2024-03-29T09:10:05Zhttps://research-repository.st-andrews.ac.uk/oai/requestoai:research-repository.st-andrews.ac.uk:10023/33412023-04-18T09:47:16Zcom_10023_196com_10023_39com_10023_28com_10023_94com_10023_879com_10023_878col_10023_197col_10023_859col_10023_98col_10023_880
St Andrews Research Repository
author
Abughazalah, Nabilah
author
Ruskuc, Nik
sponsor
EPSRC
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Pure Mathematics
institution
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
2013-02-07T12:34:47Z
2013-02-07T12:34:47Z
2013-08
Abughazalah , N & Ruskuc , N 2013 , ' On disjoint unions of finitely many copies of the free monogenic semigroup ' , Semigroup Forum , vol. 87 , no. 1 , pp. 243-256 . https://doi.org/10.1007/s00233-013-9468-9
0037-1912
PURE: 43731800
http://hdl.handle.net/10023/3341
https://doi.org/10.1007/s00233-013-9468-9
EP/I032282/1
Every semigroup which is a finite disjoint union of copies of the free monogenic semigroup (natural numbers under addition) is finitely presented and residually finite.
eng
This is an author version of this article. The final publication will be available at www.springerlink.com
QA Mathematics
On disjoint unions of finitely many copies of the free monogenic semigroup
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/3341/1/unionsns2.pdf
File
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177826
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unionsns2.pdf
URL
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File
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unionsns2.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/23752024-03-04T00:40:53Zcom_10023_196com_10023_39com_10023_28com_10023_879com_10023_878col_10023_197col_10023_859col_10023_880
St Andrews Research Repository
author
Cain, Alan James
author
Ruskuc, Nik
author
Thomas, R.M.
sponsor
EPSRC
sponsor
EPSRC
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
2012-02-28T11:01:02Z
2012-02-28T11:01:02Z
2012-06-08
Cain , A J , Ruskuc , N & Thomas , R M 2012 , ' Unary FA-presentable semigroups ' , International Journal of Algebra and Computation , vol. 22 , no. 4 , 1250038 . https://doi.org/10.1142/S0218196712500385
0218-1967
ORCID: /0000-0003-2415-9334/work/73702055
https://hdl.handle.net/10023/2375
10.1142/S0218196712500385
EP/C523229/1
Automatic presentations, also called FA-presentations, were introduced to extend nite model theory to innite structures whilst retaining the solubility of interesting decision problems. A particular focus of research has been the classication of those structures of some species that admit automatic presentations. Whilst some successes have been obtained, this appears to be a dicult problem in general. A restricted problem, also of signicant interest, is to ask this question for unary automatic presentations: auto-matic presentations over a one-letter alphabet. This paper studies unary FA-presentable semigroups. We prove the following: Every unary FA-presentable structure admits an injective unary automatic presentation where the language of representatives consists of every word over a one-letter alphabet. Unary FA-presentable semigroups are locally nite, but non-nitely generated unary FA-presentable semigroups may be innite. Every unary FA-presentable semigroup satises some Burnside identity.We describe the Green's relations in unary FA-presentable semigroups. We investigate the relationship between the class of unary FA-presentable semigroups and various semigroup constructions. A classication is given of the unary FA-presentable completely simple semigroups.
eng
Automatic presentations
Semigroups
Regular languages
QA Mathematics
Unary FA-presentable semigroups
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/2375/2/crt_unaryfa.pdf
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crt_unaryfa.pdf
URL
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crt_unaryfa.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/162602023-04-18T09:43:03Zcom_10023_165com_10023_39com_10023_28com_10023_792com_10023_95com_10023_879com_10023_878col_10023_166col_10023_859col_10023_795col_10023_100col_10023_880
St Andrews Research Repository
author
Borkin, Kerry
author
Summers, Ron
author
Thomas, Len
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Scottish Oceans Institute
institution
University of St Andrews. Centre for Research into Ecological & Environmental Modelling
institution
University of St Andrews. Marine Alliance for Science & Technology Scotland
2018-10-17T14:30:12Z
2018-10-17T14:30:12Z
2012-01-03
Borkin , K , Summers , R & Thomas , L 2012 , ' Surveying abundance and stand type associations of Formica aquilonia and F. lugubris (Hymenoptera: Formicidae) nest mounds over an extensive area : Trialing a novel method ' , European Journal of Entomology , vol. 109 , no. 1 , pp. 47-53 . https://doi.org/10.14411/eje.2012.007
PURE: 5285592
http://hdl.handle.net/10023/16260
https://doi.org/10.14411/eje.2012.007
http://www.eje.cz/pdfarticles/1679/eje_109_1_047_Borkin.pdf
Red wood ants are ecologically important members of woodland communities, and some species are of conservation concern. They occur commonly only in certain habitats in Britain, but there is limited knowledge of their numbers and distribution. This study provided baseline information at a key locality (Abernethy Forest, 37 km2) in the central Highlands of Scotland and trialed a new method of surveying red wood ant density and stand type associations: a distance sampling line transect survey of nests. This method is efficient because it allows an observer to quickly survey a large area either side of transect lines, without having to assume that all nests are detected. Instead, data collected on the distance of nests from the line are used to estimate probability of detection and the effective transect width, using the free software "Distance". Surveys took place in August and September 2003 along a total of 71.2 km of parallel, equally-spaced transects. One hundred and forty-four red wood ant nests were located, comprising 89 F. aquilonia (Yarrow, 1955) and 55 F. lugubris (Zetterstedt, 1838) nests. Estimated densities were 1.13 nests per hectare (95% CI 0.74-1.73) for F. aquilonia and 0.83 nests per hectare (95% CI 0.32-2.17) for F. lugubris. These translated to total estimated nest numbers of 4,200 (95% CI 2,700-6,400) and 3,100 (95% CI 1,200-8,100), respectively, for the whole forest. Indices of stand selection indicated that F. aquilonia had some positive association with old-growth and F. lugubris with younger stands (stem exclusion stage). No nests were found in areas that had been clear-felled, and ploughed and planted in the 1970s-1990s. The pattern of stand type association and hence distribution of F. aquilonia and F. lugubris may be due to the differing ability to disperse (F. lugubris is the faster disperser) and compete (F. aquilonia is competitively superior). We recommend using line transect sampling for extensive surveys of ants that construct nest mounds to estimate abundance and stand type association.
eng
This is an open access article distributed under the terms of the Creative Commons Attribution License (CC BY), which permits use, distribution, and reproduction in any medium, provided the original publication is properly cited. No use, distribution or reproduction is permitted which does not comply with these terms.
Distance sampling
Formica
Formicidae
Hymenoptera
Line transect
Old-growth
Pinus sylvestris
Scotland
QA Mathematics
QH301 Biology
Insect Science
Surveying abundance and stand type associations of Formica aquilonia and F. lugubris (Hymenoptera: Formicidae) nest mounds over an extensive area : Trialing a novel method
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/16260/1/Borkin20152_EJE109_SurveyingAbundance.pdf
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Borkin20152_EJE109_SurveyingAbundance.pdf
URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/16260/3/Borkin20152_EJE109_SurveyingAbundance.pdf.txt
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Borkin20152_EJE109_SurveyingAbundance.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/19572022-04-14T09:30:16Zcom_10023_165com_10023_39com_10023_28com_10023_792com_10023_309com_10023_879com_10023_878col_10023_166col_10023_859col_10023_795col_10023_311col_10023_880
St Andrews Research Repository
author
Summers, Ron W
author
Buckland, Stephen Terrence
institution
University of St Andrews. Scottish Oceans Institute
institution
University of St Andrews. Centre for Research into Ecological & Environmental Modelling
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. St Andrews Sustainability Institute
institution
University of St Andrews. Marine Alliance for Science & Technology Scotland
2011-08-10T06:36:40Z
2011-08-10T06:36:40Z
2011-06
Summers , R W & Buckland , S T 2011 , ' A first survey of the global population size and distribution of the Scottish Crossbill Loxia scotica ' , Bird Conservation International , vol. 21 , no. 2 , pp. 186-198 . https://doi.org/10.1017/S0959270909990323
0959-2709
PURE: 11461790
http://hdl.handle.net/10023/1957
https://doi.org/10.1017/S0959270909990323
A survey of Scottish Crossbills Loxia scotica was carried out in 3,506 km2 of conifer woodland in northern Scotland during January to April 2008 to provide the first estimate of the global population size for this endemic bird. Population estimates were also made for Common Crossbills L. curvirostra and Parrot Crossbills L. pytyopsittacus within this range. Crossbills were lured to systematically selected survey points for counting, sexing and recording their calls for later call-type (species) identification from sonograms. Crossbills were located at 451 of the 852 survey points, and adequate tape-recordings made at 387 of these. The Scottish Crossbill had a disjunct distribution, occurring largely within the eastern part of the study area, but also in the northwest. Common Crossbills had a mainly westerly distribution. The population size of postjuvenile Scottish Crossbills was estimated as 13,600 (95%C.I. 8,130–22,700), which will approximate to 6,800 (4,065–11,350) pairs. Common Crossbills were more abundant within this range (27,100, 95% C.I. 14,700–38,400) and Parrot Crossbills rare (about 100). The sex ratio was not significantly different from parity for Scottish Crossbills. The modal number at survey points was two but numbers were larger in January than later in the survey. The numbers and distribution of all crossbill species are likely to vary between years, depending upon the size of the cone crops of the different conifers: all were coning in 2008. Common Crossbill and Parrot Crossbill numbers will also be affected by irruptions from continental Europe. A monitoring scheme is required to detect any population trend, and further work on their habitat requirement (e.g. conifer selection at different seasons) is needed to inform habitat management of native and planted conifer forests to ensure a secure future for this endemic bird.
eng
Copyright © BirdLife International 2010. Published by Cambridge University Press, available from DOI: 10.1017/S0959270909990323
QL Zoology
A first survey of the global population size and distribution of the Scottish Crossbill Loxia scotica
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/1957/1/SummersBucklandBirdConsInt2011ScottishCrossbill.pdf
File
MD5
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198517
application/pdf
SummersBucklandBirdConsInt2011ScottishCrossbill.pdf
URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/1957/3/SummersBucklandBirdConsInt2011ScottishCrossbill.pdf.txt
File
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text/plain
SummersBucklandBirdConsInt2011ScottishCrossbill.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/89592023-04-18T10:03:44Zcom_10023_92com_10023_28com_10023_879com_10023_878col_10023_96col_10023_859col_10023_880
St Andrews Research Repository
author
E. H. Stevenson, Julie
author
E. Parnell, Clare
institution
University of St Andrews. Applied Mathematics
institution
University of St Andrews. School of Mathematics and Statistics
2016-06-09T23:32:38Z
2016-06-09T23:32:38Z
2015-12
E. H. Stevenson , J & E. Parnell , C 2015 , ' Spontaneous reconnection at a separator current layer : I. Nature of the reconnection ' , Journal of Geophysical Research: Space Physics , vol. 120 , no. 12 , pp. 10334-10352 . https://doi.org/10.1002/2015JA021730
2169-9402
PURE: 225630555
http://hdl.handle.net/10023/8959
https://doi.org/10.1002/2015JA021730
Magnetic separators, which lie on the boundary between four topologically-distinct flux domains, are prime locations in three-dimensional magnetic fields for reconnection, especially in the magnetosphere between the planetary and interplanetary magnetic fields and also in the solar atmosphere. Little is known about the details of separator reconnection and so the aim of this paper, which is the first of two, is to study the properties of magnetic reconnection at a single separator. Three-dimensional, resistive magnetohydrodynamic numerical experiments are run to study separator reconnection starting from a magnetohydrostatic equilibrium which contains a twisted current layer along a single separator linking a pair of opposite-polarity null points. The resulting reconnection occurs in two phases. The first is short involving rapid reconnection in which the current at the separator is reduced by a factor of around 2.3. Most 75% of the magnetic energy is converted during this phase, via Ohmic dissipation, directly into internal energy, with just 0.1% going into kinetic energy. During this phase the reconnection occurs along most of the separator away from its ends (the nulls), but in an asymmetric manner which changes both spatially and temporally over time. The second phase is much longer and involves slow impulsive-bursty reconnection. Again Ohmic heating dominates over viscous damping. Here the reconnection occurs in small localized bursts at random anywhere along the separator.
eng
© 2015, Publisher / the Author(s). This work is made available online in accordance with the publisher’s policies. This is the author created, accepted version manuscript following peer review and may differ slightly from the final published version. The final published version of this work is available at onlinelibrary.wiley.com / https://dx.doi.org/10.1002/2015JA021736
QB Astronomy
QC Physics
NDAS
BDC
R2C
Spontaneous reconnection at a separator current layer : I. Nature of the reconnection
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/8959/1/Stevenson_2015_JGeophysResSpacePhys_10334.pdf
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Stevenson_2015_JGeophysResSpacePhys_10334.pdf
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Stevenson_2015_JGeophysResSpacePhys_10334.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/52332022-04-05T14:30:50Zcom_10023_92com_10023_28com_10023_879com_10023_878col_10023_96col_10023_859col_10023_880
St Andrews Research Repository
author
Keppens, R.
author
Porth, O.
author
Galsgaard, K.
author
Frederiksen, J.T.
author
Restante, A.L.
author
Lapenta, G.
author
Parnell, C.
sponsor
European Commission
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Applied Mathematics
2014-08-25T16:01:34Z
2014-08-25T16:01:34Z
2013-09-13
Keppens , R , Porth , O , Galsgaard , K , Frederiksen , J T , Restante , A L , Lapenta , G & Parnell , C 2013 , ' Resistive magnetohydrodynamic reconnection : resolving long-term, chaotic dynamics ' , Physics of Plasmas , vol. 20 , no. 9 , 092109 . https://doi.org/10.1063/1.4820946
1070-664X
PURE: 143241697
http://hdl.handle.net/10023/5233
https://doi.org/10.1063/1.4820946
http://www.scopus.com/inward/record.url?eid=2-s2.0-84885027542&partnerID=8YFLogxK
263340
In this paper, we address the long-term evolution of an idealised double current system entering reconnection regimes where chaotic behavior plays a prominent role. Our aim is to quantify the energetics in high magnetic Reynolds number evolutions, enriched by secondary tearing events, multiple magnetic island coalescence, and compressive versus resistive heating scenarios. Our study will pay particular attention to the required numerical resolutions achievable by modern (grid-adaptive) computations, and comment on the challenge associated with resolving chaotic island formation and interaction. We will use shock-capturing, conservative, grid-adaptive simulations for investigating trends dominated by both physical (resistivity) and numerical (resolution) parameters, and confront them with (visco-)resistive magnetohydrodynamic simulations performed with very different, but equally widely used discretization schemes. This will allow us to comment on the obtained evolutions in a manner irrespective of the adopted discretization strategy. Our findings demonstrate that all schemes used (finite volume based shock-capturing, high order finite differences, and particle in cell-like methods) qualitatively agree on the various evolutionary stages, and that resistivity values of order 0.001 already can lead to chaotic island appearance. However, none of the methods exploited demonstrates convergence in the strong sense in these chaotic regimes. At the same time, nonperturbed tests for showing convergence over long time scales in ideal to resistive regimes are provided as well, where all methods are shown to agree. Both the advantages and disadvantages of specific discretizations as applied to this challenging problem are discussed.
eng
© 2013 AIP Publishing LLC
QC Physics
Resistive magnetohydrodynamic reconnection : resolving long-term, chaotic dynamics
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/5233/1/Galsgaard_2013_PoP_Resistive.pdf
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Galsgaard_2013_PoP_Resistive.pdf
URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/5233/3/Galsgaard_2013_PoP_Resistive.pdf.txt
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Galsgaard_2013_PoP_Resistive.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/115432024-02-26T00:43:09Zcom_10023_92com_10023_28com_10023_196com_10023_39com_10023_879com_10023_878col_10023_96col_10023_197col_10023_859col_10023_880
St Andrews Research Repository
author
O'Connor, John J.
author
Robertson, Edmund F.
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
institution
University of St Andrews. Applied Mathematics
2017-08-25T11:30:08Z
2017-08-25T11:30:08Z
2017-08-22
O'Connor , J J & Robertson , E F 2017 , ' Erwin Schrödinger and quantum wave mechanics ' , Quanta , vol. 6 , no. 1 , pp. 48-52 . https://doi.org/10.12743/quanta.v6i1.60
1314-7374
crossref: 10.12743/quanta.v6i1.60
https://hdl.handle.net/10023/11543
10.12743/quanta.v6i1.60
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.
eng
QC Physics
T-NDAS
Erwin Schrödinger and quantum wave mechanics
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/11543/1/O_Connor_2017_Quanta_QuantumWaveMechanics_CC.pdf
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O_Connor_2017_Quanta_QuantumWaveMechanics_CC.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/77722022-04-29T14:30:47Zcom_10023_165com_10023_39com_10023_28com_10023_792com_10023_309com_10023_879com_10023_878col_10023_166col_10023_859col_10023_795col_10023_311col_10023_880
St Andrews Research Repository
author
Read, Andrew, J.
author
Barco, S.
author
Bell, J.
author
Borchers, David Louis
author
Burt, M Louise
author
Cummings, E.W.
author
Dunn, J.
author
Fougeres, J.
author
Hazen, L.
author
Williams-Hodge, L.E.
author
Laura, A-M.
author
McAlarney, R.J.
author
Nilsson, P.
author
Pabst, D.A.
author
Paxton, Charles G. M.
author
Schneider, S.Z.
author
Urian, Kim
author
Waples, D.M.
author
McLellan, W.A.
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Marine Alliance for Science & Technology Scotland
institution
University of St Andrews. Scottish Oceans Institute
institution
University of St Andrews. Centre for Research into Ecological & Environmental Modelling
institution
University of St Andrews. St Andrews Sustainability Institute
2015-11-11T17:10:03Z
2015-11-11T17:10:03Z
2014
Read , A J , Barco , S , Bell , J , Borchers , D L , Burt , M L , Cummings , E W , Dunn , J , Fougeres , J , Hazen , L , Williams-Hodge , L E , Laura , A-M , McAlarney , R J , Nilsson , P , Pabst , D A , Paxton , C G M , Schneider , S Z , Urian , K , Waples , D M & McLellan , W A 2014 , ' Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA ' , Journal of Cetacean Research and Management , vol. 14 , pp. 23-35 .
1561-0713
PURE: 191849725
http://hdl.handle.net/10023/7772
https://archive.iwc.int/pages/preview.php?ref=3608&alternative=2475&k=&search=onslow%2C+bay%2C+year%3A2014&offset=0&order_by=relevance&sort=DESC&archive=0&
In this paper the occurrence, distribution and abundance of cetaceans in offshore waters of Onslow Bay, North Carolina, USA is described. Between June 2007 and June 2010 monthly aerial and shipboard line-transect surveys were conducted along ten 74km transects placed perpendicular to the shelf break. In total 42,676km of aerial trackline (218 sightings) and 5,209km of vessel trackline (100 sightings) were observed. Seven species of cetaceans were observed, but the fauna was dominated strongly by common bottlenose and Atlantic spotted dolphins. Both species were present year-round in the study area. Using photo-identification techniques, five bottlenose dolphins and one spotted dolphin were resighted during the three-year period. In general, the abundance of cetaceans in Onslow Bay was low and too few sightings were made to estimate monthly abundances for species other than bottlenose and spotted dolphins. Maximum monthly abundances of bottlenose and spotted dolphins were 4,100 (95% CI: 1,300–9,400) in May 2010 and 6,000 (95% CI: 2,500–17,400) in March 2009, respectively. Bottlenose dolphins were found throughout the study area, although they were encountered most frequently just off the shelf break. In contrast, spotted dolphins exhibited a strong preference for waters over the continental shelf and were not encountered beyond the shelf break.
eng
Copyright The Authors 2014. Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA, Read, A. J., Barco, S., Bell, J., Borchers, D. L., Burt, M. L., Cummings, E. W., Dunn, J., Fougeres, J., Hazen, L., Williams-Hodge, L. E., Laura, A-M., McAlarney, R. J., Nilsson, P., Pabst, D. A., Paxton, C. G. M., Schneider, S. Z., Urian, K., Waples, D. M. & McLellan, W. A. 2014 In : Journal of Cetacean Research and Management. 14, p. 23-35. Deposited in accordance with the journal not-for-profit open access policy.
Abundance estimate
Monitoring
Survey-combined
Trends
Photo-ID
GB Physical geography
QA Mathematics
QH301 Biology
Occurrence, distribution and abundance of cetaceans in Onslow Bay, North Carolina, USA
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/7772/1/RS3608_JCRM_14_Full_copy.pdf_14_pp023_036_Read.pdf
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97405030c12c8f74530a2fe2b3c735ef
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application/pdf
RS3608_JCRM_14_Full_copy.pdf_14_pp023_036_Read.pdf
URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/7772/3/RS3608_JCRM_14_Full_copy.pdf_14_pp023_036_Read.pdf.txt
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RS3608_JCRM_14_Full_copy.pdf_14_pp023_036_Read.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/47192023-04-18T09:51:33Zcom_10023_28com_10023_879com_10023_878col_10023_859col_10023_880
St Andrews Research Repository
author
Doostie, H.
author
Campbell, P.P.
institution
University of St Andrews. School of Mathematics and Statistics
2014-05-07T11:01:03Z
2014-05-07T11:01:03Z
2006
Doostie , H & Campbell , P P 2006 , ' On the commutator lengths of certain classes of finitely presented groups ' , International Journal of Mathematics and Mathematical Sciences , vol. 2006 , 74981 . https://doi.org/10.1155/IJMMS/2006/74981
0161-1712
PURE: 116545106
http://hdl.handle.net/10023/4719
https://doi.org/10.1155/IJMMS/2006/74981
http://www.scopus.com/inward/record.url?eid=2-s2.0-33749513941&partnerID=8YFLogxK
For a finite group G = 〈X〉 (X ≠ G), the least positive integer ML(G) is called the maximum length of G with respect to the generating set X if every element of G maybe represented as a product of at most ML(G) elements of X. The maximum length of G, denoted by ML (G), is defined to be the minimum of {ML(G) G = 〈X〉, X ≠ G, X ≠ G - {1}}. The well-known commutator length of a group G, denoted by c (G), satisfies the inequality c (G) ≤ ML(G′), where G′ is the derived subgroup of G. In this paper we study the properties of ML (G) and by using this inequality we give upper bounds for the commutator lengths of certain classes of finite groups. In some cases these upper bounds involve the interesting sequences of Fibonacci and Lucas numbers.
eng
© 2006 Doostie et al. This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are credited.
QA Mathematics
On the commutator lengths of certain classes of finitely presented groups
Journal article
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doostie2006intjmathsci74981.pdf.txt
oai:research-repository.st-andrews.ac.uk:10023/43562023-04-25T23:37:52Zcom_10023_165com_10023_39com_10023_28com_10023_879com_10023_878col_10023_166col_10023_859col_10023_880
St Andrews Research Repository
author
Schick, Robert Schilling
author
Roberts, Jason
author
Eckert, Scott
author
Clark, James
author
Bailey, Helen
author
Chai, Fei
author
Shi, Li
author
Halpin, Patrick
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Centre for Research into Ecological & Environmental Modelling
2014-01-13T10:01:05Z
2014-01-13T10:01:05Z
2013-11-20
Schick , R S , Roberts , J , Eckert , S , Clark , J , Bailey , H , Chai , F , Shi , L & Halpin , P 2013 , ' Pelagic movements of pacific leatherback turtles ( Dermochelys coriacea ) reveal the complex role of prey and ocean currents ' , Movement Ecology , vol. 1 , no. 11 , 11 . https://doi.org/10.1186/2051-3933-1-11
2051-3933
PURE: 84738893
http://hdl.handle.net/10023/4356
https://doi.org/10.1186/2051-3933-1-11
Background: Leatherback turtles are renowned for their trans-oceanic migrations. However, despite numerous movement studies, the precise drivers of movement patterns in leatherbacks remain elusive. Many previous studies of leatherback turtles as well as other diving marine predators have analyzed surface movement patterns using only surface covariates. Since turtles and other marine predators spend the vast majority of their time diving under water, an analysis of movement patterns at depth should yield insight into what drives their movements. Results: We analyzed the movement paths of 15 post-nesting adult female Pacific leatherback turtles, which were caught and tagged on three nesting beaches in Mexico. The temporal length of the tracks ranged from 32 to 436 days, and the spatial distance covered ranged from 1,532 km to 13,097 km. We analyzed these tracks using a movement model designed to yield inference on the parameters driving movement. Because the telemetry data included diving depths, we extended an earlier version of the model that examined surface only movements, and here analyze movements in 3-dimensions. We tested the effect of dynamic environmental covariates from a coupled biophysical oceanographic model on patch choice in diving leatherback turtles, and compared the effects of parameters measured at the surface and at depth. The covariates included distance to future patch, temperature, salinity, meridional current velocity (current in the north–south direction), zonal current velocity (current in the east–west direction), phytoplankton density, diatom density, micro-plankton density, and meso-zooplankton density. We found significant, i.e. non-zero, correlation between movement and the parameters for oceanic covariates in 8 of the tracks. Of particular note, for one turtle we observed a lack of correlation between movements and a modeled index of zooplankton at the surface, but a significant correlation between movements and zooplankton at depth. Two of the turtles express a preference for patches at depth with elevated diatoms, and 2 turtles prefer patches with higher mezozooplankton values at depth. In contrast, 4 turtles expressed a preference for elevated zooplankton patches at the surface, but not at depth. We suggest that our understanding of a marine predator’s response to the environment may change significantly depending upon the analytical frame of reference, i.e. whether relationships are examined at the surface, at depth, or at different temporal resolutions. Lastly, we tested the effects of accounting for ocean currents on the movement patterns and found that for 13 of the 15 turtles, the parameter governing distance to the next patch decreased. Conclusions: Our results suggest that relationships derived from the analysis of surface tracks may not entirely explain movement patterns of this highly migratory species. Accounting for choices in the water column has shown that for certain individual turtles, what appears to be favourable habitat at depth is quantitatively different from that at the surface. This has implications for the analysis of the movements and diving behaviour of any top marine predator. The leatherback turtle is a deep diving reptile, and it is important to understand the subsurface variables that influence their movements if we are to precisely map the spatial dimensions of favorable leatherback habitat. These results present a new view into the drivers of diving patterns in turtles, and in particular represent a way of analyzing movements at depth that can be extended to other diving species.
eng
© 2013 Schick et al.; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
Movement
Bayesian
Habitat suitability
Water column
Diving
Leatherback turtles
Marine predator
Dynamic covariates
Prey
Q Science
QL Zoology
SDG 14 - Life Below Water
Pelagic movements of pacific leatherback turtles (Dermochelys coriacea) reveal the complex role of prey and ocean currents
Journal article
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URL
https://research-repository.st-andrews.ac.uk/bitstream/10023/4356/1/2051_3933_1_11.pdf
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oai:research-repository.st-andrews.ac.uk:10023/40732023-04-18T09:46:34Zcom_10023_165com_10023_39com_10023_28com_10023_792com_10023_879com_10023_878col_10023_166col_10023_859col_10023_795col_10023_880
St Andrews Research Repository
author
Langrock, Roland
author
King, Ruth
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Scottish Oceans Institute
institution
University of St Andrews. Centre for Research into Ecological & Environmental Modelling
2013-10-04T13:31:01Z
2013-10-04T13:31:01Z
2013
Langrock , R & King , R 2013 , ' Maximum likelihood estimation of mark-recapture-recovery models in the presence of continuous covariates ' , Annals of Applied Statistics , vol. 7 , no. 3 , pp. 1709-1732 . https://doi.org/10.1214/13-AOAS644
1932-6157
PURE: 28450207
http://hdl.handle.net/10023/4073
https://doi.org/10.1214/13-AOAS644
http://www.e-publications.org/ims/submission/index.php/AOAS/user/submissionFile/14235?confirm=c4a65131
We consider mark-recapture-recovery (MRR) data of animals where the model parameters are a function of individual time-varying continuous covariates. For such covariates, the covariate value is unobserved if the corresponding individual is unobserved, in which case the survival probability cannot be evaluated. For continuous-valued covariates, the corresponding likelihood can only be expressed in the form of an integral that is analytically intractable, and, to date, no maximum likelihood approach that uses all the information in the data has been developed. Assuming a first-order Markov process for the covariate values, we accomplish this task by formulating the MRR setting in a state-space framework and considering an approximate likelihood approach which essentially discretizes the range of covariate values, reducing the integral to a summation. The likelihood can then be efficiently calculated and maximized using standard techniques for hidden Markov models. We initially assess the approach using simulated data before applying to real data relating to Soay sheep, specifying the survival probability as a function of body mass. Models that have previously been suggested for the corresponding covariate process are typically of the form of di.usive random walks. We consider an alternative non-di.usive AR(1)-type model which appears to provide a significantly better fit to the Soay sheep data.
eng
Copyright (c) 2013 Institute of Mathematical Statistics
Arnason-Schwarz model
Hidden Markov model
Markov chain
Missing values
Soay sheep
State-space model
QA Mathematics
Maximum likelihood estimation of mark-recapture-recovery models in the presence of continuous covariates
Journal article
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URL
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oai:research-repository.st-andrews.ac.uk:10023/20042023-04-18T09:43:52Zcom_10023_196com_10023_39com_10023_28com_10023_879com_10023_878col_10023_197col_10023_859col_10023_880
St Andrews Research Repository
author
Dolinka, Igor
author
Ruskuc, Nik
sponsor
EPSRC
institution
University of St Andrews. School of Mathematics and Statistics
institution
University of St Andrews. Centre for Interdisciplinary Research in Computational Algebra
2011-09-19T08:57:01Z
2011-09-19T08:57:01Z
2011-09
Dolinka , I & Ruskuc , N 2011 , ' Finite groups are big as semigroups ' , Archiv der Mathematik , vol. 97 , no. 3 , pp. 209-217 . https://doi.org/10.1007/s00013-011-0297-3
0003-889X
PURE: 13162230
http://hdl.handle.net/10023/2004
https://doi.org/10.1007/s00013-011-0297-3
EP/H011978/1
We prove that a finite group G occurs as a maximal proper subsemigroup of an infinite semigroup (in the terminology of Freese, Ježek, and Nation, G is a big semigroup) if and only if |G| ≥ 3. In fact, any finite semigroup whose minimal ideal contains a subgroup with at least three elements is big.
eng
This is an author version of this article. The original publication is available at www.springerlink.com copyright (c) 2011 Springer Basel AG.
Finite maximal subsemigroup
Rees matrix semigroup
QA Mathematics
Finite groups are big as semigroups
Journal article
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