, T.Yokoyama, T.In the highly structured solar corona, resonant absorption is an unavoidable mechanism of energy transfer from global transverse MHD waves to local azimuthal Alfvén waves. Due to its localised nature, a direct detection of this mechanism is extremely difficult. Yet, it is the leading theory explaining the observed fast damping of the global transverse waves. However, at odds with this theoretical prediction, recent observations indicate that in the low amplitude regime such transverse MHD waves can also appear decay-less, a yet unsolved phenomenon. Recent numerical work has shown that Kelvin-Helmholtz instabilities (KHI) often accompany transverse MHD waves. In this work, we combine 3D MHD simulations and forward modelling to show that for currently achieved spatial resolution and observed small amplitudes, an apparent decay-less oscillation is obtained. This effect results from the combination of periodic brightenings produced by the KHI and the coherent motion of the KHI vortices amplified by resonant absorption. Such effect is especially clear in emission lines forming at temperatures that capture the boundary dynamics rather than the core, and reflects the low damping character of the local azimuthal Alfvén waves resonantly coupled to the kink mode. Due to phase mixing, the detected period can vary depending on the emission line, with those sensitive to the boundary having shorter periods than those sensitive to the loop core. This allows to estimate the density contrast at the boundary.Effects of a scientific echo sounder on the behavior of short-finned pilot whales (Globicephala macrorhynchus)
http://hdl.handle.net/10023/9555
Active echo sounding devices are often employed for commercial or scientific purposes in the foraging habitats of marine mammals. We conducted an experiment off Cape Hatteras, North Carolina, USA, to assess whether the behavior of short-finned pilot whales (Globicephala macrorhynchus) changed when exposed to an EK60 scientific echo sounder. We attached digital acoustic recording tags (DTAGs) to nine individuals, five of which were exposed. A hidden Markov model to characterize diving states with and without exposure provided no evidence for a change in foraging behavior. However, generalized estimating equations to model changes in heading variance over the entire tag record under all experimental conditions showed a consistent increase in heading variance during exposure over all values of depth and pitch. This suggests that regardless of behavioral state, the whales changed their heading more frequently when the echo sounder was active. This response could represent increased vigilance in which whales maintained awareness of echo sounder location by increasing their heading variance and provides the first quantitative analysis on reactions of cetaceans to a scientific echo sounder.
This work was supported by award RC-2154 from the Strategic Environmental Research and Development Program and funding from the Naval Facilities Engineering Command Atlantic and NOAA Fisheries, Southeast Region.
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/95552017-05-01T00:00:00ZQuick, NicolaScott-Hayward, LindesaySadykova, DinaraNowacek, DougRead, AndrewActive echo sounding devices are often employed for commercial or scientific purposes in the foraging habitats of marine mammals. We conducted an experiment off Cape Hatteras, North Carolina, USA, to assess whether the behavior of short-finned pilot whales (Globicephala macrorhynchus) changed when exposed to an EK60 scientific echo sounder. We attached digital acoustic recording tags (DTAGs) to nine individuals, five of which were exposed. A hidden Markov model to characterize diving states with and without exposure provided no evidence for a change in foraging behavior. However, generalized estimating equations to model changes in heading variance over the entire tag record under all experimental conditions showed a consistent increase in heading variance during exposure over all values of depth and pitch. This suggests that regardless of behavioral state, the whales changed their heading more frequently when the echo sounder was active. This response could represent increased vigilance in which whales maintained awareness of echo sounder location by increasing their heading variance and provides the first quantitative analysis on reactions of cetaceans to a scientific echo sounder.Neutral and non-neutral collisionless plasma equilibria for twisted flux tubes : the Gold-Hoyle model in a background field
http://hdl.handle.net/10023/9539
We calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's Equation and Amp ere's Law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space and astrophysical contexts, as well as in the laboratory.
The authors gratefully acknowledge the support of the Science and Technology Facilities Council Consolidated Grants ST/K000950/1 and ST/N000609/1, as well as Doctoral Training Grant ST/K502327/1. We also gratefully acknowledge funding from Leverhulme Trust Research Project Grant F/00268/BB.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/95392016-09-01T00:00:00ZAllanson, Oliver DouglasWilson, FionaNeukirch, ThomasWe calculate exact one-dimensional collisionless plasma equilibria for a continuum of flux tube models, for which the total magnetic field is made up of the `force-free' Gold-Hoyle magnetic flux tube embedded in a uniform and anti-parallel background magnetic field. For a sufficiently weak background magnetic field, the axial component of the total magnetic field reverses at some finite radius. The presence of the background magnetic field means that the total system is not exactly force-free, but by reducing its magnitude the departure from force-free can be made as small as desired. The distribution function for each species is a function of the three constants of motion; namely the Hamiltonian and the canonical momenta in the axial and azimuthal directions. Poisson's Equation and Amp ere's Law are solved exactly, and the solution allows either electrically neutral or non-neutral configurations, depending on the values of the bulk ion and electron flows. These equilibria have possible applications in various solar, space and astrophysical contexts, as well as in the laboratory.The role of planetary waves in the tropospheric jet response to stratospheric cooling
http://hdl.handle.net/10023/9528
An idealized general circulation model is used to assess the importance of planetary-scale waves in determining the position of the tropospheric jet, specifically its tendency to shift poleward as winter stratospheric cooling is increased. Full model integrations are compared against integrations in which planetary waves are truncated in the zonal direction, and only synoptic-scale waves are retained. Two series of truncated integrations are considered, using (i) a modified radiative equilibrium temperature or (ii) a nudged-bias correction technique. Both produce tropospheric climatologies that are similar to the full model when stratospheric cooling is weak. When stratospheric cooling is increased, the results indicate that the interaction between planetary- and synoptic-scale waves plays an important role in determining the structure of the tropospheric mean flow and rule out the possibility that the jet shift occurs purely as a response to changes in the planetary- or synoptic-scale wave fields alone.
K.L.S. is funded in part by a Natural Sciences and Engineering Council of Canada Postdoctoral Fellowship. R.K.S. acknowledges support from the National Science Foundation.
Mon, 28 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/95282016-03-28T00:00:00ZSmith, Karen L.Scott, Richard K.An idealized general circulation model is used to assess the importance of planetary-scale waves in determining the position of the tropospheric jet, specifically its tendency to shift poleward as winter stratospheric cooling is increased. Full model integrations are compared against integrations in which planetary waves are truncated in the zonal direction, and only synoptic-scale waves are retained. Two series of truncated integrations are considered, using (i) a modified radiative equilibrium temperature or (ii) a nudged-bias correction technique. Both produce tropospheric climatologies that are similar to the full model when stratospheric cooling is weak. When stratospheric cooling is increased, the results indicate that the interaction between planetary- and synoptic-scale waves plays an important role in determining the structure of the tropospheric mean flow and rule out the possibility that the jet shift occurs purely as a response to changes in the planetary- or synoptic-scale wave fields alone.Modeling the sun's small-scale global photospheric magnetic field
http://hdl.handle.net/10023/9511
We present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small-scale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between small-scale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2.5 R⊙, around 10–100 times less than that determined for typical Helioseismic and Magnetic Imager synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is currently observed, and hence a much higher cosmic ray flux at Earth.
Wed, 19 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/95112016-10-19T00:00:00ZMeyer, Karen AlisonMackay, Duncan HendryWe present a new model for the Sun's global photospheric magnetic field during a deep minimum of activity, in which no active regions emerge. The emergence and subsequent evolution of small-scale magnetic features across the full solar surface is simulated, subject to the influence of a global supergranular flow pattern. Visually, the resulting simulated magnetograms reproduce the typical structure and scale observed in quiet Sun magnetograms. Quantitatively, the simulation quickly reaches a steady state, resulting in a mean field and flux distribution that are in good agreement with those determined from observations. A potential coronal magnetic field is extrapolated from the simulated full Sun magnetograms to consider the implications of such a quiet photospheric magnetic field on the corona and inner heliosphere. The bulk of the coronal magnetic field closes very low down, in short connections between small-scale features in the simulated magnetic network. Just 0.1% of the photospheric magnetic flux is found to be open at 2.5 R⊙, around 10–100 times less than that determined for typical Helioseismic and Magnetic Imager synoptic map observations. If such conditions were to exist on the Sun, this would lead to a significantly weaker interplanetary magnetic field than is currently observed, and hence a much higher cosmic ray flux at Earth.The possible impact of L5 magnetograms on non-potential solar coronal magnetic field simulations
http://hdl.handle.net/10023/9480
The proposed Carrington-L5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in non-potential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared to an L1-based field of view. A time series of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 field of view. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 field of view. Non-potential simulations for the two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can however lead to significant persistent differences in long range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux, and the location of open magnetic foot points, are sensitive to capturing the real time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the non-potential corona, interplanetary magnetic field and of solar wind source regions on the Sun.
Sat, 10 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/94802016-09-10T00:00:00ZWeinzierl, MarionMackay, Duncan HendryYeates, Anthony RobinsonPevtsov, AlexeiThe proposed Carrington-L5 mission would bring instruments to the L5 Lagrange point to provide us with crucial data for space weather prediction. To assess the importance of including a magnetograph, we consider the possible differences in non-potential solar coronal magnetic field simulations when magnetograph observations are available from the L5 point, compared to an L1-based field of view. A time series of synoptic radial magnetic field maps is constructed to capture the emergence of two active regions from the L5 field of view. These regions are initially absent in the L1 magnetic field maps, but are included once they rotate into the L1 field of view. Non-potential simulations for the two sets of input data are compared in detail. Within the bipolar active regions themselves, differences in the magnetic field structure can exist between the two simulations once the active regions are included in both. These differences tend to reduce within 5 days of the active region being included in L1. The delayed emergence in L1 can however lead to significant persistent differences in long range connectivity between the active regions and the surrounding fields, and also in the global magnetic energy. In particular, the open magnetic flux, and the location of open magnetic foot points, are sensitive to capturing the real time of emergence. These results suggest that a magnetograph at L5 could significantly improve predictions of the non-potential corona, interplanetary magnetic field and of solar wind source regions on the Sun.3D MHD modeling of twisted coronal loops
http://hdl.handle.net/10023/9475
We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the high-beta chromosphere to the low-betacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm-3. More heating is released in the low corona than the high corona and is finely structured both in space and time.
Mon, 10 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/94752016-10-10T00:00:00ZReale, F.Orlando, S.Guarrasi, M.Mignone, A.Peres, G.Hood, A. W.Priest, E. R.We perform MHD modeling of a single bright coronal loop to include the interaction with a non-uniform magnetic field. The field is stressed by random footpoint rotation in the central region and its energy is dissipated into heating by growing currents through anomalous magnetic diffusivity that switches on in the corona above a current density threshold. We model an entire single magnetic flux tube, in the solar atmosphere extending from the high-beta chromosphere to the low-betacorona through the steep transition region. The magnetic field expands from the chromosphere to the corona. The maximum resolution is ~30 km. We obtain an overall evolution typical of loop models and realistic loop emission in the EUV and X-ray bands. The plasma confined in the fluxtube is heated to active region temperatures (~3 MK) after ~2/3 hr. Upflows from the chromosphere up to ~100 km/s fill the core of the fluxtube to densities above 109 cm-3. More heating is released in the low corona than the high corona and is finely structured both in space and time.Three-dimensional forced-damped dynamical systems with rich dynamics : bifurcations, chaos and unbounded solutions
http://hdl.handle.net/10023/9468
We consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.
T.M. is supported by the Grant-in-Aid for JSPS Fellow No. 24·5312. H.O. is partially supported by JSPS KAKENHI 24244007.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/94682015-01-01T00:00:00ZMiyaji, TomoyukiOkamoto, HisashiCraik, Alexander Duncan DavidsonWe consider certain autonomous three-dimensional dynamical systems that can arise in mechanical and fluid-dynamical contexts. Extending a previous study in Craik and Okamoto (2002), to include linear forcing and damping, we find that the four-leaf structure discovered in that paper, and unbounded orbits, persist, but may now be accompanied by three distinct period-doubling cascades to chaos, and by orbits that approach stable equilibrium points. This rich structure is investigated both analytically and numerically, distinguishing three main cases determined by the damping and forcing parameter values.Sunspot rotation : II. Effects of varying the field strength and twist of an emerging flux tube
http://hdl.handle.net/10023/9442
Context. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on sub-photospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging sub-photospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a sub-photospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangian-remap code, Lare3d. We perform a parameter study by independently varying the sub-photospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.
ZS acknowledges the financial support of the Carnegie Trust for Scotland. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.
Thu, 01 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/94422016-09-01T00:00:00ZSturrock, ZoeHood, Alan WilliamContext. Observations of flux emergence indicate that rotational velocities may develop within sunspots. However, the dependence of this rotation on sub-photospheric field strength and twist remains largely unknown. Aims. We investigate the effects of varying the initial field strength and twist of an emerging sub-photospheric magnetic flux tube onthe rotation of the sunspots at the photosphere. Methods. We consider a simple model of a stratified domain with a sub-photospheric interior layer and three overlying atmospheric layers. A twisted arched flux tube is inserted in the interior and is allowed to rise into the atmosphere. To achieve this, the MHD equations are solved using the Lagrangian-remap code, Lare3d. We perform a parameter study by independently varying the sub-photospheric magnetic field strength and twist. Results. Altering the initial magnetic field strength and twist of the flux tube significantly affects the tube’s evolution and the rotational motions that develop at the photosphere. The rotation angle, vorticity, and current show a direct dependence on the initial field strength. We find that an increase in field strength increases the angle through which the fieldlines rotate, the length of the fieldlines extending into the atmosphere, and the magnetic energy transported to the atmosphere. This also affects the amount of residual twist in the interior. The length of the fieldlines is crucial as we predict the twist per unit length equilibrates to a lower value on longer fieldlines. No such direct dependence is found when we modify the twist of the magnetic field owing to the complex effect this has on the tension force acting on the tube. However, there is still a clear ordering in quantities such as the rotation angle, helicity, and free energy with higher initial twist cases being related to sunspots that rotate more rapidly, transporting more helicity and magnetic energy to the atmosphere.Uncovering the birth of a coronal mass ejection from two-viewpoint SECCHI observations
http://hdl.handle.net/10023/9428
We investigate the initiation and formation of Coronal Mass Ejections (CMEs) via a detailed two-viewpoint analysis of low corona observations of a relatively fast CME acquired by the SECCHI instruments aboard the STEREO mission. The event which occurred on 2 January 2008, was chosen because of several unique characteristics. It shows upward motions for at least four hours before the flare peak. Its speed and acceleration profiles exhibit a number of inflections which seem to have a direct counterpart in the GOES light curves. We detect and measure, in 3D, loops that collapse toward the erupting channel while the CME is increasing in size and accelerates. We suggest that these collapsing loops are our first evidence of magnetic evacuation behind the forming CME flux rope. We report the detection of a hot structure which becomes the core of the white light CME. We observe and measure unidirectional flows along the erupting filament channel which may be associated with the eruption process. Finally, we compare these observations to the predictions from the standard flare-CME model and find a very satisfactory agreement. We conclude that the standard flare-CME concept is a reliable representation of the initial stages of CMEs and that multi-viewpoint, high cadence EUV observations can be extremely useful in understanding the formation of CMEs.
Mon, 01 Oct 2012 00:00:00 GMThttp://hdl.handle.net/10023/94282012-10-01T00:00:00ZVourlidas, A.Syntelis, P.Tsinganos, K.We investigate the initiation and formation of Coronal Mass Ejections (CMEs) via a detailed two-viewpoint analysis of low corona observations of a relatively fast CME acquired by the SECCHI instruments aboard the STEREO mission. The event which occurred on 2 January 2008, was chosen because of several unique characteristics. It shows upward motions for at least four hours before the flare peak. Its speed and acceleration profiles exhibit a number of inflections which seem to have a direct counterpart in the GOES light curves. We detect and measure, in 3D, loops that collapse toward the erupting channel while the CME is increasing in size and accelerates. We suggest that these collapsing loops are our first evidence of magnetic evacuation behind the forming CME flux rope. We report the detection of a hot structure which becomes the core of the white light CME. We observe and measure unidirectional flows along the erupting filament channel which may be associated with the eruption process. Finally, we compare these observations to the predictions from the standard flare-CME model and find a very satisfactory agreement. We conclude that the standard flare-CME concept is a reliable representation of the initial stages of CMEs and that multi-viewpoint, high cadence EUV observations can be extremely useful in understanding the formation of CMEs.Study of the three-dimensional shape and dynamics of coronal loops observed by Hinode/EIS
http://hdl.handle.net/10023/9426
We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with Hinode’sEUVImaging Spectrograph (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their three-dimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the Fe viii 185 Å, Fe x 184 Å, Fe xii 195 Å, Fe xiii202 Å, and Fe xv 284 Å spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist (α<0), in agreement with the dominant twist of the region.
Mon, 01 Oct 2012 00:00:00 GMThttp://hdl.handle.net/10023/94262012-10-01T00:00:00ZSyntelis, P.Gontikakis, C.Georgoulis, M. K.Alissandrakis, C. E.Tsinganos, K.We study plasma flows along selected coronal loops in NOAA Active Region 10926, observed on 3 December 2006 with Hinode’sEUVImaging Spectrograph (EIS). From the shape of the loops traced on intensity images and the Doppler shifts measured along their length we compute their three-dimensional (3D) shape and plasma flow velocity using a simple geometrical model. This calculation was performed for loops visible in the Fe viii 185 Å, Fe x 184 Å, Fe xii 195 Å, Fe xiii202 Å, and Fe xv 284 Å spectral lines. In most cases the flow is unidirectional from one footpoint to the other but there are also cases of draining motions from the top of the loops to their footpoints. Our results indicate that the same loop may show different flow patterns when observed in different spectral lines, suggesting a dynamically complex rather than a monolithic structure. We have also carried out magnetic extrapolations in the linear force-free field approximation using SOHO/MDI magnetograms, aiming toward a first-order identification of extrapolated magnetic field lines corresponding to the reconstructed loops. In all cases, the best-fit extrapolated lines exhibit left-handed twist (α<0), in agreement with the dominant twist of the region.The spectroscopic imprint of the pre-eruptive configuration resulting into two major coronal mass ejections
http://hdl.handle.net/10023/9425
Aims: We present a spectroscopic analysis of the pre-eruptive configuration of active region NOAA 11429, prior to two very fast coronal mass ejections (CMEs) on March 7, 2012 that are associated with this active region. We study the thermal components and the dynamics associated with the ejected flux ropes. Methods: Using differential emission measure (DEM) analysis of Hinode/EIS and SDO/AIA observations, we identify the emission components of both the flux rope and the host active region. We then follow the time evolution of the flux rope emission components by using AIA observations. The plasma density and the Doppler and non-thermal velocities associated with the flux ropes are also calculated from the EIS data. Results: The eastern and western parts of the active region, in which the two different fast CMEs originated during two X-class flares, were studied separately. In both regions we identified an emission component in the temperature range of log T = 6.8-7.1 associated with the presence of flux ropes. The time evolution of the eastern region showed an increase in the mean DEM in this temperature range by an order of magnitude, 5 h prior to the first CME. This was associated with a gradual rise and heating of the flux rope as manifested by blue-shifts and increased non-thermal velocities in Ca xv 200.97 Å, respectively. An overall upward motion of the flux ropes was measured (relative blue-shifts of ~12 km s-1). The measured electron density was found to be 4× 109-2 × 1010 cm-3 (using the ratio of Ca xv 181.90 Å over Ca xv 200.97 Å). We compare our findings with other works on the same AR to provide a unified picture of its evolution.
P.S acknowledges financial support from the programme Aristotelis/SIEMENS at the NOA.
Fri, 01 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/94252016-04-01T00:00:00ZSyntelis, P.Gontikakis, C.Patsourakos, S.Tsinganos, K.Aims: We present a spectroscopic analysis of the pre-eruptive configuration of active region NOAA 11429, prior to two very fast coronal mass ejections (CMEs) on March 7, 2012 that are associated with this active region. We study the thermal components and the dynamics associated with the ejected flux ropes. Methods: Using differential emission measure (DEM) analysis of Hinode/EIS and SDO/AIA observations, we identify the emission components of both the flux rope and the host active region. We then follow the time evolution of the flux rope emission components by using AIA observations. The plasma density and the Doppler and non-thermal velocities associated with the flux ropes are also calculated from the EIS data. Results: The eastern and western parts of the active region, in which the two different fast CMEs originated during two X-class flares, were studied separately. In both regions we identified an emission component in the temperature range of log T = 6.8-7.1 associated with the presence of flux ropes. The time evolution of the eastern region showed an increase in the mean DEM in this temperature range by an order of magnitude, 5 h prior to the first CME. This was associated with a gradual rise and heating of the flux rope as manifested by blue-shifts and increased non-thermal velocities in Ca xv 200.97 Å, respectively. An overall upward motion of the flux ropes was measured (relative blue-shifts of ~12 km s-1). The measured electron density was found to be 4× 109-2 × 1010 cm-3 (using the ratio of Ca xv 181.90 Å over Ca xv 200.97 Å). We compare our findings with other works on the same AR to provide a unified picture of its evolution.The major geoeffective solar eruptions of 2012 March 7: comprehensive Sun-to-Earth analysis
http://hdl.handle.net/10023/9421
During the interval 2012 March 7-11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 kms-1) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13R⊙ to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.
Tue, 19 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/94212016-01-19T00:00:00ZPatsourakos, S.Georgoulis, M. K.Vourlidas, A.Nindos, A.Sarris, T.Anagnostopoulos, G.Anastasiadis, A.Chintzoglou, G.Daglis, I. A.Gontikakis, C.Hatzigeorgiu, N.Iliopoulos, A. C.Katsavrias, C.Kouloumvakos, A.Moraitis, K.Nieves-Chinchilla, T.Pavlos, G.Sarafopoulos, D.Syntelis, P.Tsironis, C.Tziotziou, K.Vogiatzis, I. I.Balasis, G.Georgiou, M.Karakatsanis, L. P.Malandraki, O. E.Papadimitriou, C.Odstrčil, D.Pavlos, E. G.Podlachikova, O.Sandberg, I.Turner, D. L.Xenakis, M. N.Sarris, E.Tsinganos, K.Vlahos, L.During the interval 2012 March 7-11 the geospace experienced a barrage of intense space weather phenomena including the second largest geomagnetic storm of solar cycle 24 so far. Significant ultra-low-frequency wave enhancements and relativistic-electron dropouts in the radiation belts, as well as strong energetic-electron injection events in the magnetosphere were observed. These phenomena were ultimately associated with two ultra-fast (>2000 kms-1) coronal mass ejections (CMEs), linked to two X-class flares launched on early 2012 March 7. Given that both powerful events originated from solar active region NOAA 11429 and their onsets were separated by less than an hour, the analysis of the two events and the determination of solar causes and geospace effects are rather challenging. Using satellite data from a flotilla of solar, heliospheric and magnetospheric missions a synergistic Sun-to-Earth study of diverse observational solar, interplanetary and magnetospheric data sets was performed. It was found that only the second CME was Earth-directed. Using a novel method, we estimated its near-Sun magnetic field at 13R⊙ to be in the range [0.01, 0.16] G. Steep radial fall-offs of the near-Sun CME magnetic field are required to match the magnetic fields of the corresponding interplanetary CME (ICME) at 1 AU. Perturbed upstream solar-wind conditions, as resulting from the shock associated with the Earth-directed CME, offer a decent description of its kinematics. The magnetospheric compression caused by the arrival at 1 AU of the shock associated with the ICME was a key factor for radiation-belt dynamics.Recurrence and transience for suspension flows
http://hdl.handle.net/10023/9416
We study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the renewal flow, which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.
Funding: Proyecto Fondecyt 1110040 for funding visit to PUC-Chile and partial support from NSF grant DMS 1109587.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/94162015-01-01T00:00:00ZIommi, GodofredoJordan, ThomasTodd, Michael JohnWe study the thermodynamic formalism for suspension flows over countable Markov shifts with roof functions not necessarily bounded away from zero. We establish conditions to ensure the existence and uniqueness of equilibrium measures for regular potentials. We define the notions of recurrence and transience of a potential in this setting. We define the renewal flow, which is a symbolic model for a class of flows with diverse recurrence features. We study the corresponding thermodynamic formalism, establishing conditions for the existence of equilibrium measures and phase transitions. Applications are given to suspension flows defined over interval maps having parabolic fixed points.Tracking the evolution of cancer cell populations through the mathematical lens of phenotype-structured equations
http://hdl.handle.net/10023/9363
Background: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.
This work was supported in part by the French National Research Agency through the “ANR blanche” project Kibord [ANR-13-BS01-0004].
Tue, 23 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/93632016-08-23T00:00:00ZLorenzi, TommasoChisholm, Rebecca H.Clairambault, JeanBackground: A thorough understanding of the ecological and evolutionary mechanisms that drive the phenotypic evolution of neoplastic cells is a timely and key challenge for the cancer research community. In this respect, mathematical modelling can complement experimental cancer research by offering alternative means of understanding the results of in vitro and in vivo experiments, and by allowing for a quick and easy exploration of a variety of biological scenarios through in silico studies. Results: To elucidate the roles of phenotypic plasticity and selection pressures in tumour relapse, we present here a phenotype-structured model of evolutionary dynamics in a cancer cell population which is exposed to the action of a cytotoxic drug. The analytical tractability of our model allows us to investigate how the phenotype distribution, the level of phenotypic heterogeneity, and the size of the cell population are shaped by the strength of natural selection, the rate of random epimutations, the intensity of the competition for limited resources between cells, and the drug dose in use. Conclusions: Our analytical results clarify the conditions for the successful adaptation of cancer cells faced with environmental changes. Furthermore, the results of our analyses demonstrate that the same cell population exposed to different concentrations of the same cytotoxic drug can take different evolutionary trajectories, which culminate in the selection of phenotypic variants characterised by different levels of drug tolerance. This suggests that the response of cancer cells to cytotoxic agents is more complex than a simple binary outcome, i.e., extinction of sensitive cells and selection of highly resistant cells. Also, our mathematical results formalise the idea that the use of cytotoxic agents at high doses can act as a double-edged sword by promoting the outgrowth of drug resistant cellular clones. Overall, our theoretical work offers a formal basis for the development of anti-cancer therapeutic protocols that go beyond the ‘maximum-tolerated-dose paradigm’, as they may be more effective than traditional protocols at keeping the size of cancer cell populations under control while avoiding the expansion of drug tolerant clones.A note on the probability of generating alternating or symmetric groups
http://hdl.handle.net/10023/9348
We improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.
The research of the first author is supported by the Australian Research Council grant DP120100446.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/93482015-09-01T00:00:00ZMorgan, LukeRoney-Dougal, Colva MaryWe improve on recent estimates for the probability of generating the alternating and symmetric groups An and Sn. In particular, we find the sharp lower bound if the probability is given by a quadratic in n−1. This leads to improved bounds on the largest number h(An) such that a direct product of h(An) copies of An can be generated by two elements.Evolution of magnetic helicity during eruptive flares and coronal mass ejections
http://hdl.handle.net/10023/9320
During eruptive solar flares and coronal mass ejections, a non-potential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial preeruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the pre-eruptive state,and the e.ect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry.
Funding: UK STFC, High Altitude Observatory and Montana State University.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/93202016-08-01T00:00:00ZPriest, Eric RonaldLongcope, D WJanvier, MDuring eruptive solar flares and coronal mass ejections, a non-potential magnetic arcade with much excess magnetic energy goes unstable and reconnects. It produces a twisted erupting flux rope and leaves behind a sheared arcade of hot coronal loops. We suggest that: the twist of the erupting flux rope can be determined from conservation of magnetic flux and magnetic helicity and equipartition of magnetic helicity. It depends on the geometry of the initial preeruptive structure. Two cases are considered, in the first of which a flux rope is not present initially but is created during the eruption by the reconnection. In the second case, a flux rope is present under the arcade in the pre-eruptive state,and the e.ect of the eruption and reconnection is to add an amount of magnetic helicity that depends on the fluxes of the rope and arcade and the geometry.Lengths of words in transformation semigroups generated by digraphs
http://hdl.handle.net/10023/9277
Given a simple digraph D on n vertices (with n≥2), there is a natural construction of a semigroup of transformations ⟨D⟩. For any edge (a, b) of D, let a→b be the idempotent of rank n−1 mapping a to b and fixing all vertices other than a; then, define ⟨D⟩ to be the semigroup generated by a→b for all (a,b)∈E(D). For α∈⟨D⟩, let ℓ(D,α) be the minimal length of a word in E(D) expressing α. It is well known that the semigroup Singn of all transformations of rank at most n−1 is generated by its idempotents of rank n−1. When D=Kn is the complete undirected graph, Howie and Iwahori, independently, obtained a formula to calculate ℓ(Kn,α), for any α∈⟨Kn⟩=Singn; however, no analogous non-trivial results are known when D≠Kn. In this paper, we characterise all simple digraphs D such that either ℓ(D,α) is equal to Howie–Iwahori’s formula for all α∈⟨D⟩, or ℓ(D,α)=n−fix(α) for all α∈⟨D⟩, or ℓ(D,α)=n−rk(α) for all α∈⟨D⟩. We also obtain bounds for ℓ(D,α) when D is an acyclic digraph or a strong tournament (the latter case corresponds to a smallest generating set of idempotents of rank n−1 of Singn). We finish the paper with a list of conjectures and open problems
The second and third authors were supported by the EPSRC grant EP/K033956/1.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/92772017-02-01T00:00:00ZCameron, P. J.Castillo-Ramirez, A.Gadouleau, M.Mitchell, J. D.Given a simple digraph D on n vertices (with n≥2), there is a natural construction of a semigroup of transformations ⟨D⟩. For any edge (a, b) of D, let a→b be the idempotent of rank n−1 mapping a to b and fixing all vertices other than a; then, define ⟨D⟩ to be the semigroup generated by a→b for all (a,b)∈E(D). For α∈⟨D⟩, let ℓ(D,α) be the minimal length of a word in E(D) expressing α. It is well known that the semigroup Singn of all transformations of rank at most n−1 is generated by its idempotents of rank n−1. When D=Kn is the complete undirected graph, Howie and Iwahori, independently, obtained a formula to calculate ℓ(Kn,α), for any α∈⟨Kn⟩=Singn; however, no analogous non-trivial results are known when D≠Kn. In this paper, we characterise all simple digraphs D such that either ℓ(D,α) is equal to Howie–Iwahori’s formula for all α∈⟨D⟩, or ℓ(D,α)=n−fix(α) for all α∈⟨D⟩, or ℓ(D,α)=n−rk(α) for all α∈⟨D⟩. We also obtain bounds for ℓ(D,α) when D is an acyclic digraph or a strong tournament (the latter case corresponds to a smallest generating set of idempotents of rank n−1 of Singn). We finish the paper with a list of conjectures and open problemsIdempotent rank in the endomorphism monoid of a non-uniform partition
http://hdl.handle.net/10023/9275
We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a non-uniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.
Mon, 01 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/92752016-02-01T00:00:00ZDolinka, IgorEast, JamesMitchell, James D.We calculate the rank and idempotent rank of the semigroup E(X,P) generated by the idempotents of the semigroup T(X,P), which consists of all transformations of the finite set X preserving a non-uniform partition P. We also classify and enumerate the idempotent generating sets of this minimal possible size. This extends results of the first two authors in the uniform case.Modeling the aggregated exposure and responses of bowhead whales Balaena mysticetus to multiple sources of anthropogenic underwater sound
http://hdl.handle.net/10023/9259
Potential responses of marine mammals to anthropogenic underwater sound are usually assessed by researchers and regulators on the basis of exposure to a single, relatively loud sound source. However, marine mammals typically receive sounds from multiple, dynamic sources. We developed a method to aggregate modeled sounds from multiple sources and estimate the sound levels received by individuals. To illustrate the method, we modeled the sound fields of 9 sources associated with oil development and estimated the sound received over 47 d by a population of 10 000 simulated bowhead whales Balaena mysticetus on their annual migration through the Alaskan Beaufort Sea. Empirical data were sufficient to parameterize simulations of the distribution of individual whales over time and their range of movement patterns. We ran 2 simulations to estimate the sound exposure history and distances traveled by bowhead whales: one in which they could change their movement paths (avert) in response to set levels of sound and one in which they could not avert. When animals could not avert, about 2% of the simulated population was exposed to root mean square (rms) sound pressure levels (SPL) ≥ 180 dB re 1 mu Pa, a level that regulators in the U.S. often associate with injury. When animals could avert from sound levels that regulators often associate with behavioral disturbance (rms SPL > 160 dB re 1 μPa), <1% of the simulated population was exposed to levels associated with injury. Nevertheless, many simulated bowhead whales received sound levels considerably above ambient throughout their migration. Our method enables estimates of the aggregated level of sound to which populations are exposed over extensive areas and time periods.
This work was supported in part by a contract between BP Exploration (Alaska) Inc. and the University of California, Santa Barbara (E.F.), and by the North Slope Borough.
Mon, 02 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/92592016-05-02T00:00:00ZEllison, William T.Racca, RobertoClark, Christopher W.Streever, BillFrankel, Adam S.Fleishman, EricaAngliss, RobynBerger, JoelKetten, DarleneGuerra, MelaniaLeu, MatthiasMcKenna, MeganSformo, ToddSouthall, BrandonSuydam, RobertThomas, LenPotential responses of marine mammals to anthropogenic underwater sound are usually assessed by researchers and regulators on the basis of exposure to a single, relatively loud sound source. However, marine mammals typically receive sounds from multiple, dynamic sources. We developed a method to aggregate modeled sounds from multiple sources and estimate the sound levels received by individuals. To illustrate the method, we modeled the sound fields of 9 sources associated with oil development and estimated the sound received over 47 d by a population of 10 000 simulated bowhead whales Balaena mysticetus on their annual migration through the Alaskan Beaufort Sea. Empirical data were sufficient to parameterize simulations of the distribution of individual whales over time and their range of movement patterns. We ran 2 simulations to estimate the sound exposure history and distances traveled by bowhead whales: one in which they could change their movement paths (avert) in response to set levels of sound and one in which they could not avert. When animals could not avert, about 2% of the simulated population was exposed to root mean square (rms) sound pressure levels (SPL) ≥ 180 dB re 1 mu Pa, a level that regulators in the U.S. often associate with injury. When animals could avert from sound levels that regulators often associate with behavioral disturbance (rms SPL > 160 dB re 1 μPa), <1% of the simulated population was exposed to levels associated with injury. Nevertheless, many simulated bowhead whales received sound levels considerably above ambient throughout their migration. Our method enables estimates of the aggregated level of sound to which populations are exposed over extensive areas and time periods.Ends of semigroups
http://hdl.handle.net/10023/9254
We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.
Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/92542016-10-01T00:00:00ZCraik, S.Gray, R.Kilibarda, V.Mitchell, J. D.Ruskuc, N.We define the notion of the partial order of ends of the Cayley graph of a semigroup. We prove that the structure of the ends of a semigroup is invariant under change of finite generating set and at the same time is inherited by subsemigroups and extensions of finite Rees index. We prove an analogue of Hopf's Theorem, stating that a group has 1, 2 or infinitely many ends, for left cancellative semigroups and that the cardinality of the set of ends is invariant in subsemigroups and extension of finite Green index in left cancellative semigroups.Dimension conservation for self-similar sets and fractal percolation
http://hdl.handle.net/10023/9253
We introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let K be a self-similar subset of R2 with Hausdorff dimension dimHK >1 such that the rotational components of the underlying similarities generate the full rotation group. Then for all ε >0, writing πθ for projection onto the line Lθ in direction θ, the Hausdorff dimensions of the sections satisfy dimH (K ∩ πθ-1x)> dimHK - 1 - ε for a set of x ∈ Lθ of positive Lebesgue measure, for all directions θ except for those in a set of Hausdorff dimension 0. For a class of self-similar sets we obtain a similar conclusion for all directions, but with lower box dimension replacing Hausdorff dimensions of sections. We obtain similar inequalities for the dimensions of sections of Mandelbrot percolation sets.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/92532015-01-01T00:00:00ZFalconer, Kenneth JohnJin, XiongWe introduce a technique that uses projection properties of fractal percolation to establish dimension conservation results for sections of deterministic self-similar sets. For example, let K be a self-similar subset of R2 with Hausdorff dimension dimHK >1 such that the rotational components of the underlying similarities generate the full rotation group. Then for all ε >0, writing πθ for projection onto the line Lθ in direction θ, the Hausdorff dimensions of the sections satisfy dimH (K ∩ πθ-1x)> dimHK - 1 - ε for a set of x ∈ Lθ of positive Lebesgue measure, for all directions θ except for those in a set of Hausdorff dimension 0. For a class of self-similar sets we obtain a similar conclusion for all directions, but with lower box dimension replacing Hausdorff dimensions of sections. We obtain similar inequalities for the dimensions of sections of Mandelbrot percolation sets.Sixty years of fractal projections
http://hdl.handle.net/10023/9231
Sixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.
Fri, 31 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/92312015-07-31T00:00:00ZFalconer, Kenneth JohnFraser, Jonathan MacdonaldJin, XiongSixty years ago, John Marstrand published a paper which, among other things, relates the Hausdorff dimension of a plane set to the dimensions of its orthogonal projections onto lines. For many years, the paper attracted very little attention. However, over the past 30 years, Marstrand’s projection theorems have become the prototype for many results in fractal geometry with numerous variants and applications and they continue to motivate leading research.Properties of the prominence magnetic field and plasma distributions as obtained from 3D whole-prominence fine structure modeling
http://hdl.handle.net/10023/9203
Aims. We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma beta, and mass) using the 3D whole-prominence fine structure model. Methods. The model combines a 3D magnetic field configuration of an entire prominence, obtained from non-linear force-free field simulations, with a detailed semi-empirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Results. We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D whole-prominence fine structure model to reveal the distribution of the prominence plasma, with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominence-corona transition region. We further demonstrate that the values of the plasma beta are small throughout the majority of the modeled prominence when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma beta may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed non-eruptive prominences.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/92032016-08-01T00:00:00ZGunar, StanislavMackay, Duncan HendryAims. We analyze distributions of the magnetic field strength and prominence plasma (temperature, pressure, plasma beta, and mass) using the 3D whole-prominence fine structure model. Methods. The model combines a 3D magnetic field configuration of an entire prominence, obtained from non-linear force-free field simulations, with a detailed semi-empirically derived description of the prominence plasma. The plasma is located in magnetic dips in hydrostatic equilibrium and is distributed along multiple fine structures within the 3D magnetic model. Results. We show that in the modeled prominence, the variations of the magnetic field strength and its orientation are insignificant on scales comparable to the smallest dimensions of the observed prominence fine structures. We also show the ability of the 3D whole-prominence fine structure model to reveal the distribution of the prominence plasma, with respect to its temperature within the prominence volume. This provides new insights into the composition of the prominence-corona transition region. We further demonstrate that the values of the plasma beta are small throughout the majority of the modeled prominence when realistic photospheric magnetic flux distributions and prominence plasma parameters are assumed. While this is generally true, we also find that in the region with the deepest magnetic dips, the plasma beta may increase towards unity. Finally, we show that the mass of the modeled prominence plasma is in good agreement with the mass of observed non-eruptive prominences.Hitting times and periodicity in random dynamics
http://hdl.handle.net/10023/9179
We prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/91792015-10-01T00:00:00ZTodd, Michael JohnRousseau, JeromeWe prove quenched laws of hitting time statistics for random subshifts of finite type. In particular we prove a dichotomy between the law for periodic and for non-periodic points. We show that this applies to random Gibbs measures.Automorphism groups of countable algebraically closed graphs and endomorphisms of the random graph
http://hdl.handle.net/10023/9178
We establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/91782016-05-01T00:00:00ZDolinka, IgorGray, Robert DuncanMcPhee, Jillian DawnMitchell, James DavidQuick, MartynWe establish links between countable algebraically closed graphs and the endomorphisms of the countable universal graph R. As a consequence we show that, for any countable graph Γ, there are uncountably many maximal subgroups of the endomorphism monoid of R isomorphic to the automorphism group of Γ. Further structural information about End R is established including that Aut Γ arises in uncountably many ways as a Schützenberger group. Similar results are proved for the countable universal directed graph and the countable universal bipartite graph.Motives and tensions in the release of open educational resources : the UKOER program
http://hdl.handle.net/10023/9166
Open educational resources (OER) have been promoted as a path to universal education, supporting economic development and intercultural dialogue. However, to realise these benefits requires greater understanding of the factors that influence both OER supply and use. This paper examines an aspect of the supply side of the OER lifecycle – the motives prompting release – and the resultant tensions in the release process. It draws evidence from a major program of OER release projects (UKOER) funded by the UK government. The paper sets the UKOER program within the global context of OER initiatives. It uses grounded theory to identify five candidate motive types. Then, by mapping the actions evident in the UKOER program against an organisational framework derived from an activity system, it examines tensions or contradictions encountered by the projects, revealing unstated motives. The findings will be of interest to funders, institutions and educators releasing OER as they reveal potential limitations and barriers to realising the benefits of OER
It gives us pleasure to acknowledge the support of the UK Joint Information Systems Committee and Higher Education Academy, who funded the UKOER projects upon which this paper is based.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/91662016-01-01T00:00:00ZFalconer, Isobel JessieLittlejohn, AllisonMcGill, LouBeetham, HelenOpen educational resources (OER) have been promoted as a path to universal education, supporting economic development and intercultural dialogue. However, to realise these benefits requires greater understanding of the factors that influence both OER supply and use. This paper examines an aspect of the supply side of the OER lifecycle – the motives prompting release – and the resultant tensions in the release process. It draws evidence from a major program of OER release projects (UKOER) funded by the UK government. The paper sets the UKOER program within the global context of OER initiatives. It uses grounded theory to identify five candidate motive types. Then, by mapping the actions evident in the UKOER program against an organisational framework derived from an activity system, it examines tensions or contradictions encountered by the projects, revealing unstated motives. The findings will be of interest to funders, institutions and educators releasing OER as they reveal potential limitations and barriers to realising the benefits of OERNest-building males trade off material collection costs with territory value
http://hdl.handle.net/10023/9164
Building a structurally robust nest is crucial for reproductive success in many birds. However, we know little about the criteria birds use to select material or where they go to collect it. Here we observed the material collection of male Cape Weavers (Ploceus capensis). Males typically selected long, strong material to build their nests and each male collected material from different locations. Males that built more nests nested in a different area of the colony and flew further to collect nest material than did males that built fewer nests. As these males that flew further to collect material had longer tails and wings and attracted more females to their territories than did males that flew shorter distances, they may have traded off the travel costs of collecting nest materials with benefits gained from holding a territory in a more 'desirable' part of the colony. Nest construction, then, appears to be a multi-dimensional task whereby birds take into account material's structural properties, material proximity to the nest site and territory quality. Males that do this effectively both attract more mates and provide structurally sound nests for their young.
This work was supported by the BBSRC (BB/I019502/1 to SDH and SLM) and Roslin Institute Strategic Grant funding from the BBSRC (SLM).
Mon, 25 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/91642016-01-25T00:00:00ZBailey, Ida E.Morgan, Kate V.Oschadleus, H. DieterDeRuiter, Stacy L.Meddle, Simone L.Healy, Susan D.Building a structurally robust nest is crucial for reproductive success in many birds. However, we know little about the criteria birds use to select material or where they go to collect it. Here we observed the material collection of male Cape Weavers (Ploceus capensis). Males typically selected long, strong material to build their nests and each male collected material from different locations. Males that built more nests nested in a different area of the colony and flew further to collect nest material than did males that built fewer nests. As these males that flew further to collect material had longer tails and wings and attracted more females to their territories than did males that flew shorter distances, they may have traded off the travel costs of collecting nest materials with benefits gained from holding a territory in a more 'desirable' part of the colony. Nest construction, then, appears to be a multi-dimensional task whereby birds take into account material's structural properties, material proximity to the nest site and territory quality. Males that do this effectively both attract more mates and provide structurally sound nests for their young.Impact of an L5 magnetograph on nonpotential solar global magnetic field modeling
http://hdl.handle.net/10023/9154
We present the first theoretical study to consider what improvement could be obtained in global non-potential modeling of the solar corona if magnetograph data were available from the L5 Lagrange point, in addition to from the direction of Earth. To consider this, we first carry out a "reference Sun'' simulation over two solar cycles. An important property of this simulation is that random bipole emergences are allowed across the entire solar surface at any given time (such as can occur on the Sun). Next we construct two "limited data'' simulations, where bipoles are only included when they could be seen from (i) an Earth-based magnetograph and (ii) either Earth or L5 based magnetographs. The improvement in reproducing the reference Sun simulation when an L5 view is available is quantified through considering global quantities in the limited data simulations. These include surface and polar flux, total magnetic energy, volume electric current, open flux and the number of flux ropes. Results show that when an L5 observational viewpoint is included, the accuracy of the global quantities in the limited data simulations can increase by 26-40%. This clearly shows that a magnetograph at the L5 point could significantly increase the accuracy of global non-potential modeling and with this the accuracy of future space weather forecasts.
Tue, 12 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/91542016-07-12T00:00:00ZMackay, Duncan HendryYeates, Anthony RobinsonBocquet, Francois-XavierWe present the first theoretical study to consider what improvement could be obtained in global non-potential modeling of the solar corona if magnetograph data were available from the L5 Lagrange point, in addition to from the direction of Earth. To consider this, we first carry out a "reference Sun'' simulation over two solar cycles. An important property of this simulation is that random bipole emergences are allowed across the entire solar surface at any given time (such as can occur on the Sun). Next we construct two "limited data'' simulations, where bipoles are only included when they could be seen from (i) an Earth-based magnetograph and (ii) either Earth or L5 based magnetographs. The improvement in reproducing the reference Sun simulation when an L5 view is available is quantified through considering global quantities in the limited data simulations. These include surface and polar flux, total magnetic energy, volume electric current, open flux and the number of flux ropes. Results show that when an L5 observational viewpoint is included, the accuracy of the global quantities in the limited data simulations can increase by 26-40%. This clearly shows that a magnetograph at the L5 point could significantly increase the accuracy of global non-potential modeling and with this the accuracy of future space weather forecasts.Flexible density surface estimation for spatially explicit capture-recapture surveys
http://hdl.handle.net/10023/9147
1. Existing spatially explicit capture-recapture (SECR) software does not have the ability to fit flexible nonparametric models of animal density. 2. We describe and implement in the R package secrgam, a flexible method for estimating density surfaces from SECR data, using regression splines. 3. Package secrgam is an extension of package secr to implement some models available in the generalised additive model package mvcv. It accommodates density models that are arbitrarily flexible functions of spatially- and temporally-referenced variables. This includes one-dimensional and multi-dimensional smooths of covariates and smooths with interactions. The shape and smoothness of the fitted density surfaces is data-driven and can be determined using AIC or similar criteria. We illustrate use of the package by estimating the density surface from a simulated camera trap survey of leopards. 4. Package secrgam provides a flexible tool for species distribution modelling using SECR data.
Tue, 01 Jul 2014 00:00:00 GMThttp://hdl.handle.net/10023/91472014-07-01T00:00:00ZBorchers, David LouisKidney, Darren1. Existing spatially explicit capture-recapture (SECR) software does not have the ability to fit flexible nonparametric models of animal density. 2. We describe and implement in the R package secrgam, a flexible method for estimating density surfaces from SECR data, using regression splines. 3. Package secrgam is an extension of package secr to implement some models available in the generalised additive model package mvcv. It accommodates density models that are arbitrarily flexible functions of spatially- and temporally-referenced variables. This includes one-dimensional and multi-dimensional smooths of covariates and smooths with interactions. The shape and smoothness of the fitted density surfaces is data-driven and can be determined using AIC or similar criteria. We illustrate use of the package by estimating the density surface from a simulated camera trap survey of leopards. 4. Package secrgam provides a flexible tool for species distribution modelling using SECR data.On regularity and the word problem for free idempotent generated semigroups
http://hdl.handle.net/10023/9145
The category of all idempotent generated semigroups with a prescribed structure Ɛ of their idempotents E (called the biordered set) has an initial object called the free idempotent generated semigroup over Ɛ, defined by a presentation over alphabet E, and denoted by IG(Ɛ). Recently, much effort has been put into investigating the structure of semigroups of the form IG(Ɛ), especially regarding their maximal subgroups. In this paper we take these investigations in a new direction by considering the word problem for IG(Ɛ). We prove two principal results, one positive and one negative. We show that, for a finite biordered set E, it is decidable whether a given word w ∈ E∗ represents a regular element; if in addition one assumes that all maximal subgroups of IG(Ɛ) have decidable word problems, then the word problem in IG(Ɛ) restricted to regular words is decidable. On the other hand, we exhibit a biorder Ɛ arising from a finite idempotent semigroup S, such that the word problem for IG(Ɛ) is undecidable, even though all the maximal subgroups have decidable word problems. This is achieved by relating the word problem of IG(Ɛ) to the subgroup membership problem infinitely presented groups.
The research of the first author was supported by the Ministry of Education, Science, and Technological Development of the Republic of Serbia through the grant No. 174019, and by the grant No. 0851/2015 of the Secretariat of Science and Technological Development of the Autonomous Province of Vojvodina. The research of the second author was partially supported by the EPSRC-funded project EP/N033353/1 ‘Special inverse monoids: subgroups, structure, geometry, rewriting systems and the word problem’. The research of the third author was supported by the EPSRC-funded project EP/H011978/1 ‘Automata, Languages, Decidability in Algebra’.
Fri, 03 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/91452017-03-03T00:00:00ZDolinka, IgorGray, Robert D.Ruskuc, NikolaThe category of all idempotent generated semigroups with a prescribed structure Ɛ of their idempotents E (called the biordered set) has an initial object called the free idempotent generated semigroup over Ɛ, defined by a presentation over alphabet E, and denoted by IG(Ɛ). Recently, much effort has been put into investigating the structure of semigroups of the form IG(Ɛ), especially regarding their maximal subgroups. In this paper we take these investigations in a new direction by considering the word problem for IG(Ɛ). We prove two principal results, one positive and one negative. We show that, for a finite biordered set E, it is decidable whether a given word w ∈ E∗ represents a regular element; if in addition one assumes that all maximal subgroups of IG(Ɛ) have decidable word problems, then the word problem in IG(Ɛ) restricted to regular words is decidable. On the other hand, we exhibit a biorder Ɛ arising from a finite idempotent semigroup S, such that the word problem for IG(Ɛ) is undecidable, even though all the maximal subgroups have decidable word problems. This is achieved by relating the word problem of IG(Ɛ) to the subgroup membership problem infinitely presented groups.The infinite simple group V of Richard J. Thompson : presentations by permutations
http://hdl.handle.net/10023/9143
We show one can naturally describe elements of R. Thompson's infinite finitely presented simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups; it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation, and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/91432015-01-01T00:00:00ZQuick, MartynBleak, Collin PatrickWe show one can naturally describe elements of R. Thompson's infinite finitely presented simple group V, known by Thompson to have a presentation with four generators and fourteen relations, as products of permutations analogous to transpositions. This perspective provides an intuitive explanation towards the simplicity of V and also perhaps indicates a reason as to why it was one of the first discovered infinite finitely presented simple groups; it is (in some basic sense) a relative of the finite alternating groups. We find a natural infinite presentation for V as a group generated by these "transpositions," which presentation bears comparison with Dehornoy's infinite presentation, and which enables us to develop two small presentations for V: a human-interpretable presentation with three generators and eight relations, and a Tietze-derived presentation with two generators and seven relations.The random continued fraction transformation
http://hdl.handle.net/10023/9142
We introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.
Wed, 01 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/91422015-07-01T00:00:00ZKalle, CharleneKempton, Thomas Michael WilliamVerbitskiy, EvgenyWe introduce a random dynamical system related to continued fraction expansions. It uses random combination of the Gauss map and the R\'enyi (or backwards) continued fraction map. We explore the continued fraction expansions that this system produces as well as the dynamical properties of the system.The scenery flow for self-affine measures
http://hdl.handle.net/10023/9141
We describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.
Fri, 01 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/91412015-05-01T00:00:00ZKempton, Thomas Michael WilliamWe describe the scaling scenery associated to Bernoulli measures supported on separated self-affine sets under the condition that certain projections of the measure are absolutely continuous.Computing finite semigroups
http://hdl.handle.net/10023/9138
Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and $0$-matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the $\mathscr{D}$-classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.
Wed, 07 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/91382015-10-07T00:00:00ZEast, J.Egri-Nagy, A.Mitchell, J. D.Péresse, Y.Using a variant of Schreier's Theorem, and the theory of Green's relations, we show how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups. Examples of semigroups to which these results apply include many important classes: transformation semigroups, partial permutation semigroups and inverse semigroups, partition monoids, matrix semigroups, and subsemigroups of finite regular Rees matrix and $0$-matrix semigroups over groups. For any subsemigroup of such a semigroup, it is possible to, among other things, efficiently compute its size and Green's relations, test membership, factorize elements over the generators, find the semigroup generated by the given subsemigroup and any collection of additional elements, calculate the partial order of the $\mathscr{D}$-classes, test regularity, and determine the idempotents. This is achieved by representing the given subsemigroup without exhaustively enumerating its elements. It is also possible to compute the Green's classes of an element of such a subsemigroup without determining the global structure of the semigroup.Explosive fragmentation of liquids in spherical geometry
http://hdl.handle.net/10023/9116
Rapid acceleration of a spherical shell of liquid following detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jet-like structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multi-material hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill to explosive burster (F/B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F/B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F/B yields a larger number of particle jets. A hypothetical explanation of these features based on nucleation of cavitation is explored numerically.
Fri, 08 Jul 2016 00:00:00 GMThttp://hdl.handle.net/10023/91162016-07-08T00:00:00ZMilne, Alexander MitchellLongbottom, Aaron WilliamFrost, DavidLoiseau, JasonGoroshin, SamuelPetel, OrenRapid acceleration of a spherical shell of liquid following detonation of a high explosive causes the liquid to form fine jets that are similar in appearance to the particle jets that are formed during explosive dispersal of a packed layer of solid particles. Of particular interest is determining the dependence of the scale of the jet-like structures on the physical parameters of the system, including the fluid properties (e.g., density, viscosity, surface tension) and the ratio of the mass of the liquid to that of the explosive. The present paper presents computational results from a multi-material hydrocode describing the dynamics of the explosive dispersal process. The computations are used to track the overall features of the dispersal of the liquid layer, including the wave dynamics, and motion of the spall and accretion layers. The results are compared with experimental results of spherical charges surrounded by a variety of different fluids, including water, glycerol, ethanol, and vegetable oil, which together encompass a significant range of fluid properties. The results show that the number of jet structures is not sensitive to the fluid properties, but primarily dependent on the mass ratio. Above a certain mass ratio of liquid fill to explosive burster (F/B), the number of jets is approximately constant and consistent with an empirical model based on the maximum thickness of the accretion layer. For small values of F/B, the number of liquid jets is reduced, in contrast with explosive powder dispersal, where small F/B yields a larger number of particle jets. A hypothetical explanation of these features based on nucleation of cavitation is explored numerically.Impact of flux distribution on elementary heating events
http://hdl.handle.net/10023/9109
Context. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, that can subsequently be released by magnetic reconnection. Aims. We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions. Methods. 3D MHD simulations using Lare3D are carried out, where flux-tubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The flux-tubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect. Results. Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the flux-tubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of background field between the flux-tubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two and four source cases. The two flux-tube cases are always more energetic than the corresponding four flux-tube case, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver.
This work used the COSMA Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk. This equipment was funded by a BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/K00087X/1, DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure. I.D.M was funded by the Science and Technology Facilities Council (UK). The research leading to these results has also received funding from the European Research Council (ERC) under the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214). J.O was funded by the Science and Technology Facilities Council (UK) by Doctoral Grant [ST/K502327/1].
Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/91092016-10-01T00:00:00ZO'Hara, Jennifer PatriciaDe Moortel, InekeContext. The complex magnetic field on the solar surface has been shown to contain a range of sizes and distributions of magnetic flux structures. The dynamic evolution of this magnetic carpet by photospheric flows provides a continual source of free magnetic energy into the solar atmosphere, that can subsequently be released by magnetic reconnection. Aims. We investigate how the distribution and number of magnetic flux sources impact the energy release and locations of heating through magnetic reconnection driven by slow footpoint motions. Methods. 3D MHD simulations using Lare3D are carried out, where flux-tubes are formed between positive and negative sources placed symmetrically on the lower and upper boundaries of the domain, respectively. The flux-tubes are subjected to rotational driving velocities on the boundaries and are forced to interact and reconnect. Results. Initially, simple flux distributions with two and four sources are compared. In both cases, central current concentrations are formed between the flux-tubes and Ohmic heating occurs. The reconnection and subsequent energy release is delayed in the four source case and is shown to produce more locations of heating, but with smaller magnitudes. Increasing the values of background field between the flux-tubes is shown to delay the onset of reconnection and increases the efficiency of heating in both the two and four source cases. The two flux-tube cases are always more energetic than the corresponding four flux-tube case, however the addition of the background field makes this disparity less significant. A final experiment with a larger number of smaller flux sources is considered and the field evolution and energetics are shown to be remarkably similar to the two source case, indicating the importance of the size and separation of the flux sources relative to the spatial scales of the velocity driver.Embedding right-angled Artin groups into Brin-Thompson groups
http://hdl.handle.net/10023/9080
We prove that every finitely-generated right-angled Artin group can be embedded into some Brin-Thompson group nV. It follows that many other groups can be embedded into some nV (e.g., any finite extension of any of Haglund and Wise's special groups), and that various decision problems involving subgroups of nV are unsolvable.
7 pages, no figures
Sat, 27 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/90802016-02-27T00:00:00ZBelk, JamesBleak, CollinMatucci, FrancescoWe prove that every finitely-generated right-angled Artin group can be embedded into some Brin-Thompson group nV. It follows that many other groups can be embedded into some nV (e.g., any finite extension of any of Haglund and Wise's special groups), and that various decision problems involving subgroups of nV are unsolvable.Null point distribution in global coronal potential field extrapolations
http://hdl.handle.net/10023/9063
Magnetic null points are points in space where the magnetic field is zero. Thus, they can be important sites for magnetic reconnection by virtue of the fact that they are weak points in the magnetic field and also because they are associated with topological structures, such as separators, which lie on the boundary between four topologically distinct flux domains and therefore are also locations where reconnection occurs. The number and distribution of nulls in a magnetic field acts as a measure of the complexity of the field. In this article, the numbers and distributions of null points in global potential field extrapolations from high-resolution synoptic magnetograms are examined. Extrapolations from magnetograms obtained with the Michelson Doppler Imager (MDI) are studied in depth and compared with those from high-resolution SOlar Long-time Investigations of the Sun (SOLIS) and Heliospheric Magnetic Imager (HMI). The fall-off in the density of null points with height is found to follow a power law with a slope that differs depending on whether the data are from solar maximum or solar minimum. The distribution of null points with latitude also varies with the cycle as null points form predominantly over quiet-Sun regions and avoid active-region fields. The exception to this rule are the null points that form high in the solar atmosphere, and these null points tend to form over large areas of strong flux in active regions. From case studies of data acquired with the MDI, SOLIS, and HMI, it is found that the distribution of null points is very similar between data sets, except, of course, that there are far fewer nulls observed in the SOLIS data than in the cases from MDI and HMI due to its lower resolution.
SJE would like to thank the Isle of Man Government for support during her PhD and also for the financial support of the STFC.
Sat, 18 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/90632015-07-18T00:00:00ZEdwards, S.J.Parnell, C.E.Magnetic null points are points in space where the magnetic field is zero. Thus, they can be important sites for magnetic reconnection by virtue of the fact that they are weak points in the magnetic field and also because they are associated with topological structures, such as separators, which lie on the boundary between four topologically distinct flux domains and therefore are also locations where reconnection occurs. The number and distribution of nulls in a magnetic field acts as a measure of the complexity of the field. In this article, the numbers and distributions of null points in global potential field extrapolations from high-resolution synoptic magnetograms are examined. Extrapolations from magnetograms obtained with the Michelson Doppler Imager (MDI) are studied in depth and compared with those from high-resolution SOlar Long-time Investigations of the Sun (SOLIS) and Heliospheric Magnetic Imager (HMI). The fall-off in the density of null points with height is found to follow a power law with a slope that differs depending on whether the data are from solar maximum or solar minimum. The distribution of null points with latitude also varies with the cycle as null points form predominantly over quiet-Sun regions and avoid active-region fields. The exception to this rule are the null points that form high in the solar atmosphere, and these null points tend to form over large areas of strong flux in active regions. From case studies of data acquired with the MDI, SOLIS, and HMI, it is found that the distribution of null points is very similar between data sets, except, of course, that there are far fewer nulls observed in the SOLIS data than in the cases from MDI and HMI due to its lower resolution.The dependence of coronal loop heating on the characteristics of slow photospheric motions
http://hdl.handle.net/10023/9044
The Parker hypothesis assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects the heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behavior induced by the drivers can be characterized. It is shown that heating is crucially dependent on the nature of the photospheric driver—coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events.
Mon, 06 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/90442016-06-06T00:00:00ZRitchie, M. L.Wilmot-Smith, A. L.Hornig, G.The Parker hypothesis assumes that heating of coronal loops occurs due to reconnection, induced when photospheric motions braid field lines to the point of current sheet formation. In this contribution we address the question of how the nature of photospheric motions affects the heating of braided coronal loops. We design a series of boundary drivers and quantify their properties in terms of complexity and helicity injection. We examine a series of long-duration full resistive MHD simulations in which a simulated coronal loop, consisting of initially uniform field lines, is subject to these photospheric flows. Braiding of the loop is continually driven until differences in behavior induced by the drivers can be characterized. It is shown that heating is crucially dependent on the nature of the photospheric driver—coherent motions typically lead to fewer large energy release events, while more complex motions result in more frequent but less energetic heating events.A new technique for the photospheric driving of non-potential solar coronal magnetic field simulations
http://hdl.handle.net/10023/9043
In this paper, we develop a new technique for driving global non-potential simulations of the Sun's coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an "inductive" electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface flux-transport model. The match for these cases is further improved by including the non-inductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal non-potential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available.
Mon, 23 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/90432016-05-23T00:00:00ZWeinzierl, MarionYeates, AnthonyMackay, Duncan HendryHenney, CarlArge, C. NickIn this paper, we develop a new technique for driving global non-potential simulations of the Sun's coronal magnetic field solely from sequences of radial magnetic maps of the solar photosphere. A primary challenge to driving such global simulations is that the required horizontal electric field cannot be uniquely determined from such maps. We show that an "inductive" electric field solution similar to that used by previous authors successfully reproduces specific features of the coronal field evolution in both single and multiple bipole simulations. For these cases, the true solution is known because the electric field was generated from a surface flux-transport model. The match for these cases is further improved by including the non-inductive electric field contribution from surface differential rotation. Then, using this reconstruction method for the electric field, we show that a coronal non-potential simulation can be successfully driven from a sequence of ADAPT maps of the photospheric radial field, without including additional physical observations which are not routinely available.Solar cycle variation of magnetic flux ropes in a quasi-static coronal evolution model
http://hdl.handle.net/10023/9037
The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model-in particular the flux ropes-varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.
Sat, 01 May 2010 00:00:00 GMThttp://hdl.handle.net/10023/90372010-05-01T00:00:00ZYeates, A. R.Constable, J. A.Martens, P. C. H.The structure of electric current and magnetic helicity in the solar corona is closely linked to solar activity over the 11-year cycle, yet is poorly understood. As an alternative to traditional current-free "potential field" extrapolations, we investigate a model for the global coronal magnetic field which is non-potential and time-dependent, following the build-up and transport of magnetic helicity due to flux emergence and large-scale photospheric motions. This helicity concentrates into twisted magnetic flux ropes, which may lose equilibrium and be ejected. Here, we consider how the magnetic structure predicted by this model-in particular the flux ropes-varies over the solar activity cycle, based on photospheric input data from six periods of cycle 23. The number of flux ropes doubles from minimum to maximum, following the total length of photospheric polarity inversion lines. However, the number of flux rope ejections increases by a factor of eight, following the emergence rate of active regions. This is broadly consistent with the observed cycle modulation of coronal mass ejections, although the actual rate of ejections in the simulation is about a fifth of the rate of observed events. The model predicts that, even at minimum, differential rotation will produce sheared, non-potential, magnetic structure at all latitudes.Universal sequences for the order-automorphisms of the rationals
http://hdl.handle.net/10023/9024
In this paper, we consider the group Aut(Q,≤) of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q,≤) is contained in an N-generated subgroup of Aut(Q,≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of Aut(Q,≤), we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that a and b freely generate the free semigroup {a,b}+ consisting of the non-empty words over a and b. Then we show that there exists a sequence of words w1, w2,... over {a,b} such that for every sequence f1, f2, ... ∈ Aut(Q,≤) there is a homomorphism φ : {a,b}+ → Aut(Q,≤) where (wi)φ=fi for every i. The main theorem in this paper provides an alternative proof of a result of Droste and Holland showing that the strong cofinality of Aut(Q,≤) is uncountable, or equivalently that Aut(Q,≤) has uncountable cofinality and Bergman's property.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/90242016-08-01T00:00:00ZHyde, J.Jonusas, J.Mitchell, J. D.Peresse, Y. H.In this paper, we consider the group Aut(Q,≤) of order-automorphisms of the rational numbers, proving a result analogous to a theorem of Galvin's for the symmetric group. In an announcement, Khélif states that every countable subset of Aut(Q,≤) is contained in an N-generated subgroup of Aut(Q,≤) for some fixed N ∈ N. We show that the least such N is 2. Moreover, for every countable subset of Aut(Q,≤), we show that every element can be given as a prescribed product of two generators without using their inverses. More precisely, suppose that a and b freely generate the free semigroup {a,b}+ consisting of the non-empty words over a and b. Then we show that there exists a sequence of words w1, w2,... over {a,b} such that for every sequence f1, f2, ... ∈ Aut(Q,≤) there is a homomorphism φ : {a,b}+ → Aut(Q,≤) where (wi)φ=fi for every i. The main theorem in this paper provides an alternative proof of a result of Droste and Holland showing that the strong cofinality of Aut(Q,≤) is uncountable, or equivalently that Aut(Q,≤) has uncountable cofinality and Bergman's property.Coronal density structure and its role in wave damping in loops
http://hdl.handle.net/10023/9020
It has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption or phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the self-consistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave damping processes are inhibited. For the case of phase mixing we argue that: (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient and the rapid damping of oscillations may have to be accompanied by a separate (non-wave based) heating mechanism to sustain the required density structuring.
This project has received funding from the Science and Technology Facilities Council (UK) and the European Research Council (ERC) under the European Unionʼs Horizon 2020 research and innovation program (grant agreement No 647214). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/2007-2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/about).
Thu, 19 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/90202016-05-19T00:00:00ZCargill, PeterDe Moortel, InekeKiddie, GregIt has long been established that gradients in the Alfvén speed, and in particular the plasma density, are an essential part of the damping of waves in the magnetically closed solar corona by mechanisms such as resonant absorption or phase mixing. While models of wave damping often assume a fixed density gradient, in this paper the self-consistency of such calculations is assessed by examining the temporal evolution of the coronal density. It is shown conceptually that for some coronal structures, density gradients can evolve in a way that the wave damping processes are inhibited. For the case of phase mixing we argue that: (a) wave heating cannot sustain the assumed density structure and (b) inclusion of feedback of the heating on the density gradient can lead to a highly structured density, although on long timescales. In addition, transport coefficients well in excess of classical are required to maintain the observed coronal density. Hence, the heating of closed coronal structures by global oscillations may face problems arising from the assumption of a fixed density gradient and the rapid damping of oscillations may have to be accompanied by a separate (non-wave based) heating mechanism to sustain the required density structuring.From one-dimensional fields to Vlasov equilibria : Theory and application of Hermite Polynomials
http://hdl.handle.net/10023/8992
We consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibria are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite Polynomials. Sufficient conditions are found which guarantee the convergence,boundedness and non-negativity of the candidate solution, when satisfied. These conditions are obtained by elementary means, and it is clear how to put them into practice. Illustrative examples of the use of this method with both force-free and non force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the Force-Free Harris Sheet (Allanson et al. (2015)). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for βpl = 0:05.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/89922016-06-01T00:00:00ZAllanson, Oliver DouglasNeukirch, ThomasTroscheit, SaschaWilson, FionaWe consider the theory and application of a solution method for the inverse problem in collisionless equilibria, namely that of calculating a Vlasov-Maxwell equilibrium for a given macroscopic (fluid) equilibrium. Using Jeans' Theorem, the equilibria are expressed as functions of the constants of motion, in the form of a Maxwellian multiplied by an unknown function of the canonical momenta. In this case it is possible to reduce the inverse problem to inverting Weierstrass transforms, which we achieve by using expansions over Hermite Polynomials. Sufficient conditions are found which guarantee the convergence,boundedness and non-negativity of the candidate solution, when satisfied. These conditions are obtained by elementary means, and it is clear how to put them into practice. Illustrative examples of the use of this method with both force-free and non force-free macroscopic equilibria are presented, including the full verification of a recently derived distribution function for the Force-Free Harris Sheet (Allanson et al. (2015)). In the effort to model equilibria with lower values of the plasma beta, solutions for the same macroscopic equilibrium in a new gauge are calculated, with numerical results presented for βpl = 0:05.Emergence of non-twisted magnetic fields in the Sun : jets and atmospheric response
http://hdl.handle.net/10023/8990
Aims. We study the emergence of a non-twisted flux tube from the solar interior into the solar atmosphere. We investigate whether the length of the buoyant part of the flux tube (i.e. λ) affects the emergence of the field and the dynamics of the evolving magnetic flux system. Methods. We perform three-dimensional (3D), time-dependent, resistive, compressible magnetohydrodynamic (MHD) simulations using the Lare3D code. Results. We find that there are considerable differences in the dynamics of the emergence of a magnetic flux tube when λ is varied. In the solar interior, for larger values of λ, the rising magnetic field emerges faster and expands more due to its lower magnetic tension. As a result, its field strength decreases and its emergence above the photosphere occurs later than in the smaller λ case. However, in both cases, the emerging field at the photosphere becomes unstable in two places, forming two magnetic bipoles that interact dynamically during the evolution of the system. Most of the dynamic phenomena occur at the current layer, which is formed at the interface between the interacting bipoles. We find the formation and ejection of plasmoids, the onset of successive jets from the interface, and the impulsive heating of the plasma in the solar atmosphere. We discuss the triggering mechanism of the jets and the atmospheric response to the emergence of magnetic flux in the two cases.
The authors acknowledge support by the EU (IEF-272549 grant) and the Royal Society. The present research has been co-financed by the European Union (European Social Fund-ESF) and Greek national funds through the Operational Program “Education and Lifelong Learning” of the National Strategic Reference Framework (NSRF) – Research Funding Program: Thales. Investing in knowledge society through the European Social Fund. This research has also been carried out in the frame of the research program of the RCAAM of the Academy of Athens and has been co-financed by the Program “IKY Scholarships” of the Greek national funds through the Operational Program Education and Lifelong Learning of the NSRF through the European Social Fund of ESPA 2007-2013. Finally, the work reported in this article was additionally supported by the SOLARNET project, funded by the European Commisions FP7 Capacities Program, under the Grant Agreement 312495. The simulations were performed on the STFC and SRIF funded UKMHD cluster, at the University of St Andrews.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/89902015-12-01T00:00:00ZSyntelis, P.Archontis, V.Gontikakis, C.Tsinganos, K.Aims. We study the emergence of a non-twisted flux tube from the solar interior into the solar atmosphere. We investigate whether the length of the buoyant part of the flux tube (i.e. λ) affects the emergence of the field and the dynamics of the evolving magnetic flux system. Methods. We perform three-dimensional (3D), time-dependent, resistive, compressible magnetohydrodynamic (MHD) simulations using the Lare3D code. Results. We find that there are considerable differences in the dynamics of the emergence of a magnetic flux tube when λ is varied. In the solar interior, for larger values of λ, the rising magnetic field emerges faster and expands more due to its lower magnetic tension. As a result, its field strength decreases and its emergence above the photosphere occurs later than in the smaller λ case. However, in both cases, the emerging field at the photosphere becomes unstable in two places, forming two magnetic bipoles that interact dynamically during the evolution of the system. Most of the dynamic phenomena occur at the current layer, which is formed at the interface between the interacting bipoles. We find the formation and ejection of plasmoids, the onset of successive jets from the interface, and the impulsive heating of the plasma in the solar atmosphere. We discuss the triggering mechanism of the jets and the atmospheric response to the emergence of magnetic flux in the two cases.Spontaneous reconnection at a separator current layer : 2. Nature of the waves and flows
http://hdl.handle.net/10023/8960
Sudden destabilisations of the magnetic field, such as those caused by spontaneous reconnection, will produce waves and/or flows. Here, we investigate the nature of the plasma motions resulting from spontaneous reconnection at a 3D separator. In order to clearly see the perturbations generated by the reconnection, we start from a magnetohydrostatic equilibrium containing two oppositely-signed null points joined by a generic separator along which lies a twisted current layer. The nature of the magnetic reconnection initiated in this equilibrium as a result of an anomalous resistivity is discussed in detail in \cite{Stevenson15_jgra}. The resulting sudden loss of force balance inevitably generates waves that propagate away from the diffusion region carrying the dissipated current. In their wake a twisting stagnation-flow, in planes perpendicular to the separator, feeds flux back into the original diffusion site (the separator) in order to try to regain equilibrium. This flow drives a phase of slow weak impulsive-bursty reconnection that follows on after the initial fast-reconnection phase.
JEHS would like to thank STFC for financial support during her Ph.D and continued support after on the St Andrews SMTG’s STFC consortium grant. CEP also acknowledges support from this same grant.
Thu, 10 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/89602015-12-10T00:00:00ZE. H. Stevenson, JulieE. Parnell, ClareSudden destabilisations of the magnetic field, such as those caused by spontaneous reconnection, will produce waves and/or flows. Here, we investigate the nature of the plasma motions resulting from spontaneous reconnection at a 3D separator. In order to clearly see the perturbations generated by the reconnection, we start from a magnetohydrostatic equilibrium containing two oppositely-signed null points joined by a generic separator along which lies a twisted current layer. The nature of the magnetic reconnection initiated in this equilibrium as a result of an anomalous resistivity is discussed in detail in \cite{Stevenson15_jgra}. The resulting sudden loss of force balance inevitably generates waves that propagate away from the diffusion region carrying the dissipated current. In their wake a twisting stagnation-flow, in planes perpendicular to the separator, feeds flux back into the original diffusion site (the separator) in order to try to regain equilibrium. This flow drives a phase of slow weak impulsive-bursty reconnection that follows on after the initial fast-reconnection phase.Spontaneous reconnection at a separator current layer : I. Nature of the reconnection
http://hdl.handle.net/10023/8959
Magnetic separators, which lie on the boundary between four topologically-distinct flux domains, are prime locations in three-dimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic field and also in the solar atmosphere. Little is known about the details of separator reconnection and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Three-dimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of opposite-polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid-reconnection in which the current at the separator is reduced by a factor of around 2.3. Most ($75\%$) of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just $0.1\%$ going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls), but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsive-bursty reconnection. Again Ohmic heating dominates over viscous damping. Here, the reconnection occurs in small localised bursts at random anywhere along the separator.
Wed, 27 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/89592016-01-27T00:00:00ZE. H. Stevenson, JulieE. Parnell, ClareMagnetic separators, which lie on the boundary between four topologically-distinct flux domains, are prime locations in three-dimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic field and also in the solar atmosphere. Little is known about the details of separator reconnection and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Three-dimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of opposite-polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid-reconnection in which the current at the separator is reduced by a factor of around 2.3. Most ($75\%$) of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just $0.1\%$ going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls), but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsive-bursty reconnection. Again Ohmic heating dominates over viscous damping. Here, the reconnection occurs in small localised bursts at random anywhere along the separator.A changepoint analysis of spatio-temporal point processes
http://hdl.handle.net/10023/8935
This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatio-temporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatio-temporal log-Gaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland.
As regards author Linda Altieri, the research work underlying this paper was partially funded by a FIRB 2012 grant (project no. RBFR12URQJ; title: Statistical modeling of environmental phenomena: pollution, meteorology, health and their interactions) for research projects by the Italian Ministry of Education, Universities and Research.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/89352015-01-01T00:00:00ZAltieri, LindaScott, E. MarianCocchi, DanielaIllian, Janine B.This work introduces a Bayesian approach to detecting multiple unknown changepoints over time in the inhomogeneous intensity of a spatio-temporal point process with spatial and temporal dependence within segments. We propose a new method for detecting changes by fitting a spatio-temporal log-Gaussian Cox process model using the computational efficiency and flexibility of integrated nested Laplace approximation, and by studying the posterior distribution of the potential changepoint positions. In this paper, the context of the problem and the research questions are introduced, then the methodology is presented and discussed in detail. A simulation study assesses the validity and properties of the proposed methods. Lastly, questions are addressed concerning potential unknown changepoints in the intensity of radioactive particles found on Sandside beach, Dounreay, Scotland.PReMiuM : an R package for profile regression mixture models using Dirichlet processes
http://hdl.handle.net/10023/8931
PReMiuM is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, non-parametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for post-processing of the output are also provided. In addition to tting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection.
Fri, 20 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/89312015-03-20T00:00:00ZLiverani, SilviaHastie, DavidAzizi, LamiaePapathomas, MichailRichardson, SylviaPReMiuM is a recently developed R package for Bayesian clustering using a Dirichlet process mixture model. This model is an alternative to regression models, non-parametrically linking a response vector to covariate data through cluster membership (Molitor, Papathomas, Jerrett, and Richardson 2010). The package allows binary, categorical, count and continuous response, as well as continuous and discrete covariates. Additionally, predictions may be made for the response, and missing values for the covariates are handled. Several samplers and label switching moves are implemented along with diagnostic tools to assess convergence. A number of R functions for post-processing of the output are also provided. In addition to tting mixtures, it may additionally be of interest to determine which covariates actively drive the mixture components. This is implemented in the package as variable selection.Aspects of order and congruence relations on regular semigroups
http://hdl.handle.net/10023/8926
On a regular semigroup S natural order relations have been defined
by Nambooripad and by Lallement. Different characterisations and
relationships between the Nambooripad order J, Lallement's order λ and
a certain relation k are considered in Chapter I. It is shown that on
a regular semigroup S the partial order J is left compatible if and
only if S is locally R-unipotent. This condition in the case where S
is orthodox is equivalent to saying that E(S) is a left seminormal
band. It is also proved that λ is the least compatible partial order
contained in J and that k = λ if and only if k is compatible and k
if and only if J is compatible. A description of λ and J in the
semigroups T(X) and PT(X) is presented.
In Chapter II, it is proved that in an orthodox semigroup S the
band of idempotents E(S) is left quasinormal if and only if there
exists a local isomorphism from S onto an R-unipotent semigroup. It is
shown that there exists a least R-unipotent congruence on any orthodox
semigroup, generated by a certain left compatible equivalence R. This
equivalence is a congruence if and only if E(S) is a right semiregular
band.
The last Chapter is particularly concerned with the description of
R-unipotent congruences on a regular semigroup S by means of their
kernels and traces. The lattice RC(S) of all R-unipotent congruences
on a regular semigroup S is studied. A congruence≡ on the lattice
RC(S) is considered and the greatest and the least element of each
≡-class are described.
Sat, 01 Jan 1983 00:00:00 GMThttp://hdl.handle.net/10023/89261983-01-01T00:00:00ZGomes, Gracinda Maria dos SantosOn a regular semigroup S natural order relations have been defined
by Nambooripad and by Lallement. Different characterisations and
relationships between the Nambooripad order J, Lallement's order λ and
a certain relation k are considered in Chapter I. It is shown that on
a regular semigroup S the partial order J is left compatible if and
only if S is locally R-unipotent. This condition in the case where S
is orthodox is equivalent to saying that E(S) is a left seminormal
band. It is also proved that λ is the least compatible partial order
contained in J and that k = λ if and only if k is compatible and k
if and only if J is compatible. A description of λ and J in the
semigroups T(X) and PT(X) is presented.
In Chapter II, it is proved that in an orthodox semigroup S the
band of idempotents E(S) is left quasinormal if and only if there
exists a local isomorphism from S onto an R-unipotent semigroup. It is
shown that there exists a least R-unipotent congruence on any orthodox
semigroup, generated by a certain left compatible equivalence R. This
equivalence is a congruence if and only if E(S) is a right semiregular
band.
The last Chapter is particularly concerned with the description of
R-unipotent congruences on a regular semigroup S by means of their
kernels and traces. The lattice RC(S) of all R-unipotent congruences
on a regular semigroup S is studied. A congruence≡ on the lattice
RC(S) is considered and the greatest and the least element of each
≡-class are described.SSALMON - the Solar Simulations for the Atacama Large Millimeter Observatory Network
http://hdl.handle.net/10023/8874
The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at co-ordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/88742015-12-01T00:00:00ZWedemeyer, S.Bastian, T.Brajša, R.Barta, M.Hudson, H.Fleishman, G.Loukitcheva, M.Fleck, B.Kontar, E.De Pontieu, B.Tiwari, S.Kato, Y.Soler, R.Yagoubov, P.Black, J. H.Antolin, P.Gunár, S.Labrosse, N.Benz, A. O.Nindos, A.Steffen, M.Scullion, E.Doyle, J. G.Zaqarashvili, T.Hanslmeier, A.Nakariakov, V. M.Heinzel, P.Ayres, T.Karlicky, M.The Solar Simulations for the Atacama Large Millimeter Observatory Network (SSALMON) was initiated in 2014 in connection with two ALMA development studies. The Atacama Large Millimeter/submillimeter Array (ALMA) is a powerful new tool, which can also observe the Sun at high spatial, temporal, and spectral resolution. The international SSALMONetwork aims at co-ordinating the further development of solar observing modes for ALMA and at promoting scientific opportunities for solar physics with particular focus on numerical simulations, which can provide important constraints for the observing modes and can aid the interpretation of future observations. The radiation detected by ALMA originates mostly in the solar chromosphere – a complex and dynamic layer between the photosphere and corona, which plays an important role in the transport of energy and matter and the heating of the outer layers of the solar atmosphere. Potential targets include active regions, prominences, quiet Sun regions, flares. Here, we give a brief overview over the network and potential science cases for future solar observations with ALMA.50-Year Anniversary of Papers by Cormack, Jolly and Seber
http://hdl.handle.net/10023/8872
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/88722016-05-01T00:00:00ZBuckland, Stephen TerrenceMorgan, Byron J TNumerical simulations of footpoint driven coronal heating
http://hdl.handle.net/10023/8871
Magnetic field permeates the solar atmosphere and plays a crucial role in the dynamics, energetics and structures observed. In particular, magnetic flux tubes provide the structure for coronal loops that extend from the solar surface into the corona. In this thesis, we present 3D numerical simulations examining the heating produced by reconnection between flux tubes driven by rotational footpoint motions. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. A single, twisted current layer is created in the centre of the domain and strong, localised heating is produced. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. The dynamical evolution and the resultant magnitude, distribution and timing of the heating events are examined for the different flux distributions. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the domain. A comparison of cases with two and four sources shows that there are more locations of current concentrations, but with reduced maximum current density values, for the four source case. This produces weaker reconnection and less efficient heating. In addition, for the case with two sources, we also consider the effect of splitting up one of the sources into many smaller flux fragments. The evolution and heating are shown to be very similar to the two source case. The impact of increasing the strength of the background field between the flux tubes is also examined and we find that it delays and increases the strength of the heating, although by how much depends on the distribution of the flux sources.
Fri, 24 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/88712016-06-24T00:00:00ZO'Hara, JenniferMagnetic field permeates the solar atmosphere and plays a crucial role in the dynamics, energetics and structures observed. In particular, magnetic flux tubes provide the structure for coronal loops that extend from the solar surface into the corona. In this thesis, we present 3D numerical simulations examining the heating produced by reconnection between flux tubes driven by rotational footpoint motions. The basic model consists of two, initially aligned, flux tubes that are forced to interact by rotational driving velocities on the flux concentrations on the boundaries. A single, twisted current layer is created in the centre of the domain and strong, localised heating is produced. We extend this model by altering the number, distribution and strength of the sources, while maintaining the same total magnetic flux on the boundaries. The dynamical evolution and the resultant magnitude, distribution and timing of the heating events are examined for the different flux distributions. In all cases, the magnetic field is stressed by the boundary motions and a current grows within the domain. A comparison of cases with two and four sources shows that there are more locations of current concentrations, but with reduced maximum current density values, for the four source case. This produces weaker reconnection and less efficient heating. In addition, for the case with two sources, we also consider the effect of splitting up one of the sources into many smaller flux fragments. The evolution and heating are shown to be very similar to the two source case. The impact of increasing the strength of the background field between the flux tubes is also examined and we find that it delays and increases the strength of the heating, although by how much depends on the distribution of the flux sources.A conversation with Richard M. Cormack
http://hdl.handle.net/10023/8869
Richard Melville Cormack is one of the giants who developed the theory of mark-recapture. Referring to his key paper in 1964, and the papers published back-to-back in 1965 by George Jolly and George Seber, the `Cormack-Jolly-Seber model' is central to the development of mark-recapture methods for estimating survival. Richard was born on 12 March 1935. His father was Principal of Stow College of Engineering in Glasgow. From the age of 7, Richard attended Glasgow Academy, and later entered directly into the second year at Kings College, Cambridge, intending at the time to be a theoretical astronomer. He secured first class honours in Special Mathematics from London as an external student in 1954, and second class honours in Mathematics from Cambridge in 1955. After changing direction, he left Cambridge in 1956 with a Distinction in the Diploma in Mathematical Statistics. Richard's PhD, undertaken while a lecturer at Aberdeen, was completed in 1961. Richard's period at Aberdeen (1956-66) coincided with a golden era for statistics there, and his colleagues included D.J. Finney, Bill Brass, Peter Fisk, David M.G. Wishart, Michael Sampford, Robert Curnow, George Jolly and Andrew Rutherford (the last four being members of the ARC Unit of Statistics). In common with a number of these colleagues, he moved to Edinburgh in 1966, holding a Senior Lectureship there until 1972, when he became the first Professor of Statistics at St Andrews. Richard's groundbreaking contributions to mark-recapture in the early 1960s continued when he addressed the issue of heterogeneity in capture probabilities, publishing a test for heterogeneity in Biometrics in 1966. Then in 1972, in another Biometrics paper, he showed the logic behind capture-recapture estimates, making the methods more accessible and understandable to the user community. In 1981, jointly with Philip North, Richard published important insights into mark-recovery models. His work on log-linear models for mark-recapture led to papers in Biometrika in 1984 (with Ron Sandland) and 1991 (with Peter Jupp), and in Biometrics in 1989, and additionally, to four book chapters. There was also a sequence of Biometrics capture-recapture papers in the 1990s: on modelling covariates (1990), on interval estimation (1992) and on variance estimation (1993). After retirement in 1994, his publications in mark-recapture were mostly as co-author in epidemiology studies. Richard also published on other diverse topics, often with scientists from other disciplines. His 1971 review of classification, read to the Research Committee of RSS and later appearing in JRSS A, is a classic, and while his 1988 exposition on statistical challenges in the environmental sciences (also in JRSS A) has had substantially less impact, it too showed his characteristic incisiveness. His contributions to a wide range of committees, working groups, visiting groups and scientific organisations (including council member for NERC and the Freshwater Biological Association) were substantial. He was elected a member of the ISI in 1962 and a Fellow of the Royal Society of Edinburgh in 1974. He held various offices within the Biometric Society, as Secretary of the British Region 1970-77, Regional President 1990-92 and President of the International Society 1980-81. He served on the Council and various committees of the Royal Statistical Society. Richard married Edith Whittaker on 1st September 1960, at King's College Chapel, Aberdeen. Edith is a plant ecologist, and a past chairperson of the Fife and Kinross Branch of the Scottish Wildlife Trust and of the Friends of St Andrews Botanic Garden: she was also a founding member of the Garden's Education Trust. Their son Andrew is a European Chartered Engineer working for the JANET network, while their daughter Anne is a Marketing Manager. Photography has been a passion of Richard's for many decades. He was lecturer and judge for 40 years for the Scottish Photographic Federation, and was placed on their roll of honour. He has held exhibitions in Dundee (Land of the Berbers), St Andrews (Growth and Form) and Aberdeen (Walking in the North), and has given many talks. Richard firmly established the University of St Andrews as a centre for statistical ecology, a strength that continues today.
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/88692016-05-01T00:00:00ZBuckland, Stephen TerrenceRichard Melville Cormack is one of the giants who developed the theory of mark-recapture. Referring to his key paper in 1964, and the papers published back-to-back in 1965 by George Jolly and George Seber, the `Cormack-Jolly-Seber model' is central to the development of mark-recapture methods for estimating survival. Richard was born on 12 March 1935. His father was Principal of Stow College of Engineering in Glasgow. From the age of 7, Richard attended Glasgow Academy, and later entered directly into the second year at Kings College, Cambridge, intending at the time to be a theoretical astronomer. He secured first class honours in Special Mathematics from London as an external student in 1954, and second class honours in Mathematics from Cambridge in 1955. After changing direction, he left Cambridge in 1956 with a Distinction in the Diploma in Mathematical Statistics. Richard's PhD, undertaken while a lecturer at Aberdeen, was completed in 1961. Richard's period at Aberdeen (1956-66) coincided with a golden era for statistics there, and his colleagues included D.J. Finney, Bill Brass, Peter Fisk, David M.G. Wishart, Michael Sampford, Robert Curnow, George Jolly and Andrew Rutherford (the last four being members of the ARC Unit of Statistics). In common with a number of these colleagues, he moved to Edinburgh in 1966, holding a Senior Lectureship there until 1972, when he became the first Professor of Statistics at St Andrews. Richard's groundbreaking contributions to mark-recapture in the early 1960s continued when he addressed the issue of heterogeneity in capture probabilities, publishing a test for heterogeneity in Biometrics in 1966. Then in 1972, in another Biometrics paper, he showed the logic behind capture-recapture estimates, making the methods more accessible and understandable to the user community. In 1981, jointly with Philip North, Richard published important insights into mark-recovery models. His work on log-linear models for mark-recapture led to papers in Biometrika in 1984 (with Ron Sandland) and 1991 (with Peter Jupp), and in Biometrics in 1989, and additionally, to four book chapters. There was also a sequence of Biometrics capture-recapture papers in the 1990s: on modelling covariates (1990), on interval estimation (1992) and on variance estimation (1993). After retirement in 1994, his publications in mark-recapture were mostly as co-author in epidemiology studies. Richard also published on other diverse topics, often with scientists from other disciplines. His 1971 review of classification, read to the Research Committee of RSS and later appearing in JRSS A, is a classic, and while his 1988 exposition on statistical challenges in the environmental sciences (also in JRSS A) has had substantially less impact, it too showed his characteristic incisiveness. His contributions to a wide range of committees, working groups, visiting groups and scientific organisations (including council member for NERC and the Freshwater Biological Association) were substantial. He was elected a member of the ISI in 1962 and a Fellow of the Royal Society of Edinburgh in 1974. He held various offices within the Biometric Society, as Secretary of the British Region 1970-77, Regional President 1990-92 and President of the International Society 1980-81. He served on the Council and various committees of the Royal Statistical Society. Richard married Edith Whittaker on 1st September 1960, at King's College Chapel, Aberdeen. Edith is a plant ecologist, and a past chairperson of the Fife and Kinross Branch of the Scottish Wildlife Trust and of the Friends of St Andrews Botanic Garden: she was also a founding member of the Garden's Education Trust. Their son Andrew is a European Chartered Engineer working for the JANET network, while their daughter Anne is a Marketing Manager. Photography has been a passion of Richard's for many decades. He was lecturer and judge for 40 years for the Scottish Photographic Federation, and was placed on their roll of honour. He has held exhibitions in Dundee (Land of the Berbers), St Andrews (Growth and Form) and Aberdeen (Walking in the North), and has given many talks. Richard firmly established the University of St Andrews as a centre for statistical ecology, a strength that continues today.Avoidance of wind farms by harbour seals is limited to pile driving activities
http://hdl.handle.net/10023/8856
1. As part of global efforts to reduce dependence on carbon-based energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on at-sea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts. 2. Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, south-east England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another. 3. Within an operational wind farm, there was a close-to-significant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause. 4. There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p·p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the non-piling scenario. 5. Synthesis and applications. Our spatial and temporal quantification of avoidance of wind farms by harbour seals is critical to reduce uncertainty and increase robustness in environmental impact assessments of future developments. Specifically, the results will allow policymakers to produce industry guidance on the likelihood of displacement of seals in response to pile driving; the relationship between sound levels and avoidance rates; and the duration of any avoidance, thus allowing far more accurate environmental assessments to be carried out during the consenting process. Further, our results can be used to inform mitigation strategies in terms of both the sound levels likely to cause displacement and what temporal patterns of piling would minimize the magnitude of the energetic impacts of displacement.
DJFR, GH, VMJ and BM were funded by the UK Department of Energy and Climate Change (DECC) as part of their Offshore Energy Strategic Environmental Assessment programme. DT and GH were also funded by NERC/Defra EBAO NE/J004243/1. ELJ was funded under Scottish Government grant MMSS001/01. This work was also supported by National Capability funding from the Natural Environment Research Council to SMRU (grant no. SMRU1001). Tags and their deployment in the Thames in 2006 and The Wash were funded by DECC. Tags and their deployment in the Thames in 2012 were commissioned by Zoological Society London, with funding from BBC Wildlife Fund and Sita Trust.
Thu, 01 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/88562016-12-01T00:00:00ZRussell, Deborah J. F.Hastie, Gordon D.Thompson, DavidJanik, Vincent M.Hammond, Philip S.Scott-Hayward, Lindesay A. S.Matthiopoulos, JasonJones, Esther L.McConnell, Bernie J.1. As part of global efforts to reduce dependence on carbon-based energy sources there has been a rapid increase in the installation of renewable energy devices. The installation and operation of these devices can result in conflicts with wildlife. In the marine environment, mammals may avoid wind farms that are under construction or operating. Such avoidance may lead to more time spent travelling or displacement from key habitats. A paucity of data on at-sea movements of marine mammals around wind farms limits our understanding of the nature of their potential impacts. 2. Here, we present the results of a telemetry study on harbour seals Phoca vitulina in The Wash, south-east England, an area where wind farms are being constructed using impact pile driving. We investigated whether seals avoid wind farms during operation, construction in its entirety, or during piling activity. The study was carried out using historical telemetry data collected prior to any wind farm development and telemetry data collected in 2012 during the construction of one wind farm and the operation of another. 3. Within an operational wind farm, there was a close-to-significant increase in seal usage compared to prior to wind farm development. However, the wind farm was at the edge of a large area of increased usage, so the presence of the wind farm was unlikely to be the cause. 4. There was no significant displacement during construction as a whole. However, during piling, seal usage (abundance) was significantly reduced up to 25 km from the piling activity; within 25 km of the centre of the wind farm, there was a 19 to 83% (95% confidence intervals) decrease in usage compared to during breaks in piling, equating to a mean estimated displacement of 440 individuals. This amounts to significant displacement starting from predicted received levels of between 166 and 178 dB re 1 μPa(p·p). Displacement was limited to piling activity; within 2 h of cessation of pile driving, seals were distributed as per the non-piling scenario. 5. Synthesis and applications. Our spatial and temporal quantification of avoidance of wind farms by harbour seals is critical to reduce uncertainty and increase robustness in environmental impact assessments of future developments. Specifically, the results will allow policymakers to produce industry guidance on the likelihood of displacement of seals in response to pile driving; the relationship between sound levels and avoidance rates; and the duration of any avoidance, thus allowing far more accurate environmental assessments to be carried out during the consenting process. Further, our results can be used to inform mitigation strategies in terms of both the sound levels likely to cause displacement and what temporal patterns of piling would minimize the magnitude of the energetic impacts of displacement.An efficient acoustic density estimation method with human detectors applied to gibbons in Cambodia
http://hdl.handle.net/10023/8842
Some animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capture-recapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a single-occasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multi-occasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows model-based estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multi-occasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since it only requires routine survey data. We anticipate that the low-tech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.
D. Kidney was supported by an Engineering and Physical Sciences Research Council (EPSRC) Doctoral Training Grant studentship (EPSRC grant EP/P505097/1). B. Stevenson was supported by a studentship jointly funded by the University of St Andrews and EPSRC, through the National Centre for Statistical Ecology (EPSRC grant EP/I000917/1).
Thu, 19 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/88422016-05-19T00:00:00ZKidney, DarrenRawson, Benjamin M.Borchers, David LouisStevenson, BenMarques, Tiago A.Thomas, LenSome animal species are hard to see but easy to hear. Standard visual methods for estimating population density for such species are often ineffective or inefficient, but methods based on passive acoustics show more promise. We develop spatially explicit capture-recapture (SECR) methods for territorial vocalising species, in which humans act as an acoustic detector array. We use SECR and estimated bearing data from a single-occasion acoustic survey of a gibbon population in northeastern Cambodia to estimate the density of calling groups. The properties of the estimator are assessed using a simulation study, in which a variety of survey designs are also investigated. We then present a new form of the SECR likelihood for multi-occasion data which accounts for the stochastic availability of animals. In the context of gibbon surveys this allows model-based estimation of the proportion of groups that produce territorial vocalisations on a given day, thereby enabling the density of groups, instead of the density of calling groups, to be estimated. We illustrate the performance of this new estimator by simulation. We show that it is possible to estimate density reliably from human acoustic detections of visually cryptic species using SECR methods. For gibbon surveys we also show that incorporating observers' estimates of bearings to detected groups substantially improves estimator performance. Using the new form of the SECR likelihood we demonstrate that estimates of availability, in addition to population density and detection function parameters, can be obtained from multi-occasion data, and that the detection function parameters are not confounded with the availability parameter. This acoustic SECR method provides a means of obtaining reliable density estimates for territorial vocalising species. It is also efficient in terms of data requirements since it only requires routine survey data. We anticipate that the low-tech field requirements will make this method an attractive option in many situations where populations can be surveyed acoustically by humans.Neonicotinoids target distinct nicotinic acetylcholine receptors and neurons, leading to differential risks to bumblebees
http://hdl.handle.net/10023/8793
There is growing concern over the risk to bee populations from neonicotinoid insecticides and the long-term consequences of reduced numbers of insect pollinators to essential ecosystem services and food security. Our knowledge of the risk of neonicotinoids to bees is based on studies of imidacloprid and thiamethoxam and these findings are extrapolated to clothianidin based on its higher potency at nicotinic acetylcholine receptors. This study addresses the specificity and consequences of all three neonicotinoids to determine their relative risk to bumblebees at field-relevant levels (2.5 ppb). We find compound-specific effects at all levels (individual cells, bees and whole colonies in semi-field conditions). Imidacloprid and clothianidin display distinct, overlapping, abilities to stimulate Kenyon cells, indicating the potential to differentially influence bumblebee behavior. Bee immobility was induced only by imidacloprid, and an increased vulnerability to clothianidin toxicity only occurred following chronic exposure to clothianidin or thiamethoxam. At the whole colony level, only thiamethoxam altered the sex ratio (more males present) and only clothianidin increased queen production. Finally, both imidacloprid and thiamethoxam caused deficits in colony strength, while no detrimental effects of clothianidin were observed. Given these findings, neonicotinoid risk needs to be considered independently for each compound and target species.
This research was funded jointly by BBSRC, DEFRA, NERC, the Scottish Government and The Wellcome Trust, under the Insect Pollinators Initiative (UK) grant BB/1000313/1(CNC).
Thu, 28 Apr 2016 00:00:00 GMThttp://hdl.handle.net/10023/87932016-04-28T00:00:00ZMoffat, ChristopherBuckland, Stephen T.Samson, Andrew J.McArthur, RobinChamosa Pino, VictorBollan, Karen A.Huang, Jeffrey T. -J.Connolly, Christopher N.There is growing concern over the risk to bee populations from neonicotinoid insecticides and the long-term consequences of reduced numbers of insect pollinators to essential ecosystem services and food security. Our knowledge of the risk of neonicotinoids to bees is based on studies of imidacloprid and thiamethoxam and these findings are extrapolated to clothianidin based on its higher potency at nicotinic acetylcholine receptors. This study addresses the specificity and consequences of all three neonicotinoids to determine their relative risk to bumblebees at field-relevant levels (2.5 ppb). We find compound-specific effects at all levels (individual cells, bees and whole colonies in semi-field conditions). Imidacloprid and clothianidin display distinct, overlapping, abilities to stimulate Kenyon cells, indicating the potential to differentially influence bumblebee behavior. Bee immobility was induced only by imidacloprid, and an increased vulnerability to clothianidin toxicity only occurred following chronic exposure to clothianidin or thiamethoxam. At the whole colony level, only thiamethoxam altered the sex ratio (more males present) and only clothianidin increased queen production. Finally, both imidacloprid and thiamethoxam caused deficits in colony strength, while no detrimental effects of clothianidin were observed. Given these findings, neonicotinoid risk needs to be considered independently for each compound and target species.A computational framework for particle and whole cell tracking applied to a real biological dataset
http://hdl.handle.net/10023/8783
Cell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of high-throughput, high-resolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable. In this work, we describe two approaches for automated cell tracking. Firstly, we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a non-uniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearest-neighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is rejected in the reconstructed data. The resulting mathematical problem involves the optimal control of a phase-field formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via advanced numerical methods for the solution of semilinear parabolic partial differential equations (PDEs) coupled with parallelisation and adaptive resolution techniques. Along with a detailed description of our algorithms, a number of simulation results are reported on. We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of migrating cells in a dataset which reflects many of the challenges typically encountered in microscopy data.
FY, CV, VS and AM acknowledge support from the Leverhulme Trust Research Project Grant (RPG-2014-149). The work of CV, VS and AM was partially supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1). This work (AM, ZG, EH, RZ) has also received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. The work of CV is partially supported by an EPSRC Impact Accelerator Account award.
Tue, 24 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/87832016-05-24T00:00:00ZYang, Feng WeiVenkataraman, ChandrasekharStyles, VanessaKuttenberger, VerenaHorn, Eliasvon Guttenberg, ZenoMadzvamuse, AnotidaCell tracking is becoming increasingly important in cell biology as it provides a valuable tool for analysing experimental data and hence furthering our understanding of dynamic cellular phenomena. The advent of high-throughput, high-resolution microscopy and imaging techniques means that a wealth of large data is routinely generated in many laboratories. Due to the sheer magnitude of the data involved manual tracking is often cumbersome and the development of computer algorithms for automated cell tracking is thus highly desirable. In this work, we describe two approaches for automated cell tracking. Firstly, we consider particle tracking. We propose a few segmentation techniques for the detection of cells migrating in a non-uniform background, centroids of the segmented cells are then calculated and linked from frame to frame via a nearest-neighbour approach. Secondly, we consider the problem of whole cell tracking in which one wishes to reconstruct in time whole cell morphologies. Our approach is based on fitting a mathematical model to the experimental imaging data with the goal being that the physics encoded in the model is rejected in the reconstructed data. The resulting mathematical problem involves the optimal control of a phase-field formulation of a geometric evolution law. Efficient approximation of this challenging optimal control problem is achieved via advanced numerical methods for the solution of semilinear parabolic partial differential equations (PDEs) coupled with parallelisation and adaptive resolution techniques. Along with a detailed description of our algorithms, a number of simulation results are reported on. We focus on illustrating the effectivity of our approaches by applying the algorithms to the tracking of migrating cells in a dataset which reflects many of the challenges typically encountered in microscopy data.Existence, stability and formation of baroclinic triples in quasi-geostrophic flows
http://hdl.handle.net/10023/8770
Hetons are baroclinic vortices able to transport tracers or species, and which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. Firstly, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and of two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-8) upper core. In the case of vertically distant upper and lower cores, these latter can nearly joint near the center of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small, upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/87702015-12-01T00:00:00ZReinaud, Jean NoelCarton, XavierHetons are baroclinic vortices able to transport tracers or species, and which have been observed at sea. This paper studies the offset collision of two identical hetons, often resulting in the formation of a baroclinic tripole, in a continuously stratified quasi-geostrophic model. This process is of interest since it (temporarily or definitely) stops the transport of tracers contained in the hetons. Firstly, the structure, stationarity and nonlinear stability of baroclinic tripoles composed of an upper core and of two lower (symmetric) satellites are studied analytically for point vortices and numerically for finite-area vortices. The condition for stationarity of the point vortices is obtained and it is proven that the baroclinic point tripoles are neutral. Finite-volume stationary tripoles exist with marginal states having very elongated (figure-8) upper core. In the case of vertically distant upper and lower cores, these latter can nearly joint near the center of the plane. These steady states are compared with their two-layer counterparts. Then, the nonlinear evolution of the steady states shows when they are often neutral (showing an oscillatory evolution); when they are unstable, they can either split into two hetons (by breaking of the upper core) or form a single heton (by merger of the lower satellites). These evolutions reflect the linearly unstable modes which can grow on the vorticity poles. Very tall tripoles can break up vertically due to the vertical shear mutually induced by the poles. Finally, the formation of such baroclinic tripoles from the offset collision of two identical hetons is investigated numerically. This formation occurs for hetons offset by less than the internal separation between their poles. The velocity shear during the interaction can lead to substantial filamentation by the upper core, thus forming small, upper satellites, vertically aligned with the lower ones. Finally, in the case of close and flat poles, this shear (or the baroclinic instability of the tripole) can be strong enough that the formed baroclinic tripole is short-lived and that hetons eventually emerge from the collision and drift away.Embeddings into Thompson's group V and coCF groups
http://hdl.handle.net/10023/8747
It is shown in Lehnert and Schweitzer (‘The co-word problem for the Higman–Thompson group is context-free’, Bull. London Math. Soc. 39 (2007) 235–241) that R. Thompson's group V is a co-context-free (coCF) group, thus implying that all of its finitely generated subgroups are also coCF groups. Also, Lehnert shows in his thesis that V embeds inside the coCF group QAut(T2,c), which is a group of particular bijections on the vertices of an infinite binary 2-edge-coloured tree, and he conjectures that QAut(T2,c) is a universal coCF group. We show that QAut(T2,c) embeds into V, and thus obtain a new form for Lehnert's conjecture. Following up on these ideas, we begin work to build a representation theory into R. Thompson's group V. In particular, we classify precisely which Baumslag–Solitar groups embed into V.
Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/87472016-10-01T00:00:00ZBleak, CollinMatucci, FrancescoNeunhöffer, MaxIt is shown in Lehnert and Schweitzer (‘The co-word problem for the Higman–Thompson group is context-free’, Bull. London Math. Soc. 39 (2007) 235–241) that R. Thompson's group V is a co-context-free (coCF) group, thus implying that all of its finitely generated subgroups are also coCF groups. Also, Lehnert shows in his thesis that V embeds inside the coCF group QAut(T2,c), which is a group of particular bijections on the vertices of an infinite binary 2-edge-coloured tree, and he conjectures that QAut(T2,c) is a universal coCF group. We show that QAut(T2,c) embeds into V, and thus obtain a new form for Lehnert's conjecture. Following up on these ideas, we begin work to build a representation theory into R. Thompson's group V. In particular, we classify precisely which Baumslag–Solitar groups embed into V.Gauging allowable harm limits to cumulative, sub-lethal effects of human activities on wildlife : a case-study approach using two whale populations
http://hdl.handle.net/10023/8716
As sublethal human pressures on marine wildlife and their habitats increase and interact in complex ways, there is a pressing need for methods to quantify cumulative impacts of these stressors on populations, and policy decisions about allowable harm limits. Few studies quantify population consequences of individual stressors, and fewer quantify synergistic effects. Incorporating all sources of uncertainty can cause predictions to span the range from negligible to catastrophic. Two places were identified to bound this problem through energetic mechanisms that reduce prey available to individuals. First, the US Marine Mammal Protection Act's Potential Biological Removal (PBR) equation was used as a placeholder allowable harm limit to represent the number of animals that can be removed annually without depleting a population below agreed-upon management targets. That rephrased the research question from, “How big could cumulative impacts be?” to “How big would cumulative impacts have to be to exceed an agreed-upon threshold?” Secondly, two data-rich case studies, namely Gulf of Maine humpback and northeast Pacific resident killer whales, were used as examples to parameterize the weakest link, namely between prey availability and demography. Given no additional information, the model predicted that human activities need only reduce prey available to the killer whale population by ~10% to cause a population-level take, through reduced fecundity and/or survival, equivalent to PBR. By contrast, in the humpback population, reduction in prey availability of ~50% was needed to cause a similar, PBR-sized effect. The paper describes an approach – results are merely illustrative. The two case studies differ in prey specialization, life history, and, no doubt, proximity to carrying capacity. This method of inverting the problem refocuses discussions around what the level of prey depletion – via competition with commercial fisheries, displacement from feeding areas through noise-generating activities, or acoustic masking of signals used to detect prey – would have to occur to exceed allowable harm limits set for lethal takes in fisheries or other, more easily quantifiable, human activities.
Rob Williams was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Project CONCEAL, FP7, PIIF-GA-2009-253407).
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/87162016-08-01T00:00:00ZWilliams, RobThomas, LenAshe, ErinClark, Christopher W.Hammond, Philip S.As sublethal human pressures on marine wildlife and their habitats increase and interact in complex ways, there is a pressing need for methods to quantify cumulative impacts of these stressors on populations, and policy decisions about allowable harm limits. Few studies quantify population consequences of individual stressors, and fewer quantify synergistic effects. Incorporating all sources of uncertainty can cause predictions to span the range from negligible to catastrophic. Two places were identified to bound this problem through energetic mechanisms that reduce prey available to individuals. First, the US Marine Mammal Protection Act's Potential Biological Removal (PBR) equation was used as a placeholder allowable harm limit to represent the number of animals that can be removed annually without depleting a population below agreed-upon management targets. That rephrased the research question from, “How big could cumulative impacts be?” to “How big would cumulative impacts have to be to exceed an agreed-upon threshold?” Secondly, two data-rich case studies, namely Gulf of Maine humpback and northeast Pacific resident killer whales, were used as examples to parameterize the weakest link, namely between prey availability and demography. Given no additional information, the model predicted that human activities need only reduce prey available to the killer whale population by ~10% to cause a population-level take, through reduced fecundity and/or survival, equivalent to PBR. By contrast, in the humpback population, reduction in prey availability of ~50% was needed to cause a similar, PBR-sized effect. The paper describes an approach – results are merely illustrative. The two case studies differ in prey specialization, life history, and, no doubt, proximity to carrying capacity. This method of inverting the problem refocuses discussions around what the level of prey depletion – via competition with commercial fisheries, displacement from feeding areas through noise-generating activities, or acoustic masking of signals used to detect prey – would have to occur to exceed allowable harm limits set for lethal takes in fisheries or other, more easily quantifiable, human activities.On the stability of continuously stratified quasi-geostrophic hetons
http://hdl.handle.net/10023/8709
In this paper we examine the stability of quasi-geostrophic hetons in a stably, continuously stratified fluid. To this purpose we first determinate numerically equilibrium states. Equilibrium hetons consist of two vortices of equal and opposite strength lying at different depths that are steadily translating without deforming. The situation is studied through a parameter space comprising the vertical offset between the vortices, their horizontal separation distance and their aspect ratio. The study first shows that the equilibrium vortices are not only strongly deformed in the vertical but that their instability modes are also varying within the height of the structures. The main purpose of the present contribution is to study families of equilibria which stem from the case of two vertically aligned cylindrical vortices. It is however shown that other branches of solutions exist with different properties. The paper concludes that hetons may be sensitive to baroclinic instabilities provided the separation distance between the poles of the hetons is moderate both in the horizontal and in the vertical directions. The hetons become stable and efficient ways to transport properties as fas as the poles are distant from one another. The critical separation distance in a non-trivial function of the radius-to-height aspect ratio of the poles.
Thu, 30 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/87092015-04-30T00:00:00ZReinaud, Jean NoelIn this paper we examine the stability of quasi-geostrophic hetons in a stably, continuously stratified fluid. To this purpose we first determinate numerically equilibrium states. Equilibrium hetons consist of two vortices of equal and opposite strength lying at different depths that are steadily translating without deforming. The situation is studied through a parameter space comprising the vertical offset between the vortices, their horizontal separation distance and their aspect ratio. The study first shows that the equilibrium vortices are not only strongly deformed in the vertical but that their instability modes are also varying within the height of the structures. The main purpose of the present contribution is to study families of equilibria which stem from the case of two vertically aligned cylindrical vortices. It is however shown that other branches of solutions exist with different properties. The paper concludes that hetons may be sensitive to baroclinic instabilities provided the separation distance between the poles of the hetons is moderate both in the horizontal and in the vertical directions. The hetons become stable and efficient ways to transport properties as fas as the poles are distant from one another. The critical separation distance in a non-trivial function of the radius-to-height aspect ratio of the poles.Solar prominences embedded in flux ropes : morphological features and dynamics from 3D MHD simulations
http://hdl.handle.net/10023/8702
The temporal evolution of a solar prominence inserted in a three-dimensional magnetic flux rope is investigated numerically. Using the model of Titov & Démoulin (1999) under the regime of weak twist, the cold and dense prominence counteracts gravity by modifying the initially force-free magnetic configuration. In some cases a quasi-stationary situation is achieved after the relaxation phase, characterized by the excitation of standing vertical oscillations. These oscillations show a strong attenuation with time produced by the mechanism of continuum damping due to the in homogeneous transition between the prominence and solar corona. The characteristic period of the vertical oscillations does not depend strongly on the twist of the flux rope. Nonlinearity is the responsible for triggering the Kelvin-Helmholtz instability associated to the vertical oscillations and that eventually produces horizontal structures. Contrary to other configurations in which the longitudinal axis of the prominence is permeated by a perpendicular magnetic field, like in unsheared arcades, the orientation of the prominence along the flux rope axis prevents the development of Rayleigh-Taylor instabilities and therefore the appearance of vertical structuring along this axis.
J.T. and R.S. acknowledge support from MINECO and UIB through a Ramón y Cajal grant. The authors acknowledge support by the Spanish MINECO and FEDER funds through project AYA2014-54485-P. M.L. acknowledges the support by the Spanish Ministry of Economy and Competitiveness through projects AYA2011-24808, AYA2010-18029, and AYA2014-55078-P. This work contributes to the deliverables identified in FP7 European Research Council grant agreement 277829, “Magnetic Connectivity through the Solar Partially Ionized Atmosphere” (PI: E. Khomenko). M.L., J.T., and J.L.B. also acknowledge support from the International Space Science Institute (ISSI) to the Team 314 on “Large-Amplitude Oscillation in prominences” led by M. Luna.
Wed, 30 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/87022016-03-30T00:00:00ZTerradas, J.Soler, R.Luna, M.Oliver, R.Ballester, J. L.Wright, Andrew NicholasThe temporal evolution of a solar prominence inserted in a three-dimensional magnetic flux rope is investigated numerically. Using the model of Titov & Démoulin (1999) under the regime of weak twist, the cold and dense prominence counteracts gravity by modifying the initially force-free magnetic configuration. In some cases a quasi-stationary situation is achieved after the relaxation phase, characterized by the excitation of standing vertical oscillations. These oscillations show a strong attenuation with time produced by the mechanism of continuum damping due to the in homogeneous transition between the prominence and solar corona. The characteristic period of the vertical oscillations does not depend strongly on the twist of the flux rope. Nonlinearity is the responsible for triggering the Kelvin-Helmholtz instability associated to the vertical oscillations and that eventually produces horizontal structures. Contrary to other configurations in which the longitudinal axis of the prominence is permeated by a perpendicular magnetic field, like in unsheared arcades, the orientation of the prominence along the flux rope axis prevents the development of Rayleigh-Taylor instabilities and therefore the appearance of vertical structuring along this axis.Capture-recapture abundance estimation using a semi-complete data likelihood approach
http://hdl.handle.net/10023/8690
Capture-recapture data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Model-fitting algorithms to estimate abundance most notably include a numerical approximation for the likelihood or use of a Bayesian data augmentation technique considering the complete data likelihood. We consider a Bayesian hybrid approach, defining a "semi-complete" data likelihood, composed of the product of a complete data likelihood component for individuals seen at least once within the study and a marginal data likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semi-complete likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian complete data likelihood approach) but with significantly improved computational efficiency compared to the commonly used super-population data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semi-complete likelihood approach is flexible and applicable to a range of models, including spatially explicit capture-recapture models. The model-fitting approach is applied to two different datasets corresponding to the closed population model Mh for snowshoe hare data and a spatially explicit capture-recapture model applied to gibbon data.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/86902016-03-01T00:00:00ZKing, RuthT. McClintock, BrettKidney, DarrenBorchers, DavidCapture-recapture data are often collected when abundance estimation is of interest. In the presence of unobserved individual heterogeneity, specified on a continuous scale for the capture probabilities, the likelihood is not generally available in closed form, but expressible only as an analytically intractable integral. Model-fitting algorithms to estimate abundance most notably include a numerical approximation for the likelihood or use of a Bayesian data augmentation technique considering the complete data likelihood. We consider a Bayesian hybrid approach, defining a "semi-complete" data likelihood, composed of the product of a complete data likelihood component for individuals seen at least once within the study and a marginal data likelihood component for the individuals not seen within the study, approximated using numerical integration. This approach combines the advantages of the two different approaches, with the semi-complete likelihood component specified as a single integral (over the dimension of the individual heterogeneity component). In addition, the models can be fitted within BUGS/JAGS (commonly used for the Bayesian complete data likelihood approach) but with significantly improved computational efficiency compared to the commonly used super-population data augmentation approaches (between about 10 and 77 times more efficient in the two examples we consider). The semi-complete likelihood approach is flexible and applicable to a range of models, including spatially explicit capture-recapture models. The model-fitting approach is applied to two different datasets corresponding to the closed population model Mh for snowshoe hare data and a spatially explicit capture-recapture model applied to gibbon data.Consistency in eyewitness reports of aquatic "monsters"
http://hdl.handle.net/10023/8676
Little work has been undertaken on the consistency/repeatabilityof reports of natural historical anomalies. Such information is usefulin understanding the reporting process associated with such accountsand distinguishing any underlying biological signal. Here we used intraclasscorrelation as a measure of consistency in descriptions of a variety of quantitative features from a large collection of firsthand accounts of apparentlyunknown aquatic animals (hereafter “monsters”) in each of two differentcases. In the first case, same observer, same encounter (sose), the correlationwas estimated from two different accounts of the same event from thesame witness. In the second case, the correlation was between two differentobservers of the same event (dose). Overall, levels of consistency weresurprisingly high, with length of monster, distance of monster to the witness,and duration of encounter varying between 0.63 and 1. Interestingly,there was no evidence that sose accounts generally had higher consistencythan dose accounts.
Tue, 15 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/86762016-03-15T00:00:00ZPaxton, Charles George MackayShine, Adrian J.Little work has been undertaken on the consistency/repeatabilityof reports of natural historical anomalies. Such information is usefulin understanding the reporting process associated with such accountsand distinguishing any underlying biological signal. Here we used intraclasscorrelation as a measure of consistency in descriptions of a variety of quantitative features from a large collection of firsthand accounts of apparentlyunknown aquatic animals (hereafter “monsters”) in each of two differentcases. In the first case, same observer, same encounter (sose), the correlationwas estimated from two different accounts of the same event from thesame witness. In the second case, the correlation was between two differentobservers of the same event (dose). Overall, levels of consistency weresurprisingly high, with length of monster, distance of monster to the witness,and duration of encounter varying between 0.63 and 1. Interestingly,there was no evidence that sose accounts generally had higher consistencythan dose accounts.Copulae on products of compact Riemannian manifolds
http://hdl.handle.net/10023/8672
Abstract One standard way of considering a probability distribution on the unit n -cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/86722015-09-01T00:00:00ZJupp, P.E.Abstract One standard way of considering a probability distribution on the unit n -cube, [0 , 1]n , due to Sklar (1959), is to decompose it into its marginal distributions and a copula, i.e. a probability distribution on [0 , 1]n with uniform marginals. The definition of copula was extended by Jones et al. (2014) to probability distributions on products of circles. This paper defines a copula as a probability distribution on a product of compact Riemannian manifolds that has uniform marginals. Basic properties of such copulae are established. Two fairly general constructions of copulae on products of compact homogeneous manifolds are given; one is based on convolution in the isometry group, the other using equivariant functions from compact Riemannian manifolds to their spaces of square integrable functions. Examples illustrate the use of copulae to analyse bivariate spherical data and bivariate rotational data.The effect of interstitial pressure on therapeutic agent transport : coupling with the tumor blood and lymphatic vascular systems
http://hdl.handle.net/10023/8648
Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (area-under-the curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment ? both the vasculature and the interstitium ? are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to sub-optimal outcomes.
Thu, 21 Aug 2014 00:00:00 GMThttp://hdl.handle.net/10023/86482014-08-21T00:00:00ZWu, MinFrieboes, Hermann B.Chaplain, Mark A. J.McDougall, Steven R.Cristini, VittorioLowengrub, John S.Vascularized tumor growth is characterized by both abnormal interstitial fluid flow and the associated interstitial fluid pressure (IFP). Here, we study the effect that these conditions have on the transport of therapeutic agents during chemotherapy. We apply our recently developed vascular tumor growth model which couples a continuous growth component with a discrete angiogenesis model to show that hypertensive IFP is a physical barrier that may hinder vascular extravasation of agents through transvascular fluid flux convection, which drives the agents away from the tumor. This result is consistent with previous work using simpler models without blood flow or lymphatic drainage. We consider the vascular/interstitial/lymphatic fluid dynamics to show that tumors with larger lymphatic resistance increase the agent concentration more rapidly while also experiencing faster washout. In contrast, tumors with smaller lymphatic resistance accumulate less agents but are able to retain them for a longer time. The agent availability (area-under-the curve, or AUC) increases for less permeable agents as lymphatic resistance increases, and correspondingly decreases for more permeable agents. We also investigate the effect of vascular pathologies on agent transport. We show that elevated vascular hydraulic conductivity contributes to the highest AUC when the agent is less permeable, but to lower AUC when the agent is more permeable. We find that elevated interstitial hydraulic conductivity contributes to low AUC in general regardless of the transvascular agent transport capability. We also couple the agent transport with the tumor dynamics to simulate chemotherapy with the same vascularized tumor under different vascular pathologies. We show that tumors with an elevated interstitial hydraulic conductivity alone require the strongest dosage to shrink. We further show that tumors with elevated vascular hydraulic conductivity are more hypoxic during therapy and that the response slows down as the tumor shrinks due to the heterogeneity and low concentration of agents in the tumor interior compared with the cases where other pathological effects may combine to flatten the IFP and thus reduce the heterogeneity. We conclude that dual normalizations of the micronevironment ? both the vasculature and the interstitium ? are needed to maximize the effects of chemotherapy, while normalization of only one of these may be insufficient to overcome the physical resistance and may thus lead to sub-optimal outcomes.Graph automatic semigroups
http://hdl.handle.net/10023/8645
In this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups.
We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness.
Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, Bruck-Reilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved.
Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic.
Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that Bruck-Reilly extensions are never unary graph automatic.
Fri, 24 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/86452016-06-24T00:00:00ZCarey, Rachael MarieIn this thesis we examine properties and constructions of graph automatic semigroups, a generalisation of both automatic semigroups and finitely generated FA-presentable semigroups.
We consider the properties of graph automatic semigroups, showing that they are independent of the choice of generating set, have decidable word problem, and that if we have a graph automatic structure for a semigroup then we can find one with uniqueness.
Semigroup constructions and their effect on graph automaticity are considered. We show that finitely generated direct products, free products, finitely generated Rees matrix semigroup constructions, zero unions, and ordinal sums all preserve unary graph automaticity, and examine when the converse also holds. We also demonstrate situations where semidirect products, Bruck-Reilly extensions, and semilattice constructions preserve graph automaticity, and consider the conditions we may impose on such constructions in order to ensure that graph automaticity is preserved.
Unary graph automatic semigroups, that is semigroups which have graph automatic structures over a single letter alphabet, are also examined. We consider the form of an automaton recognising multiplication by generators in such a semigroup, and use this to demonstrate various properties of unary graph automatic semigroups. We show that infinite periodic semigroups are not unary graph automatic, and show that we may always find a uniform set of normal forms for a unary graph automatic semigroup. We also determine some necessary conditions for a semigroup to be unary graph automatic, and use this to provide examples of semigroups which are not unary graph automatic.
Finally we consider semigroup constructions for unary graph automatic semigroups. We show that the free product of two semigroups is unary graph automatic if and only if both semigroups are trivial; that direct products do not always preserve unary graph automaticity; and that Bruck-Reilly extensions are never unary graph automatic.Recent advances in coronal heating
http://hdl.handle.net/10023/8643
The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.
Thu, 28 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/86432015-05-28T00:00:00ZDe Moortel, I.Browning, P.The solar corona, the tenuous outer atmosphere of the Sun, is orders of magnitude hotter than the solar surface. This 'coronal heating problem' requires the identification of a heat source to balance losses due to thermal conduction, radiation and (in some locations) convection. The review papers in this Theo Murphy meeting issue present an overview of recent observational findings, large- and small-scale numerical modelling of physical processes occurring in the solar atmosphere and other aspects which may affect our understanding of the proposed heating mechanisms. At the same time, they also set out the directions and challenges which must be tackled by future research. In this brief introduction, we summarize some of the issues and themes which reoccur throughout this issue.Is magnetic topology important for heating the solar atmosphere?
http://hdl.handle.net/10023/8642
Magnetic fields permeate the entire solar atmosphere weaving an extremely complex pattern on both local and global scales. In order to understand the nature of this tangled web of magnetic fields, its magnetic skeleton, which forms the boundaries between topologically distinct flux domains, may be determined. The magnetic skeleton consists of null points, separatrix surfaces, spines and separators. The skeleton is often used to clearly visualize key elements of the magnetic configuration, but parts of the skeleton are also locations where currents and waves may collect and dissipate. In this review, the nature of the magnetic skeleton on both global and local scales, over solar cycle time scales, is explained. The behaviour of wave pulses in the vicinity of both nulls and separators is discussed and so too is the formation of current layers and reconnection at the same features. Each of these processes leads to heating of the solar atmosphere, but collectively do they provide enough heat, spread over a wide enough area, to explain the energy losses throughout the solar atmosphere? Here, we consider this question for the three different solar regions: active regions, open-field regions and the quiet Sun. We find that the heating of active regions and open-field regions is highly unlikely to be due to reconnection or wave dissipation at topological features, but it is possible that these may play a role in the heating of the quiet Sun. In active regions, the absence of a complex topology may play an important role in allowing large energies to build up and then, subsequently, be explosively released in the form of a solar flare. Additionally, knowledge of the intricate boundaries of open-field regions (which the magnetic skeleton provides) could be very important in determining the main acceleration mechanism(s) of the solar wind.
CEP and JT acknowledge the support of STFC through the St Andrew’s SMTG consolidated grant. JEHS is supported by STFC as a PhD student. SJE is supported STFC through the Durham University Impact Acceleration Account.
Thu, 21 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/86422015-05-21T00:00:00ZE. Parnell, C.E. H. Stevenson, J.Threlfall, J.J. Edwards, S.Magnetic fields permeate the entire solar atmosphere weaving an extremely complex pattern on both local and global scales. In order to understand the nature of this tangled web of magnetic fields, its magnetic skeleton, which forms the boundaries between topologically distinct flux domains, may be determined. The magnetic skeleton consists of null points, separatrix surfaces, spines and separators. The skeleton is often used to clearly visualize key elements of the magnetic configuration, but parts of the skeleton are also locations where currents and waves may collect and dissipate. In this review, the nature of the magnetic skeleton on both global and local scales, over solar cycle time scales, is explained. The behaviour of wave pulses in the vicinity of both nulls and separators is discussed and so too is the formation of current layers and reconnection at the same features. Each of these processes leads to heating of the solar atmosphere, but collectively do they provide enough heat, spread over a wide enough area, to explain the energy losses throughout the solar atmosphere? Here, we consider this question for the three different solar regions: active regions, open-field regions and the quiet Sun. We find that the heating of active regions and open-field regions is highly unlikely to be due to reconnection or wave dissipation at topological features, but it is possible that these may play a role in the heating of the quiet Sun. In active regions, the absence of a complex topology may play an important role in allowing large energies to build up and then, subsequently, be explosively released in the form of a solar flare. Additionally, knowledge of the intricate boundaries of open-field regions (which the magnetic skeleton provides) could be very important in determining the main acceleration mechanism(s) of the solar wind.Randomization-based models for multitiered experiments : I. a chain of randomizations
http://hdl.handle.net/10023/8636
We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/86362016-06-01T00:00:00ZBailey, Rosemary AnneBrien, C. J.We derive randomization-based models for experiments with a chain of randomizations. Estimation theory for these models leads to formulae for the estimators of treatment effects, their standard errors, and expected mean squares in the analysis of variance. We discuss the practicalities in fitting these models and outline the difficulties that can occur, many of which do not arise in two-tiered experiments.Depletion of nonlinearity in the pressure force driving Navier-Stokes flows : nonlinear depletion in NS flows
http://hdl.handle.net/10023/8620
The dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between |u| and |∇|u||, among other things. Under viscous effects, such depletion may give rise to mild growth of ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.
Fri, 17 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/86202015-04-17T00:00:00ZTran, Chuong VanYu, XinweiThe dynamics of the velocity norms ||u||Lq for q ≥ 3, in Navier-Stokes flows is studied. The pressure term that drives this dynamics has a high degree of nonlinear depletion, which owes its origin to a genuine negative correlation between |u| and |∇|u||, among other things. Under viscous effects, such depletion may give rise to mild growth of ||u||Lq. We explore the possibility of non-singular growth of ||u||Lq.Memory versus effector immune responses in oncolytic virotherapies
http://hdl.handle.net/10023/8604
The main priority when designing cancer immuno-therapies has been to seek viable biological mechanisms that lead to permanent cancer eradication or cancer control. Understanding the delicate balance between the role of effector and memory cells on eliminating cancer cells remains an elusive problem in immunology. Here we make an initial investigation into this problem with the help of a mathematical model for oncolytic virotherapy; although the model can in fact be made general enough to be applied also to other immunological problems. Our results show that long-term cancer control is associated with a large number of persistent effector cells (irrespective of the initial peak in effector cell numbers). However, this large number of persistent effector cells is sustained by a relatively large number of memory cells. Moreover, we show that cancer control from a dormant state cannot be predicted by the size of the memory population.
R.E. acknowledges support from an Engineering and Physical Sciences Research Council (UK) First Grant number EP/K033689/1
Tue, 21 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/86042015-07-21T00:00:00ZMacnamara, Cicely KrystynaEftimie, RalucaThe main priority when designing cancer immuno-therapies has been to seek viable biological mechanisms that lead to permanent cancer eradication or cancer control. Understanding the delicate balance between the role of effector and memory cells on eliminating cancer cells remains an elusive problem in immunology. Here we make an initial investigation into this problem with the help of a mathematical model for oncolytic virotherapy; although the model can in fact be made general enough to be applied also to other immunological problems. Our results show that long-term cancer control is associated with a large number of persistent effector cells (irrespective of the initial peak in effector cell numbers). However, this large number of persistent effector cells is sustained by a relatively large number of memory cells. Moreover, we show that cancer control from a dormant state cannot be predicted by the size of the memory population.On the late-time behaviour of a bounded, inviscid two-dimensional flow
http://hdl.handle.net/10023/8603
Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate-wavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point-vortex model characterising the interactions between the four main vortices which emerge.
We thank the Kavli Institute for Theoretical Physics for supporting our participation in the 2014 Program “Wave-Flow Interaction in Geophysics, Climate, Astrophysics, and Plasmas” where this work was initiated. The KITP is supported in part by the NSF Grant No. NSF PHY11-25915. This work was also supported in part by the NSF under grant Nos. DMR-1306806 and CCF-1048701 (JBM and WQ).
Sun, 01 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/86032015-11-01T00:00:00ZDritschel, David GerardQi, WanmingMarston, J.B.Using complementary numerical approaches at high resolution, we study the late-time behaviour of an inviscid incompressible two-dimensional flow on the surface of a sphere. Starting from a random initial vorticity field comprised of a small set of intermediate-wavenumber spherical harmonics, we find that, contrary to the predictions of equilibrium statistical mechanics, the flow does not evolve into a large-scale steady state. Instead, significant unsteadiness persists, characterised by a population of persistent small-scale vortices interacting with a large-scale oscillating quadrupolar vorticity field. Moreover, the vorticity develops a stepped, staircase distribution, consisting of nearly homogeneous regions separated by sharp gradients. The persistence of unsteadiness is explained by a simple point-vortex model characterising the interactions between the four main vortices which emerge.Tracking marine mammals in 3D using electronic tag data
http://hdl.handle.net/10023/8591
1. Information about at-depth behaviour of marine mammals is fundamental yet very hard to obtain from direct visual observation. Animal-borne multisensor electronic tags provide a unique window of observation into such behaviours. 2. Electronic tag sensors allow the estimation of the animal's 3-dimensional (3D) orientation, depth and speed. Using tag flow noise level to provide an estimate of animal speed, we extend existing approaches of 3D track reconstruction by allowing the direction of movement to differ from that of the animal's longitudinal axis. 3. Data are processed by a hierarchical Bayesian model that allows processing of multisource data, accounting for measurement errors and testing hypotheses about animal movement by comparing models. 4. We illustrate the approach by reconstructing the 3D track of a 52-min deep dive of a Blainville's beaked whale Mesoplodon densirostris adult male fit with a digital tag (DTAG) in the Bahamas. At depth, the whale alternated regular movements at large speed (>1·5 m s-1) and more complex movements at lower speed (<1·5 m s-1) with diﬀerences between movement and longitudinal axis directions of up to 28°. The reconstructed 3D track agrees closely with independent acoustic-based localizations. 5. The approach is potentially applicable to study the underwater behaviour (e.g. response to anthropogenic disturbances) of a wide variety of species of marine mammals ﬁtted with triaxial magnetometer and accelerometer tags.
Date of Acceptance: 05/03/2015
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/85912015-09-01T00:00:00ZLaplanche, C.Marques, T.A.Thomas, L.1. Information about at-depth behaviour of marine mammals is fundamental yet very hard to obtain from direct visual observation. Animal-borne multisensor electronic tags provide a unique window of observation into such behaviours. 2. Electronic tag sensors allow the estimation of the animal's 3-dimensional (3D) orientation, depth and speed. Using tag flow noise level to provide an estimate of animal speed, we extend existing approaches of 3D track reconstruction by allowing the direction of movement to differ from that of the animal's longitudinal axis. 3. Data are processed by a hierarchical Bayesian model that allows processing of multisource data, accounting for measurement errors and testing hypotheses about animal movement by comparing models. 4. We illustrate the approach by reconstructing the 3D track of a 52-min deep dive of a Blainville's beaked whale Mesoplodon densirostris adult male fit with a digital tag (DTAG) in the Bahamas. At depth, the whale alternated regular movements at large speed (>1·5 m s-1) and more complex movements at lower speed (<1·5 m s-1) with diﬀerences between movement and longitudinal axis directions of up to 28°. The reconstructed 3D track agrees closely with independent acoustic-based localizations. 5. The approach is potentially applicable to study the underwater behaviour (e.g. response to anthropogenic disturbances) of a wide variety of species of marine mammals ﬁtted with triaxial magnetometer and accelerometer tags.Whole cell tracking through the optimal control of geometric evolution laws
http://hdl.handle.net/10023/8582
Cell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular phenomena. In this study we present a theoretical framework and an algorithm for whole cell tracking. Within this work we consider that "tracking" is equivalent to a dynamic reconstruction of the whole cell data (morphologies) from static image data sets. The novelty of our work is that the tracking algorithm is driven by a model for the motion of the cell. This model may be regarded as a simplification of a recently developed physically meaningful model for cell motility. The resulting problem is the optimal control of a geometric evolution law and we discuss the formulation and numerical approximation of the optimal control problem. The overall goal of this work is to design a framework for cell tracking within which the recovered data reflects the physics of the forward model. A number of numerical simulations are presented that illustrate the applicability of our approach.
This work (A.M., V.S. and C.V.) is supported by the Engineering and Physical Sciences Research Council, UK grant (EP/J016780/1) and the Leverhulme Trust Research Project Grant (RPG-2014-149). K.B. was partially supported by the Embirikion Foundation Grant (2011-2014) – Greece.
Tue, 15 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/85822015-09-15T00:00:00ZBlazakis, Konstantinos N.Madzvamuse, AnotidaReyes-Aldasoro, Constantino CarlosStyles, VanessaVenkataraman, ChandrasekharCell tracking algorithms which automate and systematise the analysis of time lapse image data sets of cells are an indispensable tool in the modelling and understanding of cellular phenomena. In this study we present a theoretical framework and an algorithm for whole cell tracking. Within this work we consider that "tracking" is equivalent to a dynamic reconstruction of the whole cell data (morphologies) from static image data sets. The novelty of our work is that the tracking algorithm is driven by a model for the motion of the cell. This model may be regarded as a simplification of a recently developed physically meaningful model for cell motility. The resulting problem is the optimal control of a geometric evolution law and we discuss the formulation and numerical approximation of the optimal control problem. The overall goal of this work is to design a framework for cell tracking within which the recovered data reflects the physics of the forward model. A number of numerical simulations are presented that illustrate the applicability of our approach.Solar coronal electron heating by short-wavelength dispersive shear Alfvén waves
http://hdl.handle.net/10023/8581
The electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions.
This work was partially supported by the STFC through the Centre for Fundamental Physics (CfFP) at Rutherford Appleton Laboratory, Chilton, Didcot, UK. BE acknowledges support by the Engineering and Physical Sciences Research Council (EPSRC), UK, Grant no EP/M009386/1.
Tue, 15 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/85812015-09-15T00:00:00ZBingham, R.Shukla, P. K.Eliasson, B.Cairns, A.Cairns, R AlanThe electron heating of the solar coronal plasma has remained one of the most important problems in solar physics. An explanation of the electron heating rests on the identification of the energy source and appropriate physical mechanisms via which the energy can be channelled to the electrons. Our objective here is to present an estimate for the electron heating rate in the presence of finite amplitude short-wavelength (in comparison with the ion gyroradius) dispersive shear Alfven (SWDSA) waves that propagate obliquely to the ambient magnetic field direction in the solar corona. Specifically, it is demonstrated that SWDSA waves can significantly contribute to the solar coronal electron heating via collisionless heating involving SWDSA wave-electron interactions.Constructing flag-transitive, point-imprimitive designs
http://hdl.handle.net/10023/8546
We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.
Wed, 04 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/85462016-05-04T00:00:00ZCameron, Peter JephsonPraeger, Cheryl E.We give a construction of a family of designs with a specified point-partition and determine the subgroup of automorphisms leaving invariant the point-partition. We give necessary and sufficient conditions for a design in the family to possess a flag-transitive group of automorphisms preserving the specified point-partition. We give examples of flag-transitive designs in the family, including a new symmetric 2-(1408,336,80) design with automorphism group 2^12:((3⋅M22):2) and a construction of one of the families of the symplectic designs (the designs S^−(n) ) exhibiting a flag-transitive, point-imprimitive automorphism group.Permutation groups and transformation semigroups : results and problems
http://hdl.handle.net/10023/8532
J.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single non-permutation a. Our particular concern is the influence that properties of G (related to homogeneity, transitivity and primitivity) have on the structure of the semigroup. In the first part of the paper, we consider properties of S=<G,a> such as regularity and generation. The second is a brief report on the synchronization project, which aims to decide in what circumstances S contains an element of rank 1. The paper closes with a list of open problems on permutation groups and linear groups, and some comments about the impact on semigroups are provided. These two research directions outlined above lead to very interesting and challenging problems on primitive permutation groups whose solutions require combining results from several different areas of mathematics, certainly fulfilling both of Howie's elegance and value tests in a new and fascinating way.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/85322015-10-01T00:00:00ZAraujo, JoaoCameron, Peter JephsonJ.M. Howie, the influential St Andrews semigroupist, claimed that we value an area of pure mathematics to the extent that (a) it gives rise to arguments that are deep and elegant, and (b) it has interesting interconnections with other parts of pure mathematics. This paper surveys some recent results on the transformation semigroup generated by a permutation group G and a single non-permutation a. Our particular concern is the influence that properties of G (related to homogeneity, transitivity and primitivity) have on the structure of the semigroup. In the first part of the paper, we consider properties of S=<G,a> such as regularity and generation. The second is a brief report on the synchronization project, which aims to decide in what circumstances S contains an element of rank 1. The paper closes with a list of open problems on permutation groups and linear groups, and some comments about the impact on semigroups are provided. These two research directions outlined above lead to very interesting and challenging problems on primitive permutation groups whose solutions require combining results from several different areas of mathematics, certainly fulfilling both of Howie's elegance and value tests in a new and fascinating way.Guessing games on triangle-free graphs
http://hdl.handle.net/10023/8518
The guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirected, Christofides and Markström introduced a method to bound the value of the guessing number from below using the fractional clique cover number kappa_f(G). In particular they showed gn(G) >= |V(G)| - kappa_f(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph G falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are triangle-free graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous triangle-free Higman-Sims graph has guessing number at least 77 and at most 78, while the bound given by fractional clique cover is 50.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/85182016-01-01T00:00:00ZCameron, Peter JephsonDang, AnhRiis, SorenThe guessing game introduced by Riis is a variant of the "guessing your own hats" game and can be played on any simple directed graph G on n vertices. For each digraph G, it is proved that there exists a unique guessing number gn(G) associated to the guessing game played on G. When we consider the directed edge to be bidirected, in other words, the graph G is undirected, Christofides and Markström introduced a method to bound the value of the guessing number from below using the fractional clique cover number kappa_f(G). In particular they showed gn(G) >= |V(G)| - kappa_f(G). Moreover, it is pointed out that equality holds in this bound if the underlying undirected graph G falls into one of the following categories: perfect graphs, cycle graphs or their complement. In this paper, we show that there are triangle-free graphs that have guessing numbers which do not meet the fractional clique cover bound. In particular, the famous triangle-free Higman-Sims graph has guessing number at least 77 and at most 78, while the bound given by fractional clique cover is 50.Some undecidability results for asynchronous transducers and the Brin-Thompson group 2V
http://hdl.handle.net/10023/8508
Using a result of Kari and Ollinger, we prove that the torsion problem for elements of the Brin-Thompson group 2V is undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational group R of Grigorchuk, Nekrashevich, and Sushchanskii has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements of 2V on Cantor Space. Arzhantseva, Lafont, and Minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge, 2V furnishes the first concrete example of such a group, and gives an example of a direct undecidability result in the extended family of R. Thompson type groups.
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/85082017-05-01T00:00:00ZBelk, JamesBleak, CollinUsing a result of Kari and Ollinger, we prove that the torsion problem for elements of the Brin-Thompson group 2V is undecidable. As a result, we show that there does not exist an algorithm to determine whether an element of the rational group R of Grigorchuk, Nekrashevich, and Sushchanskii has finite order. A modification of the construction gives other undecidability results about the dynamics of the action of elements of 2V on Cantor Space. Arzhantseva, Lafont, and Minasyanin prove in 2012 that there exists a finitely presented group with solvable word problem and unsolvable torsion problem. To our knowledge, 2V furnishes the first concrete example of such a group, and gives an example of a direct undecidability result in the extended family of R. Thompson type groups.The role of dimerisation and nuclear transport in the Hes1 gene regulatory network
http://hdl.handle.net/10023/8458
Hes1 is a member of the family of basic helix-loop-helix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anti-cancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.
Tue, 01 Apr 2014 00:00:00 GMThttp://hdl.handle.net/10023/84582014-04-01T00:00:00ZSturrock, MarcHellander, AndreasAldakheel, SaharPetzold, LindaChaplain, Mark A. J.Hes1 is a member of the family of basic helix-loop-helix transcription factors and the Hes1 gene regulatory network (GRN) may be described as the canonical example of transcriptional control in eukaryotic cells, since it involves only the Hes1 protein and its own mRNA. Recently, the Hes1 protein has been established as an excellent target for an anti-cancer drug treatment, with the design of a small molecule Hes1 dimerisation inhibitor representing a promising if challenging approach to therapy. In this paper, we extend a previous spatial stochastic model of the Hes1 GRN to include nuclear transport and dimerisation of Hes1 monomers. Initially, we assume that dimerisation occurs only in the cytoplasm, with only dimers being imported into the nucleus. Stochastic simulations of this novel model using the URDME software show that oscillatory dynamics in agreement with experimental studies are retained. Furthermore, we find that our model is robust to changes in the nuclear transport and dimerisation parameters. However, since the precise dynamics of the nuclear import of Hes1 and the localisation of the dimerisation reaction are not known, we consider a second modelling scenario in which we allow for both Hes1 monomers and dimers to be imported into the nucleus, and we allow dimerisation of Hes1 to occur everywhere in the cell. Once again, computational solutions of this second model produce oscillatory dynamics in agreement with experimental studies. We also explore sensitivity of the numerical solutions to nuclear transport and dimerisation parameters. Finally, we compare and contrast the two different modelling scenarios using numerical experiments that simulate dimer disruption, and suggest a biological experiment that could distinguish which model more faithfully captures the Hes1 GRN.Distance sampling with a random scale detection function
http://hdl.handle.net/10023/8454
Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the half-normal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with long-tailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes ((Formula presented.)) and compared the random scale half-normal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.
Cornelia Oedekoven was supported by a studentship jointly funded by the University of St Andrews and EP-SRC, through the National Centre for Statistical Ecology (EP-SRC Grant EP/C522702/1). Hans Skaug thanks the Center for Stock Assessment Research for facilitating his visit to University of California, Santa Cruz.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/84542015-12-01T00:00:00ZOedekoven, C.S.Laake, J.L.Skaug, H.J.Distance sampling was developed to estimate wildlife abundance from observational surveys with uncertain detection in the search area. We present novel analysis methods for estimating detection probabilities that make use of random effects models to allow for unmodeled heterogeneity in detection. The scale parameter of the half-normal detection function is modeled by means of an intercept plus an error term varying with detections, normally distributed with zero mean and unknown variance. In contrast to conventional distance sampling methods, our approach can deal with long-tailed detection functions without truncation. Compared to a fixed effect covariate approach, we think of the random effect as a covariate with unknown values and integrate over the random effect. We expand the random scale to a mixed scale model by adding fixed effect covariates. We analyzed simulated data with large sample sizes to demonstrate that the code performs correctly for random and mixed effect models. We also generated replicate simulations with more practical sample sizes ((Formula presented.)) and compared the random scale half-normal with the hazard rate detection function. As expected each estimation model was best for different simulation models. We illustrate the mixed effect modeling approach using harbor porpoise vessel survey data where the mixed effect model provided an improved model fit in comparison to a fixed effect model with the same covariates. We propose that a random or mixed effect model of the detection function scale be adopted as one of the standard approaches for fitting detection functions in distance sampling.Weak collisionless shocks in laser-plasmas
http://hdl.handle.net/10023/8442
We obtain a theory describing laminar shock-like structures in a collisionless plasma and examine the parameter limits, in terms of the ion sound Mach number and the electron/ion temperature ratio, within which these structures exist. The essential feature is the inclusion of finite ion temperature with the result that some ions are reflected from a potential ramp. This destroys the symmetry between upstream and downstream regions that would otherwise give the well-known ion solitary wave solution. We have shown earlier (Cairns et al 2014 Phys. Plasmas 21 022112) that such structures may be relevant to problems such as the existence of strong, localized electric fields observed in laser compressed pellets and laser acceleration of ions. Here we present results on the way in which these structures may produce species separation in fusion targets and suggest that it may be possible to use shock ion acceleration for fast ignition.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/84422015-04-01T00:00:00ZCairns, R. A.Bingham, R.Trines, R. G. M.Norreys, P.We obtain a theory describing laminar shock-like structures in a collisionless plasma and examine the parameter limits, in terms of the ion sound Mach number and the electron/ion temperature ratio, within which these structures exist. The essential feature is the inclusion of finite ion temperature with the result that some ions are reflected from a potential ramp. This destroys the symmetry between upstream and downstream regions that would otherwise give the well-known ion solitary wave solution. We have shown earlier (Cairns et al 2014 Phys. Plasmas 21 022112) that such structures may be relevant to problems such as the existence of strong, localized electric fields observed in laser compressed pellets and laser acceleration of ions. Here we present results on the way in which these structures may produce species separation in fusion targets and suggest that it may be possible to use shock ion acceleration for fast ignition.Effects of thermal conduction and compressive viscosity on the period ratio of the slow mode
http://hdl.handle.net/10023/8423
Aims: Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P2, between the period P1 of the fundamental mode and the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods: We consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. Results: For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. Conclusions: Damping typically has a small effect on the period ratio, suggesting that longitudinal structuring remains the most significant effect.
C.K.M. acknowledges financial support from the CarnegieTrust. Discussions with Dr. I. De Moortel and Prof. A. W. Hood are gratefully acknowledged
Tue, 01 Jun 2010 00:00:00 GMThttp://hdl.handle.net/10023/84232010-06-01T00:00:00ZMacnamara, Cicely KrystynaRoberts, BernardAims: Increasing observational evidence of wave modes brings us to a closer understanding of the solar corona. Coronal seismology allows us to combine wave observations and theory to determine otherwise unknown parameters. The period ratio, P1/2P2, between the period P1 of the fundamental mode and the period P2 of its first overtone, is one such tool of coronal seismology and its departure from unity provides information about the structure of the corona. Methods: We consider analytically the effects of thermal conduction and compressive viscosity on the period ratio for a longitudinally propagating sound wave. Results: For coronal values of thermal conduction the effect on the period ratio is negligible. For compressive viscosity the effect on the period ratio may become important for some short hot loops. Conclusions: Damping typically has a small effect on the period ratio, suggesting that longitudinal structuring remains the most significant effect.Wild attractors and thermodynamic formalism
http://hdl.handle.net/10023/8394
Fibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family ƒλ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential φt = -t log |ƒλ'|, there is a unique phase transition at some t1 ≤ 1, and the pressure P(φt ) is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a non-analytic C∞ curve (with all derivatives equal to 0 at t1 < 1) at the emergence of a wild attractor, whereas the phase transition at t1 = 1 can be of any finite order for those λ for which ƒλ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of the basin of ω(c).
MT was partially supported by NSF Grants DMS 0606343 and DMS 0908093.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/83942015-09-01T00:00:00ZBruin, HenkTodd, Michael JohnFibonacci unimodal maps can have a wild Cantor attractor, and hence be Lebesgue dissipative, depending on the order of the critical point. We present a one-parameter family ƒλ of countably piecewise linear unimodal Fibonacci maps in order to study the thermodynamic formalism of dynamics where dissipativity of Lebesgue (and conformal) measure is responsible for phase transitions. We show that for the potential φt = -t log |ƒλ'|, there is a unique phase transition at some t1 ≤ 1, and the pressure P(φt ) is analytic (with unique equilibrium state) elsewhere. The pressure is majorised by a non-analytic C∞ curve (with all derivatives equal to 0 at t1 < 1) at the emergence of a wild attractor, whereas the phase transition at t1 = 1 can be of any finite order for those λ for which ƒλ is Lebesgue conservative. We also obtain results on the existence of conformal measures and equilibrium states, as well as the hyperbolic dimension and the dimension of the basin of ω(c).Particle-in-cell simulations of collisionless magnetic reconnection with a non-uniform guide field
http://hdl.handle.net/10023/8386
Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/83862016-03-01T00:00:00ZWilson, FionaNeukirch, ThomasHesse, MichaelHarrison, Michael G.Stark, Craig R.Results are presented of a first study of collisionless magnetic reconnection starting from a recently found exact nonlinear force-free Vlasov-Maxwell equilibrium. The initial state has a Harris sheet magnetic field profile in one direction and a non-uniform guide field in a second direction, resulting in a spatially constant magnetic field strength as well as a constant initial plasma density and plasma pressure. It is found that the reconnection process initially resembles guide field reconnection, but that a gradual transition to anti-parallel reconnection happens as the system evolves. The time evolution of a number of plasma parameters is investigated, and the results are compared with simulations starting from a Harris sheet equilibrium and a Harris sheet plus constant guide field equilibrium.Description and seasonal detection of two potential whale calls recorded in the Indian Ocean
http://hdl.handle.net/10023/8382
Unidentified acoustic signals are recorded by hydrophones placed in the world's oceans. Some of these sounds are suspected to originate from marine mammals. In this study, two acoustic signals recorded by two arrays at Diego Garcia in the northern Indian Ocean are described. Data were available between January 2002 and December 2003. Signals were detected manually using long-term spectral average plots. Time and frequency measurements were taken from a sample of both signals. The first unidentified signal [Diego Garcia Downsweep (DGD)] consisted of two main components. The mean frequency range of the entire signal was 19.3-45.0 Hz, with a mean duration of 36.5 s (n = 22). Detections of DGD at the northern array peaked in the austral summer, though detections at the southern array peaked during winter and spring. The second unidentified signal [Diego Garcia Croak (DGC)] consisted of one component with a mean frequency range of 16.9-49.6 Hz. The mean duration of the signal was 13.1 s (n = 10). Detections of DGC did not follow a clear seasonal pattern. These signals followed characteristics of biological sources, suggesting that they could be whale calls. Fin whale calls and possible blue whales D-calls were also identified in the data.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/83822015-09-01T00:00:00ZSousa, Andreia GHarris, DanielleUnidentified acoustic signals are recorded by hydrophones placed in the world's oceans. Some of these sounds are suspected to originate from marine mammals. In this study, two acoustic signals recorded by two arrays at Diego Garcia in the northern Indian Ocean are described. Data were available between January 2002 and December 2003. Signals were detected manually using long-term spectral average plots. Time and frequency measurements were taken from a sample of both signals. The first unidentified signal [Diego Garcia Downsweep (DGD)] consisted of two main components. The mean frequency range of the entire signal was 19.3-45.0 Hz, with a mean duration of 36.5 s (n = 22). Detections of DGD at the northern array peaked in the austral summer, though detections at the southern array peaked during winter and spring. The second unidentified signal [Diego Garcia Croak (DGC)] consisted of one component with a mean frequency range of 16.9-49.6 Hz. The mean duration of the signal was 13.1 s (n = 10). Detections of DGC did not follow a clear seasonal pattern. These signals followed characteristics of biological sources, suggesting that they could be whale calls. Fin whale calls and possible blue whales D-calls were also identified in the data.Apparent cross-field superslow propagation of magnetohydrodynamic waves in solar plasmas
http://hdl.handle.net/10023/8377
In this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic eld. This phenomenon could be erroneously interpreted as fast mag- netosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.
TK was supported by the Program for Leading Graduate School, MEXT, Japan. This work was supported by JSPS KAKENHI Grant Number 15H03640. RS acknowledges support from MINECO through project AYA2014-54485-P and from FEDER funds. RS also acknowledges support from MINECO through a ‘Juan de la Cierva’ grant, from MECD through project CEF11-0012, and from the ‘Vicerectorat d’Investigació Postgrau’ of the UIB. JT acknowledges support from the Spanish Ministerio de Educación y Ciencia through a Ramón y Cajal grant. JT acknowledges support from MINECO through project AYA2014-54485-P and from FEDER funds. MG was supported by IAP P7/08 CHARM (Belspo) and the GOA-2015-014 (KU Leuven). TVD was supported by an Odysseus grant of the FWO Vlaanderen, the IAP P7/08 CHARM (Belspo) and the GOA-2015-014 (KU Leuven)
Thu, 15 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/83772015-10-15T00:00:00ZKaneko, TGoossens, MarcelSoler, RobertoTerradas, JaumeVan Doorsselaere, TomYokoyama, TWright, Andrew NicholasIn this paper we show that the phase mixing of continuum Alfvén waves and/or continuum slow waves in magnetic structures of the solar atmosphere as, e.g., coronal arcades, can create the illusion of wave propagation across the magnetic eld. This phenomenon could be erroneously interpreted as fast mag- netosonic waves. The cross-field propagation due to phase mixing of continuum waves is apparent because there is no real propagation of energy across the magnetic surfaces. We investigate the continuous Alfvén and slow spectra in 2D Cartesian equilibrium models with a purely poloidal magnetic field. We show that apparent superslow propagation across the magnetic surfaces in solar coronal structures is a consequence of the existence of continuum Alfvén waves and continuum slow waves that naturally live on those structures and phase mix as time evolves. The apparent cross-field phase velocity is related to the spatial variation of the local Alfvén/slow frequency across the magnetic surfaces and is slower than the Alfvén/sound velocities for typical coronal conditions. Understanding the nature of the apparent cross-field propagation is important for the correct analysis of numerical simulations and the correct interpretation of observations.Exploring dependence between categorical variables : benefits and limitations of using variable selection within Bayesian clustering in relation to log-linear modelling with interaction terms
http://hdl.handle.net/10023/8356
This manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing log-linear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the log-linear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize log-linear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.
This work was supported by MRC grant G1002319.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/83562016-06-01T00:00:00ZPapathomas, MichailRichardson, SylviaThis manuscript is concerned with relating two approaches that can be used to explore complex dependence structures between categorical variables, namely Bayesian partitioning of the covariate space incorporating a variable selection procedure that highlights the covariates that drive the clustering, and log-linear modelling with interaction terms. We derive theoretical results on this relation and discuss if they can be employed to assist log-linear model determination, demonstrating advantages and limitations with simulated and real data sets. The main advantage concerns sparse contingency tables. Inferences from clustering can potentially reduce the number of covariates considered and, subsequently, the number of competing log-linear models, making the exploration of the model space feasible. Variable selection within clustering can inform on marginal independence in general, thus allowing for a more efficient exploration of the log-linear model space. However, we show that the clustering structure is not informative on the existence of interactions in a consistent manner. This work is of interest to those who utilize log-linear models, as well as practitioners such as epidemiologists that use clustering models to reduce the dimensionality in the data and to reveal interesting patterns on how covariates combine.Stability analysis and simulations of coupled bulk-surface reaction-diffusion systems
http://hdl.handle.net/10023/8349
In this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction-diffusion system can induce patterning on the surface independent of whether the surface reaction-diffusion system produces or not, patterning. On the other hand, the surface reaction-diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction-diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.
Sun, 08 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/83492015-03-08T00:00:00ZMadzvamuse, AnotidaChung, Andy H. W.Venkataraman, ChandrasekharIn this article, we formulate new models for coupled systems of bulk-surface reaction-diffusion equations on stationary volumes. The bulk reaction-diffusion equations are coupled to the surface reaction-diffusion equations through linear Robin-type boundary conditions. We then state and prove the necessary conditions for diffusion-driven instability for the coupled system. Owing to the nature of the coupling between bulk and surface dynamics, we are able to decouple the stability analysis of the bulk and surface dynamics. Under a suitable choice of model parameter values, the bulk reaction-diffusion system can induce patterning on the surface independent of whether the surface reaction-diffusion system produces or not, patterning. On the other hand, the surface reaction-diffusion system cannot generate patterns everywhere in the bulk in the absence of patterning from the bulk reaction-diffusion system. For this case, patterns can be induced only in regions close to the surface membrane. Various numerical experiments are presented to support our theoretical findings. Our most revealing numerical result is that, Robin-type boundary conditions seem to introduce a boundary layer coupling the bulk and surface dynamics.Stellar coronal response to differential rotation and flux emergence
http://hdl.handle.net/10023/8298
We perform a numerical parameter study to determine what effect varying differential rotation and flux emergence has on a star's non-potential coronal magnetic field. In particular we consider the effects on the star's surface magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free magnetic energy, coronal heating and flux rope eruptions. To do this, we apply a magnetic flux transport model to describe the photospheric evolution, and couple this to the non-potential coronal evolution using a magnetofrictional technique. A flux emergence model is applied to add new magnetic flux on to the photosphere and into the corona. The parameters of this flux emergence model are derived from the solar flux emergence profile, however the rate of emergence can be increased to represent higher flux emergence rates than the Sun's. Overall we find that flux emergence has a greater effect on the non-potential coronal properties compared to differential rotation, with all the aforementioned properties increasing with increasing flux emergence rate. Although differential rotation has a lesser effect on the overall coronal properties compared to flux emergence, varying differential rotation does alter the coronal structure. As the differential rotation rate increases, the corona becomes more open, and more non-potential.
GPSG would like to thank the STFC for financial support. DHM would like to thank the STFC and the Leverhulme Trust for financial support. Simulations were carried out on a STFC/SRIF funded UKMHD cluster at St Andrews.
Thu, 14 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/82982016-01-14T00:00:00ZGibb, Gordon Peter SamuelMackay, Duncan HendryJardine, Moira MaryYeates, A. R.We perform a numerical parameter study to determine what effect varying differential rotation and flux emergence has on a star's non-potential coronal magnetic field. In particular we consider the effects on the star's surface magnetic flux, open magnetic flux, mean azimuthal field strength, coronal free magnetic energy, coronal heating and flux rope eruptions. To do this, we apply a magnetic flux transport model to describe the photospheric evolution, and couple this to the non-potential coronal evolution using a magnetofrictional technique. A flux emergence model is applied to add new magnetic flux on to the photosphere and into the corona. The parameters of this flux emergence model are derived from the solar flux emergence profile, however the rate of emergence can be increased to represent higher flux emergence rates than the Sun's. Overall we find that flux emergence has a greater effect on the non-potential coronal properties compared to differential rotation, with all the aforementioned properties increasing with increasing flux emergence rate. Although differential rotation has a lesser effect on the overall coronal properties compared to flux emergence, varying differential rotation does alter the coronal structure. As the differential rotation rate increases, the corona becomes more open, and more non-potential.Bayesian sequential tests of the initial size of a linear pure death process
http://hdl.handle.net/10023/8286
We provide a recursive algorithm for determining the sampling plans of invariant Bayesian sequential tests of the initial size of a linear pure death process of unknown rate. These tests compare favourably with the corresponding truncated sequential probability ratio tests.
Fri, 01 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/82862015-05-01T00:00:00ZGoudie, I.B.J.We provide a recursive algorithm for determining the sampling plans of invariant Bayesian sequential tests of the initial size of a linear pure death process of unknown rate. These tests compare favourably with the corresponding truncated sequential probability ratio tests.Head on collisions between two quasi-geostrophic hetons in a continuously stratified fluid
http://hdl.handle.net/10023/8219
We examine the interactions between two three-dimensional quasi-geostrophic hetons. The hetons are initially translating towards one another. We address the effect of the vertical distance between the two poles (vortices) constituting each heton, on the interaction. We also examine the influence of the horizontal separation between the poles within each heton. In this investigation, the two hetons are facing each other. Two configurations are possible depending on the respective location of the like-signed poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the anti-symmetric configuration corresponds to opposite-signed poles at the same depth. The first step in the investigation uses point vortices to represent the poles of the hetons. This approach allows to rapidly browse the parameter space and to estimate the possible heton trajectories. For a symmetric pair, hetons either reverse their trajectory or recombine and escape perpendicularly depending of their horizontal and vertical offsets. On the other hand, anti-symmetric hetons recombine and escape perpendicularly as same-depth dipoles. In a second part, we focus on finite core hetons (with finite volume poles). These hetons can deform and may be sensitive to horizontal shear induced deformations, or to baroclinic instability. These destabilisations depend on the vertical and horizontal offsets between the various poles, as well as on their width-to-height aspect ratios. They can modify the volume of the poles via vortex merger, breaking and/or shearing out; they compete with the advective evolution observed for singular (point) vortices. Importantly, hetons can break down or re-configure before they can drift away as expected from a point vortex approach. Thus a large variety of behaviours is observed in the parameter space. Finally, we briefly illustrate the behaviour of tall hetons which can be unstable to an azimuthal mode l=1 when many vertical modes of deformation are present on the heton.
Date of Acceptance : 21/07/2015
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/82192015-09-01T00:00:00ZReinaud, Jean NoelCarton, XavierWe examine the interactions between two three-dimensional quasi-geostrophic hetons. The hetons are initially translating towards one another. We address the effect of the vertical distance between the two poles (vortices) constituting each heton, on the interaction. We also examine the influence of the horizontal separation between the poles within each heton. In this investigation, the two hetons are facing each other. Two configurations are possible depending on the respective location of the like-signed poles of the hetons. When they lie at the same depth, we refer to the configuration as symmetric; the anti-symmetric configuration corresponds to opposite-signed poles at the same depth. The first step in the investigation uses point vortices to represent the poles of the hetons. This approach allows to rapidly browse the parameter space and to estimate the possible heton trajectories. For a symmetric pair, hetons either reverse their trajectory or recombine and escape perpendicularly depending of their horizontal and vertical offsets. On the other hand, anti-symmetric hetons recombine and escape perpendicularly as same-depth dipoles. In a second part, we focus on finite core hetons (with finite volume poles). These hetons can deform and may be sensitive to horizontal shear induced deformations, or to baroclinic instability. These destabilisations depend on the vertical and horizontal offsets between the various poles, as well as on their width-to-height aspect ratios. They can modify the volume of the poles via vortex merger, breaking and/or shearing out; they compete with the advective evolution observed for singular (point) vortices. Importantly, hetons can break down or re-configure before they can drift away as expected from a point vortex approach. Thus a large variety of behaviours is observed in the parameter space. Finally, we briefly illustrate the behaviour of tall hetons which can be unstable to an azimuthal mode l=1 when many vertical modes of deformation are present on the heton.Particle dynamics in a non-flaring solar active region model
http://hdl.handle.net/10023/8203
The aim of this work is to investigate and characterise particle behaviour in a (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flare-like behaviour in the active region, direct acceleration of electrons and protons to non-thermal energies (≲ 42 MeV) was found, yielding spectra with high-energy tails which conform to a power law. Examples of particle dynamics, including particle trapping caused by local electric rather than magnetic field effects, are observed and discussed, together with implications for future experiments which simulate non-flaring active region heating and reconnection.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/82032016-03-01T00:00:00ZThrelfall, J.-A. Bourdin, Ph.Neukirch, T.E. Parnell, C.The aim of this work is to investigate and characterise particle behaviour in a (observationally-driven) 3D MHD model of the solar atmosphere above a slowly evolving, non-flaring active region. We use a relativistic guiding-centre particle code to investigate particle acceleration in a single snapshot of the 3D MHD simulation. Despite the lack of flare-like behaviour in the active region, direct acceleration of electrons and protons to non-thermal energies (≲ 42 MeV) was found, yielding spectra with high-energy tails which conform to a power law. Examples of particle dynamics, including particle trapping caused by local electric rather than magnetic field effects, are observed and discussed, together with implications for future experiments which simulate non-flaring active region heating and reconnection.Magnetohydrostatic modelling of stellar coronae
http://hdl.handle.net/10023/8067
We introduce to the stellar physics community a method of modelling stellar coronae that can be considered to be an extension of the potential field. In this approach, the magnetic field is coupled to the background atmosphere. The model is magnetohydrostatic and is a balance between the Lorentz force, the pressure gradient and gravity. Analytical solutions are possible and we consider a particular class of equilibria in this paper. The model contains two free parameters and the effects of these on both the geometry and topology of the coronal magnetic field are investigated. A demonstration of the approach is given using a magnetogram derived from Zeeman–Doppler imaging of the 0.75 M⊙ M-dwarf star GJ 182.
Thu, 11 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/80672016-02-11T00:00:00ZMacTaggart, DavidGregory, ScottNeukirch, ThomasDonati, Jean-FrancoisWe introduce to the stellar physics community a method of modelling stellar coronae that can be considered to be an extension of the potential field. In this approach, the magnetic field is coupled to the background atmosphere. The model is magnetohydrostatic and is a balance between the Lorentz force, the pressure gradient and gravity. Analytical solutions are possible and we consider a particular class of equilibria in this paper. The model contains two free parameters and the effects of these on both the geometry and topology of the coronal magnetic field are investigated. A demonstration of the approach is given using a magnetogram derived from Zeeman–Doppler imaging of the 0.75 M⊙ M-dwarf star GJ 182.A single-station method for the detection, classification and location of fin whale calls using ocean-bottom seismic stations
http://hdl.handle.net/10023/8064
Passive seismic monitoring in the oceans uses long-term deployments of Ocean Bottom Seismometers (OBSs). An OBS usually records the three components of ground motion and pressure, typically at 100Hz. This makes the OBS an ideal tool to investigate fin and blue whales that vocalize at frequencies below 45Hz. Previous applications of OBS data to locate whale calls have relied on single channel analyses that disregard the information that is conveyed by the horizontal seismic channels. Recently, Harris, Matias, Thomas, Harwood, and Geissler [J. Acoust. Soc. Am. 134, 3522-3535 (2013)] presented a method that used all four channels recorded by one OBS to derive the range and azimuth of fin whale calls. In this work, the detection, classification, and ranging of calls using this four-channel method were further investigated, focusing on methods to increase the accuracy of range estimates to direct path arrivals. Corrections to account for the influences of the sound speed in the water layer and the velocity structure in the top strata of the seabed were considered. The single station method discussed here is best implemented when OBSs have been deployed in deep water on top of seabed strata with low P-wave velocity. These conditions maximize the ability to detect and estimate ranges to fin whale calls.
Wed, 01 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/80642015-07-01T00:00:00ZMatias, L.Harris, D.Passive seismic monitoring in the oceans uses long-term deployments of Ocean Bottom Seismometers (OBSs). An OBS usually records the three components of ground motion and pressure, typically at 100Hz. This makes the OBS an ideal tool to investigate fin and blue whales that vocalize at frequencies below 45Hz. Previous applications of OBS data to locate whale calls have relied on single channel analyses that disregard the information that is conveyed by the horizontal seismic channels. Recently, Harris, Matias, Thomas, Harwood, and Geissler [J. Acoust. Soc. Am. 134, 3522-3535 (2013)] presented a method that used all four channels recorded by one OBS to derive the range and azimuth of fin whale calls. In this work, the detection, classification, and ranging of calls using this four-channel method were further investigated, focusing on methods to increase the accuracy of range estimates to direct path arrivals. Corrections to account for the influences of the sound speed in the water layer and the velocity structure in the top strata of the seabed were considered. The single station method discussed here is best implemented when OBSs have been deployed in deep water on top of seabed strata with low P-wave velocity. These conditions maximize the ability to detect and estimate ranges to fin whale calls.An MHD avalanche in a multi-threaded coronal loop
http://hdl.handle.net/10023/8061
For the first time, we demonstrate how an MHD avalanche might occur in a multi-threaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighbouring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of \textit{nanoflares} than of constant heating.
We acknowledge the financial support of STFC through the Consolidated grants to the University of St Andrews and the University of Manchester.
Mon, 18 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/80612016-01-18T00:00:00ZHood, Alan WilliamCargill, PeterBrowning, PhilippaTam, KuanFor the first time, we demonstrate how an MHD avalanche might occur in a multi-threaded coronal loop. Considering 23 non-potential magnetic threads within a loop, we use 3D MHD simulations to show that only one thread needs to be unstable in order to start an avalanche even when the others are below marginal stability. This has significant implications for coronal heating in that it provides for energy dissipation with a trigger mechanism. The instability of the unstable thread follows the evolution determined in many earlier investigations. However, once one stable thread is disrupted, it coalesces with a neighbouring thread and this process disrupts other nearby threads. Coalescence with these disrupted threads then occurs leading to the disruption of yet more threads as the avalanche develops. Magnetic energy is released in discrete bursts as the surrounding stable threads are disrupted. The volume integrated heating, as a function of time, shows short spikes suggesting that the temporal form of the heating is more like that of \textit{nanoflares} than of constant heating.Using species proportions to quantify turnover in biodiversity
http://hdl.handle.net/10023/8033
Quantifying species turnover is an important aspect of biodiversity monitoring. Turnover measures are usually based on species presence/absence data, reflecting the rate at which species are replaced. However, measures that reflect the rate at which individuals of a species are replaced by individuals of another species are far more sensitive to change. In this paper, we propose families of turnover measures that reflect changes in species proportions. We study the properties of our measures, and use simulation to assess their success in detecting turnover. Using data on the British farmland bird community from the breeding bird survey, we evaluate our measures to quantify temporal turnover and how it varies across the British mainland.
We are very grateful to all the volunteers who have contributed to the BBS. Yuan was funded by EPSRC/NERC grant EP/1000917/1. Harrison was funded by the Scottish Government’s Centre of Expertise ClimateXChange (www.climatexchange.org.uk).
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/80332016-06-01T00:00:00ZYuan, YuanBuckland, Stephen TerrenceHarrison, PhilFoss, SergeyJohnston, AlisonQuantifying species turnover is an important aspect of biodiversity monitoring. Turnover measures are usually based on species presence/absence data, reflecting the rate at which species are replaced. However, measures that reflect the rate at which individuals of a species are replaced by individuals of another species are far more sensitive to change. In this paper, we propose families of turnover measures that reflect changes in species proportions. We study the properties of our measures, and use simulation to assess their success in detecting turnover. Using data on the British farmland bird community from the breeding bird survey, we evaluate our measures to quantify temporal turnover and how it varies across the British mainland.Particle acceleration at reconnecting separator current layers
http://hdl.handle.net/10023/8001
The aim of this work is to investigate and characterise particle behaviour in a 3D MHD model of a reconnecting magnetic separator. We use a relativistic guiding-centre test-particle code to investigate electron and proton acceleration in snapshots from 3D MHD separator reconnection experiments, and compare the results with findings from an analytical separator reconnection model studied in a previous investigation. The behaviour (and acceleration) of large distributions of particles are examined in detail for both analytical and numerical separator reconnection models. Differences in acceleration sites are recovered and discussed, together with the dependence of final particle energy ranges upon the dimensions of the models and the stage of the (time-dependent) MHD reconnection event. We discuss the implications of these results for observed magnetic separators in the solar corona.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/80012016-01-01T00:00:00ZThrelfall, J.E. H. Stevenson, J.E. Parnell, C.Neukirch, T.The aim of this work is to investigate and characterise particle behaviour in a 3D MHD model of a reconnecting magnetic separator. We use a relativistic guiding-centre test-particle code to investigate electron and proton acceleration in snapshots from 3D MHD separator reconnection experiments, and compare the results with findings from an analytical separator reconnection model studied in a previous investigation. The behaviour (and acceleration) of large distributions of particles are examined in detail for both analytical and numerical separator reconnection models. Differences in acceleration sites are recovered and discussed, together with the dependence of final particle energy ranges upon the dimensions of the models and the stage of the (time-dependent) MHD reconnection event. We discuss the implications of these results for observed magnetic separators in the solar corona.Efficient abstracting of dive profiles using a broken-stick model
http://hdl.handle.net/10023/7972
For diving animals, animal-borne sensors are used to collect time-depth information for studying behaviour, ranging patterns and foraging ecology. Often, this information needs to be compressed for storage or transmission. Widely used devices called conductivity-temperature-depth satellite relay data loggers (CTD-SRDLs) sample time and depth at high resolution during a dive and then abstract the time-depth trajectory using a broken-stick model (BSM). This approximation method can summarize efficiently the curvilinear shape of a dive, using a piecewise linear shape with a small, fixed number of vertices, or break points. We present the process of abstracting dives using the BSM and quantify its performance, by measuring the uncertainty associated with the profiles it produces. We develop a method for obtaining a confidence zone and an index for the goodness-of-fit (dive zone index, DZI) for abstracted dive profiles. We validate our results with a case study using dives from elephant seals (Mirounga spp.). We use generalized additive models (GAMs) to determine whether the DZI can be used as a proxy for an absolute measure of fit and investigate the relationship between the DZI and the dive shape. We found a strong correlation between the residual sum of squares (RSS) for the difference between the detailed and abstracted profiles, and the DZI and maximum residual (R4), for dives resulting from CTD-SRDLs (69% deviance explained). On its own, the DZI explained a lower percentage of deviance which was variable for abstracted dives with different numbers of break points. We also found evidence for systematic differences in the DZI for different dive shapes (65% deviance explained). Although the proportional loss of information in the abstraction of time-depth dive profiles by BSM is high, what remains is sufficient to infer goodness-of-fit of the abstracted profile by reversing the abstraction process. Our results suggest that together the DZI and R4 can be used as a proxy for the RSS, and we present the method for obtaining these metrics for BSM-abstracted profiles.
This work was supported by SMRU Ltd (now SMRU Marine) in the form of a PhD fellowship (T.P.). Completion of the manuscript was supported by a National Research Foundation Scarce Skills Postdoctoral Fellowship at the University of Cape Town, South Africa (T.P.). The CTD-SRDL data presented in this manuscript were collected as part of a project funded by the Natural Environment Research Council (NERC) grants NE/E018289/1 and NER/D/S/2002/00426.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/79722015-03-01T00:00:00ZPhotopoulou, T.Lovell, PhilipFedak, M.A.Thomas, L.Matthiopoulos, J.For diving animals, animal-borne sensors are used to collect time-depth information for studying behaviour, ranging patterns and foraging ecology. Often, this information needs to be compressed for storage or transmission. Widely used devices called conductivity-temperature-depth satellite relay data loggers (CTD-SRDLs) sample time and depth at high resolution during a dive and then abstract the time-depth trajectory using a broken-stick model (BSM). This approximation method can summarize efficiently the curvilinear shape of a dive, using a piecewise linear shape with a small, fixed number of vertices, or break points. We present the process of abstracting dives using the BSM and quantify its performance, by measuring the uncertainty associated with the profiles it produces. We develop a method for obtaining a confidence zone and an index for the goodness-of-fit (dive zone index, DZI) for abstracted dive profiles. We validate our results with a case study using dives from elephant seals (Mirounga spp.). We use generalized additive models (GAMs) to determine whether the DZI can be used as a proxy for an absolute measure of fit and investigate the relationship between the DZI and the dive shape. We found a strong correlation between the residual sum of squares (RSS) for the difference between the detailed and abstracted profiles, and the DZI and maximum residual (R4), for dives resulting from CTD-SRDLs (69% deviance explained). On its own, the DZI explained a lower percentage of deviance which was variable for abstracted dives with different numbers of break points. We also found evidence for systematic differences in the DZI for different dive shapes (65% deviance explained). Although the proportional loss of information in the abstraction of time-depth dive profiles by BSM is high, what remains is sufficient to infer goodness-of-fit of the abstracted profile by reversing the abstraction process. Our results suggest that together the DZI and R4 can be used as a proxy for the RSS, and we present the method for obtaining these metrics for BSM-abstracted profiles.Well quasi-order in combinatorics : embeddings and homomorphisms
http://hdl.handle.net/10023/7963
The notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between ‘tame’ and ‘wild’ such classes. In this article we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics.
Wed, 01 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/79632015-07-01T00:00:00ZHuczynska, SophieRuskuc, NikThe notion of well quasi-order (wqo) from the theory of ordered sets often arises naturally in contexts where one deals with infinite collections of structures which can somehow be compared, and it then represents a useful discriminator between ‘tame’ and ‘wild’ such classes. In this article we survey such situations within combinatorics, and attempt to identify promising directions for further research. We argue that these are intimately linked with a more systematic and detailed study of homomorphisms in combinatorics.Expert elicitation of seasonal abundance of North Atlantic right whales Eubalaena glacialis in the mid-Atlantic
http://hdl.handle.net/10023/7921
North Atlantic right whales (Eubalaena glacialis; henceforth right whales) are among the most endangered large whales. Although protected since 1935, their abundance has remained low. Right whales occupy the Atlantic Ocean from southern Greenland and the Gulf of St. Lawrence south to Florida. The highly industrialized mid-Atlantic region is part of the species’ migratory corridor. Gaps in knowledge of the species’ movements through the mid-Atlantic limit informed management of stressors to the species. To contribute to filling of these gaps, we elicited estimates of the relative abundance of adult right whales in the mid-Atlantic during four months, representing each season, from ten experts. We elicited the minimum, maximum, and mode as the number of individuals in a hypothetical population of 100 right whales, and confidence estimates as percentages. For each month-sex combination, we merged the ten experts’ answers into one distribution. The estimated modes of relative abundances of both sexes were highest in January and April (females, 29 and 59; males, 22 and 23) and lowest in July and October (females, five and nine; males, three and five). In some cases, our elicitation results were consistent with the results of studies based on sightings data. However, these studies generally did not adjust for sampling effort, which was low and likely variable. Our results supplement the results of these studies and will increase the accuracy of priors in complementary Bayesian models of right whale abundances and movements through the mid-Atlantic.
This work was supported in part by US Office of Naval Research (ONR) grants to E.F.: N00014-09-1-0896 at University of California, Santa Barbara and N00014-12-1-0274 at University of California, Davis. This work was also supported by ONR grant N000141210286 to the University of St Andrews. In addition, we gratefully acknowledge funding for this work from The Marine Alliance for Science and Technology for Scotland (MASTS). MASTS is funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Wed, 04 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/79212015-11-04T00:00:00ZOedekoven, Cornelia SabrinaFleishman, EricaHamilton, PhilipClark, James S.Schick, Robert SchillingNorth Atlantic right whales (Eubalaena glacialis; henceforth right whales) are among the most endangered large whales. Although protected since 1935, their abundance has remained low. Right whales occupy the Atlantic Ocean from southern Greenland and the Gulf of St. Lawrence south to Florida. The highly industrialized mid-Atlantic region is part of the species’ migratory corridor. Gaps in knowledge of the species’ movements through the mid-Atlantic limit informed management of stressors to the species. To contribute to filling of these gaps, we elicited estimates of the relative abundance of adult right whales in the mid-Atlantic during four months, representing each season, from ten experts. We elicited the minimum, maximum, and mode as the number of individuals in a hypothetical population of 100 right whales, and confidence estimates as percentages. For each month-sex combination, we merged the ten experts’ answers into one distribution. The estimated modes of relative abundances of both sexes were highest in January and April (females, 29 and 59; males, 22 and 23) and lowest in July and October (females, five and nine; males, three and five). In some cases, our elicitation results were consistent with the results of studies based on sightings data. However, these studies generally did not adjust for sampling effort, which was low and likely variable. Our results supplement the results of these studies and will increase the accuracy of priors in complementary Bayesian models of right whale abundances and movements through the mid-Atlantic.Coprime invariable generation and minimal-exponent groups
http://hdl.handle.net/10023/7910
A finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders |g1|,. .,|gu| are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G.We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements.Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing |S|, the product of the number kπi(S) of conjugacy classes of πi-elements satisfies. ∏i=1ukπi(S)≤|S|2|OutS|.
Colva Roney-Dougal acknowledges the support of EPSRC grant EP/I03582X/1.
Sat, 01 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/79102015-08-01T00:00:00ZDetomi, EloisaLucchini, AndreaRoney-Dougal, C.M.A finite group G is coprimely invariably generated if there exists a set of generators {g1,. .,gu} of G with the property that the orders |g1|,. .,|gu| are pairwise coprime and that for all x1,. .,xu∈G the set {g1x1,. .,guxu} generates G.We show that if G is coprimely invariably generated, then G can be generated with three elements, or two if G is soluble, and that G has zero presentation rank. As a corollary, we show that if G is any finite group such that no proper subgroup has the same exponent as G, then G has zero presentation rank. Furthermore, we show that every finite simple group is coprimely invariably generated by two elements, except for O8+(2) which requires three elements.Along the way, we show that for each finite simple group S, and for each partition π1,. .,πu of the primes dividing |S|, the product of the number kπi(S) of conjugacy classes of πi-elements satisfies. ∏i=1ukπi(S)≤|S|2|OutS|.A model for selection of eyespots on butterfly wings
http://hdl.handle.net/10023/7904
Unsolved Problem The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation. However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. Key Idea and Model We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. Result We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.
The authors acknowledge financial support from the EPSRC grant EP/J016780/1. AM and CV acknowledge financial support from the Leverhulme Trust Research Project Grant (RPG-2014-149). This research was started while CV was visiting Japan as a 2013 Japanese Society for the Promotion of Science (JSPS) Summer Fellow (http://www.jsps.go.jp/). This research was finalized whilst TS, CV and AM were participants in the Isaac Newton Institute Program, Coupling Geometric PDEs with Physics for Cell Morphology, Motility and Pattern Formation. This work (AM) has received funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. AM was partially supported by a grant from the Simons Foundation.
Wed, 04 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/79042015-11-04T00:00:00ZSekimura, ToshioVenkataraman, ChandrasekharMadzvamuse, AnotidaUnsolved Problem The development of eyespots on the wing surface of butterflies of the family Nympalidae is one of the most studied examples of biological pattern formation. However, little is known about the mechanism that determines the number and precise locations of eyespots on the wing. Eyespots develop around signaling centers, called foci, that are located equidistant from wing veins along the midline of a wing cell (an area bounded by veins). A fundamental question that remains unsolved is, why a certain wing cell develops an eyespot, while other wing cells do not. Key Idea and Model We illustrate that the key to understanding focus point selection may be in the venation system of the wing disc. Our main hypothesis is that changes in morphogen concentration along the proximal boundary veins of wing cells govern focus point selection. Based on previous studies, we focus on a spatially two-dimensional reaction-diffusion system model posed in the interior of each wing cell that describes the formation of focus points. Using finite element based numerical simulations, we demonstrate that variation in the proximal boundary condition is sufficient to robustly select whether an eyespot focus point forms in otherwise identical wing cells. We also illustrate that this behavior is robust to small perturbations in the parameters and geometry and moderate levels of noise. Hence, we suggest that an anterior-posterior pattern of morphogen concentration along the proximal vein may be the main determinant of the distribution of focus points on the wing surface. In order to complete our model, we propose a two stage reaction-diffusion system model, in which an one-dimensional surface reaction-diffusion system, posed on the proximal vein, generates the morphogen concentrations that act as non-homogeneous Dirichlet (i.e., fixed) boundary conditions for the two-dimensional reaction-diffusion model posed in the wing cells. The two-stage model appears capable of generating focus point distributions observed in nature. Result We therefore conclude that changes in the proximal boundary conditions are sufficient to explain the empirically observed distribution of eyespot focus points on the entire wing surface. The model predicts, subject to experimental verification, that the source strength of the activator at the proximal boundary should be lower in wing cells in which focus points form than in those that lack focus points. The model suggests that the number and locations of eyespot foci on the wing disc could be largely controlled by two kinds of gradients along two different directions, that is, the first one is the gradient in spatially varying parameters such as the reaction rate along the anterior-posterior direction on the proximal boundary of the wing cells, and the second one is the gradient in source values of the activator along the veins in the proximal-distal direction of the wing cell.Magneto-static modeling of the mixed plasma Beta solar atmosphere based on SUNRISE/IMaX data
http://hdl.handle.net/10023/7887
Our aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be force-free (the Lorentz-force vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken self-consistently into account and compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here we apply a linear approach, where the electric current density consists of a superposition of a field-line parallel current and a current perpendicular to the Sun’s gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a non-linear model.
TN acknowledges support by the U.K.’s Science and Technology Facilities Council and would like to thank the MPS for its hospitality during a visit in December 2014.
Tue, 01 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/78872015-12-01T00:00:00ZWiegelmann, ThomasNeukirch, ThomasNickeler, DieterSolanki, SamiMartinez Pillet, ValentinBorrero, Juan ManuleOur aim is to model the 3D magnetic field structure of the upper solar atmosphere, including regions of non-negligible plasma beta. We use high-resolution photospheric magnetic field measurements from SUNRISE/IMaX as boundary condition for a magneto-static magnetic field model. The high resolution of IMaX allows us to resolve the interface region between photosphere and corona, but modelling this region is challenging for the following reasons. While the coronal magnetic field is thought to be force-free (the Lorentz-force vanishes), this is not the case in the mixed plasma β environment in the photosphere and lower chromosphere. In our model, pressure gradients and gravity forces are taken self-consistently into account and compensate the non-vanishing Lorentz-force. Above a certain height (about 2 Mm) the non-magnetic forces become very weak and consequently the magnetic field becomes almost force-free. Here we apply a linear approach, where the electric current density consists of a superposition of a field-line parallel current and a current perpendicular to the Sun’s gravity field. We illustrate the prospects and limitations of this approach and give an outlook for an extension towards a non-linear model.The appearance, motion, and disappearance of three-dimensional magnetic null points
http://hdl.handle.net/10023/7868
While theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.
N.A.M. acknowledges support from NASA grants NNX11AB61G, NNX12AB25G, and NNX15AF43G; NASA contract NNM07AB07C; and NSF SHINE grants AGS-1156076 and AGS-1358342 to SAO. C.E.P. acknowledges support from the St Andrews 2013 STFC Consolidated grant.
Fri, 30 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/78682015-10-30T00:00:00ZA. Murphy, NicholasParnell, Clare ElizabethHaynes, Andrew LewisWhile theoretical models and simulations of magnetic reconnection often assume symmetry such that the magnetic null point when present is co-located with a flow stagnation point, the introduction of asymmetry typically leads to non-ideal flows across the null point. To understand this behavior, we present exact expressions for the motion of three-dimensional linear null points. The most general expression shows that linear null points move in the direction along which the magnetic field and its time derivative are antiparallel. Null point motion in resistive magnetohydrodynamics results from advection by the bulk plasma flow and resistive diffusion of the magnetic field, which allows non-ideal flows across topological boundaries. Null point motion is described intrinsically by parameters evaluated locally; however, global dynamics help set the local conditions at the null point. During a bifurcation of a degenerate null point into a null-null pair or the reverse, the instantaneous velocity of separation or convergence of the null-null pair will typically be infinite along the null space of the Jacobian matrix of the magnetic field, but with finite components in the directions orthogonal to the null space. Not all bifurcating null-null pairs are connected by a separator. Furthermore, except under special circumstances, there will not exist a straight line separator connecting a bifurcating null-null pair. The motion of separators cannot be described using solely local parameters because the identification of a particular field line as a separator may change as a result of non-ideal behavior elsewhere along the field line.Dimension and measure theory of self-similar structures with no separation condition
http://hdl.handle.net/10023/7854
We introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on non-overlapping self-similar sets to overlapping self-similar sets.
We investigate how the Hausdorff dimension and measure of a self-similar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a self-similar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj - ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any self-similar or graph directed self-similar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `self-similar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δ-approximate packing pre-measure coincide for sufficiently small δ > 0.
Mon, 30 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/78542015-11-30T00:00:00ZFarkas, ÁbelWe introduce methods to cope with self-similar sets when we do not assume any separation condition. For a self-similar set K ⊆ ℝᵈ we establish a similarity dimension-like formula for Hausdorff dimension regardless of any separation condition. By the application of this result we deduce that the Hausdorff measure and Hausdorff content of K are equal, which implies that K is Ahlfors regular if and only if Hᵗ (K) > 0 where t = dim[sub]H K. We further show that if t = dim[sub]H K < 1 then Hᵗ (K) > 0 is also equivalent to the weak separation property. Regarding Hausdorff dimension, we give a dimension approximation method that provides a tool to generalise results on non-overlapping self-similar sets to overlapping self-similar sets.
We investigate how the Hausdorff dimension and measure of a self-similar set
K ⊆ ℝᵈ behave under linear mappings. This depends on the nature of the group T generated by the orthogonal parts of the defining maps of K. We show that if T is finite then every linear image of K is a graph directed attractor and there exists at least one projection of K such that the dimension drops under projection. In general, with no restrictions on T we establish that Hᵗ (L ∘ O(K)) = Hᵗ (L(K)) for every element O of the closure of T , where L is a linear map and t = dim[sub]H K. We also prove that for disjoint subsets A and B of K we have that Hᵗ (L(A) ∩ L(B)) = 0. Hochman and Shmerkin showed that if T is dense in SO(d; ℝ) and the strong separation condition is satisfied then dim[sub]H (g(K)) = min {dim[sub]H K; l} for every continuously differentiable map g of rank l. We deduce the same result without any separation condition and we generalize a result of Eroğlu by obtaining that Hᵗ (g(K)) = 0.
We show that for the attractor (K1, … ,Kq) of a graph directed iterated function system, for each 1 ≤ j ≤ q and ε > 0 there exists a self-similar set K ⊆ Kj that satisfies the strong separation condition and dim[sub]H Kj - ε < dim[sub]H K. We show that we can further assume convenient conditions on the orthogonal parts and similarity ratios of the defining similarities of K. Using this property we obtain results on a range of topics including on dimensions of projections, intersections, distance sets and sums and products of sets.
We study the situations where the Hausdorff measure and Hausdorff content of a set are equal in the critical dimension. Our main result here shows that this equality holds for any subset of a set corresponding to a nontrivial cylinder of an irreducible subshift of finite type, and thus also for any self-similar or graph directed self-similar set, regardless of separation conditions. The main tool in the proof is an exhaustion lemma for Hausdorff measure based on the Vitali's Covering Theorem. We also give several examples showing that one cannot hope for the equality to hold in general if one moves in a number of the natural directions away from `self-similar'. Finally we consider an analogous version of the problem for packing measure. In this case we need the strong separation condition and can only prove that the packing measure and δ-approximate packing pre-measure coincide for sufficiently small δ > 0.Acoustic sequences in non-human animals : a tutorial review and prospectus
http://hdl.handle.net/10023/7848
Animal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the well-known example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and near-future knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorial-style introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.
Mon, 01 Feb 2016 00:00:00 GMThttp://hdl.handle.net/10023/78482016-02-01T00:00:00ZKershenbaum, ArikBlumstein, DanRoch, MarieAkçay, ÇaglarBackus, GregoryBee, Mark A.Bohn, KirstenCao, YanCarter, GeraldCäsar, CristianeCoen, MichaelDe Ruiter, Stacy LynnDoyle, LauranceEdelman, ShimonFerrer-i-Cancho, RamonFreeberg, Todd M.Garland, Ellen ClareGustison, MorganHarley, Heidi E.Huetz, ChloéHughes, MelissaBruno, Julia HylandIlany, AmiyaalJin, Dezhe Z.Johnson, MichaelJu, ChenghuiKarnowski, JeremyLohr, BernardManser, MartaMcCowan, BrendaMercado III, EduardoNarins, Peter M.Piel, AlexRice, MeganSalmi, RobertaSasahara, KazutoshiSayigh, LaelaShiu, YuTaylor, CharlesVallejo, Edgar E.Waller, SaraZamora-Gutierrez, VeronicaAnimal acoustic communication often takes the form of complex sequences, made up of multiple distinct acoustic units. Apart from the well-known example of birdsong, other animals such as insects, amphibians,and mammals (including bats, rodents, primates, and cetaceans) also generate complex acoustic sequences. Occasionally, such as with birdsong, the adaptive role of these sequences seems clear (e.g. mate attraction and territorial defence). More often however, researchers have only begun to characterise – let alone understand – the significance and meaning of acoustic sequences. Hypotheses abound, but there is little agreement as to how sequences should be defined and analysed. Our review aims to outline suitable methods for testing these hypotheses, and to describe the major limitations to our current and near-future knowledge on questions of acoustic sequences. This review and prospectus is the result of a collaborative effort between 43 scientists from the fields of animal behaviour, ecology and evolution, signal processing, machine learning,quantitative linguistics, and information theory, who gathered for a 2013 workshop entitled, ‘Analysing vocal sequences in animals’. Our goal is to present not just a review of the state of the art, but to propose a methodological framework that summarises what we suggest are the best practices for research in this field,across taxa and across disciplines. We also provide a tutorial-style introduction to some of the most promising algorithmic approaches for analysing sequences. We divide our review into three sections: identifying the distinct units of an acoustic sequence, describing the different ways that information can be contained within a sequence, and analysing the structure of that sequence. Each of these sections is further subdivided to address the key questions and approaches in that area. We propose a uniform, systematic, and comprehensive approach to studying sequences, with the goal of clarifying research terms used in different fields, and facilitating collaboration and comparative studies. Allowing greater interdisciplinary collaboration will facilitate the investigation of many important questions in the evolution of communication and sociality.Dose response severity functions for acoustic disturbance in cetaceans using recurrent event survival analysis
http://hdl.handle.net/10023/7845
Behavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of free-ranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is dose-response functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and long-finned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting dose-response severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.
Fri, 20 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/78452015-11-20T00:00:00ZHarris, Catriona MSadykova, DinaraDe Ruiter, Stacy LynnTyack, Peter LloydMiller, PatrickKvadsheim, PetterLam, Frans-PeterThomas, LenBehavioral response studies (BRSs) aim to enhance our understanding of the behavior changes made by animals in response to specific exposure levels of different stimuli, often presented in an increasing dosage. Here, we focus on BRSs that aim to understand behavioral responses of free-ranging whales and dolphins to manmade acoustic signals (although the methods are applicable more generally). One desired outcome of these studies is dose-response functions relevant to different species, signals and contexts. We adapted and applied recurrent event survival analysis (Cox proportional hazard models) to data from the 3S BRS project, where multiple behavioral responses of different severities had been observed per experimental exposure and per individual based upon expert scoring. We included species, signal type, exposure number and behavioral state prior to exposure as potential covariates. The best model included all main effect terms, with the exception of exposure number, as well as two interaction terms. The interactions between signal and behavioral state, and between species and behavioral state highlighted that the sensitivity of animals to different signal types (a 6–7 kHz upsweep sonar signal [MFAS] or a 1–2 kHz upsweep sonar signal [LFAS]) depended on their behavioral state (feeding or nonfeeding), and this differed across species. Of the three species included in this analysis (sperm whale [Physeter macrocephalus], killer whale [Orcinus orca] and long-finned pilot whale [Globicephala melas]), killer whales were consistently the most likely to exhibit behavioral responses to naval sonar exposure. We conclude that recurrent event survival analysis provides an effective framework for fitting dose-response severity functions to data from behavioral response studies. It can provide outputs that can help government and industry to evaluate the potential impacts of anthropogenic sound production in the ocean.Speed of convergence for laws of rare events and escape rates
http://hdl.handle.net/10023/7837
We obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.
MT was partially supported by NSF grant DMS 1109587. All authors are supported by FCT (Portugal) projects PTDC/MAT/099493/2008 and PTDC/MAT/120346/2010, which are financed by national and European structural funds through the programs FEDER and COMPETE. All three authors were also supported by CMUP, which is financed by FCT (Portugal) through the programs POCTI and POSI, with national and European structural funds, under the project PEst-C/MAT/UI0144/2013.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/78372015-04-01T00:00:00ZFreitas, AnaFreitas, JorgeTodd, Michael JohnWe obtain error terms on the rate of convergence to Extreme Value Laws, and to the asymptotic Hitting Time Statistics, for a general class of weakly dependent stochastic processes. The dependence of the error terms on the ‘time’ and ‘length’ scales is very explicit. Specialising to data derived from a class of dynamical systems we find even more detailed error terms, one application of which is to consider escape rates through small holes in these systems.A general framework for animal density estimation from acoustic detections across a fixed microphone array
http://hdl.handle.net/10023/7786
Acoustic monitoring can be an efficient, cheap, non-invasive alternative to physical trapping of individuals. Spatially explicit capture-recapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate time-of-arrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.
Funding for the frog survey was received from the National Geographic Society/Waitt Grants Program (No. W184-11). The EPSRC and NERC helped to fund this research through a PhD grant (No. EP/I000917/1).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/77862015-01-01T00:00:00ZStevenson, B.C.Borchers, D.L.Altwegg, R.Swift, R.J.Gillespie, D.M.Measey, G.J.Acoustic monitoring can be an efficient, cheap, non-invasive alternative to physical trapping of individuals. Spatially explicit capture-recapture (SECR) methods have been proposed to estimate calling animal abundance and density from data collected by a fixed array of microphones. However, these methods make some assumptions that are unlikely to hold in many situations, and the consequences of violating these are yet to be investigated. We generalize existing acoustic SECR methodology, enabling these methods to be used in a much wider variety of situations. We incorporate time-of-arrival (TOA) data collected by the microphone array, increasing the precision of calling animal density estimates. We use our method to estimate calling male density of the Cape Peninsula Moss Frog Arthroleptella lightfooti. Our method gives rise to an estimator of calling animal density that has negligible bias, and 95% confidence intervals with appropriate coverage. We show that using TOA information can substantially improve estimate precision. Our analysis of the A. lightfooti data provides the first statistically rigorous estimate of calling male density for an anuran population using a microphone array. This method fills a methodological gap in the monitoring of frog populations and is applicable to acoustic monitoring of other species that call or vocalize.Passive acoustic monitoring of beaked whale densities in the Gulf of Mexico
http://hdl.handle.net/10023/7779
Beaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min time-bins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.
Funding to support the tag data was also received from the MASTS pooling initiative (The Marine Alliance for Science and Technology for Scotland) funded by the Scottish Funding Council (grant reference HR09011) and contributing institutions.
Thu, 12 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/77792015-11-12T00:00:00ZHildebrand, JohnBaumann-Pickering, SimoneFrasier, KaitlinTrickey, JenniferMerkens, KarlinaWiggins, SeanMcDonald, MarkGarrison, LanceHarris, DanielleMarques, Tiago A.Thomas, LenBeaked whales are deep diving elusive animals, difficult to census with conventional visual surveys. Methods are presented for the density estimation of beaked whales, using passive acoustic monitoring data collected at sites in the Gulf of Mexico (GOM) from the period during and following the Deepwater Horizon oil spill (2010–2013). Beaked whale species detected include: Gervais’ (Mesoplodon europaeus), Cuvier’s (Ziphius cavirostris), Blainville’s (Mesoplodon densirostris) and an unknown species of Mesoplodon sp. (designated as Beaked Whale Gulf — BWG). For Gervais’ and Cuvier’s beaked whales, we estimated weekly animal density using two methods, one based on the number of echolocation clicks, and another based on the detection of animal groups during 5 min time-bins. Density estimates derived from these two methods were in good general agreement. At two sites in the western GOM, Gervais’ beaked whales were present throughout the monitoring period, but Cuvier’s beaked whales were present only seasonally, with periods of low density during the summer and higher density in the winter. At an eastern GOM site, both Gervais’ and Cuvier’s beaked whales had a high density throughout the monitoring period.On simultaneous local dimension functions of subsets of Rd
http://hdl.handle.net/10023/7778
For a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.
Date of Acceptance: 04/05/2015
Wed, 30 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/77782015-09-30T00:00:00ZOlsen, Lars Ole RonnowFor a subset E ⊑ Rd and x ∈ Rd, the local Hausdorff dimension function of E at x and the local packing dimension function of E at x are defined by (Formula presented.) where dimH and dimP denote the Hausdorff dimension and the packing dimension, respectively. In this note we give a short and simple proof showing that for any pair of continuous functions f,g: Rd → [0, d] with f ≤ g, it is possible to choose a set E that simultaneously has f as its local Hausdorff dimension function and g as its local packing dimension function.Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA
http://hdl.handle.net/10023/7772
In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard line-transect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present year-round in the study area. Using photo-identification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the three-year period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10023/77722014-01-01T00:00:00ZRead, Andrew, J.Barco, S.Bell, J.Borchers, David LouisBurt, M LouiseCummings, E.W.Dunn, J.Fougeres, J.Hazen, L.Williams-Hodge, L.E.Laura, A-M.McAlarney, R.J.Nilsson, P.Pabst, D.A.Paxton, Charles G. M.Schneider, S.Z.Urian, KimWaples, D.M.McLellan, W.A.In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard line-transect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present year-round in the study area. Using photo-identification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the three-year period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.Near-threshold electron injection in the laser-plasma wakefield accelerator leading to femtosecond bunches
http://hdl.handle.net/10023/7750
The laser-plasma wakefield accelerator is a compact source of high brightness, ultra-short duration electron bunches. Self-injection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubble-shaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from self-injection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density build-up in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultra-short electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.
We gratefully acknowledge the support of the UK EPSRC (grant no. EP/J018171/1), the EU FP7 programmes: the Extreme Light Infrastructure (ELI) project, the Laserlab-Europe (no. 284464), and the EUCARD-2 project (no. 312453).
Thu, 17 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/77502015-09-17T00:00:00ZIslam, M.R.Brunetti, E.Shanks, R.P.Ersfeld, B.Issac, R.C.Cipiccia, S.Anania, M.P.Welsh, G.H.Wiggins, S.M.Noble, A.Cairns, R AlanRaj, G.Jaroszynski, D.A.The laser-plasma wakefield accelerator is a compact source of high brightness, ultra-short duration electron bunches. Self-injection occurs when electrons from the background plasma gain sufficient momentum at the back of the bubble-shaped accelerating structure to experience sustained acceleration. The shortest duration and highest brightness electron bunches result from self-injection close to the threshold for injection. Here we show that in this case injection is due to the localized charge density build-up in the sheath crossing region at the rear of the bubble, which has the effect of increasing the accelerating potential to above a critical value. Bunch duration is determined by the dwell time above this critical value, which explains why single or multiple ultra-short electron bunches with little dark current are formed in the first bubble. We confirm experimentally, using coherent optical transition radiation measurements, that single or multiple bunches with femtosecond duration and peak currents of several kiloAmpere, and femtosecond intervals between bunches, emerge from the accelerator.Future capabilities of CME polarimetric 3D reconstructions with the METIS instrument : a numerical test
http://hdl.handle.net/10023/7748
Context. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from white-light (total and polarized brightness) images, the polarization ratio technique is widely used. The soon-to-be-launched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS white-light (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from white-light images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and white-light images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.
D.H.M. would like to thank STFC and the Leverhulme Trust for their financial support. P.P. would like to thank STFC and the Leverhulme Trust. The computational work for this paper was carried out on the joint STFC and SFC (SRIF) funded cluster at the University of St Andrews (Scotland, UK).
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/77482015-10-01T00:00:00ZPagano, PaoloBemporad, AMackay, Duncan HendryContext. Understanding the 3D structure of coronal mass ejections (CMEs) is crucial for understanding the nature and origin of solar eruptions. However, owing to the optical thinness of the solar corona we can only observe the line of sight integrated emission. As a consequence the resulting projection effects hide the true 3D structure of CMEs. To derive information on the 3D structure of CMEs from white-light (total and polarized brightness) images, the polarization ratio technique is widely used. The soon-to-be-launched METIS coronagraph on board Solar Orbiter will use this technique to produce new polarimetric images. Aims. This work considers the application of the polarization ratio technique to synthetic CME observations from METIS. In particular we determine the accuracy at which the position of the centre of mass, direction and speed of propagation, and the column density of the CME can be determined along the line of sight. Methods. We perform a 3D MHD simulation of a flux rope ejection where a CME is produced. From the simulation we (i) synthesize the corresponding METIS white-light (total and polarized brightness) images and (ii) apply the polarization ratio technique to these synthesized images and compare the results with the known density distribution from the MHD simulation. In addition, we use recent results that consider how the position of a single blob of plasma is measured depending on its projected position in the plane of the sky. From this we can interpret the results of the polarization ratio technique and give an estimation of the error associated with derived parameters. Results. We find that the polarization ratio technique reproduces with high accuracy the position of the centre of mass along the line of sight. However, some errors are inherently associated with this determination. The polarization ratio technique also allows information to be derived on the real 3D direction of propagation of the CME. The determination of this is of fundamental importance for future space weather forecasting. In addition, we find that the column density derived from white-light images is accurate and we propose an improved technique where the combined use of the polarization ratio technique and white-light images minimizes the error in the estimation of column densities. Moreover, by applying the comparison to a set of snapshots of the simulation we can also assess the errors related to the trajectory and the expansion of the CME. Conclusions. Our method allows us to thoroughly test the performance of the polarization ratio technique and allows a determination of the errors associated with it, which means that it can be used to quantify the results from the analysis of the forthcoming METIS observations in white light (total and polarized brightness). Finally, we describe a satellite observing configuration relative to the Earth that can allow the technique to be efficiently used for space weather predictions.Corotating interaction regions as seen by the STEREO Heliospheric Imagers 2007 – 2010
http://hdl.handle.net/10023/7746
NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solar-wind streams ejected from source regions on the solar surface that rotate with the Sun. High-density plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solar-wind transients associated with 40 CIRs detected by the HI instrument onboard the STEREO-A spacecraft between 2007 and 2010. We identify in-situ signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the in-situ parameters with the HI results. We note that solar-wind transients associated with CIRs appear to travel at or close to the slow solar-wind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solar-wind transients by considering variability in the solar wind.
T.M. Conlon and A.O. Williams were supported by an STFC, UK studentship and S.E. Milan was supported by STFC grant ST/K001000/1. Date of Acceptance: 08/08/2015
Sat, 01 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/77462015-08-01T00:00:00ZConlon, Thomas MichaelMilan, S.E.Davies, J.A.Williams, A.O.NASA’s Solar Terrestrial Relations Observatory (STEREO) mission has coincided with a pronounced solar minimum. This allowed for easier detection of corotating interaction regions (CIRs). CIRs are formed by the interaction between fast and slow solar-wind streams ejected from source regions on the solar surface that rotate with the Sun. High-density plasma blobs that have become entrained at the stream interface can be tracked out to large elongations in data from the Heliospheric Imager (HI) instruments onboard STEREO. These blobs act as tracers of the CIR itself such that their HI signatures can be used to estimate CIR source location and radial speed. We estimate the kinematic properties of solar-wind transients associated with 40 CIRs detected by the HI instrument onboard the STEREO-A spacecraft between 2007 and 2010. We identify in-situ signatures of these transients at L1 using the Advanced Composition Explorer (ACE) and compare the in-situ parameters with the HI results. We note that solar-wind transients associated with CIRs appear to travel at or close to the slow solar-wind speed preceding the event as measured in situ. We also highlight limitations in the commonly used analysis techniques of solar-wind transients by considering variability in the solar wind.Status and future of research on the behavioural responses of marine mammals to U.S. Navy sonar
http://hdl.handle.net/10023/7741
A review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 21-22 April 2015 in Monterey, California. Workshop attendees were key representatives of Navy-funded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of short-term behavioral response to long-term fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longer-term monitoring of animals before and after exposure is emphasized throughout.
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/77412015-01-01T00:00:00ZHarris, Catriona MThomas, LenA review of the status and future of research into behavioral responses of marine mammals to naval sonar exposure was undertaken to evaluate the return on investment of current US Navy funded programs, identify the data needs and the contributions of current research programs to meeting data needs, and determine the ability to meet outstanding data needs given the current state of technology. As part of this review, a workshop was held from 21-22 April 2015 in Monterey, California. Workshop attendees were key representatives of Navy-funded behavioral response studies, as well as three external reviewers who were selected because of their expertise in animal behavior and behavioral responses to anthropogenic stimuli in the aquatic and terrestrial environments. Prior to the workshop, a questionnaire was circulated to canvass the opinions of members of the scientific community (primarily workshop attendees exclusive of external reviewers) on each of the research approaches taken to address this topic. The workshop was then structured around the questionnaire and responses received, via a series of discussion sessions. Afterwards, each research approach was evaluated independently by the external reviewers. This report presents a synthesis of the evaluations and recommendations of the external reviewers on current and future behavioral response research relevant to naval sonar. All reviewers agreed that excellent progress has been made on this topic and that each of the research approaches has contributed to our understanding of cetacean responses to naval sonar. The report includes specific comments and recommendations of the reviewers relevant to each approach, but also includes suggestions for priority species and a comprehensive list of recommendations for the future of BRS research in general (Tables 1 and 2). In summary it was recommended that BRS research be continued and extended to increase sample sizes and experimental replication, and temporal duration and spatial scale including more research in areas where the animals are presumably more naïve than on the naval ranges. It was noted that future investigations would benefit from combining experimentation and observation to enable linkage of short-term behavioral response to long-term fitness consequences of repeated exposure. Beaked whales were the species group ranked highest in terms of research priority. The importance of baseline studies and longer-term monitoring of animals before and after exposure is emphasized throughout.Observational signatures of waves and flows in the solar corona
http://hdl.handle.net/10023/7722
Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magneto-acoustic waves and/or as quasi-periodic upflows remains unresolved. We used forward-modelling to construct observational signatures associated with a simple slow magneto-acoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) line-of-sight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be model-dependent.
DM acknowledges support of a Royal Society University Research Fellowship and a KU Leuven Research Council senior research fellowship (SF/12/008). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/2007-2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet ). TVD has been sponsored by an Odysseus grant of the FWO Vlaanderen. The research was performed in the context of the IAP P7/08 CHARM (Belspo) and the GOA-2015-014 (KU Leuven). TVD acknowledges the funding from the FP7 ERG grant with number 276808.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/77222015-02-01T00:00:00ZDe Moortel, I.Antolin, PatrickVan Doorsselaere, T.Propagating perturbations have been observed in extended coronal loop structures for a number of years, but the interpretation in terms of slow (propagating) magneto-acoustic waves and/or as quasi-periodic upflows remains unresolved. We used forward-modelling to construct observational signatures associated with a simple slow magneto-acoustic wave or periodic flow model. Observational signatures were computed for the 171 Å Fe ix and the 193 Å Fe xii spectral lines. Although there are many differences between the flow and wave models, we did not find any clear, robust observational characteristics that can be used in isolation (i.e. that do not rely on a comparison between the models). For the waves model, a relatively rapid change of the average line widths as a function of (shallow) line-of-sight angles was found, whereas the ratio of the line width amplitudes to the Doppler velocity amplitudes is relatively high for the flow model. The most robust observational signature found is that the ratio of the mean to the amplitudes of the Doppler velocity is always higher than one for the flow model. This ratio is substantially higher for flows than for waves, and for the flows model used in the study is exactly the same in the 171 Å Fe ix and the 193 Å Fe xii spectral lines. However, these potential observational signatures need to be treated cautiously because they are likely to be model-dependent.A description of LATTE outputs
http://hdl.handle.net/10023/7720
Fri, 30 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/77202015-10-30T00:00:00ZMarques, Tiago A.Thomas, LenDigit frequencies and Bernoulli convolutions
http://hdl.handle.net/10023/7719
It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).
This work was supported partly by the Dutch Organisation for Scientific Research (NWO) grant number 613.001.022 and partly by the Engineering and Physical Sciences Research Council grant number EP/K029061/1.
Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/77192014-06-27T00:00:00ZKempton, Thomas Michael WilliamIt is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).Self-affine sets with positive Lebesgue measure
http://hdl.handle.net/10023/7718
Using techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.
Fri, 27 Jun 2014 00:00:00 GMThttp://hdl.handle.net/10023/77182014-06-27T00:00:00ZDajani, KarmaJiang, KanKempton, Thomas Michael WilliamUsing techniques introduced by C. Gunturk, we prove that the attractors of a family of overlapping self-affine iterated function systems contain a neighbourhood of zero for all parameters in a certain range. This corresponds to giving conditions under which a single sequence may serve as a ‘simultaneous β-expansion’ of different numbers in different bases.Multiscale modelling of cancer progression and treatment control : the role of intracellular heterogeneities in chemotherapy treatment
http://hdl.handle.net/10023/7714
Cancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cell-cycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multi-drug and cell-cycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the sub-cellular, cellular and microenvironmental levels to study the effects of cell-cycle, phase-specific chemotherapy on the growth and progression of cancer cells.
Mon, 01 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/77142015-06-01T00:00:00ZChaplain, Mark Andrew JosephPowathil, GibinCancer is a complex, multiscale process involving interactions at intracellular, intercellular and tissue scales that are in turn susceptible to microenvironmental changes. Each individual cancer cell within a cancer cell mass is unique, with its own internal cellular pathways and biochemical interactions. These interactions contribute to the functional changes at the cellular and tissue scale, creating a heterogenous cancer cell population. Anticancer drugs are effective in controlling cancer growth by inflicting damage to various target molecules and thereby triggering multiple cellular and intracellular pathways, leading to cell death or cell-cycle arrest. One of the major impediments in the chemotherapy treatment of cancer is drug resistance driven by multiple mechanisms, including multi-drug and cell-cycle mediated resistance to chemotherapy drugs. In this article, we discuss two hybrid multiscale modelling approaches, incorporating multiple interactions involved in the sub-cellular, cellular and microenvironmental levels to study the effects of cell-cycle, phase-specific chemotherapy on the growth and progression of cancer cells.Systems oncology : towards patient-specific treatment regimes informed by multiscale mathematical modelling
http://hdl.handle.net/10023/7713
The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/77132015-02-01T00:00:00ZPowathil, Gibin G.Swat, MaciejChaplain, Mark A. J.The multiscale complexity of cancer as a disease necessitates a corresponding multiscale modelling approach to produce truly predictive mathematical models capable of improving existing treatment protocols. To capture all the dynamics of solid tumour growth and its progression, mathematical modellers need to couple biological processes occurring at various spatial and temporal scales (from genes to tissues). Because effectiveness of cancer therapy is considerably affected by intracellular and extracellular heterogeneities as well as by the dynamical changes in the tissue microenvironment, any model attempt to optimise existing protocols must consider these factors ultimately leading to improved multimodal treatment regimes. By improving existing and building new mathematical models of cancer, modellers can play important role in preventing the use of potentially sub-optimal treatment combinations. In this paper, we analyse a multiscale computational mathematical model for cancer growth and spread, incorporating the multiple effects of radiation therapy and chemotherapy in the patient survival probability and implement the model using two different cell based modelling techniques. We show that the insights provided by such multiscale modelling approaches can ultimately help in designing optimal patient-specific multi-modality treatment protocols that may increase patients quality of life.Mathematical modelling of cancer invasion : implications of cell adhesion variability for tumour infiltrative growth patterns
http://hdl.handle.net/10023/7712
Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many inter-related genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cell-cell and cell-matrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumour-induced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatio-temporal dynamics of a model of cancer invasion, where cell-cell and cell-matrix adhesion is accounted for through non-local interaction terms in a system of partial integro-differential equations. The change of adhesion properties during cancer growth and development is investigated here through time-dependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).
Fri, 21 Nov 2014 00:00:00 GMThttp://hdl.handle.net/10023/77122014-11-21T00:00:00ZDomschke, PiaTrucu, DumitruGerisch, AlfChaplain, Mark A. J.Cancer invasion, recognised as one of the hallmarks of cancer, is a complex, multiscale phenomenon involving many inter-related genetic, biochemical, cellular and tissue processes at different spatial and temporal scales. Central to invasion is the ability of cancer cells to alter and degrade an extracellular matrix. Combined with abnormal excessive proliferation and migration which is enabled and enhanced by altered cell-cell and cell-matrix adhesion, the cancerous mass can invade the neighbouring tissue. Along with tumour-induced angiogenesis, invasion is a key component of metastatic spread, ultimately leading to the formation of secondary tumours in other parts of the host body. In this paper we explore the spatio-temporal dynamics of a model of cancer invasion, where cell-cell and cell-matrix adhesion is accounted for through non-local interaction terms in a system of partial integro-differential equations. The change of adhesion properties during cancer growth and development is investigated here through time-dependent adhesion characteristics within the cell population as well as those between the cells and the components of the extracellular matrix. Our computational simulation results demonstrate a range of heterogeneous dynamics which are qualitatively similar to the invasive growth patterns observed in a number of different types of cancer, such as tumour infiltrative growth patterns (INF).Stochastic modelling of chromosomal segregation : errors can introduce correction
http://hdl.handle.net/10023/7711
Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.
Tue, 01 Jul 2014 00:00:00 GMThttp://hdl.handle.net/10023/77112014-07-01T00:00:00ZMatzavinos, AnastasiosRoitershtein, AlexanderShtylla, BlertaVoller, ZacharyLiu, SijiaChaplain, Mark A.J.Cell division is a complex process requiring the cell to have many internal checks so that division may proceed and be completed correctly. Failure to divide correctly can have serious consequences, including progression to cancer. During mitosis, chromosomal segregation is one such process that is crucial for successful progression. Accurate segregation of chromosomes during mitosis requires regulation of the interactions between chromosomes and spindle microtubules. If left uncorrected, chromosome attachment errors can cause chromosome segregation defects which have serious effects on cell fates. In early prometaphase, where kinetochores are exposed to multiple microtubules originating from the two poles, there are frequent errors in kinetochore-microtubule attachment. Erroneous attachments are classified into two categories, syntelic and merotelic. In this paper, we consider a stochastic model for a possible function of syntelic and merotelic kinetochores, and we provide theoretical evidence that merotely can contribute to lessening the stochastic noise in the time for completion of the mitotic process in eukaryotic cells.Mathematical modeling of tumor growth and treatment
http://hdl.handle.net/10023/7710
Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. So-called in silico trials that predict patient-specific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10023/77102014-01-01T00:00:00ZEnderling, HeikoChaplain, Mark A. J.Using mathematical models to simulate dynamic biological processes has a long history. Over the past couple of decades or so, quantitative approaches have also made their way into cancer research. An increasing number of mathematical, physical, computational and engineering techniques have been applied to various aspects of tumor growth, with the ultimate goal of understanding the response of the cancer population to clinical intervention. So-called in silico trials that predict patient-specific response to various dose schedules or treatment combinations and sequencing are on the way to becoming an invaluable tool to optimize patient care. Herein we describe fundamentals of mathematical modeling of tumor growth and tumor-host interactions, and summarize some of the seminal and most prominent approaches.Mean field analysis of a spatial stochastic model of a gene regulatory network
http://hdl.handle.net/10023/7709
A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/77092015-10-01T00:00:00ZSturrock, M.Murray, P. J.Matzavinos, A.Chaplain, M. A. J.A gene regulatory network may be defined as a collection of DNA segments which interact with each other indirectly through their RNA and protein products. Such a network is said to contain a negative feedback loop if its products inhibit gene transcription, and a positive feedback loop if a gene product promotes its own production. Negative feedback loops can create oscillations in mRNA and protein levels while positive feedback loops are primarily responsible for signal amplification. It is often the case in real biological systems that both negative and positive feedback loops operate in parameter regimes that result in low copy numbers of gene products. In this paper we investigate the spatio-temporal dynamics of a single feedback loop in a eukaryotic cell. We first develop a simplified spatial stochastic model of a canonical feedback system (either positive or negative). Using a Gillespie's algorithm, we compute sample trajectories and analyse their corresponding statistics. We then derive a system of equations that describe the spatio-temporal evolution of the stochastic means. Subsequently, we examine the spatially homogeneous case and compare the results of numerical simulations with the spatially explicit case. Finally, using a combination of steady-state analysis and data clustering techniques, we explore model behaviour across a subregion of the parameter space that is difficult to access experimentally and compare the parameter landscape of our spatio-temporal and spatially-homogeneous models.An exact collisionless equilibrium for the Force-Free Harris Sheet with low plasma beta
http://hdl.handle.net/10023/7691
We present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.
Funding: STFC Consolidated Grant [ST/K000950/1] (OA, TN & FW) and a Doctoral Training Grant [ST/K502327/1] (OA). EPSRC Doctoral Training Grant [EP/K503162/1] (ST).
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/76912015-10-01T00:00:00ZAllanson, Oliver DouglasNeukirch, ThomasWilson, FionaTroscheit, SaschaWe present a first discussion and analysis of the physical properties of a new exact collisionless equilibrium for a one-dimensional nonlinear force-free magnetic field, namely, the force-free Harris sheet. The solution allows any value of the plasma beta, and crucially below unity, which previous nonlinear force-free collisionless equilibria could not. The distribution function involves infinite series of Hermite polynomials in the canonical momenta, of which the important mathematical properties of convergence and non-negativity have recently been proven. Plots of the distribution function are presented for the plasma beta modestly below unity, and we compare the shape of the distribution function in two of the velocity directions to a Maxwellian distribution.3D whole-prominence fine structure modeling. II. Prominence evolution
http://hdl.handle.net/10023/7683
We use the new three-dimensional (3D) whole-prominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an arch-like region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from low-pressure, low-density plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasi-vertical small-scale feature consisting of short and deep dips, piled one above the other, is produced.
Tue, 20 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/76832015-10-20T00:00:00ZGunar, StanislavMackay, Duncan HendryWe use the new three-dimensional (3D) whole-prominence fine structure model to study the evolution of prominences and their fine structures in response to changes in the underlying photospheric magnetic flux distribution. The applied model combines a detailed 3D prominence magnetic field configuration with a realistic description of the prominence plasma distributed along multiple fine structures. In addition, we utilize an approximate Hα visualization technique to study the evolution of the visible cool prominence plasma both in emission (prominence) and absorption (filament). We show that the initial magnetic field configuration of the modeled prominence is significantly disturbed by the changing position of a single polarity of a magnetic bipole as the bipole is advected toward the main body of the filament. This leads to the creation of a barb, which becomes the dominant feature visible in the synthetic Hα images of both the prominence and filament views. The evolution of the bipole also creates conditions that lead to the disappearance and reappearance of large portions of the main body. We also show that an arch-like region containing a dark void (a bubble) can be naturally produced in the synthetic prominence Hα images. While not visible in terms of the magnetic field lines, it is due to a lack of Hα emission from low-pressure, low-density plasma located in shallow magnetic dips lying along the lines of sight intersecting the dark void. In addition, a quasi-vertical small-scale feature consisting of short and deep dips, piled one above the other, is produced.A spatially explicit capture-recapture estimator for single-catch traps
http://hdl.handle.net/10023/7680
1. Single-catch traps are frequently used in live-trapping studies of small mammals. Thus far a likelihood for single-catch traps has proven elusive and usually the likelihood for multi-catch traps is used for spatially explicit capture-recapture (SECR) analyses of such data. Previous work found the multi-catch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuous-time model for SECR to derive a likelihood for single-catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multi-catch estimator for various scenarios with non-constant density surfaces. 3. While the multi-catch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the single-catch estimator of the density surface over space, its root mean squared error is similar to that of the multi-catch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multi-catch estimator performs well with single-catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single-catch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single-catch likelihood with unknown capture times remains intractable for now, researchers using single-catch traps should aim to incorporate timing devices with their traps.
This work was part-funded by EPSRC grant EP/I000917/1.
Sun, 01 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/76802015-11-01T00:00:00ZDistiller, GregBorchers, David Louis1. Single-catch traps are frequently used in live-trapping studies of small mammals. Thus far a likelihood for single-catch traps has proven elusive and usually the likelihood for multi-catch traps is used for spatially explicit capture-recapture (SECR) analyses of such data. Previous work found the multi-catch likelihood to provide a robust estimator of average density. 2. We build on a recently developed continuous-time model for SECR to derive a likelihood for single-catch traps. We use this to develop an estimator based on observed capture times and compare its performance by simulation to that of the multi-catch estimator for various scenarios with non-constant density surfaces. 3. While the multi-catch estimator is found to be a surprisingly robust estimator of average density, its performance deteriorates with high trap saturation and increasing density gradients. Moreover, it is found to be a poor estimator of the height (but not range) of the detection function. By contrast, the single catch estimators of density, distribution and detection function parameters are found to be unbiased or nearly unbiased in all scenarios considered. This gain comes at the cost of higher variance, so that despite the lower bias of the single-catch estimator of the density surface over space, its root mean squared error is similar to that of the multi-catch estimator. 4. If there is no interest in interpreting the detection function parameters themselves, and if density is expected to be fairly constantover the survey region, then the multi-catch estimator performs well with single-catch traps. However if accurate estimation of the detection function is of interest, or if density is expected to vary substantially in space, then there is merit in using the single-catch estimator when trap saturation is above about 60%. The estimator’s performance is improved if care is taken to place traps so as to span the range of variables that affect animal distribution. As a single-catch likelihood with unknown capture times remains intractable for now, researchers using single-catch traps should aim to incorporate timing devices with their traps.Homomorphic image orders on combinatorial structures
http://hdl.handle.net/10023/7679
Combinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial well-order, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the well-known joint embedding property and amalgamation property, and are investigated here for the first time.
Wed, 01 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/76792015-07-01T00:00:00ZHuczynska, SophieRuskuc, NikCombinatorial structures have been considered under various orders, including substructure order and homomorphism order. In this paper, we investigate the homomorphic image order, corresponding to the existence of a surjective homomorphism between two structures. We distinguish between strong and induced forms of the order and explore how they behave in the context of different common combinatorial structures. We focus on three aspects: antichains and partial well-order, the joint preimage property and the dual amalgamation property. The two latter properties are natural analogues of the well-known joint embedding property and amalgamation property, and are investigated here for the first time.Formation and large-scale patterns of filament channels and filaments
http://hdl.handle.net/10023/7673
The properties and large-scale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long time-scales are described, along with the origin of the hemispheric pattern of filaments.
2015ASSL..415..355M
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/76732015-01-01T00:00:00ZMackay, Duncan HendryThe properties and large-scale patterns of filament channels and filaments are considered. Initially, the global formation locations of filament channels and filaments are discussed, along with their hemispheric pattern. Next, observations of the formation of filament channels and filaments are described where two opposing views are considered. Finally, the wide range of models that have been constructed to consider the formation of filament channels and filaments over long time-scales are described, along with the origin of the hemispheric pattern of filaments.A Hölder-type inequality on a regular rooted tree
http://hdl.handle.net/10023/7658
We establish an inequality which involves a non-negative function defined on the vertices of a finite m-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.
Sun, 15 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/76582015-03-15T00:00:00ZFalconer, Kenneth JohnWe establish an inequality which involves a non-negative function defined on the vertices of a finite m-ary regular rooted tree. The inequality may be thought of as relating an interaction energy defined on the free vertices of the tree summed over automorphisms of the tree, to a product of sums of powers of the function over vertices at certain levels of the tree. Conjugate powers arise naturally in the inequality, indeed, Hölder's inequality is a key tool in the proof which uses induction on subgroups of the automorphism group of the tree.The modelling and assessment of whale-watching impacts
http://hdl.handle.net/10023/7642
In recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whale-watching. Though perceived as 'green' or eco-friendly tourism, there is evidence that whale-watching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whale-watching is in fact a long term sustainable activity. However, an assessment of the impacts of whale-watching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of long-term whale-watching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whale-watching on cetaceans.
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/76422015-10-01T00:00:00ZNew, Leslie FrancesHall, Ailsa JaneHarcourt, R.Kaufman, G.Parsons, E.C.M.Pearson, H.C.Cosentino, A.M.Schick, Robert SchillingIn recent years there has been significant interest in modelling cumulative effects and the population consequences of individual changes in cetacean behaviour and physiology due to disturbance. One potential source of disturbance that has garnered particular interest is whale-watching. Though perceived as 'green' or eco-friendly tourism, there is evidence that whale-watching can result in statistically significant and biologically meaningful changes in cetacean behaviour, raising the question whether whale-watching is in fact a long term sustainable activity. However, an assessment of the impacts of whale-watching on cetaceans requires an understanding of the potential behavioural and physiological effects, data to effectively address the question and suitable modelling techniques. Here, we review the current state of knowledge on the viability of long-term whale-watching, as well as logistical limitations and potential opportunities. We conclude that an integrated, coordinated approach will be needed to further understanding of the possible effects of whale-watching on cetaceans.Impacts of anthropogenic noise on marine life : publication patterns, new discoveries, and future directions in research and management
http://hdl.handle.net/10023/7640
Anthropogenic underwater noise is now recognized as a world-wide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peer-reviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that non-injurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.
Funding for R. Bruintjes, J. Purser, A. N. Radford, S. D, Simpson and M. A. Wale was provided by the UK Department for Environment Food and Rural Affairs (Defra). N.D. Merchant received travel funding from Ocean Networks Canada. RW was supported by a Marie Curie International Incoming Fellowship within the 7th European Community Framework Programme (Project CONCEAL, FP7, PIIF-GA-2009-253407), and received travel funding to attend IMCC3 from the Society for Conservation Biology (SCB) Marine Section and the International Whaling Commission’s Climate Change steering group (with thanks to Mark Simmonds). A.J. Wright also received travel funding to attend IMCC3 from the SCB Marine Section. Date of Acceptance: 28/05/2015
Thu, 01 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/76402015-10-01T00:00:00ZWilliams, RobertWright, Andrew JAshe, ErinBlight, LKBruintjes, RCanessa, RClark, CWCullis-Suzuki, SDakin, DTErbe, CHammond, Philip StevenMerchant, MDO'Hara, PDPurser, JRadford, ANSimpson, SDThomas, LenWale, MAAnthropogenic underwater noise is now recognized as a world-wide problem, and recent studies have shown a broad range of negative effects in a variety of taxa. Underwater noise from shipping is increasingly recognized as a significant and pervasive pollutant with the potential to impact marine ecosystems on a global scale. We reviewed six regional case studies as examples of recent research and management activities relating to ocean noise in a variety of taxonomic groups, locations, and approaches. However, as no six projects could ever cover all taxa, sites and noise sources, a brief bibliometric analysis places these case studies into the broader historical and topical context of the peer-reviewed ocean noise literature as a whole. The case studies highlighted emerging knowledge of impacts, including the ways that non-injurious effects can still accumulate at the population level, and detailed approaches to guide ocean noise management. They build a compelling case that a number of anthropogenic noise types can affect a variety of marine taxa. Meanwhile, the bibliometric analyses revealed an increasing diversity of ocean noise topics covered and journal outlets since the 1940s. This could be seen in terms of both the expansion of the literature from more physical interests to ecological impacts of noise, management and policy, and consideration of a widening range of taxa. However, if our scientific knowledge base is ever to get ahead of the curve of rapid industrialization of the ocean, we are going to have to identify naïve populations and relatively pristine seas, and construct mechanistic models, so that we can predict impacts before they occur, and guide effective mitigation for the most vulnerable populations.On generators, relations and D-simplicity of direct products, Byleen extensions, and other semigroup constructions
http://hdl.handle.net/10023/7629
In this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a D-simple finitely presentable semigroup. We consider some well-known semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be D-simple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.
Mon, 30 Nov 2015 00:00:00 GMThttp://hdl.handle.net/10023/76292015-11-30T00:00:00ZBaynes, SamuelIn this thesis we study two different topics, both in the context of semigroup constructions. The first is the investigation of an embedding problem, specifically the problem of whether it is possible to embed any given finitely presentable semigroup into a D-simple finitely presentable semigroup. We consider some well-known semigroup constructions, investigating their properties to determine whether they might prove useful for finding a solution to our problem. We carry out a more detailed study into a more complicated semigroup construction, the Byleen extension, which has been used to solve several other embedding problems. We prove several results regarding the structure of this extension, finding necessary and sufficient conditions for an extension to be D-simple and a very strong necessary condition for an extension to be finitely presentable.
The second topic covered in this thesis is relative rank, specifically the sequence obtained by taking the rank of incremental direct powers of a given semigroup modulo the diagonal subsemigroup. We investigate the relative rank sequences of infinite Cartesian products of groups and of semigroups. We characterise all semigroups for which the relative rank sequence of an infinite Cartesian product is finite, and show that if the sequence is finite then it is bounded above by a logarithmic function. We will find sufficient conditions for the relative rank sequence of an infinite Cartesian product to be logarithmic, and sufficient conditions for it to be constant. Chapter 4 ends with the introduction of a new topic, relative presentability, which follows naturally from the topic of relative rank.Genetic censusing identifies an unexpectedly sizeable population of an endangered large mammal in a fragmented forest landscape
http://hdl.handle.net/10023/7614
Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246-321) and 319 (288-357) chimpanzees using capture-with-replacement and spatially explicit capture-recapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 8-33 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Y-chromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from small-scale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Y-chromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their long-term persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.
This study was funded by the American Society of Primatologists, the German Academic Exchange Service (DAAD), the Max Planck Society, the University of Southern California Jane Goodall Research Center and Dornsife College of Letters, Arts, and Sciences, the Nacey Maggioncalda Foundation, and Primate Conservation, Inc.
Tue, 25 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/76142015-08-25T00:00:00ZMcCarthy, M.S.Lester, J.D.Howe, Eric JohnArandjelovic, M.Stanford, C.B.Vigilant, L.Background: As habitat degradation and fragmentation continue to impact wildlife populations around the world, it is critical to understand the behavioral flexibility of species in these environments. In Uganda, the mostly unprotected forest fragment landscape between the Budongo and Bugoma Forests is a potential corridor for chimpanzees, yet little is known about the status of chimpanzee populations in these fragments. Results: From 2011 through 2013, we noninvasively collected 865 chimpanzee fecal samples across 633 km2 and successfully genotyped 662 (77%) at up to 14 microsatellite loci. These genotypes corresponded to 182 chimpanzees, with a mean of 3.5 captures per individual. We obtained population size estimates of 256 (95% confidence interval 246-321) and 319 (288-357) chimpanzees using capture-with-replacement and spatially explicit capture-recapture models, respectively. The spatial clustering of associated genotypes suggests the presence of at least nine communities containing a minimum of 8-33 individuals each. Putative community distributions defined by the locations of associated genotypes correspond well with the distribution of 14 Y-chromosome haplotypes. Conclusions: These census figures are more than three times greater than a previous estimate based on an extrapolation from small-scale nest count surveys that tend to underestimate population size. The distribution of genotype clusters and Y-chromosome haplotypes together indicate the presence of numerous male philopatric chimpanzee communities throughout the corridor habitat. Our findings demonstrate that, despite extensive habitat loss and fragmentation, chimpanzees remain widely distributed and exhibit distinct community home ranges. Our results further imply that elusive and rare species may adapt to degraded habitats more successfully than previously believed. Their long-term persistence is unlikely, however, if protection is not afforded to them and habitat loss continues unabated.Particle energisation in a collapsing magnetic trap model : the relativistic regime
http://hdl.handle.net/10023/7603
Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and non-relativistic particle dynamics.
The authors acknowledge financial support by the UK’s Science and Technology Facilities Council through a Doctoral Training Grant (SEO) and Consolidated Grant ST/K000950/1 (SEO and TN).
Tue, 01 Jul 2014 00:00:00 GMThttp://hdl.handle.net/10023/76032014-07-01T00:00:00ZEradat Oskoui, S.Neukirch, T.Context. In solar flares, a large number of charged particles is accelerated to high energies. By which physical processes this is achieved is one of the main open problems in solar physics. It has been suggested that during a flare, regions of the rapidly relaxing magnetic field can form a collapsing magnetic trap (CMT) and that this trap may contribute to particle energisation. Aims. In this Research Note we focus on a particular analytical CMT model based on kinematic magnetohydrodynamics. Previous investigations of particle acceleration for this CMT model focused on the non-relativistic energy regime. It is the specific aim of this Research Note to extend the previous work to relativistic particle energies. Methods. Particle orbits were calculated numerically using the relativistic guiding centre equations. We also calculated particle orbits using the non-relativistic guiding centre equations for comparison. Results. For mildly relativistic energies the relativistic and non-relativistic particle orbits mainly agree well, but clear deviations are seen for higher energies. In particular, the final particle energies obtained from the relativistic calculations are systematically lower than the energies reached from the corresponding non-relativistic calculations, and the mirror points of the relativistic orbits are systematically higher than for the corresponding non-relativistic orbits. Conclusions. While the overall behaviour of particle orbits in CMTs does not differ qualitatively when using the relativistic guiding centre equations, there are a few systematic quantitative differences between relativistic and non-relativistic particle dynamics.Pairwise interaction point processes for modelling bivariate spatial point patterns in the presence of interaction uncertainty
http://hdl.handle.net/10023/7583
Current ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns inter-individual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different inter-specific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/75832015-09-01T00:00:00ZNightingale, Glenna FaithIllian, Janine BaerbelKing, RuthCurrent ecological research seeks to understand the mechanisms that sustain biodiversity and allow a large number of species to coexist. Coexistence concerns inter-individual interactions. Consequently, there is an interest in identifying and quantifying interactions within and between species as reflected in the spatial pattern formed by the individuals. This study analyses the spatial pattern formed by the locations of plants in a community with high biodiversity from Western Australia. We fit a pairwise interaction Gibbs marked point process to the data using a Bayesian approach and quantify the inhibitory interactions within and between the two species. We quantitatively discriminate between competing models corresponding to different inter-specific and intraspecific interactions via posterior model probabilities. The analysis provides evidence that the intraspecific interactions for the two species of the genus Banksia are generally similar to those between the two species providing some evidence for mechanisms that sustain biodiversity.Multi-scale modelling of the dynamics of cell colonies : insights into cell-adhesion forces and cancer invasion from in silico simulations
http://hdl.handle.net/10023/7571
Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.
Sun, 01 Feb 2015 00:00:00 GMThttp://hdl.handle.net/10023/75712015-02-01T00:00:00ZSchluter, Daniela K.Ramis-Conde, IgnacioChaplain, Mark A. J.Studying the biophysical interactions between cells is crucial to understanding how normal tissue develops, how it is structured and also when malfunctions occur. Traditional experiments try to infer events at the tissue level after observing the behaviour of and interactions between individual cells. This approach assumes that cells behave in the same biophysical manner in isolated experiments as they do within colonies and tissues. In this paper, we develop a multi-scale multi-compartment mathematical model that accounts for the principal biophysical interactions and adhesion pathways not only at a cell?cell level but also at the level of cell colonies (in contrast to the traditional approach). Our results suggest that adhesion/separation forces between cells may be lower in cell colonies than traditional isolated single-cell experiments infer. As a consequence, isolated single-cell experiments may be insufficient to deduce important biological processes such as single-cell invasion after detachment from a solid tumour. The simulations further show that kinetic rates and cell biophysical characteristics such as pressure-related cell-cycle arrest have a major influence on cell colony patterns and can allow for the development of protrusive cellular structures as seen in invasive cancer cell lines independent of expression levels of pro-invasion molecules.Hopf bifurcation in a gene regulatory network model : molecular movement causes oscillations
http://hdl.handle.net/10023/7564
Gene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal inter- actions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NF-κB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.
M.A.J.C. and M.S. gratefully acknowledge the support of the ERC Advanced Investigator Grant 227619, “M5CGS — From Mutations to Metastases: Multiscale Mathematical Modelling of Cancer Growth and Spread”. M.S. would also like to thank the support from the Mathematical Biosciences Institute at the Ohio State University and NSF Grant DMS0931642.
Mon, 15 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/75642015-06-15T00:00:00ZChaplain, MarkPtashnyk, MariyaSturrock, MarcGene regulatory networks, i.e. DNA segments in a cell which interact with each other indirectly through their RNA and protein products, lie at the heart of many important intracellular signal transduction processes. In this paper, we analyze a mathematical model of a canonical gene regulatory network consisting of a single negative feedback loop between a protein and its mRNA (e.g. the Hes1 transcription factor system). The model consists of two partial differential equations describing the spatio-temporal inter- actions between the protein and its mRNA in a 1-dimensional domain. Such intracellular negative feedback systems are known to exhibit oscillatory behavior and this is the case for our model, shown initially via computational simulations. In order to investigate this behavior more deeply, we undertake a linearized stability analysis of the steady states of the model. Our results show that the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. This shows that the spatial movement of the mRNA and protein molecules alone is sufficient to cause the oscillations. Our result has implications for transcription factors such as p53, NF-κB and heat shock proteins which are involved in regulating important cellular processes such as inflammation, meiosis, apoptosis and the heat shock response, and are linked to diseases such as arthritis and cancer.Procedure description : using AUTEC’s hydrophones surrounding a DTAGed whale to obtain localizations
http://hdl.handle.net/10023/7523
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/75232015-01-01T00:00:00ZMarques, Tiago A.Shaeffer, JessicaMoretti, DavidThomas, LenMagnetospheric signatures of ionospheric density cavities observed by Cluster
http://hdl.handle.net/10023/7509
We present Cluster measurements of large amplitude electric fields corre- lated with intense downward field-aligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphere-ionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward field-aligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.
AJBR ackowledges support from STFC under consolidated grant ST/K000993/1.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/75092015-03-01T00:00:00ZRussell, Alexander John BarkwayKarlsson, TomasWright, Andrew NicholasWe present Cluster measurements of large amplitude electric fields corre- lated with intense downward field-aligned currents, observed during a nightside crossing of the auroral zone. The data are reproduced by a simple model of magnetosphere-ionosphere coupling which, under different conditions, can also produce a divergent electric field signature in the downward current region, or correlation between the electric and perturbed magnetic fields. We conclude that strong electric field associated with intense downward field-aligned current, such as this observation, is a signature of ionospheric plasma depletion caused by the downward current. It is also shown that the electric field in the downward current region correlates with downward current density if a background field is present, e.g. due to magnetospheric convection.Strategies of eradicating glioma cells : a multi-scale mathematical model with miR-451-AMPK-mTOR control
http://hdl.handle.net/10023/7503
The cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR-451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multi-scale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatio-temporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR-451-AMPK-mTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.
Wed, 28 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/75032015-01-28T00:00:00ZKim, YangjinPowathil, GibinKang, HyunjiTrucu, DumitruKim, HyeongiLawler, SeanChaplain, MarkThe cellular dispersion and therapeutic control of glioblastoma, the most aggressive type of primary brain cancer, depends critically on the migration patterns after surgery and intracellular responses of the individual cancer cells in response to external biochemical and biomechanical cues in the microenvironment. Recent studies have shown that a particular microRNA, miR-451, regulates downstream molecules including AMPK and mTOR to determine the balance between rapid proliferation and invasion in response to metabolic stress in the harsh tumor microenvironment. Surgical removal of main tumor is inevitably followed by recurrence of the tumor due to inaccessibility of dispersed tumor cells in normal brain tissue. In order to address this multi-scale nature of glioblastoma proliferation and invasion and its response to conventional treatment, we propose a hybrid model of glioblastoma that analyses spatio-temporal dynamics at the cellular level, linking individual tumor cells with the macroscopic behaviour of cell organization and the microenvironment, and with the intracellular dynamics of miR-451-AMPK-mTOR signaling within a tumour cell. The model identifies a key mechanism underlying the molecular switches between proliferative phase and migratory phase in response to metabolic stress and biophysical interaction between cells in response to fluctuating glucose levels in the presence of blood vessels (BVs). The model predicts that cell migration, therefore efficacy of the treatment, not only depends on oxygen and glucose availability but also on the relative balance between random motility and strength of chemoattractants. Effective control of growing cells near BV sites in addition to relocalization of invisible migratory cells back to the resection site was suggested as a way of eradicating these migratory cells.Sunspot rotation. I : A consequence of flux emergence
http://hdl.handle.net/10023/7497
Context. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.
ZS acknowledges the financial support of the Carnegie Trust for Scotland and CMM the support of the Royal Society of Edinburgh. This work used the DIRAC 1, UKMHD Consortium machine at the University of St Andrews and the DiRAC Data Centric system at Durham University, operated by the Institute for Computational Cosmology on behalf of the STFC DiRAC HPC Facility (www.dirac.ac.uk). This equipment was funded by BIS National E-infrastructure capital grant ST/K00042X/1, STFC capital grant ST/H008519/1, and STFC DiRAC Operations grant ST/K003267/1 and Durham University. DiRAC is part of the National E-Infrastructure.
Mon, 12 Oct 2015 00:00:00 GMThttp://hdl.handle.net/10023/74972015-10-12T00:00:00ZSturrock, ZoeHood, Alan WilliamArchontis, VasilisMcNeill, CraigContext. Solar eruptions and high flare activity often accompany the rapid rotation of sunspots. The study of sunspot rotation and the mechanisms driving this motion are therefore key to our understanding of how the solar atmosphere attains the conditions necessary for large energy release. Aims. We aim to demonstrate and investigate the rotation of sunspots in a 3D numerical experiment of the emergence of a magnetic flux tube as it rises through the solar interior and emerges into the atmosphere. Furthermore, we seek to show that the sub-photospheric twist stored in the interior is injected into the solar atmosphere by means of a definitive rotation of the sunspots. Methods. A numerical experiment is performed to solve the 3D resistive magnetohydrodynamic (MHD) equations using a Lagrangian-Remap code. We track the emergence of a toroidal flux tube as it rises through the solar interior and emerges into the atmosphere investigating various quantities related to both the magnetic field and plasma. Results. Through detailed analysis of the numerical experiment, we find clear evidence that the photospheric footprints or sunspots of the flux tube undergo a rotation. Significant vertical vortical motions are found to develop within the two polarity sources after the field emerges. These rotational motions are found to leave the interior portion of the field untwisted and twist up the atmospheric portion of the field. This is shown by our analysis of the relative magnetic helicity as a significant portion of the interior helicity is transported to the atmosphere. In addition, there is a substantial transport of magnetic energy to the atmosphere. Rotation angles are also calculated by tracing selected fieldlines; the fieldlines threading through the sunspot are found to rotate through angles of up to 353º over the course of the experiment. We explain the rotation by an unbalanced torque produced by the magnetic tension force, rather than an apparent effect.Evolution of field line helicity during magnetic reconnection
http://hdl.handle.net/10023/7485
We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.
This work was supported by the Science and Technology Facilities Council (UK) through consortium Grant Nos. ST/K000993/1 and ST/K001043 to the University of Dundee and Durham University.
Sun, 01 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/74852015-03-01T00:00:00ZRussell, A. J. B.Yeates, A. R.Hornig, G.Wilmot-Smith, A. L.We investigate the evolution of field line helicity for magnetic fields that connect two boundaries without null points, with emphasis on localized finite-B magnetic reconnection. Total ( relative) magnetic helicity is already recognized as an important topological constraint on magnetohydrodynamic processes. Field line helicity offers further advantages because it preserves all topological information and can distinguish between different magnetic fields with the same total helicity. Magnetic reconnection changes field connectivity and field line helicity reflects these changes; the goal of this paper is to characterize that evolution. We start by deriving the evolution equation for field line helicity and examining its terms, also obtaining a simplified form for cases where dynamics are localized within the domain. The main result, which we support using kinematic examples, is that during localized reconnection in a complex magnetic field, the evolution of field line helicity is dominated by a work-like term that is evaluated at the field line endpoints, namely, the scalar product of the generalized field line velocity and the vector potential. Furthermore, the flux integral of this term over certain areas is very small compared to the integral of the unsigned quantity, which indicates that changes of field line helicity happen in a well-organized pairwise manner. It follows that reconnection is very efficient at redistributing helicity in complex magnetic fields despite having little effect on the total helicity.On the theory of translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and magnetic shear
http://hdl.handle.net/10023/7484
We present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a Grad-Shafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.
Funding: STFC Doctoral Training Grant ST/K502327/1 (Jonathan Hodgson) and STFC Consolidated Grant ST/K000950/1 (Thomas Neukirch)
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/74842015-01-01T00:00:00ZHodgson, Jonathan David BrockieNeukirch, ThomasWe present an improved formalism for translationally invariant magnetohydrodynamic equilibria with anisotropic pressure and currents with a field aligned component. The derivation of a Grad-Shafranov type equation is given along with a constraint which links the shear field to the parallel pressure. The difficulties of the formalism are discussed and various methods of circumventing these difficulties are given. A simple example is then used to highlight the methods and difficulties involved.Higher moments for random multiplicative measures
http://hdl.handle.net/10023/7474
We obtain a condition for the Lq-convergence of martingales generated by random multiplicative cascade measures for q>1 without any self-similarity requirements on the cascades.
Sat, 01 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/74742015-08-01T00:00:00ZFalconer, Kenneth JohnWe obtain a condition for the Lq-convergence of martingales generated by random multiplicative cascade measures for q>1 without any self-similarity requirements on the cascades.Circular designs balanced for neighbours at distances one and two
http://hdl.handle.net/10023/7454
We define three types of neighbour-balanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding self-neighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.
Mon, 01 Dec 2014 00:00:00 GMThttp://hdl.handle.net/10023/74542014-12-01T00:00:00ZAldred, R. E. L.Bailey, R. A.Mckay, Brendan D.Wanless, Ian M.We define three types of neighbour-balanced designs for experiments where the units are arranged in a circle or single line in space or time. The designs are balanced with respect to neighbours at distance one and at distance two. The variants come from allowing or forbidding self-neighbours, and from considering neighbours to be directed or undirected. For two of the variants, we give a method of constructing a design for all values of the number of treatments, except for some small values where it is impossible. In the third case, we give a partial solution that covers all sizes likely to be used in practice.Model-based distance sampling
http://hdl.handle.net/10023/7410
Conventional distance sampling adopts a mixed approach, using model-based methods for the detection process, and design-based methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully model-based methods. Model-based methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any sub-region of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for model-based distance sampling, and show how the various model-based methods that have been proposed fit within this framework.
CSO was part-funded by EPSRC/NERC Grant EP/1000917/1.
Tue, 01 Mar 2016 00:00:00 GMThttp://hdl.handle.net/10023/74102016-03-01T00:00:00ZBuckland, Stephen TerrenceOedekoven, Cornelia SabrinaBorchers, David LouisConventional distance sampling adopts a mixed approach, using model-based methods for the detection process, and design-based methods to estimate animal abundance in the study region, given estimated probabilities of detection. In recent years, there has been increasing interest in fully model-based methods. Model-based methods are less robust for estimating animal abundance than conventional methods, but offer several advantages: they allow the analyst to explore how animal density varies by habitat or topography; abundance can be estimated for any sub-region of interest; they provide tools for analysing data from designed distance sampling experiments, to assess treatment effects. We develop a common framework for model-based distance sampling, and show how the various model-based methods that have been proposed fit within this framework.The statistical analysis of point events associated with a fixed point
http://hdl.handle.net/10023/7294
This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8-dependence models for angular-linear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed case-control models and tests. The possibility of second-order effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.
Tue, 01 Jan 1991 00:00:00 GMThttp://hdl.handle.net/10023/72941991-01-01T00:00:00ZLawson, Andrew B.This work concerns the analysis of point events which are distributed on a planar region and are thought to be related to a fixed point. Data examples are considered from Epidemiology, where morbidity events are thought to be related to a pollution source, and Ecology and Geology where events associated with a central point are to be modelled. We have developed a variety of Heterogeneous Poisson Process (HEPP) models for the above examples. In particular, I have developed interaction and 8-dependence models for angular-linear correlation, with their ML estimation and associated score/W aId tests. In the Epidemiological case we have developed case-control models and tests. The possibility of second-order effects being important has also led to the development of Bayesian Spatial Prior (BSP) models. In addition, we have developed a new deviance residual for HEPP models and explored the use of GLIM for modelling purposes. A variety of results were found in data analysis. In some cases HEPP models provide adequate descriptions of the process. In others, BSP models yield better fits. In general, the discrete case admits a simple spatial Poisson model for counts and does not require BSP model extensions.Coronal heating in multiple magnetic threads
http://hdl.handle.net/10023/7259
Context. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state. Results. The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.
We acknowledge the financial support of STFC through the Consolidated grant to the University of St Andrews.
Sat, 01 Aug 2015 00:00:00 GMThttp://hdl.handle.net/10023/72592015-08-01T00:00:00ZTam, Kuan VaiHood, Alan WilliamBrowning, PhilippaCargill, PeterContext. Heating the solar corona to several million degrees requires the conversion of magnetic energy into thermal energy. In this paper, we investigate whether an unstable magnetic thread within a coronal loop can destabilise a neighbouring magnetic thread. Aims. By running a series of simulations, we aim to understand under what conditions the destabilisation of a single magnetic thread can also trigger a release of energy in a nearby thread. Methods. The 3D magnetohydrodynamics code, Lare3d, is used to simulate the temporal evolution of coronal magnetic fields during a kink instability and the subsequent relaxation process. We assume that a coronal magnetic loop consists of non-potential magnetic threads that are initially in an equilibrium state. Results. The non-linear kink instability in one magnetic thread forms a helical current sheet and initiates magnetic reconnection. The current sheet fragments, and magnetic energy is released throughout that thread. We find that, under certain conditions, this event can destabilise a nearby thread, which is a necessary requirement for starting an avalanche of energy release in magnetic threads. Conclusions. It is possible to initiate an energy release in a nearby, non-potential magnetic thread, because the energy released from one unstable magnetic thread can trigger energy release in nearby threads, provided that the nearby structures are close to marginal stability.Are tornado-like magnetic structures able to support solar prominence plasma?
http://hdl.handle.net/10023/7202
Recent high-resolution and high-cadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornado-like structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almost-vertical structures against gravity. In this work we model analytically a tornado-like structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.
M. Luna and F. Moreno-Insertis acknowledge support by the Spanish Ministry of Economy and Competitiveness through projects AYA2011-24808 and AYA2014-55078-P. M.L. is also grateful to ERC-2011-StG 277829-SPIA. E.R.P. is grateful to the UK STFC and the Leverhulme Trust for financial support.
Mon, 20 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/72022015-07-20T00:00:00ZLuna, M.Moreno-Insertis, F.Priest, E.Recent high-resolution and high-cadence observations have surprisingly suggested that prominence barbs exhibit apparent rotating motions suggestive of a tornado-like structure. Additional evidence has been provided by Doppler measurements. The observations reveal opposite velocities for both hot and cool plasma on the two sides of a prominence barb. This motion is persistent for several hours and has been interpreted in terms of rotational motion of prominence feet. Several authors suggest that such barb motions are rotating helical structures around a vertical axis similar to tornadoes on Earth. One of the difficulties of such a proposal is how to support cool prominence plasma in almost-vertical structures against gravity. In this work we model analytically a tornado-like structure and try to determine possible mechanisms to support the prominence plasma. We have found that the Lorentz force can indeed support the barb plasma provided the magnetic structure is sufficiently twisted and/or significant poloidal flows are present.Effect of Prandtl's ration on balance in geophysical turbulence
http://hdl.handle.net/10023/7201
The fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertia-gravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ |ζ|max/f, and a small Froude number, Fr ≡ |.h|max/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freely-evolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully non-hydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PV-based Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasi-geostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasi-geostrophic turbulence for which Fr ∼ Ro ≪ 1.
Support for this research has come from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1).
Tue, 21 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/72012015-07-21T00:00:00ZDritschel, David GerardMcKiver, William JosephThe fluid dynamics of the atmosphere and oceans are to a large extent controlled by the slow evolution of a scalar field called ‘potential vorticity’, with relatively fast motions such as inertia-gravity waves playing only a minor role. This state of affairs is commonly referred to as ‘balance’. Potential vorticity (PV) is a special scalar field which is materially conserved in the absence of diabatic effects and dissipation, effects which are generally weak in the atmosphere and oceans. Moreover, in a balanced flow, PV induces the entire fluid motion and its thermodynamic structure (Hoskins et al. 1985). While exact balance is generally not achievable, it is now well established that balance holds to a high degree of accuracy in rapidly rotating and strongly stratified flows. Such flows are characterised by both a small Rossby number, Ro ≡ |ζ|max/f, and a small Froude number, Fr ≡ |.h|max/N, where ζ and .h are the relative vertical and horizontal vorticity components, while f and N are the Coriolis and buoyancy frequencies. In fact, balance can even be a good approximation when Fr < ∼ Ro ∼ O(1). In this study, we examine how balance depends specifically on Prandtl’s ratio, f/N, in unforced freely-evolving turbulence. We examine a wide variety of turbulent flows, at a mature and complex stage of their evolution, making use of the fully non-hydrostatic equations under the Boussinesq and incompressible approximations. We perform numerical simulations at exceptionally high resolution in order to carefully assess the degree to which balance holds, and to determine when it breaks down. For this purpose, it proves most useful to employ an invariant, PV-based Rossby number ε, together with f/N. For a given ε, our key finding is that — for at least tens of characteristic vortex rotation periods — the flow is insensitive to f/N for all values for which the flow remains statically stable (typically f/N < ∼1). Only the vertical velocity varies in proportion to f/N, in line with quasi-geostrophic scaling for which Fr2 ≪ Ro ≪ 1. We also find that as ε increases toward unity, the maximum f/N attainable decreases toward 0. No statically stable flows occur for ε > ∼ 1. For all stable flows, balance is found to hold to a remarkably high degree: as measured by an energy norm, imbalance never exceeds more than a few percent of the balance, even in flows where Ro > 1. The vertical velocity w remains a tiny fraction of the horizontal velocity uh, even when w is dominantly balanced. Finally, typical vertical to horizontal scale ratios H/L remain close to f/N, as found previously in quasi-geostrophic turbulence for which Fr ∼ Ro ≪ 1.On the parallel and perpendicular propagating motions visible in polar plumes : an incubator for (fast) solar wind acceleration?
http://hdl.handle.net/10023/7190
We combine observations of the Coronal Multi-channel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasi-periodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(-1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(-1), a phase speed of 830 km s(-1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.
J.L. was a student visitor at HAO. J.L. acknowledges the financial support for his visit to HAO from the Chinese Scholarship Council (CSC). The authors acknowledge support from NSFC 41131065, 41121003, 973 Key Project 2011CB811403, and CAS Key Research Program KZZD-EW-01-4. We also acknowledge support from NASA contracts NNX08BA99G, NNX11AN98G, NNM12AB40P, NNG09FA40C (IRIS), and NNM07AA01C (Hinode). The research leading to these results has also received funding from the European Commission Seventh Framework Programme (FP7/ 2007-2013) under the grant agreement SOLSPANET (project No. 269299, www.solspanet.eu/solspanet) Date of Acceptance: 25/05/2015
Sat, 20 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/71902015-06-20T00:00:00ZLiu, JiajiaMcIntosh, Scott W.De Moortel, InekeWang, YumingWe combine observations of the Coronal Multi-channel Polarimeter and the Atmospheric Imaging Assembly on board the Solar Dynamics Observatory to study the characteristic properties of (propagating) Alfvenic motions and quasi-periodic intensity disturbances in polar plumes. This unique combination of instruments highlights the physical richness of the processes taking place at the base of the (fast) solar wind. The (parallel) intensity perturbations with intensity enhancements around 1% have an apparent speed of 120 km s(-1) (in both the 171 and 193 angstrom passbands) and a periodicity of 15 minutes, while the (perpendicular) Alfvenic wave motions have a velocity amplitude of 0.5 km s(-1), a phase speed of 830 km s(-1), and a shorter period of 5 minutes on the same structures. These observations illustrate a scenario where the excited Alfvenic motions are propagating along an inhomogeneously loaded magnetic field structure such that the combination could be a potential progenitor of the magnetohydrodynamic turbulence required to accelerate the fast solar wind.Uncertainties in polarimetric 3D reconstructions of coronal mass ejections
http://hdl.handle.net/10023/7178
Aims. The aim of this work is to quantify the uncertainties in the three-dimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the so-called polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the line-of-sight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 R-circle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of halo-CMEs for space weather prediction purposes.
P.P. acknowledges STFC for financial support. Date of Acceptance: 21/01/2015
Mon, 06 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/71782015-04-06T00:00:00ZBemporad, A.Pagano, P.Aims. The aim of this work is to quantify the uncertainties in the three-dimensional (3D) reconstruction of the location of coronal mass ejections (CMEs) obtained with the so-called polarization ratio technique. The method takes advantage of the different distributions along the line of sight of total (tB) and polarized (pB) brightnesses emitted by Thomson scattering to estimate the average location of the emitting plasma. This is particularly important to correctly identify of CME propagation angles and unprojected velocities, thus allowing better capabilities for space weather forecastings. Methods. To this end, we assumed two simple electron density distributions along the line of sight (a constant density and Gaussian density profiles) for a plasma blob and synthesized the expected tB and pB for different distances z of the blob from the plane of the sky and different projected altitudes.. Reconstructed locations of the blob along the line of sight were thus compared with the real ones, allowing a precise determination of uncertainties in the method. Results. Results show that, independently of the analytical density profile, when the blob is centered at a small distance from the plane of the sky (i. e. for limb CMEs) the distance from the plane of the sky starts to be significantly overestimated. Polarization ratio technique provides the line-of-sight position of the center of mass of what we call folded density distribution, given by reflecting and summing in front of the plane of the sky the fraction of density profile located behind that plane. On the other hand, when the blob is far from the plane of the sky, but with very small projected altitudes (i. e. for halo CMEs, rho< 1.4 R-circle dot), the inferred distance from that plane is significantly underestimated. Better determination of the real blob position along the line of sight is given for intermediate locations, and in particular when the blob is centered at an angle of 20 degrees from the plane of the sky. Conclusions. These result have important consequences not only for future 3D reconstruction of CMEs with polarization ratio technique, but also for the design of future coronagraphs aimed at providing a continuous monitoring of halo-CMEs for space weather prediction purposes.Non-LTE modelling of prominence fine structures using hydrogen Lyman-line profiles
http://hdl.handle.net/10023/7177
Aims. We perform a detailed statistical analysis of the spectral Lyman-line observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profile-to-profile comparison of the synthetic Lyman spectra obtained by 2D single-thread prominence fine-structure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multi-thread fine-structure models with random positions and line-of-sight velocities of each thread to obtain a statistically significant set of synthetic Lyman-line profiles. We used for the first time multi-thread models composed of non-identical threads and viewed at line-of-sight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.
Date of Acceptance: 10/03/2015
Fri, 08 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/71772015-05-08T00:00:00ZSchwartz, P.Gunar, S.Curdt, W.Aims. We perform a detailed statistical analysis of the spectral Lyman-line observations of the quiescent prominence observed on May 18, 2005. Methods. We used a profile-to-profile comparison of the synthetic Lyman spectra obtained by 2D single-thread prominence fine-structure model as a starting point for a full statistical analysis of the observed Lyman spectra. We employed 2D multi-thread fine-structure models with random positions and line-of-sight velocities of each thread to obtain a statistically significant set of synthetic Lyman-line profiles. We used for the first time multi-thread models composed of non-identical threads and viewed at line-of-sight angles different from perpendicular to the magnetic field. Results. We investigated the plasma properties of the prominence observed with the SoHO/SUMER spectrograph on May 18, 2005 by comparing the histograms of three statistical parameters characterizing the properties of the synthetic and observed line profiles. In this way, the integrated intensity, Lyman decrement ratio, and the ratio of intensity at the central reversal to the average intensity of peaks provided insight into the column mass and the central temperature of the prominence fine structures.Large scale surveys for cetaceans : line transect assumptions, reliability of abundance estimates and improving survey efficiency – A response to MacLeod
http://hdl.handle.net/10023/7159
Sat, 01 Feb 2014 00:00:00 GMThttp://hdl.handle.net/10023/71592014-02-01T00:00:00ZHammond, Philip StevenGillespie, Douglas MichaelLovell, PhilipSamarra, Filipa Isabel PereiraSwift, Rene JamesMacleod, KellyTasker, Mark LBerggren, PerBorchers, David LouisBurt, M LouisePaxton, Charles G. M.Canadas, AnaDesportes, GenevieveDonovan, Greg PGilles, AnitaLehnert, KristinaSiebert, UrsulaGordon, Jonathan Charles DavidLeaper, RussellLeopold, MardikScheidat, MeikeOien, NilsRidoux, VincentRogan, EmerSkov, HenrikTeilmann, JonasVan Canneyt, OlivierVazquez, Jose AntonioDetectability in audio-visual surveys of tropical rainforest birds : the influence of species, weather and habitat characteristics
http://hdl.handle.net/10023/7147
Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidence-based approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for non-distance sampling data and for estimating detectability of rare species.
This research was funded by the Australian Government’s National Environmental Research Program, the Stuart Leslie Bird Research Award from Birds Australia (http://www.birdsaustralia.com.au/), the Earthwatch Institute (http://www.earthwatch.org/australia/), the Marine and Tropical Sciences Research Facility (MTSRF: http://www.rrrc.org.au/mtsrf). In addition, TAM was partially sponsored by national funds through the Fundação Nacional para a Ciência e Tecnologia, Portugal – FCT under the project (PEst-OE/MAT/UI0006/2011). Date of Acceptance: 27/04/2015
Thu, 25 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/71472015-06-25T00:00:00ZAnderson, Alexander S.Marques, Tiago A.Shoo, Luke P.Williams, Stephen E.Indices of relative abundance do not control for variation in detectability, which can bias density estimates such that ecological processes are difficult to infer. Distance sampling methods can be used to correct for detectability, but in rainforest, where dense vegetation and diverse assemblages complicate sampling, information is lacking about factors affecting their application. Rare species present an additional challenge, as data may be too sparse to fit detection functions. We present analyses of distance sampling data collected for a diverse tropical rainforest bird assemblage across broad elevational and latitudinal gradients in North Queensland, Australia. Using audio and visual detections, we assessed the influence of various factors on Effective Strip Width (ESW), an intuitively useful parameter, since it can be used to calculate an estimate of density from count data. Body size and species exerted the most important influence on ESW, with larger species detectable over greater distances than smaller species. Secondarily, wet weather and high shrub density decreased ESW for most species. ESW for several species also differed between summer and winter, possibly due to seasonal differences in calling behavior. Distance sampling proved logistically intensive in these environments, but large differences in ESW between species confirmed the need to correct for detection probability to obtain accurate density estimates. Our results suggest an evidence-based approach to controlling for factors influencing detectability, and avenues for further work including modeling detectability as a function of species characteristics such as body size and call characteristics. Such models may be useful in developing a calibration for non-distance sampling data and for estimating detectability of rare species.Evaluating the utility of B/Ca ratios in planktic foraminifera as a proxy for the carbonate system : a case study of Globigerinoides ruber
http://hdl.handle.net/10023/7133
B/Ca ratios in foraminifera have attracted considerable scientific attention as a proxy for past ocean carbonate system. However, the carbonate system controls on B/Ca ratios are not straightforward, with Δ[ CO32-] ([ CO32-]in situ - [ CO32-]at saturation) correlating best with B/Ca ratios in benthic foraminifera, rather than pH, B(OH)4-/HCO3-, or B(OH)4-/DIC (as a simple model of boron speciation in seawater and incorporation into CaCO3 would predict). Furthermore, culture experiments have shown that in planktic foraminifera properties such as salinity and [B