Mathematics & Statistics (School of)
http://hdl.handle.net/10023/28
Wed, 21 Feb 2018 01:34:01 GMT2018-02-21T01:34:01ZMathematics & Statistics (School of)http://research-repository.st-andrews.ac.uk:80/bitstream/id/13/Mathematics and statistics.gif
http://hdl.handle.net/10023/28
The coronal monsoon : thermal nonequilibrium revealed by periodic coronal rain
http://hdl.handle.net/10023/12761
We report on the discovery of periodic coronal rain in an off-limb sequence of Solar Dynamics Observatory/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6 hr) intensity pulsations of coronal loops of the sort described by Auchère et al. and Froment et al. These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation/condensation cycles resulting from a state of thermal nonequilibrium. The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain—albeit non-periodic—in several other structures within the studied field of view implies that this type of heating is at play on a large scale.
P.A. has received funding from the UK Science and Technology Facilities Council (Consolidated Grant ST/K000950/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Mon, 05 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10023/127612018-02-05T00:00:00ZAuchère, FrédéricFroment, ClaraSoubrié, ElieAntolin, PatrickOliver, RamonPelouze, GabrielWe report on the discovery of periodic coronal rain in an off-limb sequence of Solar Dynamics Observatory/Atmospheric Imaging Assembly images. The showers are co-spatial and in phase with periodic (6.6 hr) intensity pulsations of coronal loops of the sort described by Auchère et al. and Froment et al. These new observations make possible a unified description of both phenomena. Coronal rain and periodic intensity pulsations of loops are two manifestations of the same physical process: evaporation/condensation cycles resulting from a state of thermal nonequilibrium. The fluctuations around coronal temperatures produce the intensity pulsations of loops, and rain falls along their legs if thermal runaway cools the periodic condensations down and below transition-region temperatures. This scenario is in line with the predictions of numerical models of quasi-steadily and footpoint heated loops. The presence of coronal rain—albeit non-periodic—in several other structures within the studied field of view implies that this type of heating is at play on a large scale.Statistical issues in first-in-human studies on BIA 10-2474 : neglected comparison of protocol against practice
http://hdl.handle.net/10023/12740
By setting the regulatory-approved protocol for a suite of first-in-human studies on BIA 10-2474 against the subsequent French investigations, we highlight six key design and statistical issues which reinforce recommendations by a Royal Statistical Society Working Party which were made in the aftermath of cytokine release storm in six healthy volunteers in the UK in 2006. The 6 issues are dose determination, availability of pharmacokinetic results, dosing interval, stopping rules, appraisal by safety committee, and clear algorithm required if combining approvals for single and multiple ascending dose studies.
Funding information: European Union's FP7 programme, Grant/Award Number: 602552
Wed, 15 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/127402017-03-15T00:00:00ZBird, Sheila M.Bailey, Rosemary A.Grieve, Andrew P.Senn, StephenBy setting the regulatory-approved protocol for a suite of first-in-human studies on BIA 10-2474 against the subsequent French investigations, we highlight six key design and statistical issues which reinforce recommendations by a Royal Statistical Society Working Party which were made in the aftermath of cytokine release storm in six healthy volunteers in the UK in 2006. The 6 issues are dose determination, availability of pharmacokinetic results, dosing interval, stopping rules, appraisal by safety committee, and clear algorithm required if combining approvals for single and multiple ascending dose studies.A multiscale mathematical model of tumour invasive growth
http://hdl.handle.net/10023/12739
Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. 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 the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/127392017-03-01T00:00:00ZPeng, LuTrucu, DumitruLin, PingThompson, AlastairChaplain, Mark A. J.Known as one of the hallmarks of cancer (Hanahan and Weinberg in Cell 100:57–70, 2000) cancer cell invasion of human body tissue is a complicated spatio-temporal multiscale process which enables a localised solid tumour to transform into a systemic, metastatic and fatal disease. This process explores and takes advantage of the reciprocal relation that solid tumours establish with the extracellular matrix (ECM) components and other multiple distinct cell types from the surrounding microenvironment. Through the secretion of various proteolytic enzymes such as matrix metalloproteinases or the urokinase plasminogen activator (uPA), the cancer cell population alters the configuration of the surrounding ECM composition and overcomes the physical barriers to ultimately achieve local cancer spread into the surrounding tissue. The active interplay between the tissue-scale tumour dynamics and the molecular mechanics of the involved proteolytic enzymes at the cell scale underlines the biologically multiscale character of invasion and raises the challenge of modelling this process with an appropriate multiscale approach. In this paper, we present a new two-scale moving boundary model of cancer invasion that explores the tissue-scale tumour dynamics in conjunction with the molecular dynamics of the urokinase plasminogen activation system. Building on the multiscale moving boundary method proposed in Trucu et al. (Multiscale Model Simul 11(1):309–335, 2013), the modelling that we propose here allows us to study the changes in tissue-scale tumour morphology caused by the cell-scale uPA microdynamics occurring along the invasive edge of the tumour. 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 the tumour infiltrative growth patterns discussed in Ito et al. (J Gastroenterol 47:1279–1289, 2012).Sesqui-arrays, a generalisation of triple arrays
http://hdl.handle.net/10023/12725
A triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are (possibly different) non-zero constants. Deleting the condition on the letters commonto a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs ofcolumns is deleted. Thus all triple arrays are sesqui-arrays.In this paper we give three constructions for sesqui-arrays. The first gives (n+1) x n2 arrays on n(n+1) letters for n>1. (Such an array for n=2 was found by Bagchi.) This construction uses Latin squares.The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 7 x 36 sesqui-array for 42 letters. We also give a construction for K x (K-1)(K-2)/2 sesqui-arrays onK(K-1)/2 letters. This construction uses biplanes. It starts with a block of a biplane and produces an array which satisfies the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.
Tue, 13 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10023/127252018-02-13T00:00:00ZBailey, Rosemary AnneCameron, Peter JephsonNilson, TomasA triple array is a rectangular array containing letters, each letter occurring equally often with no repeats in rows or columns, such that the number of letters common to two rows, two columns, or a row and a column are (possibly different) non-zero constants. Deleting the condition on the letters commonto a row and a column gives a double array. We propose the term sesqui-array for such an array when only the condition on pairs ofcolumns is deleted. Thus all triple arrays are sesqui-arrays.In this paper we give three constructions for sesqui-arrays. The first gives (n+1) x n2 arrays on n(n+1) letters for n>1. (Such an array for n=2 was found by Bagchi.) This construction uses Latin squares.The second uses the Sylvester graph, a subgraph of the Hoffman--Singleton graph, to build a good block design for 36 treatments in 42 blocks of size 6, and then uses this in a 7 x 36 sesqui-array for 42 letters. We also give a construction for K x (K-1)(K-2)/2 sesqui-arrays onK(K-1)/2 letters. This construction uses biplanes. It starts with a block of a biplane and produces an array which satisfies the requirements for a sesqui-array except possibly that of having no repeated letters in a row or column. We show that this condition holds if and only if the Hussain chains for the selected block contain no 4-cycles. A sufficient condition for the construction to give a triple array is that each Hussain chain is a union of 3-cycles; but this condition is not necessary, and we give a few further examples. We also discuss the question of which of these arrays provide good designs for experiments.Penalized nonparametric scalar-on-function regression via principal coordinates
http://hdl.handle.net/10023/12663
A number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.
Philip Reiss, Pei-Shien Wu, and Wen-Yu Hua gratefully acknowledge the support of the U.S. National Institute of Mental Health (grant 1R01MH095836-01A1).
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/126632017-01-01T00:00:00ZReiss, Philip T.Miller, David L.Wu, Pei ShienHua, Wen YuA number of classical approaches to nonparametric regression have recently been extended to the case of functional predictors. This article introduces a new method of this type, which extends intermediate-rank penalized smoothing to scalar-on-function regression. In the proposed method, which we call principal coordinate ridge regression, one regresses the response on leading principal coordinates defined by a relevant distance among the functional predictors, while applying a ridge penalty. Our publicly available implementation, based on generalized additive modeling software, allows for fast optimal tuning parameter selection and for extensions to multiple functional predictors, exponential family-valued responses, and mixed-effects models. In an application to signature verification data, principal coordinate ridge regression, with dynamic time warping distance used to define the principal coordinates, is shown to outperform a functional generalized linear model. Supplementary materials for this article are available online.Slow and fast escape for open intermittent maps
http://hdl.handle.net/10023/12658
If a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes:(1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; (2) an intermediate regime, where the rate of mixing and escape through the hole coincide, limiting accims exist, but much of the thermodynamic picture breaks down; (3) a subexponentially mixing regime where the slow mixing means that mass simply accumulates on the parabolic fixed point. We give a complete picture of the transitions and stability properties (in the size of the hole and as we move through the family) in this class of open systems. In particular, we are able to recover a form of stability in the third regime above via the dynamics on the survivor set, even when no limiting accim exists.
MD was partially supported by NSF grant DMS 1362420. This project was started as part of an RiGs grant through ICMS, Scotland.
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/126582017-04-01T00:00:00ZDemers, Mark F.Todd, MikeIf a system mixes too slowly, putting a hole in it can completely destroy the richness of the dynamics. Here we study this instability for a class of intermittent maps with a family of slowly mixing measures. We show that there are three regimes:(1) standard hyperbolic-like behavior where the rate of mixing is faster than the rate of escape through the hole, there is a unique limiting absolutely continuous conditionally invariant measure (accim) and there is a complete thermodynamic description of the dynamics on the survivor set; (2) an intermediate regime, where the rate of mixing and escape through the hole coincide, limiting accims exist, but much of the thermodynamic picture breaks down; (3) a subexponentially mixing regime where the slow mixing means that mass simply accumulates on the parabolic fixed point. We give a complete picture of the transitions and stability properties (in the size of the hole and as we move through the family) in this class of open systems. In particular, we are able to recover a form of stability in the third regime above via the dynamics on the survivor set, even when no limiting accim exists.Module theory : an approach to linear algebra
http://hdl.handle.net/10023/12643
Originally published in 1977 by Oxford University Press, with a second edition published in 1990. This is a revised version of the second edition published for the first time in electronic form. This electronic edition is published by the University of St Andrews.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/126432018-01-01T00:00:00ZBlyth, Thomas ScottFlare particle acceleration in the interaction of twisted coronal flux ropes
http://hdl.handle.net/10023/12627
Aims. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods. We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results. The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.
The authors gratefully acknowledge the support of the U.K. Science and Technology Facilities Council. JT and AWH acknowledge the financial support of STFC through the Consolidated grant, ST/N000609/1, to the University of St Andrews. PKB acknowledges STFC support through ST/P000428/1 at the University of Manchester.
Fri, 22 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/126272017-12-22T00:00:00ZThrelfall, J.Hood, A. W.Browning, P. K.Aims. The aim of this work is to investigate and characterise non-thermal particle behaviour in a three-dimensional (3D) magnetohydrodynamical (MHD) model of unstable multi-threaded flaring coronal loops. Methods. We have used a numerical scheme which solves the relativistic guiding centre approximation to study the motion of electrons and protons. The scheme uses snapshots from high resolution numerical MHD simulations of coronal loops containing two threads, where a single thread becomes unstable and (in one case) destabilises and merges with an additional thread. Results. The particle responses to the reconnection and fragmentation in MHD simulations of two loop threads are examined in detail. We illustrate the role played by uniform background resistivity and distinguish this from the role of anomalous resistivity using orbits in an MHD simulation where only one thread becomes unstable without destabilising further loop threads. We examine the (scalable) orbit energy gains and final positions recovered at different stages of a second MHD simulation wherein a secondary loop thread is destabilised by (and merges with) the first thread. We compare these results with other theoretical particle acceleration models in the context of observed energetic particle populations during solar flares.The construction of finite soluble factor groups of finitely presented groups and its application
http://hdl.handle.net/10023/12600
Computational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.
Wed, 01 Jan 1992 00:00:00 GMThttp://hdl.handle.net/10023/126001992-01-01T00:00:00ZWegner, AlexanderComputational group theory deals with the design, analysis and computer implementation of algorithms for solving computational problems involving groups, and with the applications of the programs produced to interesting questions in group theory, in other branches of mathematics, and in other areas of science. This thesis describes an implementation of a proposal for a Soluble Quotient Algorithm, i.e. a description of the algorithms used and a report on the findings of an empirical study of the behaviour of the programs, and gives an account of an application of the programs. The programs were used for the construction of soluble groups with interesting properties, e.g. for the construction of soluble groups of large derived length which seem to be candidates for groups having efficient presentations. New finite soluble groups of derived length six with trivial Schur multiplier and efficient presentations are described. The methods for finding efficient presentations proved to be only practicable for groups of moderate order. Therefore, for a given derived length soluble groups of small order are of interest. The minimal soluble groups of derived length less than or equal to six are classified.Aggregation and travelling wave dynamics in a two-population model of cancer cell growth and invasion
http://hdl.handle.net/10023/12595
Cells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metas- tasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.
Funding: Engineering and Physical Sciences Research Council (UK) grant numbers EP/L504932/1 (VB), EP/K033689/1 (RE).
Mon, 15 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/125952018-01-15T00:00:00ZBitsouni, VasilikiTrucu, DumitruChaplain, Mark Andrew JosephEftimie, RalucaCells adhere to each other and to the extracellular matrix (ECM) through protein molecules on the surface of the cells. The breaking and forming of adhesive bonds, a process critical in cancer invasion and metas- tasis, can be influenced by the mutation of cancer cells. In this paper, we develop a nonlocal mathematical model describing cancer cell invasion and movement as a result of integrin-controlled cell-cell adhesion and cell-matrix adhesion, for two cancer cell populations with different levels of mutation. The partial differential equations for cell dynamics are coupled with ordinary differential equations describing the extracellular matrix (ECM) degradation and the production and decay of integrins. We use this model to investigate the role of cancer mutation on the possibility of cancer clonal competition with alternating dominance, or even competitive exclusion (phenomena observed experimentally). We discuss different possible cell aggregation patterns, as well as travelling wave patterns. In regard to the travelling waves, we investigate the effect of cancer mutation rate on the speed of cancer invasion.Telomerecat : a ploidy-agnostic method for estimating telomere length from whole genome sequencing data
http://hdl.handle.net/10023/12591
Telomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype.
Funding: Cancer Research UK Programme Grant to Simon Tavaré (C14303/A17197) (JHRF, AGL, MLS); European Commission through the Horizon 2020 project SOUND (Grant Agreement no. 633974) (AGL).
Mon, 22 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/125912018-01-22T00:00:00ZFarmery, JamesSmith, MikeNIHR BioResource - Rare DiseasesLynch, AndyTelomere length is a risk factor in disease and the dynamics of telomere length are crucial to our understanding of cell replication and vitality. The proliferation of whole genome sequencing represents an unprecedented opportunity to glean new insights into telomere biology on a previously unimaginable scale. To this end, a number of approaches for estimating telomere length from whole-genome sequencing data have been proposed. Here we present Telomerecat, a novel approach to the estimation of telomere length. Previous methods have been dependent on the number of telomeres present in a cell being known, which may be problematic when analysing aneuploid cancer data and non-human samples. Telomerecat is designed to be agnostic to the number of telomeres present, making it suited for the purpose of estimating telomere length in cancer studies. Telomerecat also accounts for interstitial telomeric reads and presents a novel approach to dealing with sequencing errors. We show that Telomerecat performs well at telomere length estimation when compared to leading experimental and computational methods. Furthermore, we show that it detects expected patterns in longitudinal data, repeated measurements, and cross-species comparisons. We also apply the method to a cancer cell data, uncovering an interesting relationship with the underlying telomerase genotype.Combining radiation with hyperthermia : a multiscale model informed by in vitro experiments
http://hdl.handle.net/10023/12590
Combined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.
Funding: Cancer Research UK. Research at The Institute of Cancer Research is supported by Cancer Research UK under Programme C33589/A19727. Peter Ziegenhein is supported by Cancer Research UK under Programme C33589/A19908.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/125902018-01-01T00:00:00ZBrüningk, SarahPowathil, GibinZiegenhein, PeterIjaz, JannatRivens, IanNill, S.Chaplain, Mark Andrew JosephOelfke, Uweter Haar, GailCombined radiotherapy and hyperthermia offer great potential for the successful treatment of radio-resistant tumours through thermo-radiosensitization. Tumour response heterogeneity, due to intrinsic, or micro-environmentally induced factors, may greatly influence treatment outcome, but is difficult to account for using traditional treatment planning approaches. Systems oncology simulation, using mathematical models designed to predict tumour growth and treatment response, provides a powerful tool for analysis and optimization of combined treatments. We present a framework that simulates such combination treatments on a cellular level. This multiscale hybrid cellular automaton simulates large cell populations (up to 107 cells) in vitro, while allowing individual cell-cycle progression, and treatment response by modelling radiation-induced mitotic cell death, and immediate cell kill in response to heating. Based on a calibration using a number of experimental growth, cell cycle and survival datasets for HCT116 cells, model predictions agreed well (R2 > 0.95) with experimental data within the range of (thermal and radiation) doses tested (0–40 CEM43, 0–5 Gy). The proposed framework offers flexibility for modelling multimodality treatment combinations in different scenarios. It may therefore provide an important step towards the modelling of personalized therapies using a virtual patient tumour.Quiescent prominences in the era of ALMA. II. Kinetic temperature diagnostics
http://hdl.handle.net/10023/12557
We provide the theoretical background for diagnostics of the thermal properties of solar prominences observed by the Atacama Large Millimeter/submillimeter Array (ALMA). To do this, we employ the 3D Whole-Prominence Fine Structure (WPFS) model that produces synthetic ALMA-like observations of a complex simulated prominence. We use synthetic observations derived at two different submillimeter/millimeter (SMM) wavelengths—one at a wavelength at which the simulated prominence is completely optically thin and another at a wavelength at which a significant portion of the simulated prominence is optically thick—as if these were the actual ALMA observations. This allows us to develop a technique for an analysis of the prominence plasma thermal properties from such a pair of simultaneous high-resolution ALMA observations. The 3D WPFS model also provides detailed information about the distribution of the kinetic temperature and the optical thickness along any line of sight. We can thus assess whether the measure of the kinetic temperature derived from observations accurately represents the actual kinetic temperature properties of the observed plasma. We demonstrate here that in a given pixel the optical thickness at the wavelength at which the prominence plasma is optically thick needs to be above unity or even larger to achieve a sufficient accuracy of the derived information about the kinetic temperature of the analyzed plasma. Information about the optical thickness cannot be directly discerned from observations at the SMM wavelengths alone. However, we show that a criterion that can identify those pixels in which the derived kinetic temperature values correspond well to the actual thermal properties in which the observed prominence can be established.
Funding: UK STFC, the Leverhulme Trust, and NASA (D.H.M.)
Sat, 20 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/125572018-01-20T00:00:00ZGunár, StanislavHeinzel, PetrAnzer, UlrichMackay, Duncan HendryWe provide the theoretical background for diagnostics of the thermal properties of solar prominences observed by the Atacama Large Millimeter/submillimeter Array (ALMA). To do this, we employ the 3D Whole-Prominence Fine Structure (WPFS) model that produces synthetic ALMA-like observations of a complex simulated prominence. We use synthetic observations derived at two different submillimeter/millimeter (SMM) wavelengths—one at a wavelength at which the simulated prominence is completely optically thin and another at a wavelength at which a significant portion of the simulated prominence is optically thick—as if these were the actual ALMA observations. This allows us to develop a technique for an analysis of the prominence plasma thermal properties from such a pair of simultaneous high-resolution ALMA observations. The 3D WPFS model also provides detailed information about the distribution of the kinetic temperature and the optical thickness along any line of sight. We can thus assess whether the measure of the kinetic temperature derived from observations accurately represents the actual kinetic temperature properties of the observed plasma. We demonstrate here that in a given pixel the optical thickness at the wavelength at which the prominence plasma is optically thick needs to be above unity or even larger to achieve a sufficient accuracy of the derived information about the kinetic temperature of the analyzed plasma. Information about the optical thickness cannot be directly discerned from observations at the SMM wavelengths alone. However, we show that a criterion that can identify those pixels in which the derived kinetic temperature values correspond well to the actual thermal properties in which the observed prominence can be established.Mediterranean mesocarnivores in spatially structured managed landscapes : community organisation in time and space
http://hdl.handle.net/10023/12447
In the multi-functional and biodiverse cork oak landscapes of Iberia (Montado), agro-silvo-pastoral practices promote landscape heterogeneity and create intricate habitat and resource availability patterns. We used camera-traps to investigate the temporal and spatial organisation of a mesocarnivore community in a Montado landscape in central Portugal. The target carnivore assemblage was largely dominated by three generalist species – the red fox Vulpes vulpes, the European badger Meles meles and the Egyptian mongoose Herpestes ichneumon – while remaining community members – the common genet Genetta genetta and the feral cat Felis silvestris spp. – exhibited restricted distributions. Interspecific differences in activity rhythms and habitat use were particularly marked among widespread species. Low temporal overlap was reported between the diurnal mongoose and predominantly nocturnal red fox and badger. For the latter two species, contrasting differences in habitat use were associated with anthropogenic-induced environmental heterogeneity. Whereas the red fox used more intensively Montado areas preserving dense shrubby understory and avoided semi-disturbed mosaics of sparse shrubs, the badgers displayed the opposite pattern. Our findings add to previous evidence suggesting that the spatial structure created in highly managed landscapes, particularly the diversity of resulting understory structures, promotes the abundance and spread of generalist mesocarnivore species. These may benefit from the surplus of resource amount (e.g. prey) and the creation of different human-made habitats conditions that provide particular combinations of ecological resources favourable to each species requirements. We concur the common view that maintaining understory heterogeneity in Montado landscapes, menaced by current intensification and extensification trends, is important where carnivore persistence is a relevant conservation goal, but alert for potential effects on carnivore assemblages structuring and impacts for specialist species less tolerant to disturbance.
During the final stage of the study GCS was funded by a doctoral grant from FCT (PD/BD/114037/2015). TAM thanks support by CEAUL (funded by FCT project – UID/MAT/00006/2013).
Mon, 16 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/124472017-01-16T00:00:00ZCurveira-Santos, GonçaloMarques, Tiago A.Björklund, MatsSantos-Reis, MargaridaIn the multi-functional and biodiverse cork oak landscapes of Iberia (Montado), agro-silvo-pastoral practices promote landscape heterogeneity and create intricate habitat and resource availability patterns. We used camera-traps to investigate the temporal and spatial organisation of a mesocarnivore community in a Montado landscape in central Portugal. The target carnivore assemblage was largely dominated by three generalist species – the red fox Vulpes vulpes, the European badger Meles meles and the Egyptian mongoose Herpestes ichneumon – while remaining community members – the common genet Genetta genetta and the feral cat Felis silvestris spp. – exhibited restricted distributions. Interspecific differences in activity rhythms and habitat use were particularly marked among widespread species. Low temporal overlap was reported between the diurnal mongoose and predominantly nocturnal red fox and badger. For the latter two species, contrasting differences in habitat use were associated with anthropogenic-induced environmental heterogeneity. Whereas the red fox used more intensively Montado areas preserving dense shrubby understory and avoided semi-disturbed mosaics of sparse shrubs, the badgers displayed the opposite pattern. Our findings add to previous evidence suggesting that the spatial structure created in highly managed landscapes, particularly the diversity of resulting understory structures, promotes the abundance and spread of generalist mesocarnivore species. These may benefit from the surplus of resource amount (e.g. prey) and the creation of different human-made habitats conditions that provide particular combinations of ecological resources favourable to each species requirements. We concur the common view that maintaining understory heterogeneity in Montado landscapes, menaced by current intensification and extensification trends, is important where carnivore persistence is a relevant conservation goal, but alert for potential effects on carnivore assemblages structuring and impacts for specialist species less tolerant to disturbance.The number and distribution of polar bears in the western Barents Sea
http://hdl.handle.net/10023/12440
Polar bears have experienced a rapid loss of sea-ice habitat in the Barents Sea. Monitoring this subpopulation focuses on the effects on polar bear demography. In August 2015, we conducted a survey in the Norwegian Arctic to estimate polar bear numbers and reveal population substructure. DNA profiles from biopsy samples and ear tags identified on photographs revealed that about half of the bears in Svalbard, compared to only 4.5% in the pack ice north of the archipelago, were recognized recaptures. The recaptured bears had originally been marked in Svalbard, mostly in spring. The existence of a local Svalbard stock, and another ecotype of bears using the pack ice in autumn with low likelihood of visiting Svalbard, support separate population size estimation for the two areas. Mainly by aerial survey line transect distance sampling methods, we estimated that 264 (95% CI = 199 - 363) bears were in Svalbard, close to 241 bears estimated for August 2004. The pack ice area had an estimated 709 bears (95% CI = 334 - 1026). The pack ice and the total (Svalbard + pack ice, 973 bears, 95% CI = 334 - 1026) both had higher estimates compared to August 2004 (444 and 685 bears, respectively), but the increase was not significant. There is no evidence that the fast reduction of sea-ice habitat in the area has yet led to a reduction in population size. The carrying capacity is likely reduced significantly, but recovery from earlier depletion up to 1973 may still be ongoing.
This study was funded by the Norwegian Ministry of Climate and the Environment. TAM is grateful for partial support by Centro de Estatística e Aplicações da Universidade de Lisboa, funded by the Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013.
Mon, 09 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/124402017-10-09T00:00:00ZAars, JonMarques, Tiago A.Lone, KarenAndersen, MagnusWiig, ØysteinFløystad, Ida Marie BardalenHagen, Snorre B.Buckland, Stephen T.Polar bears have experienced a rapid loss of sea-ice habitat in the Barents Sea. Monitoring this subpopulation focuses on the effects on polar bear demography. In August 2015, we conducted a survey in the Norwegian Arctic to estimate polar bear numbers and reveal population substructure. DNA profiles from biopsy samples and ear tags identified on photographs revealed that about half of the bears in Svalbard, compared to only 4.5% in the pack ice north of the archipelago, were recognized recaptures. The recaptured bears had originally been marked in Svalbard, mostly in spring. The existence of a local Svalbard stock, and another ecotype of bears using the pack ice in autumn with low likelihood of visiting Svalbard, support separate population size estimation for the two areas. Mainly by aerial survey line transect distance sampling methods, we estimated that 264 (95% CI = 199 - 363) bears were in Svalbard, close to 241 bears estimated for August 2004. The pack ice area had an estimated 709 bears (95% CI = 334 - 1026). The pack ice and the total (Svalbard + pack ice, 973 bears, 95% CI = 334 - 1026) both had higher estimates compared to August 2004 (444 and 685 bears, respectively), but the increase was not significant. There is no evidence that the fast reduction of sea-ice habitat in the area has yet led to a reduction in population size. The carrying capacity is likely reduced significantly, but recovery from earlier depletion up to 1973 may still be ongoing.Comparison of methods for modelling coronal magnetic fields
http://hdl.handle.net/10023/12438
Aims. Four different approximate approaches used to model the stressing ofcoronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements. Methods. We consider a simple model problem, comparing the full nonlinear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these,magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time-dependent. Results. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements but hassignificant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes asignificant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too large.
Funding: STFC through the Consolidated grant ST/N000609/1 (AWH); STFC studentship, ST/I505999/1 (EEG).
Fri, 03 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/124382017-11-03T00:00:00ZGoldstraw, E. E.Hood, A. W.Browning, P. K.Cargill, P. J.Aims. Four different approximate approaches used to model the stressing ofcoronal magnetic fields due to an imposed photospheric motion are compared with each other and the results from a full time-dependent magnetohydrodynamic (MHD) code. The assumptions used for each of the approximate methods are tested by considering large photospheric footpoint displacements. Methods. We consider a simple model problem, comparing the full nonlinear magnetohydrodynamic evolution, determined with the Lare2D numerical code, with four approximate approaches. Two of these,magneto-frictional relaxation and a quasi-1D Grad-Shafranov approach, assume sequences of equilibria, whilst the other two methods, a second-order linearisation of the MHD equations and Reduced MHD, are time-dependent. Results. The relaxation method is very accurate compared to full MHD for force-free equilibria for all footpoint displacements but hassignificant errors when the plasma β0 is of order unity. The 1D approach gives an extremely accurate description of the equilibria away from the photospheric boundary layers, and agrees well with Lare2D for all parameter values tested. The linearised MHD equations correctly predict the existence of photospheric boundary layers that are present in the full MHD results. As soon as the footpoint displacement becomes asignificant fraction of the loop length, the RMHD method fails to model the sequences of equilibria correctly. The full numerical solution is interesting in its own right, and care must be taken for low β0 plasmas if the viscosity is too large.Point process models for spatio-temporal distance sampling data from a large-scale survey of blue whales
http://hdl.handle.net/10023/12427
Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.
Fri, 01 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/124272017-12-01T00:00:00ZYuan, Y.Bachl, F. E.Lindgren, F.Borchers, David LouisIllian, J. B.Buckland, S. T.Rue, H.Gerrodette, T.Distance sampling is a widely used method for estimating wildlife population abundance. The fact that conventional distance sampling methods are partly design-based constrains the spatial resolution at which animal density can be estimated using these methods. Estimates are usually obtained at survey stratum level. For an endangered species such as the blue whale, it is desirable to estimate density and abundance at a finer spatial scale than stratum. Temporal variation in the spatial structure is also important. We formulate the process generating distance sampling data as a thinned spatial point process and propose model-based inference using a spatial log-Gaussian Cox process. The method adopts a flexible stochastic partial differential equation (SPDE) approach to model spatial structure in density that is not accounted for by explanatory variables, and integrated nested Laplace approximation (INLA) for Bayesian inference. It allows simultaneous fitting of detection and density models and permits prediction of density at an arbitrarily fine scale. We estimate blue whale density in the Eastern Tropical Pacific Ocean from thirteen shipboard surveys conducted over 22 years. We find that higher blue whale density is associated with colder sea surface temperatures in space, and although there is some positive association between density and mean annual temperature, our estimates are consitent with no trend in density across years. Our analysis also indicates that there is substantial spatially structured variation in density that is not explained by available covariates.Piecewise uniform potential vorticity pancake shielded vortices
http://hdl.handle.net/10023/12419
Shielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/124192017-01-01T00:00:00ZReinaud, Jean NoelShielded vortices consist of a core of potential vorticity of a given sign surrounded (or shielded) by a layer of opposite-signed potential vorticity. Such vortices have specific properties and have been the focus of numerous studies, first in two dimensional geometries (where potential vorticity is just the vertical component of the vorticity vector) and in geophysical applications (mostly in layered models). The present paper focuses on three-dimensional, spheroidal shielded vortices. In particular, we focus on vortical structures whose overall volume-integrated potential vorticity is zero. We restrict attention to vortices of piecewise uniform potential vorticity in the present research. We first revisit the problem within the quasi-geostrophic model, then we extend the results to the non-hydrostatic regime. We show that the stability of the structure depends on the ratio of potential vorticity between the inner core and the outer shield. In particular it depends on the polarity of the core and of the wavenumber of the azimuthal mode perturbed.Individual, ecological, and anthropogenic inﬂuences on activity budgets of long-ﬁnned pilot whales
http://hdl.handle.net/10023/12408
Time allocation to different activities and habitats enables individuals to modulate their perceived risks and access to resources, and can reveal important trade-offs between fitness-enhancing activities (e.g., feeding vs. social behavior). Species with long reproductive cycles and high parental investment, such as marine mammals, rely on such behavioral plasticity to cope with rapid environmental change, including anthropogenic stressors. We quantified activity budgets of free-ranging long-finned pilot whales in order to assess individual time trade-offs between foraging and other behaviors in different individual and ecological contexts, and during experimental sound exposures. The experiments included 1-2 and 6-7 kHz naval sonar exposures (a potential anthropogenic stressor), playback of killer whale (a potential predator/competitor) vocalizations, and negative controls. We combined multiple time series data from digital acoustic recording tags (DTAG) as well as group-level social behavior data from visual observations of tagged whales at the surface. The data were classified into near-surface behaviors and dive types (using a hidden Markov model for dive transitions) and aggregated into time budgets. On average, individuals (N=19) spent most of their time (69%) resting and transiting near surface, 21% in shallow dives (depth <40m), and only 10% of their time in deep foraging dives, of which 65% reached a depth 10m from the sea bottom. Individuals in the largest of three body size classes or accompanied by calves tended to spend more time foraging than others. Simultaneous tagging of pairs of individuals showed that up to 50% of the activity budget was synchronized between conspecifics with decreased synchrony during foraging periods. Individuals spent less time foraging when forming larger non-vocal aggregations of individuals in late afternoons, and more time foraging when in the mid-range of water depths (300-400m) available in the study area (50-700m). Individuals reduced foraging time by 83% (29-96%) during their first exposure to sonar, but not during killer whale sound playbacks. A relative increase in foraging during repeat sonar exposures indicated habituation or change in response tactic. We discuss the possible adaptive value of these trade-offs in time allocation to reduce individual conflict while maintaining benefits of group living.
The authors would like to thank sponsors, NL Ministry of Defence, NOR Ministry of Defence, U.S. Office of Naval Research (N00014-08-1-0984, N00014-10-1-0355, N00014-14-1-0390), FR Ministry of Defence (DGA; public market no. 15860052), World Wildlife Fund Norway (9E0682), and French Total Foundation and Bleustein-Blanchet Foundation. The statistical development work was supported by a separate grant from the U.S. Office of Naval Research (N00014-12-1-0204), under the project entitled Multi-study OCean acoustics Human effects Analysis (MOCHA).
Fri, 01 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/124082017-12-01T00:00:00ZIsojunno, S.Sadykova, D.DeRuiter, S.Curé, C.Visser, F.Thomas, L.Miller, P. J. O.Harris, C. M.Time allocation to different activities and habitats enables individuals to modulate their perceived risks and access to resources, and can reveal important trade-offs between fitness-enhancing activities (e.g., feeding vs. social behavior). Species with long reproductive cycles and high parental investment, such as marine mammals, rely on such behavioral plasticity to cope with rapid environmental change, including anthropogenic stressors. We quantified activity budgets of free-ranging long-finned pilot whales in order to assess individual time trade-offs between foraging and other behaviors in different individual and ecological contexts, and during experimental sound exposures. The experiments included 1-2 and 6-7 kHz naval sonar exposures (a potential anthropogenic stressor), playback of killer whale (a potential predator/competitor) vocalizations, and negative controls. We combined multiple time series data from digital acoustic recording tags (DTAG) as well as group-level social behavior data from visual observations of tagged whales at the surface. The data were classified into near-surface behaviors and dive types (using a hidden Markov model for dive transitions) and aggregated into time budgets. On average, individuals (N=19) spent most of their time (69%) resting and transiting near surface, 21% in shallow dives (depth <40m), and only 10% of their time in deep foraging dives, of which 65% reached a depth 10m from the sea bottom. Individuals in the largest of three body size classes or accompanied by calves tended to spend more time foraging than others. Simultaneous tagging of pairs of individuals showed that up to 50% of the activity budget was synchronized between conspecifics with decreased synchrony during foraging periods. Individuals spent less time foraging when forming larger non-vocal aggregations of individuals in late afternoons, and more time foraging when in the mid-range of water depths (300-400m) available in the study area (50-700m). Individuals reduced foraging time by 83% (29-96%) during their first exposure to sonar, but not during killer whale sound playbacks. A relative increase in foraging during repeat sonar exposures indicated habituation or change in response tactic. We discuss the possible adaptive value of these trade-offs in time allocation to reduce individual conflict while maintaining benefits of group living.Relations among partitions
http://hdl.handle.net/10023/12407
Combinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/124072017-01-01T00:00:00ZBailey, Rosemary AnneCombinatorialists often consider a balanced incomplete-block design to consist of a set of points, a set of blocks, and an incidence relation between them which satisfies certain conditions. To a statistician, such a design is a set of experimental units with two partitions, one into blocks and the other into treatments: it is the relation between these two partitions which gives the design its properties. The most common binary relations between partitions that occur in statistics are refinement, orthogonality and balance. When there are more than two partitions, the binary relations may not suffice to give all the properties of the system. I shall survey work in this area, including designs such as double Youden rectangles.JPEG2000 image compression on solar EUV images
http://hdl.handle.net/10023/12367
For future solar missions as well as ground-based telescopes, efficient ways to return and process data has become increasingly important. Solar Or-biter, e.g., the next ESA/NASA mission to explore the Sun and the heliosphere,is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals.Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand,face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000(from the Joint Photographic Experts Group 2000) image compression at different bit rates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disk and off-limb coronal loop oscillation time series observed by AIA/SDO.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/123672017-01-01T00:00:00ZFischer, CatherineMueller, DanielDe Moortel, InekeFor future solar missions as well as ground-based telescopes, efficient ways to return and process data has become increasingly important. Solar Or-biter, e.g., the next ESA/NASA mission to explore the Sun and the heliosphere,is a deep-space mission, which implies a limited telemetry rate that makes efficient onboard data compression a necessity to achieve the mission science goals.Missions like the Solar Dynamics Observatory (SDO) and future ground-based telescopes such as the Daniel K. Inouye Solar Telescope, on the other hand,face the challenge of making petabyte-sized solar data archives accessible to the solar community. New image compression standards address these challenges by implementing efficient and flexible compression algorithms that can be tailored to user requirements. We analyse solar images from the Atmospheric Imaging Assembly (AIA) instrument onboard SDO to study the effect of lossy JPEG2000(from the Joint Photographic Experts Group 2000) image compression at different bit rates. To assess the quality of compressed images, we use the mean structural similarity (MSSIM) index as well as the widely used peak signal-to noise ratio (PSNR) as metrics and compare the two in the context of solar EUV images. In addition, we perform tests to validate the scientific use of the lossily compressed images by analysing examples of an on-disk and off-limb coronal loop oscillation time series observed by AIA/SDO.Energy release in driven twisted coronal loops
http://hdl.handle.net/10023/12305
Magnetic reconnection in twisted magnetic flux tubes, representing coronal loops, is investigated. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted flux tubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric flux tubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight flux tubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along flux tubes. At the same time, the hot plasma regions in curved loops are asymmetric, and concentrate close to the loop tops. Large-scale curvature has a destabilising in influence: lower twist is needed for instability. Footpoint convergence normally delays instability slightly, although, in some cases converging flux tubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has destabilising effect.
This work is funded by Science and Technology Facilities Council (UK). This equipment was funded by a BIS National E-Infrastructure capital grant ST/K00042X/1, DiRAC Operations grant ST/K003267/1 and Durham University.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/123052016-01-01T00:00:00ZBareford, Michael RGordovskyy, MykolaBrowning, PhilippaHood, Alan WilliamMagnetic reconnection in twisted magnetic flux tubes, representing coronal loops, is investigated. The main goal is to establish the influence of the field geometry and various thermodynamic effects on the stability of twisted flux tubes and on the size and distribution of heated regions. In particular, we aim to investigate to what extent the earlier idealised models, based on the initially cylindrically symmetric flux tubes, are different from more realistic models, including the large-scale curvature, atmospheric stratification, thermal conduction and other effects. In addition, we compare the roles of Ohmic heating and shock heating in energy conversion during magnetic reconnection in twisted loops. The models with straight flux tubes show similar distribution of heated plasma during the reconnection: it initially forms a helical shape, which subsequently becomes very fragmented. The heating in these models is rather uniformly distributed along flux tubes. At the same time, the hot plasma regions in curved loops are asymmetric, and concentrate close to the loop tops. Large-scale curvature has a destabilising in influence: lower twist is needed for instability. Footpoint convergence normally delays instability slightly, although, in some cases converging flux tubes can be less stable. Finally, introducing a stratified atmosphere gives rise to decaying wave propagation, which has destabilising effect.Relaxation methods in compressible flow
http://hdl.handle.net/10023/12298
Sat, 01 Jan 1949 00:00:00 GMThttp://hdl.handle.net/10023/122981949-01-01T00:00:00ZMitchell, Andrew RonaldThe infinite simple group V of Richard J. Thompson : presentations by permutations
http://hdl.handle.net/10023/12296
We show that one can naturally describe elements of R. Thompson's finitely presented infinite 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.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/122962017-01-01T00:00:00ZBleak, CollinQuick, MartynWe show that one can naturally describe elements of R. Thompson's finitely presented infinite 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.Study on the tumor-induced angiogenesis using mathematical models
http://hdl.handle.net/10023/12256
We studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.
This work was supported by JSPS KAKENHI 16H06576 and JSPS Core-to-Core Project International Research Network.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/122562018-01-01T00:00:00ZSuzuki, TakashiMinerva, DhisaNishiyama, KoichiKoshikawa, NaohikoChaplain, Mark Andrew JosephWe studied angiogenesis using mathematical models describing the dynamics of tip cells. We reviewed the basic ideas of angiogenesis models and its numerical simulation technique to produce realistic computer graphics images of sprouting angiogenesis. We examined the classical model of Anderson-Chaplain using fundamental concepts of mass transport and chemical reaction with ECM degradation included. We then constructed two types of numerical schemes, model-faithful and model-driven ones, where new techniques of numerical simulation are introduced, such as transient probability, particle velocity, and Boolean variables.Special subgroups of regular semigroups
http://hdl.handle.net/10023/12231
Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.
This work was partially supported by the Portuguese Foundation for Science and Technology through the grant UID/MAT/00297/2013 (CMA).
Tue, 03 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/122312017-10-03T00:00:00ZBlyth, T. S.Almeida Santos, M. H.Extending the notions of inverse transversal and associate subgroup, we consider a regular semigroup S with the property that there exists a subsemigroup T which contains, for each x∈S, a unique y such that both xy and yx are idempotent. Such a subsemigroup is necessarily a group which we call a special subgroup. Here we investigate regular semigroups with this property. In particular, we determine when the subset of perfect elements is a subsemigroup and describe its structure in naturally arising situations.Regularity of Navier--Stokes flows with bounds for the pressure
http://hdl.handle.net/10023/12230
This study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.
This paper was presented at the Warwick EPSRC Symposium on PDEs in Fluid Mechanics, September 2016. Part of this research was carried out when CVT was visiting the University of Alberta, whose hospitality is gratefully acknowledged. XY was partially supported by NSERC Discovery grant RES0020476
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/122302017-05-01T00:00:00ZTran, Chuong V.Yu, XinweiThis study derives regularity criteria for solutions of the Navier–Stokes equations. Let Ω(t) := {x : |u(x, t)| > c ||u||Lr(R3) }, for some r ≥ 3 and constant c independent of t, with measure |Ω|. It is shown that if ||p + P||L3/2(Ω) becomes sufficiently small as |Ω| decreases, then||u||L(r+6)/3(R3) decays and regularity is secured. Here p is the physical pressure and P is a pressure moderator of relatively broad forms. The implications of the results are discussed and regularity criteria in terms of bounds for |p + P| within Ω are deduced.Simulating the coronal evolution of AR 11437 using SDO/HMI magnetograms
http://hdl.handle.net/10023/12226
The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. (2011). A sequence of photospheric line-of-sight magnetograms produced by SDO/HMI are used todrive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/AIA observations show that many aspects of the active region's observed coronal evolution are reproduced. In particular,it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occur on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and10 hours before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.
Funding: STFC via the Consolidated Grant SMC1/YST025 (SLY), STFC and the Levehulme Trust (DHM).
Wed, 10 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/122262018-01-10T00:00:00ZYardley, Stephanie L.Mackay, Duncan H.Green, Lucie M.The coronal magnetic field evolution of AR 11437 is simulated by applying the magnetofrictional relaxation technique of Mackay et al. (2011). A sequence of photospheric line-of-sight magnetograms produced by SDO/HMI are used todrive the simulation and continuously evolve the coronal magnetic field of the active region through a series of nonlinear force-free equilibria. The simulation is started during the first stages of the active region emergence so that its full evolution from emergence to decay can be simulated. A comparison of the simulation results with SDO/AIA observations show that many aspects of the active region's observed coronal evolution are reproduced. In particular,it shows the presence of a flux rope, which forms at the same location as sheared coronal loops in the observations. The observations show that eruptions occur on 2012 March 17 at 05:09 UT and 10:45 UT and on 2012 March 20 at14:31 UT. The simulation reproduces the first and third eruption, with the simulated flux rope erupting roughly 1 and10 hours before the observed ejections, respectively. A parameter study is conducted where the boundary and initial conditions are varied along with the physical effects of Ohmic diffusion, hyperdiffusion and an additional injection of helicity. When comparing the simulations, the evolution of the magnetic field, free magnetic energy, relative helicity and flux rope eruption timings do not change significantly. This indicates that the key element in reproducing the coronal evolution of AR 11437 is the use of line-of-sight magnetograms to drive the evolution of the coronal magnetic field.Lumped finite elements for reaction-cross-diffusion systems on stationary surfaces
http://hdl.handle.net/10023/12182
We consider a lumped surface finite element method (LSFEM) for the spatial approximation of reaction-diffusion equations on closed compact surfaces in R3 in the presence of cross-diffusion. We provide a fully-discrete scheme by applying the implicit-explicit (IMEX) Euler method. We provide sufficient conditions for the existence of polytopal invariant regions for the numerical solution after spatial and full discretisations. Furthermore, we prove optimal error bounds for the semi- and fully-discrete methods, that is the convergence rates are quadratic in the meshsize and linear in the timestep. To support our theoretical findings, we provide two numerical tests. The first test confirms that in the absence of lumping numerical solutions violate the invariant region leading to blow-up due to the nature of the kinetics. The second experiment is an example of Turing pattern formation in the presence of cross-diffusion on the sphere.
All the authors (AM, IS, CV, MF) 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). This work (AM) has received funding from the European Union's Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. AM and CV acknowledge support from the Engineering and Physical Sciences Research Council (EP/J016780/1) on Modelling, analysis and simulation of spatial patterning on evolving biological surfaces and the Leverhulme Trust Research Project Grant (RPG-2014-149) on Unravelling new mathematics for 3D cell migration. AM was partially supported by a fellowship from the Simons Foundation. AM is a Royal Society Wolfson Research Merit Award Holder, generously funded by the Wolfson Foundation.
Fri, 15 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/121822017-12-15T00:00:00ZFrittelli, MassimoMadzvamuse, AnotidaSgura, IvonneVenkataraman, ChandrasekharWe consider a lumped surface finite element method (LSFEM) for the spatial approximation of reaction-diffusion equations on closed compact surfaces in R3 in the presence of cross-diffusion. We provide a fully-discrete scheme by applying the implicit-explicit (IMEX) Euler method. We provide sufficient conditions for the existence of polytopal invariant regions for the numerical solution after spatial and full discretisations. Furthermore, we prove optimal error bounds for the semi- and fully-discrete methods, that is the convergence rates are quadratic in the meshsize and linear in the timestep. To support our theoretical findings, we provide two numerical tests. The first test confirms that in the absence of lumping numerical solutions violate the invariant region leading to blow-up due to the nature of the kinetics. The second experiment is an example of Turing pattern formation in the presence of cross-diffusion on the sphere.Return times at periodic points in random dynamics
http://hdl.handle.net/10023/12136
We prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures {µω}ω∈Ω, where the ‘driving space’ Ω is equipped with a probability measure which is invariant under a transformation θ. We assume that the fibred measures µω satisfy a generalised invariance property and are ψ-mixing. We then show that for almost every ω the return times to cylinders An at periodic points are in the limit compound Poisson distributed for a parameter ϑ which is given by the escape rate at the periodic point.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/121362017-01-01T00:00:00ZHaydn, NicolaiTodd, Michael JohnWe prove a quenched limiting law for random measures on subshifts at periodic points. We consider a family of measures {µω}ω∈Ω, where the ‘driving space’ Ω is equipped with a probability measure which is invariant under a transformation θ. We assume that the fibred measures µω satisfy a generalised invariance property and are ψ-mixing. We then show that for almost every ω the return times to cylinders An at periodic points are in the limit compound Poisson distributed for a parameter ϑ which is given by the escape rate at the periodic point.Primary education in Vietnam and pupil online engagement
http://hdl.handle.net/10023/12107
Purpose This paper focuses on exploring the disparities in social awareness and use of the Internet between urban and rural school children in the North of Vietnam. Approach A total of 525 pupils, aged 9 to 11 years old, randomly selected from 7 urban and rural schools, who are Internet users, participated in the study and consented to responding to a questionnaire adapted from an equivalent European Union (EU) study. A comparative statistical analysis of the responses was then carried out, using IBM SPSS v21, which consisted of a descriptive analysis, an identification of personal self-development opportunities, as well as issues related to pupils’ digital prowess and knowledge of Internet use, and Internet safety, including parental engagement in their offspring’s online activities. Findings The study highlights the fact that children from both the urban and rural regions of the North of Vietnam mostly access the Internet from home, but with more children in the urbanized areas accessing it at school than their rural counterparts. Although children from the rural areas scored lower on all the Internet indicators, such as digital access and online personal experience and awareness, there was no disparity in awareness of Internet risks between the two sub-samples. It is noteworthy that there was no statistically significant gender difference towards online activities that support self-development. In relation to safe Internet usage, children are likely to seek advice from their parents, rather than through teachers or friends. However, they are not yet provided with an effective safety net while exposing themselves to the digital world.
Mon, 08 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/121072018-01-08T00:00:00ZNguyen, QuynhNaguib, RaoufDas, AshishPapathomas, MichailVallar, EdgarWickramasinghe, NilminiSantos, Gil NonatoGalvez, Maria CeciliaNguyen, VietPurpose This paper focuses on exploring the disparities in social awareness and use of the Internet between urban and rural school children in the North of Vietnam. Approach A total of 525 pupils, aged 9 to 11 years old, randomly selected from 7 urban and rural schools, who are Internet users, participated in the study and consented to responding to a questionnaire adapted from an equivalent European Union (EU) study. A comparative statistical analysis of the responses was then carried out, using IBM SPSS v21, which consisted of a descriptive analysis, an identification of personal self-development opportunities, as well as issues related to pupils’ digital prowess and knowledge of Internet use, and Internet safety, including parental engagement in their offspring’s online activities. Findings The study highlights the fact that children from both the urban and rural regions of the North of Vietnam mostly access the Internet from home, but with more children in the urbanized areas accessing it at school than their rural counterparts. Although children from the rural areas scored lower on all the Internet indicators, such as digital access and online personal experience and awareness, there was no disparity in awareness of Internet risks between the two sub-samples. It is noteworthy that there was no statistically significant gender difference towards online activities that support self-development. In relation to safe Internet usage, children are likely to seek advice from their parents, rather than through teachers or friends. However, they are not yet provided with an effective safety net while exposing themselves to the digital world.Modelling the spatial dynamics of non-state terrorism : world study, 2002-2013
http://hdl.handle.net/10023/12067
To this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/120672017-12-07T00:00:00ZPython, AndréTo this day, terrorism perpetrated by non-state actors persists as a worldwide threat, as exemplified by the recent lethal attacks in Paris, London, Brussels, and the ongoing massacres perpetrated by the Islamic State in Iraq, Syria and neighbouring countries. In response, states deploy various counterterrorism policies, the costs of which could be reduced through more efficient preventive measures. The literature has not applied statistical models able to account for complex spatio-temporal dependencies, despite their potential for explaining and preventing non-state terrorism at the sub-national level. In an effort to address this shortcoming, this thesis employs Bayesian hierarchical models, where the spatial random field is represented by a stochastic partial differential equation. The results show that lethal terrorist attacks perpetrated by non-state actors tend to be concentrated in areas located within failed states from which they may diffuse locally, towards neighbouring areas. At the sub-national level, the propensity of attacks to be lethal and the frequency of lethal attacks appear to be driven by antagonistic mechanisms. Attacks are more likely to be lethal far away from large cities, at higher altitudes, in less economically developed areas, and in locations with higher ethnic diversity. In contrast, the frequency of lethal attacks tends to be higher in more economically developed areas, close to large cities, and within democratic countries.Above the noise : the search for periodicities in the inner heliosphere
http://hdl.handle.net/10023/12054
Remote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.
Wed, 01 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/120542017-11-01T00:00:00ZThrelfall, James WilliamDe Moortel, InekeConlon, Thomas MichaelRemote sensing of coronal and heliospheric periodicities can provide vital insight into the local conditions and dynamics of the solar atmosphere. We seek to trace long (one hour or longer) periodic oscillatory signatures (previously identified above the limb in the corona by, e.g., Telloni et al., 2013, Astrophys. J., 767, 138) from their origin at the solar surface out into the heliosphere. To do this, we combine on-disk measurements taken by the Atmospheric Imaging Assembly (AIA) onboard the Solar Dynamics Observatory (SDO) and concurrent extreme ultra-violet (EUV) and coronagraph data from one of the Solar Terrestrial Relations Observatory (STEREO) spacecraft to study the evolution of two active regions in the vicinity of an equatorial coronal hole over several days in early 2011. Fourier and wavelet analysis of signals are performed. Applying white-noise-based confidence levels to the power spectra associated with detrended intensity time series yields detections of oscillatory signatures with periods from 6 − 13 hours in both AIA and STEREO data. As was found by Telloni et al. (2013), these signatures are aligned with local magnetic structures. However, typical spectral power densities all vary substantially as a function of period, indicating spectra dominated by red (rather than white) noise. Contrary to the white-noise-based results, applying global confidence levels based on a generic background noise model (allowing a combination of white noise, red noise, and transients following Auch`ere et al., 2016, Astrophys. J., 825, 110) without detrending the time series, uncovers only sporadic, spatially uncorrelated evidence of periodic signatures in either instrument. Automating this method to individual pixels in the STEREO/COR coronagraph field of view is non-trivial.Vortex scaling ranges in two-dimensional turbulence
http://hdl.handle.net/10023/12029
We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.
Wed, 01 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/120292017-11-01T00:00:00ZBurgess, B. H.Dritschel, D. G.Scott, R. K.We survey the role of coherent vortices in two-dimensional turbulence, including formation mechanisms, implications for classical similarity and inertial range theories, and characteristics of the vortex populations. We review early work on the spatial and temporal scaling properties of vortices in freely evolving turbulence and more recent developments, including a spatiotemporal scaling theory for vortices in the forced inverse energy cascade. We emphasize that Kraichnan-Batchelor similarity theories and vortex scaling theories are best viewed as complementary and together provide a more complete description of two-dimensional turbulence. In particular, similarity theory has a continued role in describing the weak filamentary sea between the vortices. Moreover, we locate both classical inertial and vortex scaling ranges within the broader framework of scaling in far-from-equilibrium systems, which generically exhibit multiple fixed point solutions with distinct scaling behaviour. We describe how stationary transport in a range of scales comoving with the dilatation of flow features, as measured by the growth in vortex area, constrains the vortex number density in both freely evolving and forced two-dimensional turbulence. The new theories for coherent vortices reveal previously hidden nontrivial scaling, point to new dynamical understanding, and provide a novel exciting window into two-dimensional turbulence.Counting subwords and other results related to the generalised star-height problem for regular languages
http://hdl.handle.net/10023/12024
The Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one.
Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one.
Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups.
Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form 𝐴 ⋊ ℤ[sub]𝑟, where 𝐴 is an abelian group and ℤ[sub]𝑟 is the cyclic group of order 𝑟.
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/120242017-12-07T00:00:00ZBourne, ThomasThe Generalised Star-Height Problem is an open question in the field of formal language theory that concerns a measure of complexity on the class of regular languages; specifically, it asks whether or not there exists an algorithm to determine the generalised star-height of a given regular language. Rather surprisingly, it is not yet known whether there exists a regular language of generalised star-height greater than one.
Motivated by a theorem of Thérien, we first take a combinatorial approach to the problem and consider the languages in which every word features a fixed contiguous subword an exact number of times. We show that these languages are all of generalised star-height zero. Similarly, we consider the languages in which every word features a fixed contiguous subword a prescribed number of times modulo a fixed number and show that these languages are all of generalised star-height at most one.
Using these combinatorial results, we initiate work on identifying the generalised star-height of the languages that are recognised by finite semigroups. To do this, we establish the generalised star-height of languages recognised by Rees zero-matrix semigroups over nilpotent groups of classes zero and one before considering Rees zero-matrix semigroups over monogenic semigroups.
Finally, we explore the generalised star-height of languages recognised by finite groups of a given order. We do this through the use of finite state automata and 'count arrows' to examine semidirect products of the form 𝐴 ⋊ ℤ[sub]𝑟, where 𝐴 is an abelian group and ℤ[sub]𝑟 is the cyclic group of order 𝑟.Preserving invariance properties of reaction-diffusion systems on stationary surfaces
http://hdl.handle.net/10023/12021
We propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in ℝ3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves the maximum principle. On the application of a fully discrete scheme using the implicit–explicit Euler method in time, we prove that invariant regions of the continuous problem are preserved (i) at the spatially discrete level with no restriction on the meshsize and (ii) at the fully discrete level under a timestep restriction. We further prove optimal error bounds for the semidiscrete and fully discrete methods, that is, the convergence rates are quadratic in the meshsize and linear in the timestep. Numerical experiments are provided to support the theoretical findings. We provide examples in which, in the absence of lumping, the numerical solution violates the invariant region leading to blow-up.
This work (AM, CV) is partly supported by the EPSRC grant number EP/J016780/1 and the Leverhulme Trust Research Project Grant (RPG-2014-149). The authors (MF, AM, IS CV) would like to 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] supported by EPSRC Grant Number EP/K032208/1. AM acknowledges funding from the European Union Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866 and was partially supported by a grant from the Simons Foundation. AM is a Royal Society Wolfson Research Merit Award Holder funded generously by the Wolfson Foundation.
Fri, 27 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/120212017-10-27T00:00:00ZFrittelli, MassimoMadzvamuse, AnotideSgura, IvonneVenkataraman, ChandrasekharWe propose and analyse a lumped surface finite element method for the numerical approximation of reaction–diffusion systems on stationary compact surfaces in ℝ3. The proposed method preserves the invariant regions of the continuous problem under discretization and, in the special case of scalar equations, it preserves the maximum principle. On the application of a fully discrete scheme using the implicit–explicit Euler method in time, we prove that invariant regions of the continuous problem are preserved (i) at the spatially discrete level with no restriction on the meshsize and (ii) at the fully discrete level under a timestep restriction. We further prove optimal error bounds for the semidiscrete and fully discrete methods, that is, the convergence rates are quadratic in the meshsize and linear in the timestep. Numerical experiments are provided to support the theoretical findings. We provide examples in which, in the absence of lumping, the numerical solution violates the invariant region leading to blow-up.Modelling complex dependencies inherent in spatial and spatio-temporal point pattern data
http://hdl.handle.net/10023/12009
Point processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.
Fri, 23 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/120092017-06-23T00:00:00ZJones-Todd, Charlotte MPoint processes are mechanisms that beget point patterns. Realisations of point processes are observed in many contexts, for example, locations of stars in the sky, or locations of trees in a forest. Inferring the mechanisms that drive point processes relies on the development of models that appropriately account for the dependencies inherent in the data. Fitting models that adequately capture the complex dependency structures in either space, time, or both is often problematic. This is commonly due to—but not restricted to—the intractability of the likelihood function, or computational burden of the required numerical operations.
This thesis primarily focuses on developing point process models with some hierarchical structure, and specifically where this is a latent structure that may be considered as one of the following: (i) some unobserved construct assumed to be generating the observed structure, or (ii) some stochastic process describing the structure of the point pattern. Model fitting procedures utilised in this thesis include either (i) approximate-likelihood techniques to circumvent intractable likelihoods, (ii) stochastic partial differential equations to model continuous spatial latent structures, or (iii) improving computational speed in numerical approximations by exploiting automatic differentiation.
Moreover, this thesis extends classic point process models by considering multivariate dependencies. This is achieved through considering a general class of joint point process model, which utilise shared stochastic structures. These structures account for the dependencies inherent in multivariate point process data. These models are applied to data originating from various scientific fields; in particular, applications are considered in ecology, medicine, and geology. In addition, point process models that account for the second order behaviour of these assumed stochastic structures are also considered.Bifurcations and chaotic dynamics in a tumour-immune-virus system
http://hdl.handle.net/10023/11999
Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.
Wed, 07 Dec 2016 00:00:00 GMThttp://hdl.handle.net/10023/119992016-12-07T00:00:00ZEftimie, R.Macnamara, C. K.Dushoff, JonathanBramson, J. L.Earn, D. J. D.Despite mounting evidence that oncolytic viruses can be effective in treating cancer, understanding the details of the interactions between tumour cells, oncolytic viruses and immune cells that could lead to tumour control or tumour escape is still an open problem. Mathematical modelling of cancer oncolytic therapies has been used to investigate the biological mechanisms behind the observed temporal patterns of tumour growth. However, many models exhibit very complex dynamics, which renders them difficult to investigate. In this case, bifurcation diagrams could enable the visualisation of model dynamics by identifying (in the parameter space) the particular transition points between different behaviours. Here, we describe and investigate two simple mathematical models for oncolytic virus cancer therapy, with constant and immunity-dependent carrying capacity. While both models can exhibit complex dynamics, namely fixed points, periodic orbits and chaotic behaviours, only the model with immunity-dependent carrying capacity can exhibit them for biologically realistic situations, i.e., before the tumour grows too large and the experiment is terminated. Moreover, with the help of the bifurcation diagrams we uncover two unexpected behaviours in virus-tumour dynamics: (i) for short virus half-life, the tumour size seems to be too small to be detected, while for long virus half-life the tumour grows to larger sizes that can be detected; (ii) some model parameters have opposite effects on the transient and asymptotic dynamics of the tumour.Inhomogeneous self-similar sets with overlaps
http://hdl.handle.net/10023/11995
It is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and the condensation set. First, we prove that this 'expected formula' does not hold in general if there are overlaps in the construction. We demonstrate this via two different types of counterexample: the first is a family of overlapping inhomogeneous self-similar sets based upon Bernoulli convolutions; and the second applies in higher dimensions and makes use of a spectral gap property that holds for certain subgroups of SO(d) for d≥3. We also obtain new upper bounds for the upper box dimension of an inhomogeneous self-similar set which hold in general. Moreover, our counterexamples demonstrate that these bounds are optimal. In the final section we show that if the weak separation property is satisfied, that is, the overlaps are controllable, then the 'expected formula' does hold.
Thu, 04 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/119952017-05-04T00:00:00ZBaker, SimonFraser, Jonathan M.Máthé, AndrásIt is known that if the underlying iterated function system satisfies the open set condition, then the upper box dimension of an inhomogeneous self-similar set is the maximum of the upper box dimensions of the homogeneous counterpart and the condensation set. First, we prove that this 'expected formula' does not hold in general if there are overlaps in the construction. We demonstrate this via two different types of counterexample: the first is a family of overlapping inhomogeneous self-similar sets based upon Bernoulli convolutions; and the second applies in higher dimensions and makes use of a spectral gap property that holds for certain subgroups of SO(d) for d≥3. We also obtain new upper bounds for the upper box dimension of an inhomogeneous self-similar set which hold in general. Moreover, our counterexamples demonstrate that these bounds are optimal. In the final section we show that if the weak separation property is satisfied, that is, the overlaps are controllable, then the 'expected formula' does hold.On interfaces between cell populations with different mobilities
http://hdl.handle.net/10023/11980
Partial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/119802017-03-01T00:00:00ZLorenzi, TommasoLorz, AlexanderPerthame, BenoitPartial differential equations describing the dynamics of cell population densities from a fluid mechanical perspective can model the growth of avascular tumours. In this framework, we consider a system of equations that describes the interaction between a population of dividing cells and a population of non-dividing cells. The two cell populations are characterised by different mobilities. We present the results of numerical simulations displaying two-dimensional spherical waves with sharp interfaces between dividing and non-dividing cells. Furthermore, we numerically observe how different ratios between the mobilities change the morphology of the interfaces, and lead to the emergence of finger-like patterns of invasion above a threshold. Motivated by these simulations, we study the existence of one-dimensional travelling wave solutions.Arithmetic patches, weak tangents, and dimension
http://hdl.handle.net/10023/11978
We investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure of tangent sets, and the Assouad dimension. We begin by extending a recent result of Dyatlov and Zahl by showing that a set cannot contain arbitrarily large arithmetic progressions (patches) if it has Assouad dimension strictly smaller than the ambient spatial dimension. Seeking a partial converse, we go on to prove that having Assouad dimension equal to the ambient spatial dimension is equivalent to having weak tangents with non-empty interior and to ‘asymptotically’ containing arbitrarily large arithmetic patches. We present some applications of our results concerning sets of integers, which include a weak solution to the Erdös–Turán conjecture on arithmetic progressions.
The first named author is supported by a Leverhulme Trust Research Fellowship (RF-2016-500) and the second named author is supported by a PhD scholarship provided bythe School of Mathematics in the University of St Andrews
Wed, 01 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/119782017-11-01T00:00:00ZFraser, Jonathan MacDonaldYu, HanWe investigate the relationships between several classical notions in arithmetic combinatorics and geometry including the presence (or lack of) arithmetic progressions (or patches in dimensions at least 2), the structure of tangent sets, and the Assouad dimension. We begin by extending a recent result of Dyatlov and Zahl by showing that a set cannot contain arbitrarily large arithmetic progressions (patches) if it has Assouad dimension strictly smaller than the ambient spatial dimension. Seeking a partial converse, we go on to prove that having Assouad dimension equal to the ambient spatial dimension is equivalent to having weak tangents with non-empty interior and to ‘asymptotically’ containing arbitrarily large arithmetic patches. We present some applications of our results concerning sets of integers, which include a weak solution to the Erdös–Turán conjecture on arithmetic progressions.A path reconstruction method integrating dead-reckoning and position fixes applied to humpback whales
http://hdl.handle.net/10023/11976
BACKGROUND: Detailed information about animal location and movement is often crucial in studies of natural behaviour and how animals respond to anthropogenic activities. Dead-reckoning can be used to infer such detailed information, but without additional positional data this method results in uncertainty that grows with time. Combining dead-reckoning with new Fastloc-GPS technology should provide good opportunities for reconstructing georeferenced fine-scale tracks, and should be particularly useful for marine animals that spend most of their time under water. We developed a computationally efficient, Bayesian state-space modelling technique to estimate humpback whale locations through time, integrating dead-reckoning using on-animal sensors with measurements of whale locations using on-animal Fastloc-GPS and visual observations. Positional observation models were based upon error measurements made during calibrations. RESULTS: High-resolution 3-dimensional movement tracks were produced for 13 whales using a simple process model in which errors caused by water current movements, non-location sensor errors, and other dead-reckoning errors were accumulated into a combined error term. Positional uncertainty quantified by the track reconstruction model was much greater for tracks with visual positions and few or no GPS positions, indicating a strong benefit to using Fastloc-GPS for track reconstruction. Compared to tracks derived only from position fixes, the inclusion of dead-reckoning data greatly improved the level of detail in the reconstructed tracks of humpback whales. Using cross-validation, a clear improvement in the predictability of out-of-set Fastloc-GPS data was observed compared to more conventional track reconstruction methods. Fastloc-GPS observation errors during calibrations were found to vary by number of GPS satellites received and by orthogonal dimension analysed; visual observation errors varied most by distance to the whale. CONCLUSIONS: By systematically accounting for the observation errors in the position fixes, our model provides a quantitative estimate of location uncertainty that can be appropriately incorporated into analyses of animal movement. This generic method has potential application for a wide range of marine animal species and data recording systems.
PW received a PhD studentship with matched funding from The Netherlands Ministry of Defence (administered by TNO) and the UK Natural Environment Research Council (NE/J500276/1). The 3S2 project was funded by the US Office of Naval Research (N00014-10-1-0355), the Norwegian Ministry of Defence, and The Netherlands Ministry of Defence. Part of this work was supported by the Multi-study Ocean acoustics Human effects Analysis (MOCHA) project funded by the US Office of Naval Research (N00014-12-1-0204).
Mon, 21 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/119762015-09-21T00:00:00ZWensveen, Paul J.Thomas, LenMiller, Patrick J OBACKGROUND: Detailed information about animal location and movement is often crucial in studies of natural behaviour and how animals respond to anthropogenic activities. Dead-reckoning can be used to infer such detailed information, but without additional positional data this method results in uncertainty that grows with time. Combining dead-reckoning with new Fastloc-GPS technology should provide good opportunities for reconstructing georeferenced fine-scale tracks, and should be particularly useful for marine animals that spend most of their time under water. We developed a computationally efficient, Bayesian state-space modelling technique to estimate humpback whale locations through time, integrating dead-reckoning using on-animal sensors with measurements of whale locations using on-animal Fastloc-GPS and visual observations. Positional observation models were based upon error measurements made during calibrations. RESULTS: High-resolution 3-dimensional movement tracks were produced for 13 whales using a simple process model in which errors caused by water current movements, non-location sensor errors, and other dead-reckoning errors were accumulated into a combined error term. Positional uncertainty quantified by the track reconstruction model was much greater for tracks with visual positions and few or no GPS positions, indicating a strong benefit to using Fastloc-GPS for track reconstruction. Compared to tracks derived only from position fixes, the inclusion of dead-reckoning data greatly improved the level of detail in the reconstructed tracks of humpback whales. Using cross-validation, a clear improvement in the predictability of out-of-set Fastloc-GPS data was observed compared to more conventional track reconstruction methods. Fastloc-GPS observation errors during calibrations were found to vary by number of GPS satellites received and by orthogonal dimension analysed; visual observation errors varied most by distance to the whale. CONCLUSIONS: By systematically accounting for the observation errors in the position fixes, our model provides a quantitative estimate of location uncertainty that can be appropriately incorporated into analyses of animal movement. This generic method has potential application for a wide range of marine animal species and data recording systems.The interaction of two surface vortices near a topographic slope in a stratified ocean
http://hdl.handle.net/10023/11972
We study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity, and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it, or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other, and thus favour merger. The topographic wave and vortices exert a deformation on these cyclones, which filament. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting, and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper vortices, or to the strong shear that the former exert on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with opposite signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its mixing in regions of vortex merger. The trajectories of particles indicates how the fluid initially in the vortices is finally partitioned.
Fri, 01 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/119722017-12-01T00:00:00Zde Marez, CharlyCarton, XavierMorvan, MathieuReinaud, Jean NoelWe study the influence of bottom topography on the interaction of two identical vortices in a two-layer, quasi-geostrophic model. The two vortices have piecewise-uniform potential vorticity, and are lying in the upper layer of the model. The topography is a smooth bottom slope. For two cyclones, topography modifies the merger critical distance and the merger efficiency: the topographic wave and vortices can advect the two cyclones along the shelf when they are initially far from it, or towards the shelf when they are initially closer to it. They can also advect the two cyclones towards each other, and thus favour merger. The topographic wave and vortices exert a deformation on these cyclones, which filament. Regimes of partial vortex merger or of vortex splitting are then observed. The interaction of the vorticity poles in the two layers are analysed to explain the evolution of the two upper layer cyclones. For taller topography, two new regimes appear: vortex drift and splitting, and filamentation and asymmetric merger. They are due to the hetonic coupling of lower layer vorticity with the upper vortices, or to the strong shear that the former exert on the latter. The interaction of two anticyclones shows regimes of co-rotation or merger, but specifically, it leads to the drift of the two vortices away from the slope, via a hetonic coupling with opposite signed vorticity in the lower layer. This vorticity originates in the breaking of the topographic wave. The analysis of passive tracer evolution confirms the inshore or offshore drift of the fluid, the formation of tracer fronts along filaments and its mixing in regions of vortex merger. The trajectories of particles indicates how the fluid initially in the vortices is finally partitioned.New aspects of particle acceleration in collapsing magnetic traps
http://hdl.handle.net/10023/11954
Collapsing magnetic traps (CMTs) have been suggested as one of the mechanisms that could contribute to particle energisation in solar flares. The basic idea behind CMTs is that charged particles will be trapped on the magnetic field lines below the reconnection region of a flare. This thesis discusses a number of important new aspects in particle energisation processes in CMTs, based on the model by Giuliani et al. (2005). In particular, we extend previous studies of particle acceleration in this CMT model to the relativistic regime and compare our results obtained using relativistic guiding centre theory with results obtained using the non-relativistic guiding centre theory. The similarities and differences found are discussed. We then present a detailed study of the question, what leads to the trapping or escape of particle orbits from CMTs. The answer to this question is investigated by using results from the non-relativistic orbit calculations with guiding centre theory and a number of simple models for particle energy gain in CMTs. We find that there is a critical pitch angle dividing trapped particle orbits from the escaping particle orbits and that this critical pitch angle does not coincide with the initial loss cone angle. Furthermore, we also present a calculation of the time evolution of an anisotropic pressure tensor and of the plasma density under the assumptions that they evolve in line with our kinematic MHD CMT model and that the pressure tensor satisfies the double-adiabatic Chew-Goldburger-Low (CGL) theory.
Finally, we make a first step to introduce Coulomb scattering by a Maxwellian background plasma into our guiding centre equations by changing them into a set of stochastic differential equations. We study the influence of a static background plasma onto selected particle orbits by pitch angle scattering and energy losses, and look at its effect on the particle energy and the trapping conditions.
Wed, 01 Jan 2014 00:00:00 GMThttp://hdl.handle.net/10023/119542014-01-01T00:00:00ZEradat Oskoui, SolmazCollapsing magnetic traps (CMTs) have been suggested as one of the mechanisms that could contribute to particle energisation in solar flares. The basic idea behind CMTs is that charged particles will be trapped on the magnetic field lines below the reconnection region of a flare. This thesis discusses a number of important new aspects in particle energisation processes in CMTs, based on the model by Giuliani et al. (2005). In particular, we extend previous studies of particle acceleration in this CMT model to the relativistic regime and compare our results obtained using relativistic guiding centre theory with results obtained using the non-relativistic guiding centre theory. The similarities and differences found are discussed. We then present a detailed study of the question, what leads to the trapping or escape of particle orbits from CMTs. The answer to this question is investigated by using results from the non-relativistic orbit calculations with guiding centre theory and a number of simple models for particle energy gain in CMTs. We find that there is a critical pitch angle dividing trapped particle orbits from the escaping particle orbits and that this critical pitch angle does not coincide with the initial loss cone angle. Furthermore, we also present a calculation of the time evolution of an anisotropic pressure tensor and of the plasma density under the assumptions that they evolve in line with our kinematic MHD CMT model and that the pressure tensor satisfies the double-adiabatic Chew-Goldburger-Low (CGL) theory.
Finally, we make a first step to introduce Coulomb scattering by a Maxwellian background plasma into our guiding centre equations by changing them into a set of stochastic differential equations. We study the influence of a static background plasma onto selected particle orbits by pitch angle scattering and energy losses, and look at its effect on the particle energy and the trapping conditions.Spatial distribution of citizen science casuistic observations for different taxonomic groups
http://hdl.handle.net/10023/11933
Opportunistic citizen science databases are becoming an important way of gathering information on species distributions. These data are temporally and spatially dispersed and could have limitations regarding biases in the distribution of the observations in space and/or time. In this work, we test the influence of landscape variables in the distribution of citizen science observations for eight taxonomic groups. We use data collected through a Portuguese citizen science database (biodiversity4all.org). We use a zero-inflated negative binomial regression to model the distribution of observations as a function of a set of variables representing the landscape features plausibly influencing the spatial distribution of the records. Results suggest that the density of paths is the most important variable, having a statistically significant positive relationship with number of observations for seven of the eight taxa considered. Wetland coverage was also identified as having a significant, positive relationship, for birds, amphibians and reptiles, and mammals. Our results highlight that the distribution of species observations, in citizen science projects, is spatially biased. Higher frequency of observations is driven largely by accessibility and by the presence of water bodies. We conclude that efforts are required to increase the spatial evenness of sampling effort from volunteers.
PT acknowledges support from the Portuguese Foundation for Science and Technology (FCT/MCTES) (SFRH/BD/89543/2012). ACH acknowledges support from the Portuguese Foundation for Science and Technology (FCT/MCTES) (UID/BIA/50027/2013) and from FEDER through the Operational Programme for Competitiveness Factors – COMPETE (POCI-01-0145-FEDER-006821). TAM thanks partial support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013). CC acknowledges support from the Portuguese Foundation for Science and Technology (FCT) FCT for funds to GHTM - UID/Multi/04413/2013. We thank all volunteers who participate in BioDiversity4All project.
Mon, 16 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/119332017-10-16T00:00:00ZTiago, PatríciaCeia-Hasse, AnaMarques, Tiago A.Capinha, CésarPereira, Henrique M.Opportunistic citizen science databases are becoming an important way of gathering information on species distributions. These data are temporally and spatially dispersed and could have limitations regarding biases in the distribution of the observations in space and/or time. In this work, we test the influence of landscape variables in the distribution of citizen science observations for eight taxonomic groups. We use data collected through a Portuguese citizen science database (biodiversity4all.org). We use a zero-inflated negative binomial regression to model the distribution of observations as a function of a set of variables representing the landscape features plausibly influencing the spatial distribution of the records. Results suggest that the density of paths is the most important variable, having a statistically significant positive relationship with number of observations for seven of the eight taxa considered. Wetland coverage was also identified as having a significant, positive relationship, for birds, amphibians and reptiles, and mammals. Our results highlight that the distribution of species observations, in citizen science projects, is spatially biased. Higher frequency of observations is driven largely by accessibility and by the presence of water bodies. We conclude that efforts are required to increase the spatial evenness of sampling effort from volunteers.DESNT : a poor prognosis category of human prostate cancer
http://hdl.handle.net/10023/11922
Background : A critical problem in the clinical management of prostate cancer is that it is highly heterogeneous. Accurate prediction of individual cancer behaviour is therefore not achievable at the time of diagnosis leading to substantial overtreatment. It remains an enigma that, in contrast to breast cancer, unsupervised analyses of global expression profiles have not currently defined robust categories of prostate cancer with distinct clinical outcomes. Objective: To devise a novel classification framework for human prostate cancer based on unsupervised mathematical approaches. Design, setting, and participants: Our analyses are based on the hypothesis that previous attempts to classify prostate cancer have been unsuccessful because individual samples of prostate cancer frequently have heterogeneous compositions. To address this issue, we applied an unsupervised Bayesian procedure called Latent Process Decomposition to four independent prostate cancer transcriptome datasets obtained using samples from prostatectomy patients and containing between 78 and 182 participants. Outcome measurements and statistical analysis: Biochemical failure was assessed using log-rank analysis and Cox regression analysis. Results and limitations: Application of Latent Process Decomposition identified a common process in all four independent datasets examined. Cancers assigned to this process (designated DESNT cancers) are characterized by low expression of a core set of 45 genes, many encoding proteins involved in the cytoskeleton machinery, ion transport, and cell adhesion. For the three datasets with linked prostate-specific antigen failure data following prostatectomy, patients with DESNT cancer exhibited poor outcome relative to other patients (p = 2.65 × 10−5, p = 4.28 × 10−5, and p = 2.98 × 10−8). When these three datasets were combined the independent predictive value of DESNT membership was p = 1.61 × 10−7 compared with p = 1.00 × 10−5 for Gleason sum. A limitation of the study is that only prediction of prostate-specific antigen failure was examined. Conclusions: Our results demonstrate the existence of a novel poor prognosis category of human prostate cancer and will assist in the targeting of therapy, helping avoid treatment-associated morbidity in men with indolent disease. Patient Summary: Prostate cancer, unlike breast cancer, does not have a robust classification framework. We propose that this failure has occurred because prostate cancer samples selected for analysis frequently have heterozygous compositions (individual samples are made up of many different parts that each have different characteristics). Applying a mathematical approach that can overcome this problem we identify a novel poor prognosis category of human prostate cancer called DESNT.
his work was funded by the Bob Champion Cancer Trust, The Masonic Charitable Foundation successor to The Grand Charity, The King Family, and The University of East Anglia. We acknowledge support from Movember, from Prostate Cancer UK, Callum Barton, and from The Andy Ripley Memorial Fund. We would like to acknowledge the support of the National Institute for Health Research which funds the Cambridge Bio-medical Research Centre, Cambridge UK.
Mon, 06 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/119222017-03-06T00:00:00ZLuca, Bogdan-AlexandruBrewer, Daniel S.Edwards, Dylan R.Edwards, SandraWhitaker, Hayley C.Merson, SueDennis, NeningCooper, Rosalin A.Hazell, StevenWarren, Anne Y.Eeles, RosalindLynch, Andy G.Ross-Adams, HelenLamb, Alastair D.Neal, David E.Sethia, KrishnaMills, Robert D.Ball, Richard Y.Curley, HelenClark, JeremyMoulton, VincentCooper, Colin S.Background : A critical problem in the clinical management of prostate cancer is that it is highly heterogeneous. Accurate prediction of individual cancer behaviour is therefore not achievable at the time of diagnosis leading to substantial overtreatment. It remains an enigma that, in contrast to breast cancer, unsupervised analyses of global expression profiles have not currently defined robust categories of prostate cancer with distinct clinical outcomes. Objective: To devise a novel classification framework for human prostate cancer based on unsupervised mathematical approaches. Design, setting, and participants: Our analyses are based on the hypothesis that previous attempts to classify prostate cancer have been unsuccessful because individual samples of prostate cancer frequently have heterogeneous compositions. To address this issue, we applied an unsupervised Bayesian procedure called Latent Process Decomposition to four independent prostate cancer transcriptome datasets obtained using samples from prostatectomy patients and containing between 78 and 182 participants. Outcome measurements and statistical analysis: Biochemical failure was assessed using log-rank analysis and Cox regression analysis. Results and limitations: Application of Latent Process Decomposition identified a common process in all four independent datasets examined. Cancers assigned to this process (designated DESNT cancers) are characterized by low expression of a core set of 45 genes, many encoding proteins involved in the cytoskeleton machinery, ion transport, and cell adhesion. For the three datasets with linked prostate-specific antigen failure data following prostatectomy, patients with DESNT cancer exhibited poor outcome relative to other patients (p = 2.65 × 10−5, p = 4.28 × 10−5, and p = 2.98 × 10−8). When these three datasets were combined the independent predictive value of DESNT membership was p = 1.61 × 10−7 compared with p = 1.00 × 10−5 for Gleason sum. A limitation of the study is that only prediction of prostate-specific antigen failure was examined. Conclusions: Our results demonstrate the existence of a novel poor prognosis category of human prostate cancer and will assist in the targeting of therapy, helping avoid treatment-associated morbidity in men with indolent disease. Patient Summary: Prostate cancer, unlike breast cancer, does not have a robust classification framework. We propose that this failure has occurred because prostate cancer samples selected for analysis frequently have heterozygous compositions (individual samples are made up of many different parts that each have different characteristics). Applying a mathematical approach that can overcome this problem we identify a novel poor prognosis category of human prostate cancer called DESNT.Theory of one-dimensional Vlasov-Maxwell equilibria: with applications to collisionless current sheets and flux tubes
http://hdl.handle.net/10023/11916
Vlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models.
The ‘inverse problem’ is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation
of the plasma, and make conjectures for all classes.
The inverse problem is considered for nonlinear ‘force-free Harris sheets’. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging’ process.
We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets’, and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations.
We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle’ model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/119162017-12-07T00:00:00ZAllanson, Oliver DouglasVlasov-Maxwell equilibria are characterised by the self-consistent descriptions of the steady-states of collisionless plasmas in particle phase-space, and balanced macroscopic forces. We study the theory of Vlasov-Maxwell equilibria in one spatial dimension, as well as its application to current sheet and flux tube models.
The ‘inverse problem’ is that of determining a Vlasov-Maxwell equilibrium distribution function self-consistent with a given magnetic field. We develop the theory of inversion using expansions in Hermite polynomial functions of the canonical momenta. Sufficient conditions for the convergence of a Hermite expansion are found, given a pressure tensor. For large classes of DFs, we prove that non-negativity of the distribution function is contingent on the magnetisation
of the plasma, and make conjectures for all classes.
The inverse problem is considered for nonlinear ‘force-free Harris sheets’. By applying the Hermite method, we construct new models that can describe sub-unity values of the plasma beta (βpl) for the first time. Whilst analytical convergence is proven for all βpl, numerical convergence is attained for βpl = 0.85, and then βpl = 0.05 after a ‘re-gauging’ process.
We consider the properties that a pressure tensor must satisfy to be consistent with ‘asymmetric Harris sheets’, and construct new examples. It is possible to analytically solve the inverse problem in some cases, but others must be tackled numerically. We present new exact Vlasov-Maxwell equilibria for asymmetric current sheets, which can be written as a sum of shifted Maxwellian distributions. This is ideal for implementations in particle-in-cell simulations.
We study the correspondence between the microscopic and macroscopic descriptions of equilibrium in cylindrical geometry, and then attempt to find Vlasov-Maxwell equilibria for the nonlinear force-free ‘Gold-Hoyle’ model. However, it is necessary to include a background field, which can be arbitrarily weak if desired. The equilibrium can be electrically non-neutral, depending on the bulk flows.Global warming and ocean stratification : a potential result of large extraterrestrial impacts
http://hdl.handle.net/10023/11915
The prevailing paradigm for the climatic effects of large asteroid or comet impacts is a reduction in sunlight and significant short-term cooling caused by atmospheric aerosol loading. Here we show, using global climate model experiments, that the large increases in stratospheric water vapor that can occur upon impact with the ocean cause radiative forcings of over +20 W m−2 in the case of 10 km sized bolides. The result of such a positive forcing is rapid climatic warming, increased upper ocean stratification, and potentially disruption of upper ocean ecosystems. Since two thirds of the world's surface is ocean, we suggest that some bolide impacts may actually warm climate overall. For impacts producing both stratospheric water vapor and aerosol loading, radiative forcing by water vapor can reduce or even cancel out aerosol-induced cooling, potentially causing 1–2 decades of increased temperatures in both the upper ocean and on the land surface. Such a response, which depends on the ratio of aerosol to water vapor radiative forcing, is distinct from many previous scenarios for the climatic effects of large bolide impacts, which mostly account for cooling from aerosol loading. Finally, we discuss how water vapor forcing from bolide impacts may have contributed to two well-known phenomena: extinction across the Cretaceous/Paleogene boundary and the deglaciation of the Neoproterozoic snowball Earth.
We acknowledge the support of resources provided by UK National Centre for Atmospheric Science (NCAS), the High Performance Computing Cluster supported by the Research and Specialist Computing Support service at the University of East Anglia, UK Natural Environment Research Council (NERC), grants "CPE" (NE/K014757/1), and "Paleopolar" (NE/I005722/1). Data can be obtained from MJ on request. ACM acknowledges support from an AXA Postdoctoral Fellowship and the ERC ACCI grant Project No 267760, and NERC grant NE/M018199/1.
Fri, 28 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/119152017-04-28T00:00:00ZJoshi, Manojvon Glasow, RolandSmith, Robin S.Paxton, Charles G. M.Maycock, Amanda C.Lunt, Daniel J.Loptson, ClaireMarkwick, PaulThe prevailing paradigm for the climatic effects of large asteroid or comet impacts is a reduction in sunlight and significant short-term cooling caused by atmospheric aerosol loading. Here we show, using global climate model experiments, that the large increases in stratospheric water vapor that can occur upon impact with the ocean cause radiative forcings of over +20 W m−2 in the case of 10 km sized bolides. The result of such a positive forcing is rapid climatic warming, increased upper ocean stratification, and potentially disruption of upper ocean ecosystems. Since two thirds of the world's surface is ocean, we suggest that some bolide impacts may actually warm climate overall. For impacts producing both stratospheric water vapor and aerosol loading, radiative forcing by water vapor can reduce or even cancel out aerosol-induced cooling, potentially causing 1–2 decades of increased temperatures in both the upper ocean and on the land surface. Such a response, which depends on the ratio of aerosol to water vapor radiative forcing, is distinct from many previous scenarios for the climatic effects of large bolide impacts, which mostly account for cooling from aerosol loading. Finally, we discuss how water vapor forcing from bolide impacts may have contributed to two well-known phenomena: extinction across the Cretaceous/Paleogene boundary and the deglaciation of the Neoproterozoic snowball Earth.Can substorm particle acceleration be applied to solar flares?
http://hdl.handle.net/10023/11912
Using test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.
Fri, 20 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/119122017-10-20T00:00:00ZBirn, JoachimBattaglia, MarinaFletcher, LyndsayHesse, MichaelNeukirch, ThomasUsing test particle studies in the electromagnetic fields of three-dimensional magnetohydrodynamic (MHD) simulations of magnetic reconnection, we study the energization of charged particles in the context of the standard two-ribbon flare picture in analogy to the standard magnetospheric substorm paradigm. In particular, we investigate the effects of the collapsing field ("collapsing magnetic trap") below a reconnection site, which has been demonstrated to be the major acceleration mechanism that causes energetic particle acceleration and injections observed in Earth's magnetotail associated with substorms and other impulsive events. We contrast an initially force-free, high-shear field (low beta) with low and moderate shear, finite-pressure (high-beta) arcade structures, where beta represents the ratio between gas (plasma) and magnetic pressure. We demonstrate that the energization affects large numbers of particles, but the acceleration is modest in the presence of a significant shear field. Without incorporating loss mechanisms, the effect on particles at different energies is similar, akin to adiabatic heating, and thus is not a likely mechanism to generate a power-law tail onto a (heated or not heated) Maxwellian velocity distribution.Correlation estimation using components of Japanese candlesticks
http://hdl.handle.net/10023/11901
Using the wick's difference from the classical Japanese candlestick representation of daily open, high, low, close prices brings efficiency when estimating the correlation in a bivariate Brownian motion. An interpretation of the correlation estimator in Rogers and Zhou (2008) in the light of wicks' difference allows us to suggest modifications, which lead to an increased efficiency and robustness against the baseline model. An empirical study on four major financial markets confirms the advantages of the modified estimator.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/119012016-01-01T00:00:00ZPopov, Valentin MinaUsing the wick's difference from the classical Japanese candlestick representation of daily open, high, low, close prices brings efficiency when estimating the correlation in a bivariate Brownian motion. An interpretation of the correlation estimator in Rogers and Zhou (2008) in the light of wicks' difference allows us to suggest modifications, which lead to an increased efficiency and robustness against the baseline model. An empirical study on four major financial markets confirms the advantages of the modified estimator.Collisionless current sheet equilibria
http://hdl.handle.net/10023/11890
Current sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.
The authors acknowledge financial support by the UK Science and Technology Facilities Council Consolidated Grants ST/K000950/1 and and ST/N000609/1, as well as Doctoral Training Grant ST/K502327/1. OA also acknowledges support by the UK Natural Environment Research Council Grant NE/P017274/1.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/118902018-01-01T00:00:00ZNeukirch, ThomasWilson, FionaAllanson, Oliver DouglasCurrent sheets are important for the structure and dynamics of many plasma systems. In space and astrophysical plasmas they play a crucial role in activity processes, for example by facilitating the release of magnetic energy via processes such as magnetic reconnection. In this contribution we will focus on collisionless plasma systems. A sensible first step in any investigation of physical processes involving current sheets is to find appropriate equilibrium solutions. The theory of collisionless plasma equilibria is well established, but over the past few years there has been a renewed interest in finding equilibrium distribution functions for collisionless current sheets with particular properties, for example for cases where the current density is parallel to the magnetic field (force-free current sheets). This interest is due to a combination of scientific curiosity and potential applications to space and astrophysical plasmas. In this paper we will give an overview of some of the recent developments, discuss their potential applications and address a number of open questions.Parallel algorithms for computing finite semigroups
http://hdl.handle.net/10023/11879
In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing a finite semigroup. If U is any semigroup, and A be a subset of U, then we denote by ⟨A⟩ the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about ⟨A⟩, that has been found using the Froidure-Pin Algorithm, to compute the semigroup ⟨A, B⟩. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for ⟨A, B⟩ from that for ⟨A⟩. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup they output.
Mon, 19 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/118792017-06-19T00:00:00ZJonusas, JuliusMitchell, J. D.Pfeiffer, M.In this paper, we present two algorithms based on the Froidure-Pin Algorithm for computing a finite semigroup. If U is any semigroup, and A be a subset of U, then we denote by ⟨A⟩ the least subsemigroup of U containing A. If B is any other subset of U, then, roughly speaking, the first algorithm we present describes how to use any information about ⟨A⟩, that has been found using the Froidure-Pin Algorithm, to compute the semigroup ⟨A, B⟩. More precisely, we describe the data structure for a finite semigroup S given by Froidure and Pin, and how to obtain such a data structure for ⟨A, B⟩ from that for ⟨A⟩. The second algorithm is a lock-free concurrent version of the Froidure-Pin Algorithm. As was the case with the original algorithm of Froidure and Pin, the algorithms presented here produce the left and right Cayley graphs, a confluent terminating rewriting system, and a reduced word of the rewriting system for every element of the semigroup they output.Vertical structure of tropospheric winds on gas giants
http://hdl.handle.net/10023/11850
Zonal mean zonal velocity profiles from cloud-tracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloud-tops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.
Support for this work was generously provided by the National Science Foundation.
Sun, 16 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/118502017-04-16T00:00:00ZScott, R. K.Dunkerton, T. J.Zonal mean zonal velocity profiles from cloud-tracking observations on Jupiter and Saturn are used to infer latitudinal variations of potential temperature consistent with a shear stable potential vorticity distribution. Immediately below the cloud tops, density stratification is weaker on the poleward and stronger on the equatorward flanks of midlatitude jets, while at greater depth the opposite relation holds. Thermal wind balance then yields the associated vertical shears of midlatitude jets in an altitude range bounded above by the cloud-tops and bounded below by the level where the latitudinal gradient of static stability changes sign. The inferred vertical shear below the cloud tops is consistent with existing thermal profiling of the upper troposphere.The sense of the associated mean meridional circulation in the upper troposphere is discussed and expected magnitudes are given based on existing estimates of the radiative timescale on each planet.On the Fourier analytic structure of the Brownian graph
http://hdl.handle.net/10023/11846
In a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/118462018-01-01T00:00:00ZFraser, Jonathan MacDonaldSahlsten, TuomasIn a previous article (Int. Math. Res. Not. 2014:10 (2014), 2730–2745) T. Orponen and the authors proved that the Fourier dimension of the graph of any real-valued function on R is bounded above by 1. This partially answered a question of Kahane (1993) by showing that the graph of the Wiener process Wt (Brownian motion) is almost surely not a Salem set. In this article we complement this result by showing that the Fourier dimension of the graph of Wt is almost surely 1. In the proof we introduce a method based on Itô calculus to estimate Fourier transforms by reformulating the question in the language of Itô drift-diffusion processes and combine it with the classical work of Kahane on Brownian images.Notes on a semigroup related to the dicyclic group Qn
http://hdl.handle.net/10023/11837
We consider certain properties of the semigroup S defined by the Presentation S = 〈a,b : a2ⁿ⁻¹ = 1,b2 = a2ⁿ⁻², ba = ab2ⁿ⁻¹-1〉, (n ≥ 3).
Thu, 21 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/118372017-09-21T00:00:00ZSorouhesh, Mohammad R.Campbell, Colin M.We consider certain properties of the semigroup S defined by the Presentation S = 〈a,b : a2ⁿ⁻¹ = 1,b2 = a2ⁿ⁻², ba = ab2ⁿ⁻¹-1〉, (n ≥ 3).Root sets of polynomials and power series with finite choice of coefficients
http://hdl.handle.net/10023/11822
Given H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H, {z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0}, and the set of zeros of a power series with coefficients in H, {z∈C:∃(an)∈HN,∑n=0∞anzn=0}. In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any r∈(1/2,1), if H is 2cos−1(5−4|r|24)-dense in S1, then the set of zeros of polynomials with coefficients in H is dense in {z∈C:|z|∈[r,r−1]}, and the set of zeros of power series with coefficients in H contains the annulus {z∈C:|z|∈[r,1)}. These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.
The first author is supported by the EPSRC Grant EP/M001903/1. The second author is supported by a PhD scholarship provided by the School of Mathematics in the University of St Andrews.
Mon, 09 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/118222017-10-09T00:00:00ZBaker, SimonYu, HanGiven H⊆C two natural objects to study are the set of zeros of polynomials with coefficients in H, {z∈C:∃k>0,∃(an)∈Hk+1,∑n=0kanzn=0}, and the set of zeros of a power series with coefficients in H, {z∈C:∃(an)∈HN,∑n=0∞anzn=0}. In this paper, we consider the case where each element of H has modulus 1. The main result of this paper states that for any r∈(1/2,1), if H is 2cos−1(5−4|r|24)-dense in S1, then the set of zeros of polynomials with coefficients in H is dense in {z∈C:|z|∈[r,r−1]}, and the set of zeros of power series with coefficients in H contains the annulus {z∈C:|z|∈[r,1)}. These two statements demonstrate quantitatively how the set of polynomial zeros/power series zeros fill out the natural annulus containing them as H becomes progressively more dense.Appraising the relevance of DNA copy number loss and gain in prostate cancer using whole genome DNA sequence data
http://hdl.handle.net/10023/11812
A variety of models have been proposed to explain regions of recurrent somatic copy number alteration (SCNA) in human cancer. Our study employs Whole Genome DNA Sequence (WGS) data from tumor samples (n = 103) to comprehensively assess the role of the Knudson two hit genetic model in SCNA generation in prostate cancer. 64 recurrent regions of loss and gain were detected, of which 28 were novel, including regions of loss with more than 15% frequency at Chr4p15.2-p15.1 (15.53%), Chr6q27 (16.50%) and Chr18q12.3 (17.48%). Comprehensive mutation screens of genes, lincRNA encoding sequences, control regions and conserved domains within SCNAs demonstrated that a two-hit genetic model was supported in only a minor proportion of recurrent SCNA losses examined (15/40). We found that recurrent breakpoints and regions of inversion often occur within Knudson model SCNAs, leading to the identification of ZNF292 as a target gene for the deletion at 6q14.3-q15 and NKX3.1 as a two-hit target at 8p21.3-p21.2. The importance of alterations of lincRNA sequences was illustrated by the identification of a novel mutational hotspot at the KCCAT42, FENDRR, CAT1886 and STCAT2 loci at the 16q23.1-q24.3 loss. Our data confirm that the burden of SCNAs is predictive of biochemical recurrence, define nine individual regions that are associated with relapse, and highlight the possible importance of ion channel and G-protein coupled-receptor (GPCR) pathways in cancer development. We concluded that a two-hit genetic model accounts for about one third of SCNA indicating that mechanisms, such haploinsufficiency and epigenetic inactivation, account for the remaining SCNA losses.
We acknowledge support from Cancer Research UK (C5047/A22530, C309/A11566, C368/A6743, A368/A7990, C14303/A17197) and the Dallaglio Foundation. We also acknowledge support from the National Institute of Health Research (NIHR) (The Biomedical Research Centre at The Institute of Cancer Research & The Royal Marsden NHS Foundation Trust and the project "Prostate Cancer: Mechanisms of Progression and Treatment (PROMPT)" [G0500966/75466]). We thank the Wellcome Trust, Bob Champion Cancer Trust, The Orchid Cancer appeal, The RoseTrees Trust, The North West Cancer Research Fund, Big C, The King family, and The Masonic Charitable Foundation for funding. This research is supported by the Francis Crick Institute which receives its core funding from Cancer Research UK (FC001202), the UK Medical Research Council (FC001202), and the Wellcome Trust (FC001202).
Mon, 25 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/118122017-09-25T00:00:00ZCamacho, NiedzicaVan Loo, PeterEdwards, SandraKay, Jonathan D.Matthews, LucyHaase, KerstinClark, JeremyDennis, NeningThomas, SarahKremeyer, BarbaraZamora, JorgeButler, Adam P.Gundem, GunesMerson, SueLuxton, HayleyHawkins, SteveGhori, MohammedMarsden, LukeLambert, AdamKaraszi, KatalinPelvender, GillMassie, Charlie E.Kote-Jarai, ZSofiaRaine, KeiranJones, DavidHowat, William J.Hazell, StevenLivni, NaomiFisher, CyrilOgden, ChristopherKumar, PardeepThompson, AlanNicol, DavidMayer, ErikDudderidge, TimYu, YongweiZhang, HongweiShah, Nimish C.Gnanapragasam, Vincent J.Group, The CRUK-ICGC ProstateIsaacs, WilliamVisakorpi, TapioHamdy, FreddieBerney, DanVerrill, ClareWarren, Anne Y.Wedge, David C.Lynch, Andrew G.Foster, Christopher S.Lu, Yong JieBova, G. StevenWhitaker, Hayley C.McDermott, UltanNeal, David E.Eeles, RosalindCooper, Colin S.Brewer, Daniel S.A variety of models have been proposed to explain regions of recurrent somatic copy number alteration (SCNA) in human cancer. Our study employs Whole Genome DNA Sequence (WGS) data from tumor samples (n = 103) to comprehensively assess the role of the Knudson two hit genetic model in SCNA generation in prostate cancer. 64 recurrent regions of loss and gain were detected, of which 28 were novel, including regions of loss with more than 15% frequency at Chr4p15.2-p15.1 (15.53%), Chr6q27 (16.50%) and Chr18q12.3 (17.48%). Comprehensive mutation screens of genes, lincRNA encoding sequences, control regions and conserved domains within SCNAs demonstrated that a two-hit genetic model was supported in only a minor proportion of recurrent SCNA losses examined (15/40). We found that recurrent breakpoints and regions of inversion often occur within Knudson model SCNAs, leading to the identification of ZNF292 as a target gene for the deletion at 6q14.3-q15 and NKX3.1 as a two-hit target at 8p21.3-p21.2. The importance of alterations of lincRNA sequences was illustrated by the identification of a novel mutational hotspot at the KCCAT42, FENDRR, CAT1886 and STCAT2 loci at the 16q23.1-q24.3 loss. Our data confirm that the burden of SCNAs is predictive of biochemical recurrence, define nine individual regions that are associated with relapse, and highlight the possible importance of ion channel and G-protein coupled-receptor (GPCR) pathways in cancer development. We concluded that a two-hit genetic model accounts for about one third of SCNA indicating that mechanisms, such haploinsufficiency and epigenetic inactivation, account for the remaining SCNA losses.On the star-height of subword counting languages and their relationship to Rees zero-matrix semigroups
http://hdl.handle.net/10023/11811
Given a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.
Tue, 15 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/118112016-11-15T00:00:00ZBourne, TomRuškuc, NikGiven a word w over a finite alphabet, we consider, in three special cases, the generalised star-height of the languages in which w occurs as a contiguous subword (factor) an exact number of times and of the languages in which w occurs as a contiguous subword modulo a fixed number, and prove that in each case it is at most one. We use these combinatorial results to show that any language recognised by a Rees (zero-)matrix semigroup over an abelian group is of generalised star-height at most one.Vortex merger near a topographic slope in a homogeneous rotating fluid
http://hdl.handle.net/10023/11779
The effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.
This work is a contribution to the PHYSINDIEN research program. It was supported by CNRS-RFBR contract PRC 1069/16-55-150001.
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/117792017-10-01T00:00:00ZCarton, XavierMorvan, MathieuReinaud, Jean NoelSokolovskiy, MikhailL'Hégaret, PierreVic, ClémentThe effect of a bottom slope on the merger of two identical Rankine vortices is investigated in a two dimensional, quasi-geostrophic, incompressible fluid. When two cyclones initially lie parallel to the slope, and more than two vortex diameters away from the slope, the critical merger distance is unchanged. When the cyclones are closer to the slope, they can merge at larger distances, but they lose more mass into filaments, thus weakening the efficiency of merger. Several effects account for this: the topographic Rossby wave advects the cyclones, reduces their mutual distance and deforms them. This along shelf wave breaks into filaments and into secondary vortices which shear out the initial cyclones. The global motion of fluid towards the shallow domain and the erosion of the two cyclones are confirmed by the evolution of particles seeded both in the cyclone sand near the topographic slope. The addition of tracer to the flow indicates that diffusion is ballistic at early times. For two anticyclones, merger is also facilitated because one vortex is ejected offshore towards the other, via coupling with a topographic cyclone. Again two anticyclones can merge at large distance but they are eroded in the process. Finally, for taller topographies, the critical merger distance is again increased and the topographic influence can scatter or completely erode one of the two initial cyclones. Conclusions are drawn on possible improvements of the model configuration for an application to the ocean.Emergence of spatial patterns in a mathematical model for the co-culture dynamics of epithelial-like and mesenchymal-like cells
http://hdl.handle.net/10023/11775
Accumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/117752017-02-01T00:00:00ZDelitala, MarcelloLorenzi, TommasoAccumulating evidence indicates that the interaction between epithelial and mesenchymal cells plays a pivotal role in cancer development and metastasis formation. Here we propose an integro-differential model for the co-culture dynamics of epithelial-like and mesenchymal-like cells. Our model takes into account the effects of chemotaxis, adhesive interactions between epithelial-like cells, proliferation and competition for nutrients. We present a sample of numerical results which display the emergence of spots, stripes and honeycomb patterns, depending on parameters and initial data. These simulations also suggest that epithelial-like and mesenchymal-like cells can segregate when there is little competition for nutrients. Furthermore, our computational results provide a possible explanation for how the concerted action between epithelial-cell adhesion and mesenchymal-cell spreading can precipitate the formation of ring-like structures, which resemble the fibrous capsules frequently observed in hepatic tumours.Spatio-temporal models of synthetic genetic oscillators
http://hdl.handle.net/10023/11774
Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. 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). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/117742017-02-01T00:00:00ZMacnamara, Cicely K.Chaplain, Mark A. J.Signal transduction pathways play a major role in many important aspects of cellular function e.g. cell division, apoptosis. One important class of signal transduction pathways is gene regulatory networks (GRNs). In many GRNs, proteins bind to gene sites in the nucleus thereby altering the transcription rate. Such proteins are known as transcription factors. 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). Recent computational modelling has demonstrated that spatial movement of the molecules is a vital component of GRNs and may cause the oscillations. These numerical findings have subsequently been proved rigorously i.e. the diffusion coefficient of the protein/mRNA acts as a bifurcation parameter and gives rise to a Hopf bifurcation. In this paper we first present a model of the canonical GRN (the Hes1 protein) and show the effect of varying the spatial location of gene and protein production sites on the oscillations. We then extend the approach to examine spatio-temporal models of synthetic gene regulatory networks e.g. n-gene repressilators and activator-repressor systems.The eruption of a small-scale emerging flux rope as the driver of an M-class flare and of a coronal mass ejection
http://hdl.handle.net/10023/11761
Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling of the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions.
This work is sponsored by the National Science Foundation of China (NSFC) under the grant numbers 11373066, 11603071, 11503080, 11633008, 11533008, by the Key Laboratory of Solar Activity of CAS under numbers KLSA201603, KLSA201508, by the Yunnan Science Foundation of China under number 2013FB086, CAS "Light of West China" Program, by the Youth Innovation Promotion Association CAS (No.2011056), and the national basic research program of China (973 program, 2011CB811400). The BBSO operation is supported by NJIT, US NSF AGS-1250818, and NASA NNX13AG14G grants, and the NST operation is partly supported by the Korea Astronomy and Space Science Institute and Seoul National University and by the strategic priority research program of CAS with Grant No. XDB09000000.
Thu, 10 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/117612017-08-10T00:00:00ZYan, X. L.Jiang, C. W.Xue, Z. K.Wang, J. C.Priest, E. R.Yang, L. H.Kong, D. F.Cao, W. D.Ji, H. S.Solar flares and coronal mass ejections are the most powerful explosions in the Sun. They are major sources of potentially destructive space weather conditions. However, the possible causes of their initiation remain controversial. Using high-resolution data observed by the New Solar Telescope of Big Bear Solar Observatory, supplemented by Solar Dynamics Observatory observations, we present unusual observations of a small-scale emerging flux rope near a large sunspot, whose eruption produced an M-class flare and a coronal mass ejection. The presence of the small-scale flux rope was indicated by static nonlinear force-free field extrapolation as well as data-driven magnetohydrodynamics modeling of the dynamic evolution of the coronal three-dimensional magnetic field. During the emergence of the flux rope, rotation of satellite sunspots at the footpoints of the flux rope was observed. Meanwhile, the Lorentz force, magnetic energy, vertical current, and transverse fields were increasing during this phase. The free energy from the magnetic flux emergence and twisting magnetic fields is sufficient to power the M-class flare. These observations present, for the first time, the complete process, from the emergence of the small-scale flux rope, to the production of solar eruptions.Open population maximum likelihood spatial capture-recapture
http://hdl.handle.net/10023/11758
Open population capture-recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modelling with spatial capture-recapture, allowing for estimation ofthe effective area sampled and population density. Here, open population spatial capture-recapture, both Cormack-Jolly-Seber and Jolly-Seber models, is formulated as a hidden Markov model, allowing inference by maximum likelihood. The method is applied to a twelve-year survey of male jaguars (Panthera onca) in the Cockscomb Wildlife Sanctuary Basin, Belize, to estimate the apparent survival and population abundance over time. The hidden Markov model approach is compared with Bayesian data augmentation, demonstrating it to be substantially more efficient. A simulation study shows maximum likelihood inference to be negligibly biased for small sample sizes and recapture rates.
Mon, 04 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/117582017-09-04T00:00:00ZGlennie, RichardBorchers, David LouisMurchie, MatthewHarmsen, BartFoster, RebeccaOpen population capture-recapture models are widely used to estimate population demographics and abundance over time. Bayesian methods exist to incorporate open population modelling with spatial capture-recapture, allowing for estimation ofthe effective area sampled and population density. Here, open population spatial capture-recapture, both Cormack-Jolly-Seber and Jolly-Seber models, is formulated as a hidden Markov model, allowing inference by maximum likelihood. The method is applied to a twelve-year survey of male jaguars (Panthera onca) in the Cockscomb Wildlife Sanctuary Basin, Belize, to estimate the apparent survival and population abundance over time. The hidden Markov model approach is compared with Bayesian data augmentation, demonstrating it to be substantially more efficient. A simulation study shows maximum likelihood inference to be negligibly biased for small sample sizes and recapture rates.Incorporating animal movement into distance sampling
http://hdl.handle.net/10023/11757
Distance sampling is a popular statistical method to estimate the density of wild animal populations. Conventional distance sampling represents animals as fixed points in space that are detected with an unknown probability that depends on the distance between the observer and the animal. Animal movement, responsive or non-responsive to the observer, can cause substantial bias in density estimation. Methods to correct for responsive animal movement exist, but none account for non-responsive movement independent of the observer. Here, an explicit animal movement model is incorporated into distance sampling, combining distance sampling survey data with independently obtained animal telemetry data.A detection probability that depends on the entire unobserved path the animal travels is derived in continuous space-time. The intractable integration overall possible animal paths is approximated by a hidden Markov model. A simulation study shows the method to be negligibly biased (less than 5%) in scenarios where conventional distance sampling overestimates abundance by up to 100%.The method is applied to a line transect survey of spotted dolphins (Stenella attenuata attenuata) in the eastern tropical Pacific.
Fri, 08 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/117572017-09-08T00:00:00ZGlennie, RichardBuckland, Stephen TerrenceLangrock, RolandGerrodette, TimBallance, LisaChivers, SusanScott, MichaelPerrin, WilliamDistance sampling is a popular statistical method to estimate the density of wild animal populations. Conventional distance sampling represents animals as fixed points in space that are detected with an unknown probability that depends on the distance between the observer and the animal. Animal movement, responsive or non-responsive to the observer, can cause substantial bias in density estimation. Methods to correct for responsive animal movement exist, but none account for non-responsive movement independent of the observer. Here, an explicit animal movement model is incorporated into distance sampling, combining distance sampling survey data with independently obtained animal telemetry data.A detection probability that depends on the entire unobserved path the animal travels is derived in continuous space-time. The intractable integration overall possible animal paths is approximated by a hidden Markov model. A simulation study shows the method to be negligibly biased (less than 5%) in scenarios where conventional distance sampling overestimates abundance by up to 100%.The method is applied to a line transect survey of spotted dolphins (Stenella attenuata attenuata) in the eastern tropical Pacific.Title redacted
http://hdl.handle.net/10023/11739
Thu, 07 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/117392017-12-07T00:00:00ZSharifi Far, ServehInteraction between a surface quasi-geostrophic buoyancy filament and an internal vortex
http://hdl.handle.net/10023/11727
This paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.
Fri, 23 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/117272016-09-23T00:00:00ZReinaud, Jean NoelDritschel, David GerardCarton, XavierThis paper focuses on the nonlinear interaction between a surface quasi-geostrophic buoyancy filament and an internal vortex. We first revisit the stability of an isolated buoyancy filament. The buoyancy profile considered is continuous and leads to a continuous velocity field, albeit one with infinite shear just outside its edge. The stability properties of an isolated filament help to interpret the unsteady interaction with a sub-surface (internal) vortex studied next. We find that, in all cases, the filament breaks into billows, analogous in form to those occurring in Kelvin-Helmholtz shear instability. For intense buoyancy filaments, the vortex itself may undergo strong deformations, including being split into several pieces. Generally, the nonlinear interaction causes both the filament and the vortex to lose their respective ‘self’-energies to the energy of interaction. The flow evolution depends sensitively on whether the vertical vorticity of the filament and the vortex have the same or opposite signs — termed “cooperative” and “adverse” shear respectively. In cooperative shear, the filament rolls up into a coherent surface eddy above a vortex initially placed below it, whereas in adverse shear, buoyancy is expelled above the vortex. Although sufficiently great shear induced by the buoyancy filament may split the vortex in both cases, adverse shear is significantly more destructive.Particle acceleration with anomalous pitch angle scattering in 2D magnetohydrodynamic reconnection simulations
http://hdl.handle.net/10023/11714
The conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and non-thermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of two-dimensional (2D) X-point reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivity-independent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.
A.B. would like to thank the University of St Andrews for financial support from the 7th Century Scholarship and the Scottish Government for support from the Saltire Scholarship. E.P.K.’s work is partially supported by a STFC consolidated grant ST/L000741/1. J.T. and T.N. gratefully acknowledge the support of the UK STFC (consolidated grant SN/N000609/1).
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/117142017-09-01T00:00:00ZBorissov, AlexeiKontar, EduardThrelfall, James WilliamNeukirch, ThomasThe conversion of magnetic energy into other forms (such as plasma heating, bulk plasma flows, and non-thermal particles) during solar flares is one of the outstanding open problems in solar physics. It is generally accepted that magnetic reconnection plays a crucialrole in these conversion processes. In order to achieve the rapid energy release required in solar flares, an anomalous resistivity, which is orders of magnitude higher than the Spitzer resistivity, is often used in magnetohydrodynamic (MHD) simulations of reconnection in the corona. The origin of Spitzer resistivity is based on Coulomb scattering, which becomes negligible at the high energies achieved by accelerated particles. As a result, simulations of particle acceleration in reconnection events are often performed in the absence of any interaction between accelerated particles and any background plasma. This need not be the case for scattering associated with anomalous resistivity caused by turbulence within solar flares, as the higher resistivity implies an elevated scattering rate. We present results of test particle calculations, with and without pitch angle scattering, subject to fields derived from MHD simulations of two-dimensional (2D) X-point reconnection. Scattering rates proportional to the ratio of the anomalous resistivity to the local Spitzer resistivity, as well as at fixed values, are considered. Pitch angle scattering, which is independent of the anomalous resistivity, causes higher maximum energies in comparison to those obtained without scattering. Scattering rates which are dependent on the local anomalous resistivity tend to produce fewer highly energised particles due to weaker scattering in the separatrices, even though scattering in the current sheet may be stronger when compared to resistivity-independent scattering. Strong scattering also causes an increase in the number of particles exiting the computational box in the reconnection outflow region, as opposed to along the separatrices as is the case in the absence of scattering.Spatio-temporal variation in click production rates of beaked whales : implications for passive acoustic density estimation
http://hdl.handle.net/10023/11712
Passive acoustic monitoring has become an increasingly prevalent tool for estimating density of marine mammals, such as beaked whales, which vocalize often but are difficult to survey visually. Counts of acoustic cues (e.g., vocalizations), when corrected for detection probability, can be translated into animal density estimates by applying an individual cue production rate multiplier. It is essential to understand variation in these rates to avoid biased estimates. The most direct way to measure cue production rate is with animal-mounted acoustic recorders. This study utilized data from sound recording tags deployed on Blainville's (Mesoplodon densirostris, 19 deployments) and Cuvier's (Ziphius cavirostris, 16 deployments) beaked whales, in two locations per species, to explore spatial and temporal variation in click production rates. No spatial or temporal variation was detected within the average click production rate of Blainville's beaked whales when calculated over dive cycles (including silent periods between dives); however, spatial variation was detected when averaged only over vocal periods. Cuvier's beaked whales exhibited significant spatial and temporal variation in click production rates within vocal periods and when silent periods were included. This evidence of variation emphasizes the need to utilize appropriate cue production rates when estimating density from passive acoustic data.
T.A.M. was funded under Grant No. N000141010382 from the Office of Naval Research (LATTE project) and thanks support by CEAUL (funded by FCT - Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013). M.P.J. was funded by a Marie Curie Career Integration Grant and M.P.J. and P.L.T. were funded by MASTS (The Marine Alliance for Science and Technology for Scotland, a research pooling initiative funded by the Scottish Funding Council under grant HR09011 and contributing institutions). L.S.H. thanks the BRS Bahamas team that helped collect the Bahamas data, and A. Bocconcelli. D.H. and L.T. were funded by the Office of Naval Research (Award No. N00014-14-1-0394). N.A.S. was funded by an EU-Horizon 2020 Marie Slodowska Curie fellowship (project ECOSOUND). DTAG data in the Canary Islands were collected with funds from the U.S. Office of Naval Research and Fundación Biodiversidad (EU project LIFE INDEMARES) with permit from the Canary Islands and Spanish governments.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/117122017-03-01T00:00:00ZWarren, Victoria E.Marques, Tiago A.Harris, DanielleThomas, LenTyack, Peter L.Aguilar de Soto, NatachaHickmott, Leigh S.Johnson, Mark P.Passive acoustic monitoring has become an increasingly prevalent tool for estimating density of marine mammals, such as beaked whales, which vocalize often but are difficult to survey visually. Counts of acoustic cues (e.g., vocalizations), when corrected for detection probability, can be translated into animal density estimates by applying an individual cue production rate multiplier. It is essential to understand variation in these rates to avoid biased estimates. The most direct way to measure cue production rate is with animal-mounted acoustic recorders. This study utilized data from sound recording tags deployed on Blainville's (Mesoplodon densirostris, 19 deployments) and Cuvier's (Ziphius cavirostris, 16 deployments) beaked whales, in two locations per species, to explore spatial and temporal variation in click production rates. No spatial or temporal variation was detected within the average click production rate of Blainville's beaked whales when calculated over dive cycles (including silent periods between dives); however, spatial variation was detected when averaged only over vocal periods. Cuvier's beaked whales exhibited significant spatial and temporal variation in click production rates within vocal periods and when silent periods were included. This evidence of variation emphasizes the need to utilize appropriate cue production rates when estimating density from passive acoustic data.The theoretical foundation of 3D Alfvén resonances : time dependent solutions
http://hdl.handle.net/10023/11706
We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.
Both authors were funded in part by STFC (through Consolidated Grant ST/N000609/1) and The Leverhulme Trust (through Research Grant RPG-2016-071).
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/117062017-03-01T00:00:00ZElsden, T.Wright, A. N.We present results from a 3D numerical simulation which investigates the coupling of fast and Alfvén magnetohydrodynamic (MHD) waves in a nonuniform dipole equilibrium. This represents the time dependent extension of the normal mode (∝ exp(−iωt)) analysis of Wright and Elsden [2016], and provides a theoretical basis for understanding 3D Alfvén resonances. Wright and Elsden [2016] show that these are fundamentally different to resonances in 1D and 2D. We demonstrate the temporal behaviour of the Alfvén resonance, which is formed within the ‘Resonant Zone’; a channel of the domain where a family of solutions exists such that the natural Alfvén frequency matches the fast mode frequency. At early times, phase mixing leads to the production of prominent ridges in the energy density, whose shape is determined by the Alfvén speed profile and the chosen background magnetic field geometry. These off resonant ridges decay in time, leaving only a main 3D resonant sheet in the steady state. We show that the width of the 3D resonance in time and in space can be accurately estimated by adapting previous analytical estimates from 1D theory. We further provide an analytical estimate for the resonance amplitude in 3D, based upon extending 2D theory.Fine-scale harbour seal usage for informed marine spatial planning
http://hdl.handle.net/10023/11695
High-resolution species distribution maps are required for marine spatial planning, consenting, and licensing to assess interactions between anthropogenic activities and ecosystems. This approach can inform conservation measures for protected species and facilitate commercial developments needed for economic growth. A case study centred on Orkney, UK, is an area where concern for a declining harbour seal population has led to constraints being placed on tidal energy generation developments. Telemetry data from 54 animals tagged between 2003 and 2015 were combined with terrestrial counts from 2008 to 2015 to produce density estimation maps. Predictive habitat models using GAM-GEEs provided robust predictions in areas where telemetry data were absent, and were combined with density estimation maps. Harbour seal usage maps with confidence intervals were produced around Orkney and the North coast of Scotland. The selected habitat model showed that distance from haul out, proportion of sand in seabed sediment, and peak flow of tidal current were important predictors of space-use. Fine-scale usage maps can be used in consenting and licensing of anthropogenic developments to determine local abundance. When quantifying anthropogenic impacts through changes to species distributions, usage maps could be spatially explicitly linked to individual-based models to inform predicted movement and behaviour.
The work was funded through Scottish Government MSQ0174 contract CR/2014/11; CREEM, University of St Andrews; the National Capability fund from the Natural Environment Research Council to the Sea Mammal Research Unit (grant no. SMRU1001); and MASTS pooling initiative, which is funded by the Scottish Funding Council (grant reference HR09011).
Thu, 14 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/116952017-09-14T00:00:00ZJones, Esther LaneSparling, Carol ElizabethMcConnell, Bernie JMorris, ChristopherSmout, Sophie CarolineHigh-resolution species distribution maps are required for marine spatial planning, consenting, and licensing to assess interactions between anthropogenic activities and ecosystems. This approach can inform conservation measures for protected species and facilitate commercial developments needed for economic growth. A case study centred on Orkney, UK, is an area where concern for a declining harbour seal population has led to constraints being placed on tidal energy generation developments. Telemetry data from 54 animals tagged between 2003 and 2015 were combined with terrestrial counts from 2008 to 2015 to produce density estimation maps. Predictive habitat models using GAM-GEEs provided robust predictions in areas where telemetry data were absent, and were combined with density estimation maps. Harbour seal usage maps with confidence intervals were produced around Orkney and the North coast of Scotland. The selected habitat model showed that distance from haul out, proportion of sand in seabed sediment, and peak flow of tidal current were important predictors of space-use. Fine-scale usage maps can be used in consenting and licensing of anthropogenic developments to determine local abundance. When quantifying anthropogenic impacts through changes to species distributions, usage maps could be spatially explicitly linked to individual-based models to inform predicted movement and behaviour.Synthetic lethality between androgen receptor signalling and the PARP pathway in prostate cancer
http://hdl.handle.net/10023/11680
Emerging data demonstrate homologous recombination (HR) defects in castration-resistant prostate cancers, rendering these tumours sensitive to PARP inhibition. Here we demonstrate a direct requirement for the androgen receptor (AR) to maintain HR gene expression and HR activity in prostate cancer. We show that PARP-mediated repair pathways are upregulated in prostate cancer following androgen-deprivation therapy (ADT). Furthermore, upregulation of PARP activity is essential for the survival of prostate cancer cells and we demonstrate a synthetic lethality between ADT and PARP inhibition in vivo. Our data suggest that ADT can functionally impair HR prior to the development of castration resistance and that, this potentially could be exploited therapeutically using PARP inhibitors in combination with androgen-deprivation therapy upfront in advanced or high-risk prostate cancer.Tumours with homologous recombination (HR) defects become sensitive to PARPi. Here, the authors show that androgen receptor (AR) regulates HR and AR inhibition activates the PARP pathway in vivo, thus inhibition of both AR and PARP is required for effective treatment of high risk prostate cancer.
This study was supported by the National Cancer Research Institute (National Institute of Health Research (NIHR) Collaborative Study: ‘Prostate Cancer: Mechanisms of Progression and Treatment (PROMPT)” (grant G0500966/75466). This work was funded by a Cancer Research UK program grant (D.N.), the Swedish Research Council (T.H.), AFA insurance (T.H.), Swedish Cancer Society (T.H.), the Swedish Pain Relief Foundation (T.H.), the Torsten and Ragnar Söderberg Foundation (T.H.), AstraZeneca (T.H.) Centre for Clinical Research (CKF) (F.T.), the Västmanland Research Foundation for Cancer in Vasteras (F.T.), the Henning and Ida Persson Research Foundation (F.T.).
Tue, 29 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/116802017-08-29T00:00:00ZAsim, MohammadTarish, FirasZecchini, Heather ISanjiv, KumarGelali, EleniMassie, Charles EBaridi, AjoebWarren, Anne YZhao, WanfengOgris, ChristophMcDuffus, Leigh-AnneMascalchi, PatriceShaw, GregDev, HarveerWadhwa, KaranWijnhoven, PaulForment, Josep VLyons, Scott RLynch, Andy GO'Neill, CormacZecchini, Vincent RRennie, Paul SBaniahmad, AriaTavaré, SimonMills, Ian GGalanty, YaronCrosetto, NicolaSchultz, NiklasNeal, DavidHelleday, ThomasEmerging data demonstrate homologous recombination (HR) defects in castration-resistant prostate cancers, rendering these tumours sensitive to PARP inhibition. Here we demonstrate a direct requirement for the androgen receptor (AR) to maintain HR gene expression and HR activity in prostate cancer. We show that PARP-mediated repair pathways are upregulated in prostate cancer following androgen-deprivation therapy (ADT). Furthermore, upregulation of PARP activity is essential for the survival of prostate cancer cells and we demonstrate a synthetic lethality between ADT and PARP inhibition in vivo. Our data suggest that ADT can functionally impair HR prior to the development of castration resistance and that, this potentially could be exploited therapeutically using PARP inhibitors in combination with androgen-deprivation therapy upfront in advanced or high-risk prostate cancer.Tumours with homologous recombination (HR) defects become sensitive to PARPi. Here, the authors show that androgen receptor (AR) regulates HR and AR inhibition activates the PARP pathway in vivo, thus inhibition of both AR and PARP is required for effective treatment of high risk prostate cancer.Wave of chaos in a spatial eco-epidemiological system : generating realistic patterns of patchiness in rabbit-lynx dynamics
http://hdl.handle.net/10023/11666
In the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.
AM and CV would like to acknowledge support from the Engineering and Physical Sciences Research Council grant (EP/J016780/1) and the Leverhulme Trust Research Project Grant (RPG-2014-149).
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/116662016-11-01T00:00:00ZUpadhyay, RanjitRoy, ParimitaVenkataraman, C.Madzvamuse, AnotidaIn the present paper, we propose and analyse an eco-epidemiological model with diffusion to study the dynamics of rabbit populations which are consumed by lynx populations. Existence, boundedness, stability and bifurcation analyses of solutions for the proposed rabbit-lynx model are performed. Results show that in the presence of diffusion the model has the potential of exhibiting Turing instability. Numerical results (finite difference and finite element methods) reveal the existence of the wave of chaos and this appears to be a dominant mode of disease dispersal. We also show the mechanism of spatiotemporal pattern formation resulting from the Hopf bifurcation analysis, which can be a potential candidate for understanding the complex spatiotemporal dynamics of eco-epidemiological systems. Implications of the asymptotic transmission rate on disease eradication among rabbit population which in turn enhances the survival of Iberian lynx are discussed.On the energetics of a two-layer baroclinic flow
http://hdl.handle.net/10023/11637
The formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.
Sat, 01 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/116372017-04-01T00:00:00ZJougla, ThibaultDritschel, David GerardThe formation, evolution and co-existence of jets and vortices in turbulent planetary atmospheres is examined using a two-layer quasi-geostrophic β -channel shallow-water model. The study in particular focuses on the vertical structure of jets. Following Panetta & Held (J. Atmos. Sci., vol. 45 (22), 1988, pp. 3354–3365), a vertical shear arising from latitudinal heating variations is imposed on the flow and maintained by thermal damping. Idealised convection between the upper and lower layers is implemented by adding cyclonic/anti-cyclonic pairs, called hetons, to the flow, though the qualitative flow evolution is evidently not sensitive to this or other small-scale stochastic forcing. A very wide range of simulations have been conducted. A characteristic simulation which exhibits alternation between two different phases, quiescent and turbulent, is examined in detail. We study the energy transfers between different components and modes, and find the classical picture of barotropic/baroclinic energy transfers to be too simplistic. We also discuss the dependence on thermal damping and on the imposed vertical shear. Both have a strong influence on the flow evolution. Thermal damping is a major factor affecting the stability of the flow while vertical shear controls the number of jets in the domain, qualitatively through the Rhines scale LRh = √U/β.Self-similar sets: projections, sections and percolation
http://hdl.handle.net/10023/11629
We survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/116292017-01-01T00:00:00ZFalconer, Kenneth JohnJin, XiongWe survey some recent results on the dimension of orthogonal projections of self-similar sets and of random subsets obtained by percolation on self-similar sets. In particular we highlight conditions when the dimension of the projections takes the generic value for all, or very nearly all, projections. We then describe a method for deriving dimensional properties of sections of deterministic self-similar sets by utilising projection properties of random percolation subsets.Exact Vlasov-Maxwell equilibria for asymmetric current sheets
http://hdl.handle.net/10023/11626
The NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.
Funding: Science and Technology Facilities Council Consolidated Grant Nos. ST/K000950/1 and ST/N000609/1 (O.A., T.N., J.D.B.H.and F.W.), the Science and Technology Facilities Council Doctoral Training Grant No. ST/K502327/1 (O.A. and J.D.B.H), the Natural Environment Research Council Grant No. NE/P017274/1 (Rad-Sat) (O.A.)
Sat, 16 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/116262017-09-16T00:00:00ZAllanson, O.Wilson, F.Neukirch, T.Liu, Yi-HsinHodgson, J. D. B.The NASA Magnetospheric Multiscale mission has made in-situ diffusion region and kinetic-scale resolution measurements of asymmetric magnetic reconnection for the first time [Burch et al., 2016], in the Earth’s magnetopause. The principal theoretical tool currently used to model collisionless asymmetric reconnection is particle-in-cell simulations. Many particle-in-cell simulations of asymmetric collisionless reconnection start from an asymmetric Harris-type magnetic field, but with distribution functions that are not exact equilibrium solutions of the Vlasov equation. We present new and exact equilibrium solutions of the Vlasov-Maxwell system that are self-consistent with one-dimensional asymmetric current sheets, with an asymmetric Harris-type magnetic field profile, plus a constant non-zero guide field. The distribution functions can be represented as a combination of four shifted Maxwellian distribution functions. This equilibrium describes a magnetic field configuration with more freedom than the previously known exact solution [Alpers, 1969], and has different bulk flow properties.Spatial variation in boundary conditions can govern selection and location of eyespots in butterfly wings
http://hdl.handle.net/10023/11618
Despite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reaction-diffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/116182017-01-01T00:00:00ZVenkataraman, ChandrasekharSekimura, ToshioDespite being the subject of widespread study, many aspects of the development of eyespot patterns in butterfly wings remain poorly understood. In this work, we examine, through numerical simulations, a mathematical model for eyespot focus point formation in which a reaction-diffusion system is assumed to play the role of the patterning mechanism. In the model, changes in the boundary conditions at the veins at the proximal boundary alone are capable of determining whether or not an eyespot focus forms in a given wing cell and the eventual position of focus points within the wing cell. Furthermore, an auxiliary surface reaction diffusion system posed along the entire proximal boundary of the wing cells is proposed as the mechanism that generates the necessary changes in the proximal boundary profiles. In order to illustrate the robustness of the model, we perform simulations on a curved wing geometry that is somewhat closer to a biological realistic domain than the rectangular wing cells previously considered, and we also illustrate the ability of the model to reproduce experimental results on artificial selection of eyespots.Force-free collisionless current sheet models with non-uniform temperature and density profiles
http://hdl.handle.net/10023/11614
We present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk- ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.
The authors acknowledge the support of the Science and Technology Facilities Council via the consolidated grants ST/K000950/1 and ST/N000609/1 and the doctoral training grant ST/K502327/1 (O. A.), and the Natural Environment Research Council via grant no. NE/P017274/1 (Rad-Sat) (O. A.). F. W. and T. N. would also like to thank the University of St Andrews for general financial support
Thu, 17 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/116142017-08-17T00:00:00ZWilson, FionaNeukirch, ThomasAllanson, Oliver DouglasWe present a class of one-dimensional, strictly neutral, Vlasov-Maxwell equilibrium distribution functions for force-free current sheets, with magnetic fields defined in terms of Jacobian elliptic functions, extending the results of Abraham-Shrauner48 to allow for non-uniform density and temperature pro les. To achieve this, we use an approach previously applied to the force-free Harris sheet by Kolotkov et al.49. In one limit of the parameters, we recover the model of Kolotkov et al.49, while another limit gives a linear force-free field. We discuss conditions on the parameters such that the distribution functions are always positive, and give expressions for the pressure, density, temperature and bulk- ow velocities of the equilibrium, discussing differences from previous models. We also present some illustrative plots of the distribution function in velocity space.Inference from randomized (factorial) experiments
http://hdl.handle.net/10023/11606
This is a contribution to the discussion of the interesting paper by Ding [Statist. Sci. 32 (2017) 331–345], which contrasts approaches attributed to Neyman and Fisher. I believe that Fisher’s usual assumption was unit-treatment additivity, rather than the “sharp null hypothesis” attributed to him. Fisher also developed the notion of interaction in factorial experiments. His explanation leads directly to the concept of marginality, which is essential for the interpretation of data from any factorial experiment.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/116062017-01-01T00:00:00ZBailey, Rosemary AnneThis is a contribution to the discussion of the interesting paper by Ding [Statist. Sci. 32 (2017) 331–345], which contrasts approaches attributed to Neyman and Fisher. I believe that Fisher’s usual assumption was unit-treatment additivity, rather than the “sharp null hypothesis” attributed to him. Fisher also developed the notion of interaction in factorial experiments. His explanation leads directly to the concept of marginality, which is essential for the interpretation of data from any factorial experiment.Near-complete external difference families
http://hdl.handle.net/10023/11576
We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/115762017-09-01T00:00:00ZDavis, James A.Huczynska, SophieMullen, Gary L.We introduce and explore near-complete external difference families, a partitioning of the nonidentity elements of a group so that each nonidentity element is expressible as a difference of elements from distinct subsets a fixed number of times. We show that the existence of such an object implies the existence of a near-resolvable design. We provide examples and general constructions of these objects, some of which lead to new parameter families of near-resolvable designs on a non-prime-power number of points. Our constructions employ cyclotomy, partial difference sets, and Galois rings.Genomic evolution of breast cancer metastasis and relapse
http://hdl.handle.net/10023/11553
Patterns of genomic evolution between primary and metastatic breast cancer have not been studied in large numbers, despite patients with metastatic breast cancer having dismal survival. We sequenced whole genomes or a panel of 365 genes on 299 samples from 170 patients with locally relapsed or metastatic breast cancer. Several lines of analysis indicate that clones seeding metastasis or relapse disseminate late from primary tumors, but continue to acquire mutations, mostly accessing the same mutational processes active in the primary tumor. Most distant metastases acquired driver mutations not seen in the primary tumor, drawing from a wider repertoire of cancer genes than early drivers. These include a number of clinically actionable alterations and mutations inactivating SWI-SNF and JAK2-STAT3 pathways.
A.G.L. and J.H.R.F. were supported by a Cancer Research UK Program Grant to Simon Tavaré (C14303/A17197).
Mon, 14 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/115532017-08-14T00:00:00ZYates, Lucy R.Knappskog, StianWedge, DavidFarmery, James H. R.Gonzalez, SantiagoMartincorena, InigoAlexandrov, Ludmil B.Van Loo, PeterHaugland, Hans KristianLilleng, Peer KaareGundem, GunesGerstung, MoritzPappaemmanuil, ElliGazinska, PatrycjaBhosle, Shriram GJones, DavidRaine, KeiranMudie, LauraLatimer, CalliSawyer, ElinorDesmedt, ChristineSotiriou, ChristosStratton, Michael R.Sieuwerts, Anieta M.Lynch, Andy G.Martens, John W.Richardson, Andrea L.Tutt, AndrewLønning, Per EysteinCampbell, Peter J.Patterns of genomic evolution between primary and metastatic breast cancer have not been studied in large numbers, despite patients with metastatic breast cancer having dismal survival. We sequenced whole genomes or a panel of 365 genes on 299 samples from 170 patients with locally relapsed or metastatic breast cancer. Several lines of analysis indicate that clones seeding metastasis or relapse disseminate late from primary tumors, but continue to acquire mutations, mostly accessing the same mutational processes active in the primary tumor. Most distant metastases acquired driver mutations not seen in the primary tumor, drawing from a wider repertoire of cancer genes than early drivers. These include a number of clinically actionable alterations and mutations inactivating SWI-SNF and JAK2-STAT3 pathways.Underwater ambient noise in a baleen whale migratory habitat off the Azores
http://hdl.handle.net/10023/11545
Assessment of underwater noise is of particular interest given the increase in noise-generating human activities and the potential negative effects on marine mammals which depend on sound for many vital processes. The Azores archipelago is an important migratory and feeding habitat for blue (Balaenoptera musculus), fin (Balaenoptera physalus) and sei whales (Balaenoptera borealis) en route to summering grounds in northern Atlantic waters. High levels of low frequency noise in this area could displace whales or interfere with foraging behavior, impacting energy intake during a critical stage of their annual cycle. In this study, bottom-mounted Ecological Acoustic Recorders were deployed at three Azorean seamounts (Condor, Açores and Gigante) to measure temporal variations in background noise levels and ship noise in the 18-1,000 Hz frequency band, used by baleen whales to emit and receive sounds. Monthly average noise levels ranged from 90.3 dB re 1 μPa (Açores seamount) to 103.1 dB re 1 μPa (Condor seamount) and local ship noise was present up to 13% of the recording time in Condor. At this location, average contribution of local boat noise to background noise levels is almost 10 dB higher than wind contribution, which might temporally affect detection ranges for baleen whale calls and difficult communication at long ranges. Given the low time percentatge with noise levels above 120 dB re 1μPa found here (3.3 % at Condor), we woud expect limited behavioural responses to ships from baleen whales. Sound pressure levels measured in the Azores are lower than those reported for the Mediterranean basin and the Strait of Gibraltar. However, the currently unknown effects of baleen whale vocalization masking and the increasing presence of boats at the monitored sites underline the need for continuous monitoring to understand any long-term impacts on whales.
TM is a member of CEA/UL (Funded by FCT- Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013).
Tue, 25 Apr 2017 00:00:00 GMThttp://hdl.handle.net/10023/115452017-04-25T00:00:00ZRomagosa, MiriamCascão, IrmaMerchant, Nathan D.Lammers, Marc O.Giacomello, EvaMarques, Tiago A.Silva, Mónica A.Assessment of underwater noise is of particular interest given the increase in noise-generating human activities and the potential negative effects on marine mammals which depend on sound for many vital processes. The Azores archipelago is an important migratory and feeding habitat for blue (Balaenoptera musculus), fin (Balaenoptera physalus) and sei whales (Balaenoptera borealis) en route to summering grounds in northern Atlantic waters. High levels of low frequency noise in this area could displace whales or interfere with foraging behavior, impacting energy intake during a critical stage of their annual cycle. In this study, bottom-mounted Ecological Acoustic Recorders were deployed at three Azorean seamounts (Condor, Açores and Gigante) to measure temporal variations in background noise levels and ship noise in the 18-1,000 Hz frequency band, used by baleen whales to emit and receive sounds. Monthly average noise levels ranged from 90.3 dB re 1 μPa (Açores seamount) to 103.1 dB re 1 μPa (Condor seamount) and local ship noise was present up to 13% of the recording time in Condor. At this location, average contribution of local boat noise to background noise levels is almost 10 dB higher than wind contribution, which might temporally affect detection ranges for baleen whale calls and difficult communication at long ranges. Given the low time percentatge with noise levels above 120 dB re 1μPa found here (3.3 % at Condor), we woud expect limited behavioural responses to ships from baleen whales. Sound pressure levels measured in the Azores are lower than those reported for the Mediterranean basin and the Strait of Gibraltar. However, the currently unknown effects of baleen whale vocalization masking and the increasing presence of boats at the monitored sites underline the need for continuous monitoring to understand any long-term impacts on whales.Erwin Schrödinger and quantum wave mechanics
http://hdl.handle.net/10023/11543
The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.
Tue, 22 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/115432017-08-22T00:00:00ZO'Connor, John J.Robertson, Edmund F.The fathers of matrix quantum mechanics believed that the quantum particles are unanschaulich (unvisualizable) and that quantum particles pop into existence only when we measure them. Challenging the orthodoxy, in 1926 Erwin Schrödinger developed his wave equation that describes the quantum particles as a packet of quantum probability amplitudes evolving in space and time. Thus, Schrödinger visualized the unvisualizable and lifted the veil that has been obscuring the wonders of the quantum world.The stability of Mars' annular polar vortex
http://hdl.handle.net/10023/11541
The Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Mars-like annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.
This research was partially supported by a NASA grant from the Mars Fundamental Research Program (NNX14AG53G).
Mon, 01 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/115412017-05-01T00:00:00ZSeviour, WilliamWaugh, DarrynScott, Richard KirknessThe Martian polar atmosphere is known to have a persistent local minimum in potential vorticity (PV) near the winter pole, with a region of high PV encircling it. This finding is surprising since an isolated band of PV is barotropically unstable, a result going back to Rayleigh. Here we investigate the stability of a Mars-like annular vortex using numerical integrations of the rotating shallow water equations. We show how the mode of instability and its growth rate depends upon the latitude and width of the annulus. By introducing thermal relaxation towards an annular equilibrium profile with a time scale similar to that of the instability, we are able to simulate a persistent annular vortex with similar characteristics as that observed in the Martian atmosphere. This time scale, typically 0.5-2 sols, is similar to radiative relaxation time scales for Mars’ polar atmosphere. We also demonstrate that the persistence of an annular vortex is robust to topographic forcing, as long as it is below a certain amplitude. We hence propose that the persistence of this barotropically unstable annular vortex is permitted due to the combination of short radiative relaxation time scales and relatively weak topographic forcing in the Martian polar atmosphere.Measuring temporal trends in biodiversity
http://hdl.handle.net/10023/11534
In 2002, nearly 200 nations signed up to the 2010 target of the Convention for Biological Diversity, ‘to significantly reduce the rate of biodiversity loss by 2010’. In order to assess whether the target was met, it became necessary to quantify temporal trends in measures of diversity. This resulted in a marked shift in focus for biodiversity measurement. We explore the developments in measuring biodiversity that were prompted by the 2010 target. We consider measures based on species proportions, and also explain why a geometric mean of relative abundance estimates was preferred to such measures for assessing progress towards the target. We look at the use of diversity profiles, and consider how species similarity can be incorporated into diversity measures. We also discuss measures of turnover that can be used to quantify shifts in community composition arising for example from climate change.
Yuan was part-funded by EPSRC/NERC Grant EP/1000917/1 and Marcon by ANR-10-LABX-25-01.
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/115342017-10-01T00:00:00ZBuckland, S. T.Yuan, Y.Marcon, EricIn 2002, nearly 200 nations signed up to the 2010 target of the Convention for Biological Diversity, ‘to significantly reduce the rate of biodiversity loss by 2010’. In order to assess whether the target was met, it became necessary to quantify temporal trends in measures of diversity. This resulted in a marked shift in focus for biodiversity measurement. We explore the developments in measuring biodiversity that were prompted by the 2010 target. We consider measures based on species proportions, and also explain why a geometric mean of relative abundance estimates was preferred to such measures for assessing progress towards the target. We look at the use of diversity profiles, and consider how species similarity can be incorporated into diversity measures. We also discuss measures of turnover that can be used to quantify shifts in community composition arising for example from climate change.Editing Cavendish : Maxwell and The Electrical Researches of Henry Cavendish
http://hdl.handle.net/10023/11531
During the last five years of his life, 1874-79, James Clerk Maxwell was absorbed in editing the electrical researches of Henry Cavendish, performed 100 years earlier. This endeavour is often assumed to be a work of duty to the Cavendish family, and an unfortunate waste of Maxwell's time. By looking at the history of Cavendish's papers, and the editorial choices that Maxwell made, this paper questions this assumption, considering the importance of Cavendish's experiments in Maxwell's electrical programme, and the implications that he may have derived for developing a doctrine of experimental method.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/115312017-01-01T00:00:00ZFalconer, IsobelDuring the last five years of his life, 1874-79, James Clerk Maxwell was absorbed in editing the electrical researches of Henry Cavendish, performed 100 years earlier. This endeavour is often assumed to be a work of duty to the Cavendish family, and an unfortunate waste of Maxwell's time. By looking at the history of Cavendish's papers, and the editorial choices that Maxwell made, this paper questions this assumption, considering the importance of Cavendish's experiments in Maxwell's electrical programme, and the implications that he may have derived for developing a doctrine of experimental method.Synchronization and separation in the Johnson schemes
http://hdl.handle.net/10023/11525
Recently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that S(t,k,n) exists whenever the necessary divisibility conditions on the parameters are satisfied and n is sufficiently large in terms of k and t. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called synchronizing and separating) lying between primitive and 2-homogeneous are defined. A big open question is how the permutation group induced by Sn on k-subsets of {1,...,n} fits in this hierarchy; our conjecture would give a solution to this problem for n large in terms of k.
Fri, 09 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10023/115252018-02-09T00:00:00ZAljohani, MohammedBamberg, JohnCameron, Peter JephsonRecently Peter Keevash solved asymptotically the existence question for Steiner systems by showing that S(t,k,n) exists whenever the necessary divisibility conditions on the parameters are satisfied and n is sufficiently large in terms of k and t. The purpose of this paper is to make a conjecture which if true would be a significant extension of Keevash's theorem, and to give some theoretical and computational evidence for the conjecture. We phrase the conjecture in terms of the notions (which we define here) of synchronization and separation for association schemes. These definitions are based on those for permutation groups which grow out of the theory of synchronization in finite automata. In this theory, two classes of permutation groups (called synchronizing and separating) lying between primitive and 2-homogeneous are defined. A big open question is how the permutation group induced by Sn on k-subsets of {1,...,n} fits in this hierarchy; our conjecture would give a solution to this problem for n large in terms of k.Multimodality imaging and mathematical modelling of drug delivery to glioblastomas
http://hdl.handle.net/10023/11513
Patients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from anti-angiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.
MAJC would like to 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” supported by EPSRC Grant Number EP/K032208/1.
Thu, 06 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/115132016-10-06T00:00:00ZBoujelben, AhmedWatson, MichaelMcDougall, StevenYen, Yi-FenGerstner, ElizabethCatana, CiprianDeisboeck, ThomasBatchelor, TracyBoas, DavidRosen, BruceKalpathy-Cramer, JayashreeChaplain, Mark Andrew JosephPatients diagnosed with glioblastoma, an aggressive brain tumour, have a poor prognosis, with a median overall survival of less than 15 months. Vasculature within these tumours is typically abnormal, with increased tortuosity, dilation and disorganization and they typically exhibit a disrupted blood brain barrier. Although it has been hypothesized that the “normalization” of the vasculature resulting from anti-angiogenic therapies could improve drug delivery through improved blood flow, there is also evidence that suggests that the restoration of blood brain barrier integrity might limit the delivery of therapeutic agents and hence their effectiveness. In this paper we apply mathematical models of blood flow, vascular permeability and diffusion within the tumour microenvironment to investigate the effect of these competing factors on drug delivery. Preliminary results from the modelling indicate that all three physiological parameters investigated – flow rate, vessel permeability, and tissue diffusion coefficient – interact nonlinearly to produce the observed average drug concentration in the microenvironment.Pressure moderation and effective pressure in Navier-Stokes flows
http://hdl.handle.net/10023/11499
We study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.
Wed, 17 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/114992016-08-17T00:00:00ZTran, Chuong VanYu, XinweiWe study the Cauchy problem of the Navier–Stokes equations by both semi-analytic and classical energy methods. The former approach provides a physical picture of how viscous effects may or may not be able to suppress singularity development. In the latter approach, we examine the pressure term that drives the dynamics of the velocity norms ||u||Lq , for q ≥ 3. A key idea behind this investigation is due to the fact that the pressure p in this term is determined upto a function of both space and |u|, say Ƥ(x, |u|), which may assume relatively broad forms. This allows us to use Ƥ as a pressure moderator in the evolution equation for ||u||Lq , whereby optimal regularity criteria can be sought by varying Ƥ within its admissible classes. New regularity criteria are derived with and without making use of the moderator. The results obtained in the absence of the moderator feature some improvement over existing criteria in the literature. Several criteria are derived in terms of the moderated (effective) pressure p+Ƥ. A simple moderation scheme and the plausibility of the present approach to the problem of Navier–Stokes regularity are discussed.Authentication and characterisation of a new oesophageal adenocarcinoma cell line : MFD-1
http://hdl.handle.net/10023/11487
New biological tools are required to understand the functional significance of genetic events revealed by whole genome sequencing (WGS) studies in oesophageal adenocarcinoma (OAC). The MFD-1 cell line was isolated from a 55-year-old male with OAC without recombinant-DNA transformation. Somatic genetic variations from MFD-1, tumour, normal oesophagus, and leucocytes were analysed with SNP6. WGS was performed in tumour and leucocytes. RNAseq was performed in MFD-1, and two classic OAC cell lines FLO1 and OE33. Transposase-accessible chromatin sequencing (ATAC-seq) was performed in MFD-1, OE33, and non-neoplastic HET1A cells. Functional studies were performed. MFD-1 had a high SNP genotype concordance with matched germline/tumour. Parental tumour and MFD-1 carried four somatically acquired mutations in three recurrent mutated genes in OAC: TP53, ABCB1 and SEMA5A, not present in FLO-1 or OE33. MFD-1 displayed high expression of epithelial and glandular markers and a unique fingerprint of open chromatin. MFD-1 was tumorigenic in SCID mouse and proliferative and invasive in 3D cultures. The clinical utility of whole genome sequencing projects will be delivered using accurate model systems to develop molecular-phenotype therapeutics. We have described the first such system to arise from the oesophageal International Cancer Genome Consortium project.
Wed, 07 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/114872016-09-07T00:00:00ZGarcia, EdwinHayden, AnnetteBirts, CharlesBritton, EdwardCowie, AndrewPickard, KarenMellone, MassimilianoChoh, ClarisaDerouet, MathieuDuriez, PatrickNoble, FergusWhite, Michael J.Primrose, John N.Strefford, Jonathan C.Rose-Zerilli, MatthewThomas, Gareth J.Ang, YengSharrocks, Andrew D.Fitzgerald, Rebecca C.Underwood, Timothy J.Lynch, Andy G.New biological tools are required to understand the functional significance of genetic events revealed by whole genome sequencing (WGS) studies in oesophageal adenocarcinoma (OAC). The MFD-1 cell line was isolated from a 55-year-old male with OAC without recombinant-DNA transformation. Somatic genetic variations from MFD-1, tumour, normal oesophagus, and leucocytes were analysed with SNP6. WGS was performed in tumour and leucocytes. RNAseq was performed in MFD-1, and two classic OAC cell lines FLO1 and OE33. Transposase-accessible chromatin sequencing (ATAC-seq) was performed in MFD-1, OE33, and non-neoplastic HET1A cells. Functional studies were performed. MFD-1 had a high SNP genotype concordance with matched germline/tumour. Parental tumour and MFD-1 carried four somatically acquired mutations in three recurrent mutated genes in OAC: TP53, ABCB1 and SEMA5A, not present in FLO-1 or OE33. MFD-1 displayed high expression of epithelial and glandular markers and a unique fingerprint of open chromatin. MFD-1 was tumorigenic in SCID mouse and proliferative and invasive in 3D cultures. The clinical utility of whole genome sequencing projects will be delivered using accurate model systems to develop molecular-phenotype therapeutics. We have described the first such system to arise from the oesophageal International Cancer Genome Consortium project.Mutational signatures of ionizing radiation in second malignancies
http://hdl.handle.net/10023/11484
Ionizing radiation is a potent carcinogen, inducing cancer through DNA damage. The signatures of mutations arising in human tissues following in vivo exposure to ionizing radiation have not been documented. Here, we searched for signatures of ionizing radiation in 12 radiation-associated second malignancies of different tumour types. Two signatures of somatic mutation characterize ionizing radiation exposure irrespective of tumour type. Compared with 319 radiation-naive tumours, radiation-associated tumours carry a median extra 201 deletions genome-wide, sized 1-100 base pairs often with microhomology at the junction. Unlike deletions of radiation-naive tumours, these show no variation in density across the genome or correlation with sequence context, replication timing or chromatin structure. Furthermore, we observe a significant increase in balanced inversions in radiation-associated tumours. Both small deletions and inversions generate driver mutations. Thus, ionizing radiation generates distinctive mutational signatures that explain its carcinogenic potential.
Sequencing data have been deposited at the European Genome-Phenome Archive (EGA, http://www.ebi.ac.uk/ega/), which is hosted by the European Bioinformatics Institute; accession numbers EGAS00001000138; EGAS00001000147; EGAS00001000195.
Mon, 12 Sep 2016 00:00:00 GMThttp://hdl.handle.net/10023/114842016-09-12T00:00:00ZBehjati, SamGundem, GunesWedge, David C.Roberts, Nicola D.Tarpey, Patrick S.Cooke, Susanna L.Van Loo, PeterAlexandrov, Ludmil B.Ramakrishna, ManasaDavies, HelenNik-Zainal, SerenaHardy, ClaireLatimer, CalliRaine, Keiran M.Stebbings, LucyMenzies, AndyJones, DavidShepherd, RebeccaButler, Adam P.Teague, Jon W.Jorgensen, MetteKhatri, BhavishaPillay, NischalanShlien, AdamFutreal, P. AndrewBadie, ChristopheMcDermott, UltanBova, G. StevenRichardson, Andrea L.Flanagan, Adrienne M.Stratton, Michael R.Campbell, Peter J.Lynch, Andrew G.Ionizing radiation is a potent carcinogen, inducing cancer through DNA damage. The signatures of mutations arising in human tissues following in vivo exposure to ionizing radiation have not been documented. Here, we searched for signatures of ionizing radiation in 12 radiation-associated second malignancies of different tumour types. Two signatures of somatic mutation characterize ionizing radiation exposure irrespective of tumour type. Compared with 319 radiation-naive tumours, radiation-associated tumours carry a median extra 201 deletions genome-wide, sized 1-100 base pairs often with microhomology at the junction. Unlike deletions of radiation-naive tumours, these show no variation in density across the genome or correlation with sequence context, replication timing or chromatin structure. Furthermore, we observe a significant increase in balanced inversions in radiation-associated tumours. Both small deletions and inversions generate driver mutations. Thus, ionizing radiation generates distinctive mutational signatures that explain its carcinogenic potential.Whole-genome sequencing of nine esophageal adenocarcinoma cell lines
http://hdl.handle.net/10023/11480
Esophageal adenocarcinoma (EAC) is highly mutated and molecularly heterogeneous. The number of cell lines available for study is limited and their genome has been only partially characterized. The availability of an accurate annotation of their mutational landscape is crucial for accurate experimental design and correct interpretation of genotype-phenotype findings. We performed high coverage, paired end whole genome sequencing on eight EAC cell lines-ESO26, ESO51, FLO-1, JH-EsoAd1, OACM5.1 C, OACP4 C, OE33, SK-GT-4-all verified against original patient material, and one esophageal high grade dysplasia cell line, CP-D. We have made available the aligned sequence data and report single nucleotide variants (SNVs), small insertions and deletions (indels), and copy number alterations, identified by comparison with the human reference genome and known single nucleotide polymorphisms (SNPs). We compare these putative mutations to mutations found in primary tissue EAC samples, to inform the use of these cell lines as a model of EAC.
This work was funded by an MRC Programme Grant to R.C.F. and a Cancer Research UK grant to PAWE. The pipeline for mutation calling is funded by Cancer Research UK as part of the International Cancer Genome Consortium. G.C. is a National Institute for Health Research Lecturer as part of a NIHR professorship grant to R.C.F. AGL is supported by a Cancer Research UK programme grant (C14303/A20406) to Simon Tavaré and the European Commission through the Horizon 2020 project SOUND (Grant Agreement no. 633974).
Fri, 10 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/114802016-06-10T00:00:00ZContino, GianmarcoEldridge, Matthew D.Secrier, MariaBower, LawrenceElliott, Rachael FelsWeaver, JamieLynch, Andy G.Edwards, Paul A.W.Fitzgerald, Rebecca C.Esophageal adenocarcinoma (EAC) is highly mutated and molecularly heterogeneous. The number of cell lines available for study is limited and their genome has been only partially characterized. The availability of an accurate annotation of their mutational landscape is crucial for accurate experimental design and correct interpretation of genotype-phenotype findings. We performed high coverage, paired end whole genome sequencing on eight EAC cell lines-ESO26, ESO51, FLO-1, JH-EsoAd1, OACM5.1 C, OACP4 C, OE33, SK-GT-4-all verified against original patient material, and one esophageal high grade dysplasia cell line, CP-D. We have made available the aligned sequence data and report single nucleotide variants (SNVs), small insertions and deletions (indels), and copy number alterations, identified by comparison with the human reference genome and known single nucleotide polymorphisms (SNPs). We compare these putative mutations to mutations found in primary tissue EAC samples, to inform the use of these cell lines as a model of EAC.Decomposition of mutational context signatures using quadratic programming methods
http://hdl.handle.net/10023/11479
Methods for inferring signatures of mutational contexts from large cancer sequencing data sets are invaluable for biological research, but impractical for clinical application where we require tools that decompose the context data for an individual into signatures. One such method has recently been published using an iterative linear modelling approach. A natural alternative places the problem within a quadratic programming framework and is presented here, where it is seen to offer advantages of speed and accuracy.
AGL was supported in this work by a Cancer Research UK programme grant [C14303/A20406] to Simon Tavaré. AGL acknowledges the support of the University of Cambridge, Cancer Research UK and Hutchison Whampoa Limited. Whole-genome sequencing of oesophageal adenocarcinoma was part of the oesophageal International Cancer Genome Consortium (ICGC) project. The oesophageal ICGC project was funded through a programme and infrastructure grant to Rebecca Fitzgerald as part of the OCCAMS collaboration.
Tue, 07 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/114792016-06-07T00:00:00ZLynch, Andy G.Methods for inferring signatures of mutational contexts from large cancer sequencing data sets are invaluable for biological research, but impractical for clinical application where we require tools that decompose the context data for an individual into signatures. One such method has recently been published using an iterative linear modelling approach. A natural alternative places the problem within a quadratic programming framework and is presented here, where it is seen to offer advantages of speed and accuracy.A tumor DNA complex aberration index is an independent predictor of survival in breast and ovarian cancer
http://hdl.handle.net/10023/11478
Complex focal chromosomal rearrangements in cancer genomes, also called "firestorms", can be scored from DNA copy number data. The complex arm-wise aberration index (CAAI) is a score that captures DNA copy number alterations that appear as focal complex events in tumors, and has potential prognostic value in breast cancer. This study aimed to validate this DNA-based prognostic index in breast cancer and test for the first time its potential prognostic value in ovarian cancer. Copy number alteration (CNA) data from 1950 breast carcinomas (METABRIC cohort) and 508 high-grade serous ovarian carcinomas (TCGA dataset) were analyzed. Cases were classified as CAAI positive if at least one complex focal event was scored. Complex alterations were frequently localized on chromosome 8p (n = 159), 17q (n = 176) and 11q (n = 251). CAAI events on 11q were most frequent in estrogen receptor positive (ER+) cases and on 17q in estrogen receptor negative (ER) cases. We found only a modest correlation between CAAI and the overall rate of genomic instability (GII) and number of breakpoints (r = 0.27 and r = 0.42, p <0.001). Breast cancer specific survival (BCSS), overall survival (OS) and ovarian cancer progression free survival (PUS) were used as clinical end points in Cox proportional hazard model survival analyses. CAAI positive breast cancers (43%) had higher mortality: hazard ratio (HR) of 1.94 (95%CI, 1.62-2.32) for BCSS, and of 1.49 (95%CI, 1.30-1.71) for OS. Representations of the 70-gene and the 21-gene predictors were compared with CAAI in multivariable models and CAAI was independently significant with a Cox adjusted HR of 1.56 (95%CI, 1.23-1.99) for ER+ and 1.55 (95%CI, 1.11-2.18) for ER disease. None of the expression-based predictors were prognostic in the ER subset. We found that a model including CAM and the two expression-based prognostic signatures outperformed a model including the 21-gene and 70-gene signatures but excluding CAAL Inclusion of CAAI in the clinical prognostication tool PREDICT significantly improved its performance. CAAI positive ovarian cancers (52%) also had worse prognosis: HRs of 1.3 (95%CI, 1.1-1.7) for PFS and 1.3 (95%CI, 1.1-1.6) for OS. This study validates CAM as an independent predictor of survival in both ER+ and ER breast cancer and reveals a significant prognostic value for CAAI in high-grade serous ovarian cancer. (C) 2014 The Authors. Published by Elsevier B.V. on behalf of Federation of European Biochemical Societies. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).
Thu, 01 Jan 2015 00:00:00 GMThttp://hdl.handle.net/10023/114782015-01-01T00:00:00ZVollan, Hans Kristian MoenRueda, Oscar M.Chin, Suet-FeungCurtis, ChristinaTurashuili, GulisaShah, SohrabLingjaerde, Ole ChristianYuan, YinyinNg, Charlotte K.Dunning, Mark J.Dicks, EdProvenzano, ElenaSammut, StephenMcKinney, StevenEllis, Ian O.Pinder, SarahPurushotham, ArnieMurphy, Leigh C.Kristensen, Vessela N.Brenton, James D.Pharoah, Paul D. P.Borresen-Dale, Anne-LiseAparicio, SamuelCaldas, CarlosLynch, AndyComplex focal chromosomal rearrangements in cancer genomes, also called "firestorms", can be scored from DNA copy number data. The complex arm-wise aberration index (CAAI) is a score that captures DNA copy number alterations that appear as focal complex events in tumors, and has potential prognostic value in breast cancer. This study aimed to validate this DNA-based prognostic index in breast cancer and test for the first time its potential prognostic value in ovarian cancer. Copy number alteration (CNA) data from 1950 breast carcinomas (METABRIC cohort) and 508 high-grade serous ovarian carcinomas (TCGA dataset) were analyzed. Cases were classified as CAAI positive if at least one complex focal event was scored. Complex alterations were frequently localized on chromosome 8p (n = 159), 17q (n = 176) and 11q (n = 251). CAAI events on 11q were most frequent in estrogen receptor positive (ER+) cases and on 17q in estrogen receptor negative (ER) cases. We found only a modest correlation between CAAI and the overall rate of genomic instability (GII) and number of breakpoints (r = 0.27 and r = 0.42, p <0.001). Breast cancer specific survival (BCSS), overall survival (OS) and ovarian cancer progression free survival (PUS) were used as clinical end points in Cox proportional hazard model survival analyses. CAAI positive breast cancers (43%) had higher mortality: hazard ratio (HR) of 1.94 (95%CI, 1.62-2.32) for BCSS, and of 1.49 (95%CI, 1.30-1.71) for OS. Representations of the 70-gene and the 21-gene predictors were compared with CAAI in multivariable models and CAAI was independently significant with a Cox adjusted HR of 1.56 (95%CI, 1.23-1.99) for ER+ and 1.55 (95%CI, 1.11-2.18) for ER disease. None of the expression-based predictors were prognostic in the ER subset. We found that a model including CAM and the two expression-based prognostic signatures outperformed a model including the 21-gene and 70-gene signatures but excluding CAAL Inclusion of CAAI in the clinical prognostication tool PREDICT significantly improved its performance. CAAI positive ovarian cancers (52%) also had worse prognosis: HRs of 1.3 (95%CI, 1.1-1.7) for PFS and 1.3 (95%CI, 1.1-1.6) for OS. This study validates CAM as an independent predictor of survival in both ER+ and ER breast cancer and reveals a significant prognostic value for CAAI in high-grade serous ovarian cancer. (C) 2014 The Authors. Published by Elsevier B.V. on behalf of Federation of European Biochemical Societies. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/3.0/).Phenotype specific analyses reveal distinct regulatory mechanism for chronically activated p53
http://hdl.handle.net/10023/11475
The downstream functions of the DNA binding tumor suppressor p53 vary depending on the cellular context, and persistent p53 activation has recently been implicated in tumor suppression and senescence. However, genome-wide information about p53-target gene regulation has been derived mostly from acute genotoxic conditions. Using ChIP-seq and expression data, we have found distinct p53 binding profiles between acutely activated (through DNA damage) and chronically activated (in senescent or pro-apoptotic conditions) p53. Compared to the classical ‘acute’ p53 binding profile, ‘chronic’ p53 peaks were closely associated with CpG-islands. Furthermore, the chronic CpG-island binding of p53 conferred distinct expression patterns between senescent and pro-apoptotic conditions. Using the p53 targets seen in the chronic conditions together with external high-throughput datasets, we have built p53 networks that revealed extensive self-regulatory ‘p53 hubs’ where p53 and many p53 targets can physically interact with each other. Integrating these results with public clinical datasets identified the cancer-associated lipogenic enzyme, SCD, which we found to be directly repressed by p53 through the CpG-island promoter, providing a mechanistic link between p53 and the ‘lipogenic phenotype’, a hallmark of cancer. Our data reveal distinct phenotype associations of chronic p53 targets that underlie specific gene regulatory mechanisms.
This work was supported by the University of Cambridge; Cancer Research UK (C14303/A17197); Hutchison Whampoa. In addition, MasasN and TO were supported by the Human Frontier Science Program (RGY0078/2010); HK was supported by MEXT KAKENHI (Grant Numbers 25116005 and 26291071); KT was supported by the Japan Society for the Promotion of Science (24–8563).
Thu, 19 Mar 2015 00:00:00 GMThttp://hdl.handle.net/10023/114752015-03-19T00:00:00ZKirschner, KristinaSamarajiwa, Shamith A.Cairns, Jonathan M.Menon, SurajPérez-Mancera, Pedro A.Tomimatsu, KosukeBermejo-Rodriguez, CaminoIto, YokoChandra, TamirNarita, MasakoLyons, Scott K.Lynch, Andy G.Kimura, HiroshiOhbayashi, TetsuyaTavaré, SimonNarita, MasashiThe downstream functions of the DNA binding tumor suppressor p53 vary depending on the cellular context, and persistent p53 activation has recently been implicated in tumor suppression and senescence. However, genome-wide information about p53-target gene regulation has been derived mostly from acute genotoxic conditions. Using ChIP-seq and expression data, we have found distinct p53 binding profiles between acutely activated (through DNA damage) and chronically activated (in senescent or pro-apoptotic conditions) p53. Compared to the classical ‘acute’ p53 binding profile, ‘chronic’ p53 peaks were closely associated with CpG-islands. Furthermore, the chronic CpG-island binding of p53 conferred distinct expression patterns between senescent and pro-apoptotic conditions. Using the p53 targets seen in the chronic conditions together with external high-throughput datasets, we have built p53 networks that revealed extensive self-regulatory ‘p53 hubs’ where p53 and many p53 targets can physically interact with each other. Integrating these results with public clinical datasets identified the cancer-associated lipogenic enzyme, SCD, which we found to be directly repressed by p53 through the CpG-island promoter, providing a mechanistic link between p53 and the ‘lipogenic phenotype’, a hallmark of cancer. Our data reveal distinct phenotype associations of chronic p53 targets that underlie specific gene regulatory mechanisms.Frequent somatic transfer of mitochondrial DNA into the nuclear genome of human cancer cells
http://hdl.handle.net/10023/11474
Mitochondrial genomes are separated from the nuclear genome for most of the cell cycle by the nuclear double membrane, intervening cytoplasm, and the mitochondrial double membrane. Despite these physical barriers, we show that somatically acquired mitochondrial-nuclear genome fusion sequences are present in cancer cells. Most occur in conjunction with intranuclear genomic rearrangements, and the features of the fusion fragments indicate that nonhomologous end joining and/or replication-dependent DNA double-strand break repair are the dominant mechanisms involved. Remarkably, mitochondrial-nuclear genome fusions occur at a similar rate per base pair of DNA as interchromosomal nuclear rearrangements, indicating the presence of a high frequency of contact between mitochondrial and nuclear DNA in some somatic cells. Transmission of mitochondrial DNA to the nuclear genome occurs in neoplastically transformed cells, but we do not exclude the possibility that some mitochondrial-nuclear DNA fusions observed in cancer occurred years earlier in normal somatic cells.
Mon, 01 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/114742015-06-01T00:00:00ZJu, Young SeokTubio, Jose M.C.Mifsud, WilliamFu, BeiyuanDavies, Helen R.Ramakrishna, ManasaLi, YilongYates, LucyGundem, GunesTarpey, Patrick S.Behjati, SamPapaemmanuil, ElliMartin, SanchaFullam, AnthonyGerstung, MoritzNangalia, JyotiGreen, Anthony R.Caldas, CarlosBorg, ÅkeTutt, AndrewMichael Lee, Ming TaVan'T Veer, Laura J.Tan, Benita K.T.Aparicio, SamuelSpan, Paul N.Martens, John W.M.Knappskog, StianVincent-Salomon, AnneBørresen-Dale, Anne LiseEyfjörd, Jórunn ErlaFlanagan, Adrienne M.Foster, ChristopherNeal, David E.Cooper, ColinEeles, RosalindLakhani, Sunil R.Desmedt, ChristineThomas, GillesRichardson, Andrea L.Purdie, Colin A.Thompson, Alastair M.McDermott, UltanYang, FengtangNik-Zainal, SerenaCampbell, Peter J.Stratton, Michael R.Lynch, AndyMitochondrial genomes are separated from the nuclear genome for most of the cell cycle by the nuclear double membrane, intervening cytoplasm, and the mitochondrial double membrane. Despite these physical barriers, we show that somatically acquired mitochondrial-nuclear genome fusion sequences are present in cancer cells. Most occur in conjunction with intranuclear genomic rearrangements, and the features of the fusion fragments indicate that nonhomologous end joining and/or replication-dependent DNA double-strand break repair are the dominant mechanisms involved. Remarkably, mitochondrial-nuclear genome fusions occur at a similar rate per base pair of DNA as interchromosomal nuclear rearrangements, indicating the presence of a high frequency of contact between mitochondrial and nuclear DNA in some somatic cells. Transmission of mitochondrial DNA to the nuclear genome occurs in neoplastically transformed cells, but we do not exclude the possibility that some mitochondrial-nuclear DNA fusions observed in cancer occurred years earlier in normal somatic cells.Mobile element insertions are frequent in oesophageal adenocarcinomas and can mislead paired-end sequencing analysis
http://hdl.handle.net/10023/11473
Background: Mobile elements are active in the human genome, both in the germline and cancers, where they can mutate driver genes. Results: While analysing whole genome paired-end sequencing of oesophageal adenocarcinomas to find genomic rearrangements, we identified three ways in which new mobile element insertions appear in the data, resembling translocation or insertion junctions: inserts where unique sequence has been transduced by an L1 (Long interspersed element 1) mobile element; novel inserts that are confidently, but often incorrectly, mapped by alignment software to L1s or polyA tracts in the reference sequence; and a combination of these two ways, where different sequences within one insert are mapped to different loci. We identified nine unique sequences that were transduced by neighbouring L1s, both L1s in the reference genome and L1s not present in the reference. Many of the resulting inserts were small fragments that include little or no recognisable mobile element sequence. We found 6 loci in the reference genome to which sequence reads from inserts were frequently mapped, probably erroneously, by alignment software: these were either L1 sequence or particularly long polyA runs. Inserts identified from such apparent rearrangement junctions averaged 16 inserts/tumour, range 0-153 insertions in 43 tumours. However, many inserts would not be detected by mapping the sequences to the reference genome, because they do not include sufficient mappable sequence. To estimate total somatic inserts we searched for polyA sequences that were not present in the matched normal or other normals from the same tumour batch, and were not associated with known polymorphisms. Samples of these candidate inserts were verified by sequencing across them or manual inspection of surrounding reads: at least 85 % were somatic and resembled L1-mediated events, most including L1Hs sequence. Approximately 100 such inserts were detected per tumour on average (range zero to approximately 700). Conclusions: Somatic mobile elements insertions are abundant in these tumours, with over 75 % of cases having a number of novel inserts detected. The inserts create a variety of problems for the interpretation of paired-end sequencing data.
Funding was primarily from Cancer Research UK program grants to RCF and ST (C14478/A15874 and C14303/A17197), with additional support awarded to RCF from UK Medical Research Council, NHS National Institute for Health Research (NIHR), the Experimental Cancer Medicine Centre Network and the NIHR Cambridge Biomedical Research Centre, and Cancer Research UK Project grant C1023/A14545 to PAWE. JMJW was funded by a Wellcome Trust Translational Medicine and Therapeutics grant.
Fri, 10 Jul 2015 00:00:00 GMThttp://hdl.handle.net/10023/114732015-07-10T00:00:00ZPaterson, Anna L.Weaver, Jamie M. J.Eldridge, Matthew D.Tavare, SimonFitzgerald, Rebecca C.Edwards, Paul A. W.Lynch, AndyBackground: Mobile elements are active in the human genome, both in the germline and cancers, where they can mutate driver genes. Results: While analysing whole genome paired-end sequencing of oesophageal adenocarcinomas to find genomic rearrangements, we identified three ways in which new mobile element insertions appear in the data, resembling translocation or insertion junctions: inserts where unique sequence has been transduced by an L1 (Long interspersed element 1) mobile element; novel inserts that are confidently, but often incorrectly, mapped by alignment software to L1s or polyA tracts in the reference sequence; and a combination of these two ways, where different sequences within one insert are mapped to different loci. We identified nine unique sequences that were transduced by neighbouring L1s, both L1s in the reference genome and L1s not present in the reference. Many of the resulting inserts were small fragments that include little or no recognisable mobile element sequence. We found 6 loci in the reference genome to which sequence reads from inserts were frequently mapped, probably erroneously, by alignment software: these were either L1 sequence or particularly long polyA runs. Inserts identified from such apparent rearrangement junctions averaged 16 inserts/tumour, range 0-153 insertions in 43 tumours. However, many inserts would not be detected by mapping the sequences to the reference genome, because they do not include sufficient mappable sequence. To estimate total somatic inserts we searched for polyA sequences that were not present in the matched normal or other normals from the same tumour batch, and were not associated with known polymorphisms. Samples of these candidate inserts were verified by sequencing across them or manual inspection of surrounding reads: at least 85 % were somatic and resembled L1-mediated events, most including L1Hs sequence. Approximately 100 such inserts were detected per tumour on average (range zero to approximately 700). Conclusions: Somatic mobile elements insertions are abundant in these tumours, with over 75 % of cases having a number of novel inserts detected. The inserts create a variety of problems for the interpretation of paired-end sequencing data.Mining human prostate cancer datasets : the “camcAPP” shiny app
http://hdl.handle.net/10023/11472
Funding: Core CRUK funding: MD, AGL, ADL. Academy of Medical Sciences Clinical Lecturer Starter Grant SGCL11 (prinicipal funder of this work): ADL.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/114722017-03-01T00:00:00ZDunning, Mark J.Vowler, Sarah L.Lalonde, EmilieRoss-Adams, HelenBoutros, PaulMills, Ian G.Lynch, Andy G.Lamb, Alastair D.HES5 silencing is an early and recurrent change in prostate tumourigenesis
http://hdl.handle.net/10023/11471
Prostate cancer is the most common cancer in men, resulting in over 10 000 deaths/year in the UK. Sequencing and copy number analysis of primary tumours has revealed heterogeneity within tumours and an absence of recurrent founder mutations, consistent with non-genetic disease initiating events. Using methylation profiling in a series of multifocal prostate tumours, we identify promoter methylation of the transcription factor HES5 as an early event in prostate tumourigenesis. We confirm that this epigenetic alteration occurs in 86-97% of cases in two independent prostate cancer cohorts (n=49 and n=39 tumour-normal pairs). Treatment of prostate cancer cells with the demethylating agent 5-aza-2′-deoxycytidine increased HES5 expression and downregulated its transcriptional target HES6, consistent with functional silencing of the HES5 gene in prostate cancer. Finally, we identify and test a transcriptional module involving the AR, ERG, HES1 and HES6 and propose a model for the impact of HES5 silencing on tumourigenesis as a starting point for future functional studies.
The ICGC Prostate UK Group is funded by Cancer Research UK Grant C5047/A14835, by the Dallaglio Foundation, and by The Wellcome Trust. The Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre.
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/114712015-04-01T00:00:00ZMassie, Charles E.Spiteri, InmaculadaRoss-Adams, HelenLuxton, HayleyKay, JonathanWhitaker, Hayley C.Dunning, Mark J.Lamb, Alastair D.Ramos-Montoya, AntonioBrewer, Daniel S.Cooper, Colin S.Eeles, RosalindWarren, Anne Y.Tavaré, SimonNeal, David E.Lynch, Andy G.UK Prostate ICGC GroupProstate cancer is the most common cancer in men, resulting in over 10 000 deaths/year in the UK. Sequencing and copy number analysis of primary tumours has revealed heterogeneity within tumours and an absence of recurrent founder mutations, consistent with non-genetic disease initiating events. Using methylation profiling in a series of multifocal prostate tumours, we identify promoter methylation of the transcription factor HES5 as an early event in prostate tumourigenesis. We confirm that this epigenetic alteration occurs in 86-97% of cases in two independent prostate cancer cohorts (n=49 and n=39 tumour-normal pairs). Treatment of prostate cancer cells with the demethylating agent 5-aza-2′-deoxycytidine increased HES5 expression and downregulated its transcriptional target HES6, consistent with functional silencing of the HES5 gene in prostate cancer. Finally, we identify and test a transcriptional module involving the AR, ERG, HES1 and HES6 and propose a model for the impact of HES5 silencing on tumourigenesis as a starting point for future functional studies.Seals and shipping : quantifying population risk and individual exposure to vessel noise
http://hdl.handle.net/10023/11459
1. Vessels can have acute and chronic impacts on marine species. The rate of increase in commercial shipping is accelerating, and there is a need to quantify and potentially manage the risk of these impacts. 2. Usage maps characterising densities of grey and harbour seals and ships around the British Isles were used to produce risk maps of seal co-occurrence with shipping traffic. Acoustic exposure to individual harbour seals was modelled in a study area using contemporaneous movement data from 28 animals fitted with UHF global positioning satellite telemetry tags and automatic identification system data from all ships during 2014 and 2015. Data from four acoustic recorders were used to validate sound exposure predictions. 3. Across the British Isles, rates of co-occurrence were highest within 50 km of the coast, close to seal haul-outs. Areas identified with high risk of exposure included 11 Special Areas of Conservation (SAC; from a possible 25). Risk to harbour seal populations was highest, affecting half of all SACs associated with the species. 4. Predicted cumulative sound exposure level, cSELs(Mpw), over all seals was 176·8 dB re 1 μPa2 s (95% CI 163·3–190·4), ranging from 170·2 dB re 1μPa2 s (95% CI 168·4–171·9) to 189·3 dB re 1 μPa2 s (95% CI 172·6–206·0) for individuals. This represented an increase in 28·3 dB re 1 μPa2 s over measured ambient noise. For 20 of 28 animals in the study, 95% CI for cSELs(Mpw) had upper bounds above levels known to induce temporary threshold shift. Predictions of broadband received sound pressure levels were underestimated on average by 0·7 dB re 1 μPa (±3·3). 5. Synthesis and applications. We present a framework to allow shipping noise, an important marine anthropogenic stressor, to be explicitly incorporated into spatial planning. Potentially sensitive areas are identified through quantifying risk to marine species of exposure to shipping traffic, and individual noise exposure is predicted with associated uncertainty in an area with varying rates of co-occurrence. The detailed approach taken here facilitates spatial planning with regard to underwater noise within areas protected through the Habitats Directive, and could be used to provide evidence for further designations. This framework may have utility in assessing whether underwater noise levels are at Good Environmental Status under the Marine Strategy Framework Directive.
The work was funded under Scottish Government grant MMSS/001/11 and contract CR/2014/04, and supported by National Capability funding from NERC to SMRU (grant no. SMRU1001). Seal at-sea usage maps, location data for individual seals, locations and source levels for vessels, and SPLs from monitoring data used for acoustic validations are available from the Pure repository, https://doi.org/10.17630/89ac9345-240a-41bb-8f53-b3f14bb114c0.
Fri, 01 Dec 2017 00:00:00 GMThttp://hdl.handle.net/10023/114592017-12-01T00:00:00ZJones, Esther L.Hastie, Gordon D.Smout, SophieOnoufriou, JosephMerchant, Nathan D.Brookes, Kate L.Thompson, David1. Vessels can have acute and chronic impacts on marine species. The rate of increase in commercial shipping is accelerating, and there is a need to quantify and potentially manage the risk of these impacts. 2. Usage maps characterising densities of grey and harbour seals and ships around the British Isles were used to produce risk maps of seal co-occurrence with shipping traffic. Acoustic exposure to individual harbour seals was modelled in a study area using contemporaneous movement data from 28 animals fitted with UHF global positioning satellite telemetry tags and automatic identification system data from all ships during 2014 and 2015. Data from four acoustic recorders were used to validate sound exposure predictions. 3. Across the British Isles, rates of co-occurrence were highest within 50 km of the coast, close to seal haul-outs. Areas identified with high risk of exposure included 11 Special Areas of Conservation (SAC; from a possible 25). Risk to harbour seal populations was highest, affecting half of all SACs associated with the species. 4. Predicted cumulative sound exposure level, cSELs(Mpw), over all seals was 176·8 dB re 1 μPa2 s (95% CI 163·3–190·4), ranging from 170·2 dB re 1μPa2 s (95% CI 168·4–171·9) to 189·3 dB re 1 μPa2 s (95% CI 172·6–206·0) for individuals. This represented an increase in 28·3 dB re 1 μPa2 s over measured ambient noise. For 20 of 28 animals in the study, 95% CI for cSELs(Mpw) had upper bounds above levels known to induce temporary threshold shift. Predictions of broadband received sound pressure levels were underestimated on average by 0·7 dB re 1 μPa (±3·3). 5. Synthesis and applications. We present a framework to allow shipping noise, an important marine anthropogenic stressor, to be explicitly incorporated into spatial planning. Potentially sensitive areas are identified through quantifying risk to marine species of exposure to shipping traffic, and individual noise exposure is predicted with associated uncertainty in an area with varying rates of co-occurrence. The detailed approach taken here facilitates spatial planning with regard to underwater noise within areas protected through the Habitats Directive, and could be used to provide evidence for further designations. This framework may have utility in assessing whether underwater noise levels are at Good Environmental Status under the Marine Strategy Framework Directive.multiSNV : a probabilistic approach for improving detection of somatic point mutations from multiple related tumour samples
http://hdl.handle.net/10023/11447
Somatic variant analysis of a tumour sample and its matched normal has been widely used in cancer research to distinguish germline polymorphisms from somatic mutations. However, due to the extensive intratumour heterogeneity of cancer, sequencing data from a single tumour sample may greatly underestimate the overall mutational landscape. In recent studies, multiple spatially or temporally separated tumour samples from the same patient were sequenced to identify the regional distribution of somatic mutations and study intratumour heterogeneity. There are a number of tools to perform somatic variant calling from matched tumour-normal next-generation sequencing (NGS) data; however none of these allow joint analysis of multiple same-patient samples. We discuss the benefits and challenges of multisample somatic variant calling and present multiSNV, a software package for calling single nucleotide variants (SNVs) using NGS data from multiple same-patient samples. Instead of performing multiple pairwise analyses of a single tumour sample and a matched normal, multiSNV jointly considers all available samples under a Bayesian framework to increase sensitivity of calling shared SNVs. By leveraging information from all available samples, multiSNV is able to detect rare mutations with variant allele frequencies down to 3% from whole-exome sequencing experiments.
Funding: Cancer Research UK grant C14303/A17197. Funding for open access charge: University of Cambridge.
Tue, 19 May 2015 00:00:00 GMThttp://hdl.handle.net/10023/114472015-05-19T00:00:00ZJosephidou, MalvinaLynch, Andy G.Tavaré, SimonSomatic variant analysis of a tumour sample and its matched normal has been widely used in cancer research to distinguish germline polymorphisms from somatic mutations. However, due to the extensive intratumour heterogeneity of cancer, sequencing data from a single tumour sample may greatly underestimate the overall mutational landscape. In recent studies, multiple spatially or temporally separated tumour samples from the same patient were sequenced to identify the regional distribution of somatic mutations and study intratumour heterogeneity. There are a number of tools to perform somatic variant calling from matched tumour-normal next-generation sequencing (NGS) data; however none of these allow joint analysis of multiple same-patient samples. We discuss the benefits and challenges of multisample somatic variant calling and present multiSNV, a software package for calling single nucleotide variants (SNVs) using NGS data from multiple same-patient samples. Instead of performing multiple pairwise analyses of a single tumour sample and a matched normal, multiSNV jointly considers all available samples under a Bayesian framework to increase sensitivity of calling shared SNVs. By leveraging information from all available samples, multiSNV is able to detect rare mutations with variant allele frequencies down to 3% from whole-exome sequencing experiments.5-hydroxymethylcytosine marks promoters in colon that resist DNA hypermethylation in cancer
http://hdl.handle.net/10023/11446
Background : The discovery of cytosine hydroxymethylation (5hmC) as a mechanism that potentially controls DNA methylation changes typical of neoplasia prompted us to investigate its behaviour in colon cancer. 5hmC is globally reduced in proliferating cells such as colon tumours and the gut crypt progenitors, from which tumours can arise. Results : Here, we show that colorectal tumours and cancer cells express Ten-Eleven-Translocation (TET) transcripts at levels similar to normal tissues. Genome-wide analyses show that promoters marked by 5hmC in normal tissue, and those identified as TET2 targets in colorectal cancer cells, are resistant to methylation gain in cancer. In vitro studies of TET2 in cancer cells confirm that these promoters are resistant to methylation gain independently of sustained TET2 expression. We also find that a considerable number of the methylation gain-resistant promoters marked by 5hmC in normal colon overlap with those that are marked with poised bivalent histone modifications in embryonic stem cells. Conclusions : Together our results indicate that promoters that acquire 5hmC upon normal colon differentiation are innately resistant to neoplastic hypermethylation by mechanisms that do not require high levels of 5hmC in tumours. Our study highlights the potential of cytosine modifications as biomarkers of cancerous cell proliferation.
The authors would like to acknowledge the support of The University of Cambridge, Cancer Research UK (CRUK SEB-Institute Group Award A ref10182; CRUK Senior fellowship C10112/A11388 to AEKI) and Hutchison Whampoa Limited. The Human Research Tissue Bank is supported by the NIHR Cambridge Biomedical Research Centre. FF is a ULB Professor funded by grants from the F.N.R.S. and Télévie, the IUAP P7/03 programme, the ARC (AUWB-2010-2015 ULB-No 7), the WB Health program and the Fonds Gaston Ithier. Data access: http://www.ncbi.nlm.nih.gov/geo/query/acc.cgi?token=jpwzvsowiyuamzs&acc=GSE47592
Wed, 01 Apr 2015 00:00:00 GMThttp://hdl.handle.net/10023/114462015-04-01T00:00:00ZUribe-Lewis, SantiagoStark, RoryCarroll, ThomasDunning, Mark J.Bachman, MartinIto, YokoStojic, LovorkaHalim, SilviaVowler, Sarah L.Lynch, Andy G.Delatte, Benjaminde Bony, Eric J.Colin, LaurenceDefrance, MatthieuKrueger, FelixSilva, Ana Luisaten Hoopen, RogierIbrahim, Ashraf E.K.Fuks, FrançoisMurrell, AdeleBackground : The discovery of cytosine hydroxymethylation (5hmC) as a mechanism that potentially controls DNA methylation changes typical of neoplasia prompted us to investigate its behaviour in colon cancer. 5hmC is globally reduced in proliferating cells such as colon tumours and the gut crypt progenitors, from which tumours can arise. Results : Here, we show that colorectal tumours and cancer cells express Ten-Eleven-Translocation (TET) transcripts at levels similar to normal tissues. Genome-wide analyses show that promoters marked by 5hmC in normal tissue, and those identified as TET2 targets in colorectal cancer cells, are resistant to methylation gain in cancer. In vitro studies of TET2 in cancer cells confirm that these promoters are resistant to methylation gain independently of sustained TET2 expression. We also find that a considerable number of the methylation gain-resistant promoters marked by 5hmC in normal colon overlap with those that are marked with poised bivalent histone modifications in embryonic stem cells. Conclusions : Together our results indicate that promoters that acquire 5hmC upon normal colon differentiation are innately resistant to neoplastic hypermethylation by mechanisms that do not require high levels of 5hmC in tumours. Our study highlights the potential of cytosine modifications as biomarkers of cancerous cell proliferation.Epigenetic and oncogenic regulation of SLC16A7 (MCT2) results in protein over-expression, impacting on signalling and cellular phenotypes in prostate cancer
http://hdl.handle.net/10023/11445
Monocarboxylate Transporter 2 (MCT2) is a major pyruvate transporter encoded by the SLC16A7 gene. Recent studies pointed to a consistent overexpression of MCT2 in prostate cancer (PCa) suggesting MCT2 as a putative biomarker and molecular target. Despite the importance of this observation the mechanisms involved in MCT2 regulation are unknown. Through an integrative analysis we have discovered that selective demethylation of an internal SLC16A7/MCT2 promoter is a recurrent event in independent PCa cohorts. This demethylation is associated with expression of isoforms differing only in 5'-UTR translational control motifs, providing one contributing mechanism for MCT2 protein overexpression in PCa. Genes co-expressed with SLC16A7/MCT2 also clustered in oncogenic-related pathways and effectors of these signalling pathways were found to bind at the SLC16A7/MCT2 gene locus. Finally, MCT2 knock-down attenuated the growth of PCa cells. The present study unveils an unexpected epigenetic regulation of SLC16A7/MCT2 isoforms and identifies a link between SLC16A7/MCT2, Androgen Receptor (AR), ETS-related gene (ERG) and other oncogenic pathways in PCa. These results underscore the importance of combining data from epigenetic, transcriptomic and protein level changes to allow more comprehensive insights into the mechanisms underlying protein expression, that in our case provide additional weight to MCT2 as a candidate biomarker and molecular target in PCa.
Felisbino S. received a fellowship from the Sao Paulo Research Foundation (FAPESP) ref. 2013/08830-2 and 2013/06802-1. Anne Y Warren research time funded by: Cambridge Biomedical Research Centre.
Tue, 02 Jun 2015 00:00:00 GMThttp://hdl.handle.net/10023/114452015-06-02T00:00:00ZPértega-Gomes, NelmaVizcaino, Jose R.Felisbino, SergioWarren, Anne Y.Shaw, GregKay, JonathanWhitaker, HayleyLynch, Andy G.Fryer, LeeNeal, David E.Massie, Charles E.Monocarboxylate Transporter 2 (MCT2) is a major pyruvate transporter encoded by the SLC16A7 gene. Recent studies pointed to a consistent overexpression of MCT2 in prostate cancer (PCa) suggesting MCT2 as a putative biomarker and molecular target. Despite the importance of this observation the mechanisms involved in MCT2 regulation are unknown. Through an integrative analysis we have discovered that selective demethylation of an internal SLC16A7/MCT2 promoter is a recurrent event in independent PCa cohorts. This demethylation is associated with expression of isoforms differing only in 5'-UTR translational control motifs, providing one contributing mechanism for MCT2 protein overexpression in PCa. Genes co-expressed with SLC16A7/MCT2 also clustered in oncogenic-related pathways and effectors of these signalling pathways were found to bind at the SLC16A7/MCT2 gene locus. Finally, MCT2 knock-down attenuated the growth of PCa cells. The present study unveils an unexpected epigenetic regulation of SLC16A7/MCT2 isoforms and identifies a link between SLC16A7/MCT2, Androgen Receptor (AR), ETS-related gene (ERG) and other oncogenic pathways in PCa. These results underscore the importance of combining data from epigenetic, transcriptomic and protein level changes to allow more comprehensive insights into the mechanisms underlying protein expression, that in our case provide additional weight to MCT2 as a candidate biomarker and molecular target in PCa.Energetics of the Kelvin-Helmholtz instability induced by transverse waves in twisted coronal loops
http://hdl.handle.net/10023/11444
Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, density-enhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube’s magnetic field. Results. The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop’s density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a non-zero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode. Conclusions. The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures.
The research leading to these results has received funding from the UK Science and Technology Facilities Council (consolidated grant ST/N000609/1) and the European Union Horizon 2020 research and innovation programme (grant agreement No. 647214).
Thu, 16 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/114442017-11-16T00:00:00ZHowson, T. A.De Moortel, I.Antolin, P.Aims. We quantify the effects of twisted magnetic fields on the development of the magnetic Kelvin-Helmholtz instability (KHI) in transversely oscillating coronal loops. Methods. We modelled a fundamental standing kink mode in a straight, density-enhanced magnetic flux tube using the magnetohydrodynamics code, Lare3d. In order to evaluate the impact of an azimuthal component of the magnetic field, various degrees of twist were included within the flux tube’s magnetic field. Results. The process of resonant absorption is only weakly affected by the presence of a twisted magnetic field. However, the subsequent evolution of the KHI is sensitive to the strength of the azimuthal component of the field. Increased twist values inhibit the deformation of the loop’s density profile, which is associated with the growth of the instability. Despite this, much smaller scales in the magnetic field are generated when there is a non-zero azimuthal component present. Hence, the instability is more energetic in cases with (even weakly) twisted fields. Field aligned flows at the loop apex are established in a twisted regime once the instability has formed. Further, in the straight field case, there is no net vertical component of vorticity when integrated across the loop. However, the inclusion of azimuthal magnetic field generates a preferred direction for the vorticity which oscillates during the kink mode. Conclusions. The KHI may have implications for wave heating in the solar atmosphere due to the creation of small length scales and the generation of a turbulent regime. Whilst magnetic twist does suppress the development of the vortices associated with the instability, the formation of the KHI in a twisted regime will be accompanied by greater Ohmic dissipation due to the larger currents that are produced, even if only weak twist is present. The presence of magnetic twist will likely make the instability more difficult to detect in the corona, but will enhance its contribution to heating the solar atmosphere. Further, the development of velocities along the loop may have observational applications for inferring the presence of magnetic twist within coronal structures.Integration of copy number and transcriptomics provides risk stratification in prostate cancer : a discovery and validation cohort study
http://hdl.handle.net/10023/11443
Background : Understanding the heterogeneous genotypes and phenotypes of prostate cancer is fundamental to improving the way we treat this disease. As yet, there are no validated descriptions of prostate cancer subgroups derived from integrated genomics linked with clinical outcome. Methods : In a study of 482 tumour, benign and germline samples from 259 men with primary prostate cancer, we used integrative analysis of copy number alterations (CNA) and array transcriptomics to identify genomic loci that affect expression levels of mRNA in an expression quantitative trait loci (eQTL) approach, to stratify patients into subgroups that we then associated with future clinical behaviour, and compared with either CNA or transcriptomics alone. Findings : We identified five separate patient subgroups with distinct genomic alterations and expression profiles based on 100 discriminating genes in our separate discovery and validation sets of 125 and 103 men. These subgroups were able to consistently predict biochemical relapse (p = 0.0017 and p = 0.016 respectively) and were further validated in a third cohort with long-term follow-up (p = 0.027). We show the relative contributions of gene expression and copy number data on phenotype, and demonstrate the improved power gained from integrative analyses. We confirm alterations in six genes previously associated with prostate cancer ( MAP3K7, MELK, RCBTB2, ELAC2, TPD52, ZBTB4), and also identify 94 genes not previously linked to prostate cancer progression that would not have been detected using either transcript or copy number data alone. We confirm a number of previously published molecular changes associated with high risk disease, including MYC amplification, and NKX3-1, RB1 and PTEN deletions, as well as over-expression of PCA3 and AMACR, and loss of MSMB in tumour tissue. A subset of the 100 genes outperforms established clinical predictors of poor prognosis (PSA, Gleason score), as well as previously published gene signatures (p = 0.0001). We further show how our molecular profiles can be used for the early detection of aggressive cases in a clinical setting, and inform treatment decisions. Interpretation : For the first time in prostate cancer this study demonstrates the importance of integrated genomic analyses incorporating both benign and tumour tissue data in identifying molecular alterations leading to the generation of robust gene sets that are predictive of clinical outcome in independent patient cohorts.
Study data are deposited in NCBI GEO (unique identifier number GSE70770).
Tue, 01 Sep 2015 00:00:00 GMThttp://hdl.handle.net/10023/114432015-09-01T00:00:00ZRoss-Adams, H.Lamb, A. D.Dunning, M. J.Halim, S.Lindberg, J.Massie, C. M.Egevad, L. A.Russell, R.Ramos-Montoya, A.Vowler, S. L.Sharma, N. L.Kay, J.Whitaker, H.Clark, J.Hurst, R.Gnanapragasam, V. J.Shah, N. C.Warren, A. Y.Cooper, C. S.Lynch, A. G.Stark, R.Mills, I. G.Grönberg, H.Neal, D. E.Shaw, GregHori, SatoshiBaridi, AjoebTran, MaxineWadhwa, KaranNelson, AdamPatel, KevalThomas, BenjaminLuxton, HayleyGnanpragasam, VincentDoble, AndrewKastner, ChristofAho, TevitaHaynes, BeverleyPartridge, WendyCromwell, ElizabethSangrasi, AsifBurge, JoGeorge, AnneStearn, SaraCorcoran, MarieCoret, HansleyBasnett, GillianFrancis, InduWhitington, ThomasYuan, YinyinRueda, OscarHadfield, JamesHowat, WillMiller, JodiBrewer, DanielCamCaP Study GroupBackground : Understanding the heterogeneous genotypes and phenotypes of prostate cancer is fundamental to improving the way we treat this disease. As yet, there are no validated descriptions of prostate cancer subgroups derived from integrated genomics linked with clinical outcome. Methods : In a study of 482 tumour, benign and germline samples from 259 men with primary prostate cancer, we used integrative analysis of copy number alterations (CNA) and array transcriptomics to identify genomic loci that affect expression levels of mRNA in an expression quantitative trait loci (eQTL) approach, to stratify patients into subgroups that we then associated with future clinical behaviour, and compared with either CNA or transcriptomics alone. Findings : We identified five separate patient subgroups with distinct genomic alterations and expression profiles based on 100 discriminating genes in our separate discovery and validation sets of 125 and 103 men. These subgroups were able to consistently predict biochemical relapse (p = 0.0017 and p = 0.016 respectively) and were further validated in a third cohort with long-term follow-up (p = 0.027). We show the relative contributions of gene expression and copy number data on phenotype, and demonstrate the improved power gained from integrative analyses. We confirm alterations in six genes previously associated with prostate cancer ( MAP3K7, MELK, RCBTB2, ELAC2, TPD52, ZBTB4), and also identify 94 genes not previously linked to prostate cancer progression that would not have been detected using either transcript or copy number data alone. We confirm a number of previously published molecular changes associated with high risk disease, including MYC amplification, and NKX3-1, RB1 and PTEN deletions, as well as over-expression of PCA3 and AMACR, and loss of MSMB in tumour tissue. A subset of the 100 genes outperforms established clinical predictors of poor prognosis (PSA, Gleason score), as well as previously published gene signatures (p = 0.0001). We further show how our molecular profiles can be used for the early detection of aggressive cases in a clinical setting, and inform treatment decisions. Interpretation : For the first time in prostate cancer this study demonstrates the importance of integrated genomic analyses incorporating both benign and tumour tissue data in identifying molecular alterations leading to the generation of robust gene sets that are predictive of clinical outcome in independent patient cohorts.A comprehensive assessment of somatic mutation detection in cancer using whole-genome sequencing
http://hdl.handle.net/10023/11442
As whole-genome sequencing for cancer genome analysis becomes a clinical tool, a full understanding of the variables affecting sequencing analysis output is required. Here using tumour-normal sample pairs from two different types of cancer, chronic lymphocytic leukaemia and medulloblastoma, we conduct a benchmarking exercise within the context of the International Cancer Genome Consortium. We compare sequencing methods, analysis pipelines and validation methods. We show that using PCR-free methods and increasing sequencing depth to similar to 100 x shows benefits, as long as the tumour: control coverage ratio remains balanced. We observe widely varying mutation call rates and low concordance among analysis pipelines, reflecting the artefact-prone nature of the raw data and lack of standards for dealing with the artefacts. However, we show that, using the benchmark mutation set we have created, many issues are in fact easy to remedy and have an immediate positive impact on mutation detection accuracy.
Sequence data for this study have been deposited in the European Genome-phenome Archive (EGA) under the accession number EGAS00001001539.
Wed, 09 Dec 2015 00:00:00 GMThttp://hdl.handle.net/10023/114422015-12-09T00:00:00ZAlioto, Tyler S.Buchhalter, IvoDerdak, SophiaHutter, BarbaraEldridge, Matthew D.Hovig, EivindHeisler, Lawrence E.Beck, Timothy A.Simpson, Jared T.Tonon, LaurieSertier, Anne-SophiePatch, Ann-MarieJaeger, NatalieGinsbach, PhilipDrews, RubenParamasivam, NagarajanKabbe, RolfChotewutmontri, SasithornDiessl, NicollePreviti, ChristopherSchmidt, SabineBrors, BenediktFeuerbach, LarsHeinold, MichaelGroebner, SusanneKorshunov, AndreyTarpey, Patrick S.Butler, Adam P.Hinton, JonathanJones, DavidMenzies, AndrewRaine, KeiranShepherd, RebeccaStebbings, LucyTeague, Jon W.Ribeca, PaoloGiner, Francesc CastroBeltran, SergiRaineri, EmanueleDabad, MarcHeath, Simon C.Gut, MartaDenroche, Robert E.Harding, Nicholas J.Yamaguchi, Takafumi N.Fujimoto, AkihiroNakagawa, HidewakiQuesada, CtorValdes-Mas, RafaelNakken, SigveVodak, DanielBower, LawrenceLynch, Andrew G.Anderson, Charlotte L.Waddell, NicolaPearson, John V.Grimmond, Sean M.Peto, MyronSpellman, PaulHe, MinghuiKandoth, CyriacLee, SeminZhang, JohnLetourneau, LouisMa, SingerSeth, SahilTorrents, DavidXi, LiuWheeler, David A.Lopez-Otin, CarlosCampo, EliasCampbell, Peter J.Boutros, Paul C.Puente, Xose S.Gerhard, Daniela S.Pfister, Stefan M.McPherson, John D.Hudson, Thomas J.Schlesner, MatthiasLichter, PeterEils, RolandJones, David T. W.Gut, Ivo G.As whole-genome sequencing for cancer genome analysis becomes a clinical tool, a full understanding of the variables affecting sequencing analysis output is required. Here using tumour-normal sample pairs from two different types of cancer, chronic lymphocytic leukaemia and medulloblastoma, we conduct a benchmarking exercise within the context of the International Cancer Genome Consortium. We compare sequencing methods, analysis pipelines and validation methods. We show that using PCR-free methods and increasing sequencing depth to similar to 100 x shows benefits, as long as the tumour: control coverage ratio remains balanced. We observe widely varying mutation call rates and low concordance among analysis pipelines, reflecting the artefact-prone nature of the raw data and lack of standards for dealing with the artefacts. However, we show that, using the benchmark mutation set we have created, many issues are in fact easy to remedy and have an immediate positive impact on mutation detection accuracy.Lianas and soil nutrients predict fine-scale distribution of above-ground biomass in a tropical moist forest
http://hdl.handle.net/10023/11437
1. Prediction of carbon dynamics in response to global climate change requires an understanding of the processes that govern the distribution of carbon stocks. Above ground biomass (AGB) in tropical forests is regulated by variation in soil fertility, climate, species composition and topography at regional scales, but the drivers of fine-scale variation in tropical forest AGB are poorly understood. The factors that control the growth and mortality of individual trees may be obscured by the low resolution of studies at regional scales. 2. In this paper, we evaluate the effects of soil nutrients, topography and liana abundance on the fine-scale spatial distribution of AGB and density of trees for a lowland tropical moist forest in Panama using additive regression models. 3. Areas with larger values of AGB were negatively associated with the presence of lianas, which may reflect competition with lianas and/or the association of lianas with disturbed or open canopy patches within forests. AGB was positively associated with soils possessing higher pH and K concentrations, reflecting the importance of below-ground resource availability on AGB independently of stem density. 4. Synthesis: Our results shed new light the factors that influence fine-scale tree AGB and carbon stocks in tropical forests: liana abundance is the strongest predictor, having a negative impact on tree AGB. The availability of soil nutrients was also revealed as an important driver of fine-scale spatial variation in tree AGB.
This study was supported by the FP7-PEOPLE-2013-IEF Marie-Curie Action – SPATFOREST. Tree data from BCI were provided by the Center for Tropical Forest Science of the Smithsonian Tropical Research Institute and the primary granting agencies that have supported the BCI plot tree census. Data for the liana censuses were supported by the US National Science Foundation grants: DEB-0613666, DEB-0845071, and DEB-1019436 (to SAS). Soil data was funded by the National Science Foundation grants DEB021104, DEB021115, DEB0212284 and DEB0212818 supporting soils mapping in the BCI plot.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/114372016-11-01T00:00:00ZLedo, AliciaIllian, Janine B.Schnitzer, Stefan A.Wright, S. JosephDalling, James W.Burslem, David F. R. P.1. Prediction of carbon dynamics in response to global climate change requires an understanding of the processes that govern the distribution of carbon stocks. Above ground biomass (AGB) in tropical forests is regulated by variation in soil fertility, climate, species composition and topography at regional scales, but the drivers of fine-scale variation in tropical forest AGB are poorly understood. The factors that control the growth and mortality of individual trees may be obscured by the low resolution of studies at regional scales. 2. In this paper, we evaluate the effects of soil nutrients, topography and liana abundance on the fine-scale spatial distribution of AGB and density of trees for a lowland tropical moist forest in Panama using additive regression models. 3. Areas with larger values of AGB were negatively associated with the presence of lianas, which may reflect competition with lianas and/or the association of lianas with disturbed or open canopy patches within forests. AGB was positively associated with soils possessing higher pH and K concentrations, reflecting the importance of below-ground resource availability on AGB independently of stem density. 4. Synthesis: Our results shed new light the factors that influence fine-scale tree AGB and carbon stocks in tropical forests: liana abundance is the strongest predictor, having a negative impact on tree AGB. The availability of soil nutrients was also revealed as an important driver of fine-scale spatial variation in tree AGB.The importance of DNA methylation in prostate cancer development
http://hdl.handle.net/10023/11435
After briefly reviewing the nature of DNA methylation, its general role in cancer and the tools available to interrogate it, we consider the literature surrounding DNA methylation as relating to prostate cancer. Specific consideration is given to recurrent alterations. A list of frequently reported genes is synthesized from 17 studies that have reported on methylation changes in malignant prostate tissue, and we chart the timing of those changes in the diseases history through amalgamation of several previously published data sets. We also review associations with genetic alterations and hormone signalling, before the practicalities of investigating prostate cancer methylation using cell lines are assessed. We conclude by outlining the interplay between DNA methylation and prostate cancer metabolism and their regulation by androgen receptor, with a specific discussion of the mitochondria and their associations with DNA methylation.
Wed, 01 Feb 2017 00:00:00 GMThttp://hdl.handle.net/10023/114352017-02-01T00:00:00ZMassie, Charles E.Mills, Ian G.Lynch, Andy G.After briefly reviewing the nature of DNA methylation, its general role in cancer and the tools available to interrogate it, we consider the literature surrounding DNA methylation as relating to prostate cancer. Specific consideration is given to recurrent alterations. A list of frequently reported genes is synthesized from 17 studies that have reported on methylation changes in malignant prostate tissue, and we chart the timing of those changes in the diseases history through amalgamation of several previously published data sets. We also review associations with genetic alterations and hormone signalling, before the practicalities of investigating prostate cancer methylation using cell lines are assessed. We conclude by outlining the interplay between DNA methylation and prostate cancer metabolism and their regulation by androgen receptor, with a specific discussion of the mitochondria and their associations with DNA methylation.The early effects of rapid androgen deprivation on human prostate cancer
http://hdl.handle.net/10023/11434
The androgen receptor (AR) is the dominant growth factor in prostate cancer (PCa). Therefore, understanding how ARs regulate the human transcriptome is of paramount importance. The early effects of castration on human PCa have not previously been studied 27 patients medically castrated with degarelix 7 d before radical prostatectomy. We used mass spectrometry, immunohistochemistry, and gene expression array (validated by reverse transcription-polymerase chain reaction) to compare resected tumour with matched, controlled, untreated PCa tissue. All patients had levels of serum androgen, with reduced levels of intraprostatic androgen at prostatectomy. We observed differential expression of known androgen-regulated genes (TMPRSS2, KLK3, CAMKK2, FKBP5). We identified 749 genes downregulated and 908 genes upregulated following castration. AR regulation of α-methylacyl-CoA racemase expression and three other genes (FAM129A, RAB27A, and KIAA0101) was confirmed. Upregulation of oestrogen receptor 1 (ESR1) expression was observed in malignant epithelia and was associated with differential expression of ESR1-regulated genes and correlated with proliferation (Ki-67 expression). Patient summary : This first-in-man study defines the rapid gene expression changes taking place in prostate cancer (PCa) following castration. Expression levels of the genes that the androgen receptor regulates are predictive of treatment outcome. Upregulation of oestrogen receptor 1 is a mechanism by which PCa cells may survive despite castration.
The authors thank CRUK; the NIHR; the Academy of Medical Sciences (RG:63397); the National Cancer Research Prostate Cancer: Mechanisms of Progression and Treatment (ProMPT) collaborative (G0500966/75466); Hutchison Whampoa Limited; the Human Research Tissue Bank (Addenbrooke’s Hospital, supported by the NIHR Cambridge BRC); and Cancer Research UK.
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/114342016-08-01T00:00:00ZShaw, Greg L.Whitaker, HayleyCorcoran, MarieDunning, Mark J.Luxton, HayleyKay, JonathanMassie, Charlie E.Miller, Jodi L.Lamb, Alastair D.Ross-Adams, HelenRussell, RoslinNelson, Adam W.Eldridge, Matthew D.Lynch, Andrew G.Ramos-Montoya, AntonioMills, Ian G.Taylor, Angela E.Arlt, WiebkeShah, NimishWarren, Anne Y.Neal, David E.The androgen receptor (AR) is the dominant growth factor in prostate cancer (PCa). Therefore, understanding how ARs regulate the human transcriptome is of paramount importance. The early effects of castration on human PCa have not previously been studied 27 patients medically castrated with degarelix 7 d before radical prostatectomy. We used mass spectrometry, immunohistochemistry, and gene expression array (validated by reverse transcription-polymerase chain reaction) to compare resected tumour with matched, controlled, untreated PCa tissue. All patients had levels of serum androgen, with reduced levels of intraprostatic androgen at prostatectomy. We observed differential expression of known androgen-regulated genes (TMPRSS2, KLK3, CAMKK2, FKBP5). We identified 749 genes downregulated and 908 genes upregulated following castration. AR regulation of α-methylacyl-CoA racemase expression and three other genes (FAM129A, RAB27A, and KIAA0101) was confirmed. Upregulation of oestrogen receptor 1 (ESR1) expression was observed in malignant epithelia and was associated with differential expression of ESR1-regulated genes and correlated with proliferation (Ki-67 expression). Patient summary : This first-in-man study defines the rapid gene expression changes taking place in prostate cancer (PCa) following castration. Expression levels of the genes that the androgen receptor regulates are predictive of treatment outcome. Upregulation of oestrogen receptor 1 is a mechanism by which PCa cells may survive despite castration.A comparative analysis of whole genome sequencing of esophageal adenocarcinoma pre- and post-chemotherapy
http://hdl.handle.net/10023/11433
The scientific community has avoided using tissue samples from patients that have been exposed to systemic chemotherapy to infer the genomic landscape of a given cancer. Esophageal adenocarcinoma is a heterogeneous, chemoresistant tumor for which the availability and size of pretreatment endoscopic samples are limiting. This study compares whole-genome sequencing data obtained from chemo-naive and chemo-treated samples. The quality of whole-genomic sequencing data is comparable across all samples regardless of chemotherapy status. Inclusion of samples collected post-chemotherapy increased the proportion of late-stage tumors. When comparing matched pre- and post-chemotherapy samples from 10 cases, the mutational signatures, copy number, and SNV mutational profiles reflect the expected heterogeneity in this disease. Analysis of SNVs in relation to allele-specific copy-number changes pinpoints the common ancestor to a point prior to chemotherapy. For cases in which pre- and post-chemotherapy samples do show substantial differences, the timing of the divergence is near-synchronous with endoreduplication. Comparison across a large prospective cohort (62 treatment-naive, 58 chemotherapy-treated samples) reveals no significant differences in the overall mutation rate, mutation signatures, specific recurrent point mutations, or copy-number events in respect to chemotherapy status. In conclusion, whole-genome sequencing of samples obtained following neoadjuvant chemotherapy is representative of the genomic landscape of esophageal adenocarcinoma. Excluding these samples reduces the material available for cataloging and introduces a bias toward the earlier stages of cancer.
The whole-genome sequencing data from this study have been submitted to the European Genome-phenome Archive (EGA; https://www.ebi.ac.uk/ega/home) under accession number EGAD00001002241. Mutation calls can be found within the ICGC data portal (https://dcc.icgc.org/) under project ID ESADUK and library IDs listed in Supplemental Table S2.
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/114332017-06-01T00:00:00ZNoorani, AyeshaBornschein, JanLynch, Andy GSecrier, MariaAchilleos, AchilleasEldridge, MatthewBower, LawrenceWeaver, Jamie M.J.Crawte, JasonOng, Chin-AnnShannon, NicholasMacRae, ShonaGrehan, NicolaNutzinger, BarbaraO'Donovan, MariaHardwick, RichardTavaré, SimonFitzgerald, Rebecca C.on behalf of the Oesophageal Cancer Clinical and Molecular Stratification (OCCAMS) ConsortiumThe scientific community has avoided using tissue samples from patients that have been exposed to systemic chemotherapy to infer the genomic landscape of a given cancer. Esophageal adenocarcinoma is a heterogeneous, chemoresistant tumor for which the availability and size of pretreatment endoscopic samples are limiting. This study compares whole-genome sequencing data obtained from chemo-naive and chemo-treated samples. The quality of whole-genomic sequencing data is comparable across all samples regardless of chemotherapy status. Inclusion of samples collected post-chemotherapy increased the proportion of late-stage tumors. When comparing matched pre- and post-chemotherapy samples from 10 cases, the mutational signatures, copy number, and SNV mutational profiles reflect the expected heterogeneity in this disease. Analysis of SNVs in relation to allele-specific copy-number changes pinpoints the common ancestor to a point prior to chemotherapy. For cases in which pre- and post-chemotherapy samples do show substantial differences, the timing of the divergence is near-synchronous with endoreduplication. Comparison across a large prospective cohort (62 treatment-naive, 58 chemotherapy-treated samples) reveals no significant differences in the overall mutation rate, mutation signatures, specific recurrent point mutations, or copy-number events in respect to chemotherapy status. In conclusion, whole-genome sequencing of samples obtained following neoadjuvant chemotherapy is representative of the genomic landscape of esophageal adenocarcinoma. Excluding these samples reduces the material available for cataloging and introduces a bias toward the earlier stages of cancer.New model for estimating glomerular filtration rate in patients with cancer
http://hdl.handle.net/10023/11432
Purpose: The glomerular filtration rate (GFR) is essential for carboplatin chemotherapy dosing; however, the best method to estimate GFR in patients with cancer is unknown. We identify the most accurate and least biased method. Methods: We obtained data on age, sex, height, weight, serum creatinine concentrations, and results for GFR from chromium-51 (51Cr) EDTA excretion measurements (51Cr-EDTA GFR) from white patients ≥ 18 years of age with histologically confirmed cancer diagnoses at the Cambridge University Hospital NHS Trust, United Kingdom. We developed a new multivariable linear model for GFR using statistical regression analysis. 51Cr-EDTA GFR was compared with the estimated GFR (eGFR) from seven published models and our new model, using the statistics root-mean-squared-error (RMSE) and median residual and on an internal and external validation data set. We performed a comparison of carboplatin dosing accuracy on the basis of an absolute percentage error > 20%. Results: Between August 2006 and January 2013, data from 2,471 patients were obtained. The new model improved the eGFR accuracy (RMSE, 15.00 mL/min; 95% CI, 14.12 to 16.00 mL/min) compared with all published models. Body surface area (BSA)?adjusted chronic kidney disease epidemiology (CKD-EPI) was the most accurate published model for eGFR (RMSE, 16.30 mL/min; 95% CI, 15.34 to 17.38 mL/min) for the internal validation set. Importantly, the new model reduced the fraction of patients with a carboplatin dose absolute percentage error > 20% to 14.17% in contrast to 18.62% for the BSA-adjusted CKD-EPI and 25.51% for the Cockcroft-Gault formula. The results were externally validated. Conclusion: In a large data set from patients with cancer, BSA-adjusted CKD-EPI is the most accurate published model to predict GFR. The new model improves this estimation and may present a new standard of care.
T.J. was supported by the Wellcome Trust Translational Medicine and Therapeutics Programme and the University of Cambridge, Department of Oncology (RJAG/076). H.E. was supported by the National Institute of Health Research Cambridge Biomedical Research Centre and the University of Cambridge.
Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/114322017-08-01T00:00:00ZJanowitz, TobiasWilliams, Edward H.Marshall, AndreaAinsworth, NicolaThomas, Peter B.Sammut, Stephen J.Shepherd, ScottWhite, JeffMark, Patrick B.Lynch, Andy G.Jodrell, Duncan I.Tavaré, SimonEarl, HelenaPurpose: The glomerular filtration rate (GFR) is essential for carboplatin chemotherapy dosing; however, the best method to estimate GFR in patients with cancer is unknown. We identify the most accurate and least biased method. Methods: We obtained data on age, sex, height, weight, serum creatinine concentrations, and results for GFR from chromium-51 (51Cr) EDTA excretion measurements (51Cr-EDTA GFR) from white patients ≥ 18 years of age with histologically confirmed cancer diagnoses at the Cambridge University Hospital NHS Trust, United Kingdom. We developed a new multivariable linear model for GFR using statistical regression analysis. 51Cr-EDTA GFR was compared with the estimated GFR (eGFR) from seven published models and our new model, using the statistics root-mean-squared-error (RMSE) and median residual and on an internal and external validation data set. We performed a comparison of carboplatin dosing accuracy on the basis of an absolute percentage error > 20%. Results: Between August 2006 and January 2013, data from 2,471 patients were obtained. The new model improved the eGFR accuracy (RMSE, 15.00 mL/min; 95% CI, 14.12 to 16.00 mL/min) compared with all published models. Body surface area (BSA)?adjusted chronic kidney disease epidemiology (CKD-EPI) was the most accurate published model for eGFR (RMSE, 16.30 mL/min; 95% CI, 15.34 to 17.38 mL/min) for the internal validation set. Importantly, the new model reduced the fraction of patients with a carboplatin dose absolute percentage error > 20% to 14.17% in contrast to 18.62% for the BSA-adjusted CKD-EPI and 25.51% for the Cockcroft-Gault formula. The results were externally validated. Conclusion: In a large data set from patients with cancer, BSA-adjusted CKD-EPI is the most accurate published model to predict GFR. The new model improves this estimation and may present a new standard of care.Animal Counting Toolkit : a practical guide to small-boat surveys for estimating abundance of coastal marine mammals
http://hdl.handle.net/10023/11430
Small cetaceans (dolphins and porpoises) face serious anthropogenic threats in coastal habitats. These include bycatch in fisheries; exposure to noise, plastic and chemical pollution; disturbance from boaters; and climate change. Generating reliable abundance estimates is essential to assess sustainability of bycatch in fishing gear or any other form of anthropogenic removals and to design conservation and recovery plans for endangered species. Cetacean abundance estimates are lacking from many coastal waters of many developing countries. Lack of funding and training opportunities makes it difficult to fill in data gaps. Even if international funding were found for surveys in developing countries, building local capacity would be necessary to sustain efforts over time to detect trends and monitor biodiversity loss. Large-scale, shipboard surveys can cost tens of thousands of US dollars each day. We focus on methods to generate preliminary abundance estimates from low-cost, small-boat surveys that embrace a ‘training-while-doing’ approach to fill in data gaps while simultaneously building regional capacity for data collection. Our toolkit offers practical guidance on simple design and field data collection protocols that work with small boats and small budgets, but expect analysis to involve collaboration with a quantitative ecologist or statistician. Our audience includes independent scientists, government conservation agencies, NGOs and indigenous coastal communities, with a primary focus on fisheries bycatch. We apply our Animal Counting Toolkit to a small-boat survey in Canada’s Pacific coastal waters to illustrate the key steps in collecting line transect survey data used to estimate and monitor marine mammal abundance.
The authors thank Synchronicity Earth, Marisla Foundation, and the US Marine Mammal Commission for seed funding for this program.
Thu, 10 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/114302017-08-10T00:00:00ZWilliams, RobAshe, Erin ElizabethGaut, KatieGryba, RowennaMoore, Jeffrey E.Rexstad, EricSandilands, DougSteventon, JustinReeves, RandallSmall cetaceans (dolphins and porpoises) face serious anthropogenic threats in coastal habitats. These include bycatch in fisheries; exposure to noise, plastic and chemical pollution; disturbance from boaters; and climate change. Generating reliable abundance estimates is essential to assess sustainability of bycatch in fishing gear or any other form of anthropogenic removals and to design conservation and recovery plans for endangered species. Cetacean abundance estimates are lacking from many coastal waters of many developing countries. Lack of funding and training opportunities makes it difficult to fill in data gaps. Even if international funding were found for surveys in developing countries, building local capacity would be necessary to sustain efforts over time to detect trends and monitor biodiversity loss. Large-scale, shipboard surveys can cost tens of thousands of US dollars each day. We focus on methods to generate preliminary abundance estimates from low-cost, small-boat surveys that embrace a ‘training-while-doing’ approach to fill in data gaps while simultaneously building regional capacity for data collection. Our toolkit offers practical guidance on simple design and field data collection protocols that work with small boats and small budgets, but expect analysis to involve collaboration with a quantitative ecologist or statistician. Our audience includes independent scientists, government conservation agencies, NGOs and indigenous coastal communities, with a primary focus on fisheries bycatch. We apply our Animal Counting Toolkit to a small-boat survey in Canada’s Pacific coastal waters to illustrate the key steps in collecting line transect survey data used to estimate and monitor marine mammal abundance.A new approach for modelling chromospheric evaporation in response to enhanced coronal heating : II. Non-uniform heating
http://hdl.handle.net/10023/11427
We proposed that the use of an approximate “jump condition” at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region.
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).
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/114272017-09-01T00:00:00ZJohnston, C. D.Hood, A. W.Cargill, P. J.De Moortel, I.We proposed that the use of an approximate “jump condition” at the solar transition region permits fast and accurate numerical solutions of the one dimensional hydrodynamic equations when the corona undergoes impulsive heating. In particular, it eliminates the need for the very short timesteps imposed by a highly resolved numerical grid. This paper presents further examples of the applicability of the method for cases of non-uniform heating, in particular, nanoflare trains (uniform in space but non-uniform in time) and spatially localised impulsive heating, including at the loop apex and base of the transition region. In all cases the overall behaviour of the coronal density and temperature shows good agreement with a fully resolved one dimensional model and is significantly better than the equivalent results from a 1D code run without using the jump condition but with the same coarse grid. A detailed assessment of the errors introduced by the jump condition is presented showing that the causes of discrepancy with the fully resolved code are (i) the neglect of the terms corresponding to the rate of change of total energy in the unresolved atmosphere; (ii) mass motions at the base of the transition region and (iii) for some cases with footpoint heating, an over-estimation of the radiative losses in the transition region.N-body dynamics on closed surfaces : the axioms of mechanics
http://hdl.handle.net/10023/11426
A major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).
D.G.D. gratefully acknowledges support for this research from CNPq (Conselho Nacional de Desenvolvimento Cientifico e Tecnologico ) and FINEP (Inovação e Pesquisa) in Brazil, and from the UK Engineering and Physical Sciences Research Council (grant no. EP/H001794/1)
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/114262016-08-01T00:00:00ZBoatto, StefanellaDritschel, David GerardSchaefer, Rodrigo GA major challenge for our understanding of the mathematical basis of particle dynamics is the formulation of N-body and N-vortex dynamics on Riemann surfaces. In this paper, we show how the two problems are, in fact, closely related when considering the role played by the intrinsic geometry of the surface. This enables a straightforward deduction of the dynamics of point masses, using recently derived results for point vortices on general closed differentiable surfaces M endowed with a metric g. We find, generally, that Kepler's Laws do not hold. What is more, even Newton's First Law (the law of inertia) fails on closed surfaces with variable curvature (e.g. the ellipsoid).Interaction of a mode-2 internal solitary wave with narrow isolated topography
http://hdl.handle.net/10023/11406
Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a/ℓ. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ℓ.
This research was supported by the Natural Sciences and Engineering Research Council of Canada through a Discovery Grant (MS), and the Government of Ontario through a Queen Elizabeth II Graduate Scholarship in Science and Technology (DD). The experimental work was conducted at The University of Dundee by DD and MC with the aid of grants provided by The University of Dundee, the University of St Andrews, and the University of Waterloo.
Mon, 31 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/114062017-07-31T00:00:00ZDeepwell, DavidStastna, MarekCarr, MagdaDavies, Peter A.Numerical and experimental studies of the transit of a mode-2 internal solitary wave over an isolated ridge are presented. All studies used a quasi-two-layer fluid with a pycnocline centred at the mid-depth. The wave amplitude and total fluid depth were both varied, while the topography remained fixed. The strength of the interaction between the internal solitary waves and the hill was found to be characterized by three regimes: weak, moderate, and strong interactions. The weak interaction exhibited negligible wave modulation and bottom surface stress. The moderate interaction generated weak and persistent vorticity in the lower layer, in addition to negligible wave modulation. The strong interaction clearly showed material from the trapped core of the mode-2 wave extracted in the form of a thin filament while generating a strong vortex at the hill. A criterion for the strength of the interaction was found by non-dimensionalizing the wave amplitude by the lower layer depth, a/ℓ. A passive tracer was used to measure the conditions for resuspension of boundary material due to the interaction. The speed and prevalence of cross boundary layer transport increased with a/ℓ.Interaction between a surface quasi-geostrophic buoyancy anomaly jet and internal vortices
http://hdl.handle.net/10023/11404
This paper addresses the dynamical coupling of the ocean's surface and the ocean's interior. In particular, we investigate the dynamics of an oceanic surface jet, and its interaction with vortices at depth. The jet is induced by buoyancy (density) anomalies at the surface. We first focus on the jet alone. The linear stability indicates there are two modes of instability: the sinuous and the varicose modes. When a vortex in present below the jet, it interacts with it. The velocity field induced by the vortex perturbs the jet and triggers its destabilisation. The jet also influences the vortex by pushing it under a region of co-operative shear. Strong jets may also partially shear out the vortex. We also investigate the interaction between a surface jet and a vortex dipole in the interior. Again, strong jets may partially shear out the vortex structure. The jet also modifies the trajectory of the dipole. Dipoles travelling towards the jet at shallow incidence angles may be reflected by the jet. Vortices travelling at moderate incidence angles normally cross below the jet. This is related to the displacement of the two vortices of the dipole by the shear induced by the jet. Intense jets may also destabilise early and form streets of billows. These billows can pair with the vortices and separate the dipole.
Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/114042017-08-01T00:00:00ZReinaud, Jean NoelDritschel, David GerardCarton, XavierThis paper addresses the dynamical coupling of the ocean's surface and the ocean's interior. In particular, we investigate the dynamics of an oceanic surface jet, and its interaction with vortices at depth. The jet is induced by buoyancy (density) anomalies at the surface. We first focus on the jet alone. The linear stability indicates there are two modes of instability: the sinuous and the varicose modes. When a vortex in present below the jet, it interacts with it. The velocity field induced by the vortex perturbs the jet and triggers its destabilisation. The jet also influences the vortex by pushing it under a region of co-operative shear. Strong jets may also partially shear out the vortex. We also investigate the interaction between a surface jet and a vortex dipole in the interior. Again, strong jets may partially shear out the vortex structure. The jet also modifies the trajectory of the dipole. Dipoles travelling towards the jet at shallow incidence angles may be reflected by the jet. Vortices travelling at moderate incidence angles normally cross below the jet. This is related to the displacement of the two vortices of the dipole by the shear induced by the jet. Intense jets may also destabilise early and form streets of billows. These billows can pair with the vortices and separate the dipole.Orbits of primitive k-homogenous groups on (n-k)-partitions with applications to semigroups
http://hdl.handle.net/10023/11403
The purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation groups (those which act transitively on the subsets of size k of their domain X) where |X|=n and k<n/2. In the process we obtain, for k-homogeneous groups, results on the minimum numbers of generators, the numbers of orbits on k-partitions, and their normalizers in the symmetric group. As a sample result, we show that every finite 2-homogeneous group is 2-generated. Underlying our investigations on automorphisms of transformation semigroups is the following conjecture: If a transformation semigroup S contains singular maps, and its group of units is a primitive group G of permutations, then its automorphisms are all induced (under conjugation) by the elements in the normalizer of G in the symmetric group. For the special case that S contains all constant maps, this conjecture was proved correct, more than 40 years ago. In this paper, we prove that the conjecture also holds for the case of semigroups containing a map of rank 3 or less. The effort in establishing this result suggests that further improvements might be a great challenge. This problem and several additional} ones on permutation groups, transformation semigroups and computational algebra, are proposed in the end of the paper.
This work was developed within FCT project CEMAT-CIÊNCIAS (UID/Multi/04621/2013).
Tue, 09 May 2017 00:00:00 GMThttp://hdl.handle.net/10023/114032017-05-09T00:00:00ZAraújo, JoãoBentz, WolframCameron, Peter JephsonThe purpose of this paper is to advance our knowledge of two of the most classic and popular topics in transformation semigroups: automorphisms and the size of minimal generating sets. In order to do this, we examine the k-homogeneous permutation groups (those which act transitively on the subsets of size k of their domain X) where |X|=n and k<n/2. In the process we obtain, for k-homogeneous groups, results on the minimum numbers of generators, the numbers of orbits on k-partitions, and their normalizers in the symmetric group. As a sample result, we show that every finite 2-homogeneous group is 2-generated. Underlying our investigations on automorphisms of transformation semigroups is the following conjecture: If a transformation semigroup S contains singular maps, and its group of units is a primitive group G of permutations, then its automorphisms are all induced (under conjugation) by the elements in the normalizer of G in the symmetric group. For the special case that S contains all constant maps, this conjecture was proved correct, more than 40 years ago. In this paper, we prove that the conjecture also holds for the case of semigroups containing a map of rank 3 or less. The effort in establishing this result suggests that further improvements might be a great challenge. This problem and several additional} ones on permutation groups, transformation semigroups and computational algebra, are proposed in the end of the paper.Recurrence statistics for the space of interval exchange maps and the Teichmüller flow on the space of translation surfaces
http://hdl.handle.net/10023/11400
In this paper we show that the transfer operator of a Rauzy–Veech–Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and its associated Teichmüller flow. We establish Borel–Cantelli lemmas, Extreme Value statistics and return time statistics for the map and flow. Previous results have established quasicompactness in Hölder or analytic function spaces, for example the work of M. Pollicott and T. Morita. The quasi-Hölder function space is particularly useful for investigating return time statistics. In particular we establish the shrinking target property for nested balls in the setting of Teichmüller flow. Our point of view, approach and terminology derive from the work of M. Pollicott augmented by that of M. Viana.
MT was partially supported by NSF grant DMS 110958.
Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/114002017-08-01T00:00:00ZAimino, RomainNicol, MatthewTodd, Michael JohnIn this paper we show that the transfer operator of a Rauzy–Veech–Zorich renormalization map acting on a space of quasi-Hölder functions is quasicompact and derive certain statistical recurrence properties for this map and its associated Teichmüller flow. We establish Borel–Cantelli lemmas, Extreme Value statistics and return time statistics for the map and flow. Previous results have established quasicompactness in Hölder or analytic function spaces, for example the work of M. Pollicott and T. Morita. The quasi-Hölder function space is particularly useful for investigating return time statistics. In particular we establish the shrinking target property for nested balls in the setting of Teichmüller flow. Our point of view, approach and terminology derive from the work of M. Pollicott augmented by that of M. Viana.Fractal, group theoretic, and relational structures on Cantor space
http://hdl.handle.net/10023/11370
Cantor space, the set of infinite words over a finite alphabet, is a type of metric space
with a `self-similar' structure. This thesis explores three areas concerning Cantor space
with regard to fractal geometry, group theory, and topology.
We find first results on the dimension of intersections of fractal sets within the Cantor
space. More specifically, we examine the intersection of a subset E of the n-ary Cantor
space, C[sub]n with the image of another subset Funder a random isometry. We obtain
almost sure upper bounds for the Hausdorff and upper box-counting dimensions of the
intersection, and a lower bound for the essential supremum of the Hausdorff dimension.
We then consider a class of groups, denoted by V[sub]n(G), of homeomorphisms of the
Cantor space built from transducers. These groups can be seen as homeomorphisms
that respect the self-similar and symmetric structure of C[sub]n, and are supergroups of the
Higman-Thompson groups V[sub]n. We explore their isomorphism classes with our primary
result being that V[sub]n(G) is isomorphic to (and conjugate to) V[sub]n if and only if G is a
semiregular subgroup of the symmetric group on n points.
Lastly, we explore invariant relations on Cantor space, which have quotients homeomorphic to fractals in many different classes. We generalize a method of describing these
quotients by invariant relations as an inverse limit, before characterizing a specific class
of fractals known as Sierpiński relatives as invariant factors. We then compare relations
arising through edge replacement systems to invariant relations, detailing the conditions
under which they are the same.
Fri, 01 Jan 2016 00:00:00 GMThttp://hdl.handle.net/10023/113702016-01-01T00:00:00ZDonoven, Casey RyallCantor space, the set of infinite words over a finite alphabet, is a type of metric space
with a `self-similar' structure. This thesis explores three areas concerning Cantor space
with regard to fractal geometry, group theory, and topology.
We find first results on the dimension of intersections of fractal sets within the Cantor
space. More specifically, we examine the intersection of a subset E of the n-ary Cantor
space, C[sub]n with the image of another subset Funder a random isometry. We obtain
almost sure upper bounds for the Hausdorff and upper box-counting dimensions of the
intersection, and a lower bound for the essential supremum of the Hausdorff dimension.
We then consider a class of groups, denoted by V[sub]n(G), of homeomorphisms of the
Cantor space built from transducers. These groups can be seen as homeomorphisms
that respect the self-similar and symmetric structure of C[sub]n, and are supergroups of the
Higman-Thompson groups V[sub]n. We explore their isomorphism classes with our primary
result being that V[sub]n(G) is isomorphic to (and conjugate to) V[sub]n if and only if G is a
semiregular subgroup of the symmetric group on n points.
Lastly, we explore invariant relations on Cantor space, which have quotients homeomorphic to fractals in many different classes. We generalize a method of describing these
quotients by invariant relations as an inverse limit, before characterizing a specific class
of fractals known as Sierpiński relatives as invariant factors. We then compare relations
arising through edge replacement systems to invariant relations, detailing the conditions
under which they are the same.Constructing 2-generated subgroups of the group of homeomorphisms of Cantor space
http://hdl.handle.net/10023/11362
We study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the
group of homeomorphisms of Cantor space.
In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generated, simple, vigorous subgroups of H[sub]c is closed under several natural constructions.
In Chapter 4 we use a generalised notion of word and the tight completion construction from [13] to construct a family of subgroups of H[sub]c which generalise Thompson's group V . We give necessary conditions for these groups to be finitely generated and simple. Of these we show which are vigorous. Finally we give some examples.
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/113622017-01-01T00:00:00ZHyde, James ThomasWe study finite generation, 2-generation and simplicity of subgroups of H[sub]c, the
group of homeomorphisms of Cantor space.
In Chapter 1 and Chapter 2 we run through foundational concepts and notation. In Chapter 3 we study vigorous subgroups of H[sub]c. A subgroup G of H[sub]c is vigorous if for any non-empty clopen set A with proper non-empty clopen subsets B and C there exists g ∈ G with supp(g) ⊑ A and Bg ⊆ C. It is a corollary of the main theorem of Chapter 3 that all finitely generated simple vigorous subgroups of H[sub]c are in fact 2-generated. We show the family of finitely generated, simple, vigorous subgroups of H[sub]c is closed under several natural constructions.
In Chapter 4 we use a generalised notion of word and the tight completion construction from [13] to construct a family of subgroups of H[sub]c which generalise Thompson's group V . We give necessary conditions for these groups to be finitely generated and simple. Of these we show which are vigorous. Finally we give some examples.Observations and numerical models of coronal heating associated with spicules
http://hdl.handle.net/10023/11358
Spicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of short-lived transient brightenings in the corona that are associated with spicules,these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules.We use high-resolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and of the corona with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures associated with spicular mass ejections and heating of plasma to transition region and coronal temperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our observations are supported by 2.5D radiative MHD simulations that show heating to coronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment.
Sun, 20 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/113582017-08-20T00:00:00ZDe Pontieu, BartDe Moortel, InekeMartinez-Sykora, JuanMcIntosh, ScottSpicules have been proposed as significant contributors to the mass and energy balance of the corona. While previous observations have provided a glimpse of short-lived transient brightenings in the corona that are associated with spicules,these observations have been contested and are the subject of a vigorous debate both on the modeling and the observational side. Therefore, it remains unclear whether plasma is heated to coronal temperatures in association with spicules.We use high-resolution observations of the chromosphere and transition region with the Interface Region Imaging Spectrograph (IRIS) and of the corona with the Atmospheric Imaging Assembly (AIA) on board the Solar Dynamics Observatory (SDO) to show evidence of the formation of coronal structures associated with spicular mass ejections and heating of plasma to transition region and coronal temperatures. Our observations suggest that a significant fraction of the highly dynamic loop fan environment associated with plage regions may be the result of the formation of such new coronal strands, a process that previously had been interpreted as the propagation of transient propagating coronal disturbances (PCD)s. Our observations are supported by 2.5D radiative MHD simulations that show heating to coronal temperatures in association with spicules. Our results suggest that heating and strong flows play an important role in maintaining the substructure of loop fans, in addition to the waves that permeate this low coronal environment.Evolutionary dynamics of phenotype-structured populations : from individual-level mechanisms to population-level consequences
http://hdl.handle.net/10023/11328
Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.
This research was supported in part by the Australian Research Council (DP140100339) and by the French National Research Agency through the ANR blanche project Kibord [ANR-13-BS01-0004] and the “ANR JC” project Modevol [ANR-13-JS01-0009]. TL was also supported in part by the Hadamard Mathematics Labex, backed by the Fondation Mathématique Jacques Hadamard, through a grant overseen by the French National Research Agency [ANR-11-LABX-0056-LMH]. LD was also supported in part by Université Sorbonne Paris Cité “Investissements d’Avenir”[ANR-11-IDEX-0005].
Mon, 01 Aug 2016 00:00:00 GMThttp://hdl.handle.net/10023/113282016-08-01T00:00:00ZChisholm, Rebecca H.Lorenzi, TommasoDesvillettes, LaurentHughes, Barry D.Epigenetic mechanisms are increasingly recognised as integral to the adaptation of species that face environmental changes. In particular, empirical work has provided important insights into the contribution of epigenetic mechanisms to the persistence of clonal species, from which a number of verbal explanations have emerged that are suited to logical testing by proof-of-concept mathematical models. Here, we present a stochastic agent-based model and a related deterministic integrodifferential equation model for the evolution of a phenotype-structured population composed of asexually-reproducing and competing organisms which are exposed to novel environmental conditions. This setting has relevance to the study of biological systems where colonising asexual populations must survive and rapidly adapt to hostile environments, like pathogenesis, invasion and tumour metastasis. We explore how evolution might proceed when epigenetic variation in gene expression can change the reproductive capacity of individuals within the population in the new environment. Simulations and analyses of our models clarify the conditions under which certain evolutionary paths are possible, and illustrate that whilst epigenetic mechanisms may facilitate adaptation in asexual species faced with environmental change, they can also lead to a type of “epigenetic load” and contribute to extinction. Moreover, our results offer a formal basis for the claim that constant environments favour individuals with low rates of stochastic phenotypic variation. Finally, our model provides a “proof of concept” of the verbal hypothesis that phenotypic stability is a key driver in rescuing the adaptive potential of an asexual lineage, and supports the notion that intense selection pressure can, to an extent, offset the deleterious effects of high phenotypic instability and biased epimutations, and steer an asexual population back from the brink of an evolutionary dead end.A new insight for monitoring ungulates : density surface modelling of roe deer in a Mediterranean habitat
http://hdl.handle.net/10023/11325
Ungulates are especially difficult to monitor, and population estimates are challenging to obtain; nevertheless, such information is fundamental for effective management. This is particularly important for expanding species such as roe deer (Capreolus capreolus), whose populations dramatically increased in number and geographic distribution over the last decades. In an attempt to follow population trends and assess species ecology, important methodological advances were recently achieved by combining line or point sampling with geographic information systems (GIS). In this study, we combined density surface modelling (DSM) with line transect survey to predict roe deer density in northeastern Portugal. This was based on modelling pellet group counts as a function of environmental factors while taking into account the probability of detecting pellets and conversion factors to relate pellet density to animal density. We estimated a global density of 3.01 animals/100 ha (95 % CI 0.37–3.51) with a 32.82 % CV. Roe deer densities increased with increasing distance to roads as well as with higher percentage of cover areas and decreased with increasing distance to human populations. This recently developed spatial method can be advantageous to predict density over space through the identification of key factors influencing species abundance. Furthermore, surface maps for subset areas will enable to visually depict abundance distribution of wild populations. This will enable the assessment of areas where ungulate impacts should be minimized, allowing an adaptive management through time.
We would like to thank the University of Aveiro (Department of Biology) and FCT/MEC for the financial support to CESAM RU (UID/AMB/50017) through national funds and, where applicable, co-financed by the FEDER, within the PT2020 Partnership Agreement. TAM is partially funded by FCT, Fundação para a Ciência e a Tecnologia, Portugal, through the project UID/MAT/00006/2013.
Sat, 01 Oct 2016 00:00:00 GMThttp://hdl.handle.net/10023/113252016-10-01T00:00:00ZValente, Ana M.Marques, Tiago A.Fonseca, CarlosTorres, Rita TinocoUngulates are especially difficult to monitor, and population estimates are challenging to obtain; nevertheless, such information is fundamental for effective management. This is particularly important for expanding species such as roe deer (Capreolus capreolus), whose populations dramatically increased in number and geographic distribution over the last decades. In an attempt to follow population trends and assess species ecology, important methodological advances were recently achieved by combining line or point sampling with geographic information systems (GIS). In this study, we combined density surface modelling (DSM) with line transect survey to predict roe deer density in northeastern Portugal. This was based on modelling pellet group counts as a function of environmental factors while taking into account the probability of detecting pellets and conversion factors to relate pellet density to animal density. We estimated a global density of 3.01 animals/100 ha (95 % CI 0.37–3.51) with a 32.82 % CV. Roe deer densities increased with increasing distance to roads as well as with higher percentage of cover areas and decreased with increasing distance to human populations. This recently developed spatial method can be advantageous to predict density over space through the identification of key factors influencing species abundance. Furthermore, surface maps for subset areas will enable to visually depict abundance distribution of wild populations. This will enable the assessment of areas where ungulate impacts should be minimized, allowing an adaptive management through time.Extremal problems in combinatorial semigroup theory
http://hdl.handle.net/10023/11322
In this thesis we shall consider three types of extremal problems (i.e. problems involving maxima and minima) concerning semigroups. In the first chapter we show how to construct a minimal semigroup presentation that defines a group of non-negative deficiency given a minimal group presentation for that group. This demonstrates that the semigroup deficiency of a group of non-negative deficiency is equal to the group deficiency of that group. Given a finite monoid we find a necessary and sufficient condition for the monoid deficiency to equal the semigroup deficiency. We give a class of infinite monoids for which this equality also holds. The second type of problem we consider concerns infinite semigroups of relations and transformations. We find the relative rank of the full transformation semigroup, over an infinite set, modulo some standard subsets and subsemigroups, including the set of contraction maps and the set of order preserving maps (for some infinite ordered sets). We also find the relative rank of the semigroup of all binary relations (over an infinite set) modulo the partial transformation semigroup, the full transformation semigroup, the symmetric inverse semigroup, the symmetric group and the set of idempotent relations. Analogous results are also proven for the symmetric inverse semigroup. The third, and final, type of problem studied concerns generalising notions of independence from linear algebra to semigroups and groups. We determine the maximum cardinality of an independent set in finite abelian groups, Brandt semigroups, free nilpotent semigroups, and some examples of infinite groups.
Mon, 01 Jul 2002 00:00:00 GMThttp://hdl.handle.net/10023/113222002-07-01T00:00:00ZMitchell, James DavidIn this thesis we shall consider three types of extremal problems (i.e. problems involving maxima and minima) concerning semigroups. In the first chapter we show how to construct a minimal semigroup presentation that defines a group of non-negative deficiency given a minimal group presentation for that group. This demonstrates that the semigroup deficiency of a group of non-negative deficiency is equal to the group deficiency of that group. Given a finite monoid we find a necessary and sufficient condition for the monoid deficiency to equal the semigroup deficiency. We give a class of infinite monoids for which this equality also holds. The second type of problem we consider concerns infinite semigroups of relations and transformations. We find the relative rank of the full transformation semigroup, over an infinite set, modulo some standard subsets and subsemigroups, including the set of contraction maps and the set of order preserving maps (for some infinite ordered sets). We also find the relative rank of the semigroup of all binary relations (over an infinite set) modulo the partial transformation semigroup, the full transformation semigroup, the symmetric inverse semigroup, the symmetric group and the set of idempotent relations. Analogous results are also proven for the symmetric inverse semigroup. The third, and final, type of problem studied concerns generalising notions of independence from linear algebra to semigroups and groups. We determine the maximum cardinality of an independent set in finite abelian groups, Brandt semigroups, free nilpotent semigroups, and some examples of infinite groups.Our dynamic sun : 2017 Hannes Alfvén Medal lecture at the EGU
http://hdl.handle.net/10023/11320
This lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A small-scale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic fine-scale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fast-particle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.
Fri, 14 Jul 2017 00:00:00 GMThttp://hdl.handle.net/10023/113202017-07-14T00:00:00ZPriest, EricThis lecture summarises how our understanding of many aspects of the Sun has been revolutionised over the past few years by new observations and models. Much of the dynamic behaviour of the Sun is driven by the magnetic field since, in the outer atmosphere, it represents the largest source of energy by far. The interior of the Sun possesses a strong shear layer at the base of the convection zone, where sunspot magnetic fields are generated. A small-scale dynamo may also be operating near the surface of the Sun, generating magnetic fields that thread the lowest layer of the solar atmosphere, the turbulent photosphere. Above the photosphere lies the highly dynamic fine-scale chromosphere, and beyond that is the rare corona at high temperatures exceeding 1 million degrees K. Possible magnetic mechanisms for heating the corona and driving the solar wind (two intriguing and unsolved puzzles) are described. Other puzzles include the structure of giant flux ropes, known as prominences, which have complex fine structure. Occasionally, they erupt and produce huge ejections of mass and magnetic fields (coronal mass ejections), which can disrupt the space environment of the Earth. When such eruptions originate in active regions around sunspots, they are also associated with solar flares, in which magnetic energy is converted to kinetic energy, heat and fast-particle energy. A new theory will be presented for the origin of the twist that is observed in erupting prominences and for the nature of reconnection in the rise phase of an eruptive flare or coronal mass ejection.Optimized automated survey design in wildlife population assessment
http://hdl.handle.net/10023/11318
Increased pressure on the environment has placed numerous ecological populations under threat of extinction. Management schemes dedicated to the future conservation of wildlife populations rely on effective monitoring of the size of those populations. This requires that accurate and precise abundance estimates are obtained for the purposes of wildlife population assessment. The accuracy and precision of estimates are determined to a large extent by the survey design used to obtain population samples. Methods for optimizing the survey design process are detailed, with a particular- focus on automating the sui-vey designs using computer software. The technique of automated survey design is a simulation-based tool, which provides the means to assess the properties of any type of survey design, permits the evaluation of abundance estimates over sui-vey regions with assumed population densities, and from a practical standpoint facilitates the creation of a survey plan that can be implemented in the field. Survey design properties include the probability of a particular location being included in the sample, the spatial distribution of the sampling locations within the survey region, and the distances covered by observers to obtain the sample data. The design properties are directly linked to the accuracy and precision of estimates, as well as the efficiency, achieved by a type of design. A comparative study of a number of different survey designs that can be broadly classified as systematic or non-systematic is presented. The simulation results show their performance with regard to the above-mentioned properties and the abundance estimates obtained if the designs are applied to some known population densities. Due to the more even spatial distribution of the systematic designs the estimates they produce are potentially more precise and the distances covered by observers less variable as well. It is also shown how biased estimates can result if the probability of a particular location being included in the sample is assumed to be even over the entire survey region when it is not. The problems associated with surveying along the boundary of a survey region and within non-convex regions are addressed. The methods are illustrated with a number of survey design examples.
Tue, 01 May 2001 00:00:00 GMThttp://hdl.handle.net/10023/113182001-05-01T00:00:00ZStrindberg, SamanthaIncreased pressure on the environment has placed numerous ecological populations under threat of extinction. Management schemes dedicated to the future conservation of wildlife populations rely on effective monitoring of the size of those populations. This requires that accurate and precise abundance estimates are obtained for the purposes of wildlife population assessment. The accuracy and precision of estimates are determined to a large extent by the survey design used to obtain population samples. Methods for optimizing the survey design process are detailed, with a particular- focus on automating the sui-vey designs using computer software. The technique of automated survey design is a simulation-based tool, which provides the means to assess the properties of any type of survey design, permits the evaluation of abundance estimates over sui-vey regions with assumed population densities, and from a practical standpoint facilitates the creation of a survey plan that can be implemented in the field. Survey design properties include the probability of a particular location being included in the sample, the spatial distribution of the sampling locations within the survey region, and the distances covered by observers to obtain the sample data. The design properties are directly linked to the accuracy and precision of estimates, as well as the efficiency, achieved by a type of design. A comparative study of a number of different survey designs that can be broadly classified as systematic or non-systematic is presented. The simulation results show their performance with regard to the above-mentioned properties and the abundance estimates obtained if the designs are applied to some known population densities. Due to the more even spatial distribution of the systematic designs the estimates they produce are potentially more precise and the distances covered by observers less variable as well. It is also shown how biased estimates can result if the probability of a particular location being included in the sample is assumed to be even over the entire survey region when it is not. The problems associated with surveying along the boundary of a survey region and within non-convex regions are addressed. The methods are illustrated with a number of survey design examples.Helioseismology and diagnostics of internal magnetic layers
http://hdl.handle.net/10023/11315
Solar magnetic fields, as well as temperature changes, introduce pressure deviations that play a significant role in modulating the resonant frequencies of p-mode oscillations. Those pressure deviations occurring in the atmosphere or sub-surface of the Sun can explain the frequency shifts observed on the timescale of the solar activity cycle. A separate study of the contribution of internal magnetic layers can clarify the relative importance of surface effects. Results from helioseismology provide realistic constraints for choosing parameters suitable to represent the magnetic layers buried in the solar interior and available for modelling, i.e. at the base of the convection zone and in the sunspots’ anchoring zone. Diagnostics of the internal magnetic layers are obtained through a schematic model in which the Sun is plane-stratified. The influence of a buried magnetic field on p-modes is explored, and the nature of various waves and instabilities that can arise on such a buried magnetic field is assessed. By treating the effects of internal magnetic layers, this thesis contributes to the building of a bridge between theories and observations. On the one hand, the theoretical analysis is explored carefully in the course of its formulation, which generates new hypotheses that were not obvious so far. On the other hand, observations help to understand which explanations of the solar cycle frequency shifts may apply.
Fri, 01 Mar 2002 00:00:00 GMThttp://hdl.handle.net/10023/113152002-03-01T00:00:00ZFoullon, Claire-Uriel Armelle Marie AlineSolar magnetic fields, as well as temperature changes, introduce pressure deviations that play a significant role in modulating the resonant frequencies of p-mode oscillations. Those pressure deviations occurring in the atmosphere or sub-surface of the Sun can explain the frequency shifts observed on the timescale of the solar activity cycle. A separate study of the contribution of internal magnetic layers can clarify the relative importance of surface effects. Results from helioseismology provide realistic constraints for choosing parameters suitable to represent the magnetic layers buried in the solar interior and available for modelling, i.e. at the base of the convection zone and in the sunspots’ anchoring zone. Diagnostics of the internal magnetic layers are obtained through a schematic model in which the Sun is plane-stratified. The influence of a buried magnetic field on p-modes is explored, and the nature of various waves and instabilities that can arise on such a buried magnetic field is assessed. By treating the effects of internal magnetic layers, this thesis contributes to the building of a bridge between theories and observations. On the one hand, the theoretical analysis is explored carefully in the course of its formulation, which generates new hypotheses that were not obvious so far. On the other hand, observations help to understand which explanations of the solar cycle frequency shifts may apply.Magnetohydrodynamic waves and instabilities in solar magnetic structures
http://hdl.handle.net/10023/11308
Motions of plasma in magnetic structures in the solar atmosphere may be successfully modelled using the theory of magnetohydrodynamics (MHD) describing oscillatory motion, in the form of standing and propagating waves, and unstable behaviour. In this thesis we consider two forms of magnetic structuring, the current sheet and the thin magnetic flux tube. The current sheet finds particular application in the solar corona and solar wind; the thin flux tube is of particular importance in solar photospheric magnetism. A model of a current sheet with a continuous magnetic field profile is studied as a waveguide. The equation of motion for small perturbations to a current sheet equilibrium is obtained from the equations of ideal linear MHD and solved numerically to determine the nature of magnetoacoustic waves propagating parallel to the applied magnetic field. A number of approximation methods are used to shed light on the significance of the numerical results. We consider a variation of this model, applicable to the solar corona, and examine the possibility of impulsively generated magnetohydro dynamic waves in the sheet. Such waves exhibit wavepacket properties, similar to those found in slab models of magnetic structures. The process of convective collapse in a vertical magnetic flux tube located in the solar photospheric network is treated using the thin flux tube equations of ideal linear MED. We consider the critical stability of a thin flux tube embedded in convection zone models of varying complexity, taking into account the effects of an overlying chromospheric atmosphere and temperature imbalance between the flux tube and its environment. The dependence of the instability on various sets of boundary conditions is discussed; the choice of boundary conditions is a subject of some debate in the current literature. Possible future directions for work which extends the description of dynamic phenomena in both the current sheet and thin flux tube structure is discussed and ideas for linking these areas of research are presented.
Fri, 01 Jun 2001 00:00:00 GMThttp://hdl.handle.net/10023/113082001-06-01T00:00:00ZBoddie, DavidMotions of plasma in magnetic structures in the solar atmosphere may be successfully modelled using the theory of magnetohydrodynamics (MHD) describing oscillatory motion, in the form of standing and propagating waves, and unstable behaviour. In this thesis we consider two forms of magnetic structuring, the current sheet and the thin magnetic flux tube. The current sheet finds particular application in the solar corona and solar wind; the thin flux tube is of particular importance in solar photospheric magnetism. A model of a current sheet with a continuous magnetic field profile is studied as a waveguide. The equation of motion for small perturbations to a current sheet equilibrium is obtained from the equations of ideal linear MHD and solved numerically to determine the nature of magnetoacoustic waves propagating parallel to the applied magnetic field. A number of approximation methods are used to shed light on the significance of the numerical results. We consider a variation of this model, applicable to the solar corona, and examine the possibility of impulsively generated magnetohydro dynamic waves in the sheet. Such waves exhibit wavepacket properties, similar to those found in slab models of magnetic structures. The process of convective collapse in a vertical magnetic flux tube located in the solar photospheric network is treated using the thin flux tube equations of ideal linear MED. We consider the critical stability of a thin flux tube embedded in convection zone models of varying complexity, taking into account the effects of an overlying chromospheric atmosphere and temperature imbalance between the flux tube and its environment. The dependence of the instability on various sets of boundary conditions is discussed; the choice of boundary conditions is a subject of some debate in the current literature. Possible future directions for work which extends the description of dynamic phenomena in both the current sheet and thin flux tube structure is discussed and ideas for linking these areas of research are presented.Field line resonances in the earth's magnetosphere driven by convectively unstable magnetospheric waveguide modes
http://hdl.handle.net/10023/11303
Shear flow instabilities, such as Kelvin-Helmholtz instabilities, occurring on the Earth’s magnetospheric flanks may cause fast magnetosonic wave modes to propagate through the non-homogeneous environment of the Earth’s magnetospheric cavity. The non-uniformity in this plasma environment means the fast wave mode couples to a standing Alfvén wave mode along a closed field line in the magnetosphere with natural frequency equal to the fast wave frequency. The one-dimensional hydromagnetic box model of Southwood (1974), which treats the Earth’s magnetic field as a set of straight field lines between two ionospheric boundaries which are not perfectly reflecting, is used to model the resonance. There is a finite height-integrated Pedersen conductivity, Σp, at the boundaries of the one-dimensional box which is responsible for the damping of the field line resonance. The coupling process between the fast and Alfvén modes is represented by a simple harmonic oscillator equation driven by a time-dependent function representing the fast mode azimuthal pressure gradient, Wright (1992a,b). A fourth-order Runge-Kutta numerical integration technique is used to obtain the solution to the simple harmonic oscillation. These numerical routines are verified using analytically derived solutions for a test case of a simple driving function d{t) = Dsin(wdt). Following this test of the numerical routines, realistic driving functions from Wright et al (2002), which represent convectively unstable fast wave modes propagating through the magnetospheric cavity as a result of a Kelvin-Helmholtz instability occurring on the flanks of the magnetosphere, are used to drive the simple harmonic system. Four different unstable drivers are used, these being the fundamental and the second harmonic mode for two different values of azimuthal coordinate. For all four drivers clear resonance characteristics emerged, suggesting these may drive field line resonances in the Earth’s magnetosphere.
Mon, 01 Jul 2002 00:00:00 GMThttp://hdl.handle.net/10023/113032002-07-01T00:00:00ZMcRobbie, Mairi CatrionaShear flow instabilities, such as Kelvin-Helmholtz instabilities, occurring on the Earth’s magnetospheric flanks may cause fast magnetosonic wave modes to propagate through the non-homogeneous environment of the Earth’s magnetospheric cavity. The non-uniformity in this plasma environment means the fast wave mode couples to a standing Alfvén wave mode along a closed field line in the magnetosphere with natural frequency equal to the fast wave frequency. The one-dimensional hydromagnetic box model of Southwood (1974), which treats the Earth’s magnetic field as a set of straight field lines between two ionospheric boundaries which are not perfectly reflecting, is used to model the resonance. There is a finite height-integrated Pedersen conductivity, Σp, at the boundaries of the one-dimensional box which is responsible for the damping of the field line resonance. The coupling process between the fast and Alfvén modes is represented by a simple harmonic oscillator equation driven by a time-dependent function representing the fast mode azimuthal pressure gradient, Wright (1992a,b). A fourth-order Runge-Kutta numerical integration technique is used to obtain the solution to the simple harmonic oscillation. These numerical routines are verified using analytically derived solutions for a test case of a simple driving function d{t) = Dsin(wdt). Following this test of the numerical routines, realistic driving functions from Wright et al (2002), which represent convectively unstable fast wave modes propagating through the magnetospheric cavity as a result of a Kelvin-Helmholtz instability occurring on the flanks of the magnetosphere, are used to drive the simple harmonic system. Four different unstable drivers are used, these being the fundamental and the second harmonic mode for two different values of azimuthal coordinate. For all four drivers clear resonance characteristics emerged, suggesting these may drive field line resonances in the Earth’s magnetosphere.Three dimensional numerical simulations of non-linear MHD instabilities in the solar corona
http://hdl.handle.net/10023/11297
The aim of this thesis has been to carry out 3D MHD simulations to investigate nonlinear MHD instabilities and the behaviour of solar coronal loops. The simulations have been carried out on a parallel computer using a new shock-capturing Lagrangian-remap code, LareSd. As part of the PhD this code has been extended to include resistivity allowing the study of the non-linear resistive evolution of the instability. In particular the kink instability in line-tied coronal loops has been studied. This was suggested as a possible explanation of compact loop flares, sudden brightenings of a coronal loop due to a release of energy which does not destroy the loop. For the kink instability to explain such flares it must drive reconnection. This requires high current densities, i.e. current sheets. The results presented in this thesis suggest that the formation of current sheets during the non-linear evolution of the kink instability is more complicated than was previously believed. Indeed, if the loop is allowed to evolve slowly until the instability is triggered than the current appears to saturate at a finite value. This suggests that the kink instability cannot explain a compact loop flare. LareSd has also been used to model space observations from NASA’s SoHO (a joint NASA/ESA satellite) and TRACE satellites. These observations showed a group of rotating sunspots and their overlying system of loops. The simulations will allow further investigations of this behaviour to be carried out.
Tue, 01 Jan 2002 00:00:00 GMThttp://hdl.handle.net/10023/112972002-01-01T00:00:00ZGerrard, Catherine LouiseThe aim of this thesis has been to carry out 3D MHD simulations to investigate nonlinear MHD instabilities and the behaviour of solar coronal loops. The simulations have been carried out on a parallel computer using a new shock-capturing Lagrangian-remap code, LareSd. As part of the PhD this code has been extended to include resistivity allowing the study of the non-linear resistive evolution of the instability. In particular the kink instability in line-tied coronal loops has been studied. This was suggested as a possible explanation of compact loop flares, sudden brightenings of a coronal loop due to a release of energy which does not destroy the loop. For the kink instability to explain such flares it must drive reconnection. This requires high current densities, i.e. current sheets. The results presented in this thesis suggest that the formation of current sheets during the non-linear evolution of the kink instability is more complicated than was previously believed. Indeed, if the loop is allowed to evolve slowly until the instability is triggered than the current appears to saturate at a finite value. This suggests that the kink instability cannot explain a compact loop flare. LareSd has also been used to model space observations from NASA’s SoHO (a joint NASA/ESA satellite) and TRACE satellites. These observations showed a group of rotating sunspots and their overlying system of loops. The simulations will allow further investigations of this behaviour to be carried out.An investigation of rotating magnetospheres
http://hdl.handle.net/10023/11294
In this thesis we will construct simple models of rotating stellar and planetary magnetospheres within the framework of ideal MHD. These models will take the basic outline of a stellar magnetosphere that we have outlined above as a starting point from which to proceed further. In summary, this simple magnetosphere will be that of a single, rapidly rotating star' with an axisymmetric dipole magnetic field at the base of its corona and with an axis that is in alignment with that of the rotation axis. It is the isothermal plasma associated with this field that will give rise to the magnetospheric emission and which is held in strict corotation with the stellar surface. Equatorial and rotational symmetry reduce the domain to one quarter of a two dimensional quadrant. We will consider timescales that are much longer than the typical time scales of the system, which will allow us to model the evolution of the system quasi-statically by calculating sequences of MHS equilibria. This is achieved by numerical solution of the Grad-Shafranov equation (in terms of the flux function. A) Which requires us to specify a suitable surface pressure distribution and specify the toroidal component of the magnetic field as a function of A. The second chapter will outline the numerical procedure that will be employed to calculate these equilibrium sequences, and the practical realisation of this procedure. The third chapter will discuss different models which will be characterised by different surface pressure distributions but all of which will lack a toroidal magnetic field component. The fourth chapter will discuss results from a model which includes a toroidal magnetic field component. The models successfully reproduce the observed saturation and supersaturation of stellar emission with rotation. The fifth chapter will address the question of analytically constructing three dimensional equilibria that may be of use in the modelling of magnetospheres with magnetic field geometries that are not in alignment with their rotation axes or which are displaced from the centre of the rotating body, such as the giant gas planets Uranus and Neptune. The last section of the thesis will be a brief discussion of our conclusions, a review of the work of the thesis and will consider the outlook for further development, extension and refinement of our models.
Fri, 01 Nov 2002 00:00:00 GMThttp://hdl.handle.net/10023/112942002-11-01T00:00:00ZRyan, Richard DanielIn this thesis we will construct simple models of rotating stellar and planetary magnetospheres within the framework of ideal MHD. These models will take the basic outline of a stellar magnetosphere that we have outlined above as a starting point from which to proceed further. In summary, this simple magnetosphere will be that of a single, rapidly rotating star' with an axisymmetric dipole magnetic field at the base of its corona and with an axis that is in alignment with that of the rotation axis. It is the isothermal plasma associated with this field that will give rise to the magnetospheric emission and which is held in strict corotation with the stellar surface. Equatorial and rotational symmetry reduce the domain to one quarter of a two dimensional quadrant. We will consider timescales that are much longer than the typical time scales of the system, which will allow us to model the evolution of the system quasi-statically by calculating sequences of MHS equilibria. This is achieved by numerical solution of the Grad-Shafranov equation (in terms of the flux function. A) Which requires us to specify a suitable surface pressure distribution and specify the toroidal component of the magnetic field as a function of A. The second chapter will outline the numerical procedure that will be employed to calculate these equilibrium sequences, and the practical realisation of this procedure. The third chapter will discuss different models which will be characterised by different surface pressure distributions but all of which will lack a toroidal magnetic field component. The fourth chapter will discuss results from a model which includes a toroidal magnetic field component. The models successfully reproduce the observed saturation and supersaturation of stellar emission with rotation. The fifth chapter will address the question of analytically constructing three dimensional equilibria that may be of use in the modelling of magnetospheres with magnetic field geometries that are not in alignment with their rotation axes or which are displaced from the centre of the rotating body, such as the giant gas planets Uranus and Neptune. The last section of the thesis will be a brief discussion of our conclusions, a review of the work of the thesis and will consider the outlook for further development, extension and refinement of our models.On the application of numerical continuation methods to two- and three-dimensional solar and astrophysical problems
http://hdl.handle.net/10023/11293
In this thesis, applications of a numerical continuation method to two- and three-dimensional bifurcation problems are presented. The 2D problems are motivated by solar applications. In particular, it is shown that the bifurcation properties of a previously studied model for magnetic arcades depend strongly on the pressure function used in the model. The bifurcation properties of a straight flux model for coronal loops are investigated and compared with the results of linear ideal MHD stability analysis. It is shown that for line-tied boundary conditions, the method for the calculation of the equilibrium sequence determines whether the first or the second bifurcation point coincides with the linear stability threshold. Also, in this thesis, the 3D version of the continuation code is applied for the first time. The problems treated with the 3D code are therefore chosen with the intention to demonstrate the general capabilities of the code and to see where its limitations are. Whereas the code performs as expected for relatively simple albeit nonlinear bifurcation problems, a clear need for further development is shown by more involved problems.
Sat, 01 Jun 2002 00:00:00 GMThttp://hdl.handle.net/10023/112932002-06-01T00:00:00ZRomeou, ZahareniaIn this thesis, applications of a numerical continuation method to two- and three-dimensional bifurcation problems are presented. The 2D problems are motivated by solar applications. In particular, it is shown that the bifurcation properties of a previously studied model for magnetic arcades depend strongly on the pressure function used in the model. The bifurcation properties of a straight flux model for coronal loops are investigated and compared with the results of linear ideal MHD stability analysis. It is shown that for line-tied boundary conditions, the method for the calculation of the equilibrium sequence determines whether the first or the second bifurcation point coincides with the linear stability threshold. Also, in this thesis, the 3D version of the continuation code is applied for the first time. The problems treated with the 3D code are therefore chosen with the intention to demonstrate the general capabilities of the code and to see where its limitations are. Whereas the code performs as expected for relatively simple albeit nonlinear bifurcation problems, a clear need for further development is shown by more involved problems.Investigations of current build up in topologically simple magnetic fields
http://hdl.handle.net/10023/11291
The solar corona is a highly conductive plasma which is dominated by the coronal magnetic field. Observations show that important solar phenomena like flares or the heating of the corona are driven by magnetic energy, probably through the process of magnetic reconnection. The release of magnetic energy by reconnection requires that non-ideal processes take place in contradiction to the high conductivity of the corona. One possibility to overcome this problem is to generate strong electrical currents in strongly localised regions. In this thesis we investigate how such localised currents can be formed by slow ideal evolution of topologically simple magnetic fields. To this purpose numerical simulations are carried out using an Eulerian and a Lagrangian MHD relaxation code. We first use a simple example (twisting of a uniform field) to investigate the advantages and disadvantages of both codes and to discover possible limitations for their application. We show that for the problems addressed in this thesis the Lagrangian code is more suited because it can resolve the localised current densities much better than the Eulerian code. We then focus in particular on magnetic fields containing a so-called Hyperbolic Flux Tube (HPT). A recently proposed analytical theory predicts that HFT’s are sites where under certain conditions strong current build-up can be expected. We use our code to carry out a systematic parametric study of the dependence of current growth for a typical HFT configuration. We have also developed a completely new version of the analytical theory which is directly based on the set-up of our numerical simulations. We find that the simulations agree with the analytical prediction in a quantitative way but that the analytical theory underestimates the current growth quite substantially, probably by not taking into account the non-linear character of the full problem.
Wed, 01 Jun 2005 00:00:00 GMThttp://hdl.handle.net/10023/112912005-06-01T00:00:00ZBocquet, Francois-XavierThe solar corona is a highly conductive plasma which is dominated by the coronal magnetic field. Observations show that important solar phenomena like flares or the heating of the corona are driven by magnetic energy, probably through the process of magnetic reconnection. The release of magnetic energy by reconnection requires that non-ideal processes take place in contradiction to the high conductivity of the corona. One possibility to overcome this problem is to generate strong electrical currents in strongly localised regions. In this thesis we investigate how such localised currents can be formed by slow ideal evolution of topologically simple magnetic fields. To this purpose numerical simulations are carried out using an Eulerian and a Lagrangian MHD relaxation code. We first use a simple example (twisting of a uniform field) to investigate the advantages and disadvantages of both codes and to discover possible limitations for their application. We show that for the problems addressed in this thesis the Lagrangian code is more suited because it can resolve the localised current densities much better than the Eulerian code. We then focus in particular on magnetic fields containing a so-called Hyperbolic Flux Tube (HPT). A recently proposed analytical theory predicts that HFT’s are sites where under certain conditions strong current build-up can be expected. We use our code to carry out a systematic parametric study of the dependence of current growth for a typical HFT configuration. We have also developed a completely new version of the analytical theory which is directly based on the set-up of our numerical simulations. We find that the simulations agree with the analytical prediction in a quantitative way but that the analytical theory underestimates the current growth quite substantially, probably by not taking into account the non-linear character of the full problem.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.
Tue, 01 Nov 2016 00:00:00 GMThttp://hdl.handle.net/10023/112632016-11-01T00:00:00ZCain, 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.
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/112592018-01-01T00:00:00ZHarris, 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.
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/112532017-10-01T00:00:00ZIllian, 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.
Fri, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/111622017-09-01T00:00:00ZBitsouni, 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
Sun, 01 Jan 2017 00:00:00 GMThttp://hdl.handle.net/10023/111342017-01-01T00:00:00ZAraújo, 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).
Fri, 25 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/111222017-08-25T00:00:00ZKarampelas, 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, 01 Sep 2017 00:00:00 GMThttp://hdl.handle.net/10023/108902017-09-01T00:00:00ZPrieto 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.
Thu, 01 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/108822017-06-01T00:00:00ZHeide-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.
Wed, 01 Jun 2016 00:00:00 GMThttp://hdl.handle.net/10023/106252016-06-01T00:00:00ZPotts, 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, 01 Feb 2018 00:00:00 GMThttp://hdl.handle.net/10023/105432018-02-01T00:00:00ZCuthbertson, 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.
Tue, 01 Aug 2017 00:00:00 GMThttp://hdl.handle.net/10023/105392017-08-01T00:00:00ZLucchini, 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).
Sun, 01 May 2016 00:00:00 GMThttp://hdl.handle.net/10023/102732016-05-01T00:00:00ZErichson, 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.
The authors were financially supported by an LMS Scheme 4 Research in Pairs grant. The second author also acknowledges financial support from the EPSRC grant EP/K029061/1, and the first author acknowledges financial support from a Leverhulme Trust Research Fellowship (RF-2016-500).
Mon, 01 Jan 2018 00:00:00 GMThttp://hdl.handle.net/10023/101652018-01-01T00:00:00ZFraser, Jonathan M.Kempton, 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).
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/101162017-10-01T00:00:00ZBorchers, 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.
Wed, 01 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/100862017-03-01T00:00:00ZIommi, 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.
Sun, 01 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/100692017-10-01T00:00:00ZAllen, 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.
Fri, 16 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/100612017-06-16T00:00:00ZFraser, Jonathan M.Jordan, 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.
Thu, 12 Oct 2017 00:00:00 GMThttp://hdl.handle.net/10023/99382017-10-12T00:00:00ZTaylor, 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.
Thu, 15 Jun 2017 00:00:00 GMThttp://hdl.handle.net/10023/98852017-06-15T00:00:00ZBorchers, 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.
Tue, 21 Mar 2017 00:00:00 GMThttp://hdl.handle.net/10023/98692017-03-21T00:00:00ZLehmann, 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, 01 Nov 2017 00:00:00 GMThttp://hdl.handle.net/10023/97112017-11-01T00:00:00ZAwang, 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 equil