2024-03-28T08:37:01Z
https://eprints.maths.manchester.ac.uk/cgi/oai2
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:103
2017-10-20T14:12:02Z
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https://eprints.maths.manchester.ac.uk/103/
Interpretation, coordination and conformity
Hosni, Hykel
03 Mathematical logic and foundations
91 Game theory, economics, social and behavioral sciences
The aim of this note is to investigate a very general problem of (radical) interpretation in terms of a simple coordination game: the conformity game. We show how, within our mathematical framework, the solution concept for the conformity game does indeed provide an algorithmic procedure facilitating triangulation, in the sense of Davidson.
Springer
Pietarinen, Ahti-Veikko
Majer, Ondrej
Tulenheimo, Tero
2005-06
Book Section
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/103/1/interpretation_coordination_and_conformity.pdf
Hosni, Hykel (2005) Interpretation, coordination and conformity. In: Logic and Games: Foundational Perspectives. Springer. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:120
2017-11-08T23:18:16Z
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https://eprints.maths.manchester.ac.uk/120/
Universal connection and curvature for statistical manifold geometry
Arwini, Khadiga
Del Riego, L
Dodson, CTJ
53 Differential geometry
62 Statistics
Statistical manifolds are representations of smooth families of
probability density functions
that allow differential geometric methods to be applied to
problems in stochastic processes, mathematical statistics and
information theory. It is common to have to consider a number of
linear connections on a given statistical manifold and so it is
important to know the corresponding universal connection and
curvature; then all linear connections and their curvatures are
pullbacks. An important class of statistical manifolds is that
arising from the exponential families and one particular family is
that of gamma distributions, which we showed recently to have
important uniqueness properties in stochastic processes. Here we
provide formulae for universal connections and curvatures on
exponential families and give an explicit example for the manifold
of gamma distributions.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/120/1/univconexpf.pdf
Arwini, Khadiga and Del Riego, L and Dodson, CTJ (2005) Universal connection and curvature for statistical manifold geometry. Houston Journal of Mathematics, In pre. ISSN 0362-1588 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:127
2017-10-20T14:12:03Z
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https://eprints.maths.manchester.ac.uk/127/
Isomorphism classes for Banach vector bundle structures of second
tangents
Dodson, CTJ
Galanis, GN
Vassiliou, E
53 Differential geometry
58 Global analysis, analysis on manifolds
On a smooth Banach manifold M,$the equivalence classes of curves
that agree up to acceleration form the second order tangent bundle
T^2M of M.
This is a vector bundle in the presence of a linear connection on
M and the corresponding local structure is heavily dependent on
the choice of connection. In this paper we study the extent of this
dependence and we prove that it is closely related to the notions
of conjugate connections and
second order differentials. In particular, the vector bundle structure on
T^2M remains invariant under conjugate connections with respect
to diffeomorphisms of M.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/127/1/isomt2m.pdf
Dodson, CTJ and Galanis, GN and Vassiliou, E (2005) Isomorphism classes for Banach vector bundle structures of second tangents. Math. Proc. Camb. Phil. Soc.. ISSN 0305-0041 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:185
2017-10-20T14:12:05Z
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https://eprints.maths.manchester.ac.uk/185/
Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves.
Parnell, William J
Abrahams, I David
35 Partial differential equations
74 Mechanics of deformable solids
The effective response of a periodic fibre reinforced material to SH wave propagation is studied using the method of asymptotic homogenization, complex variable theory and multipole expansions. The quasi-static limit of the effective properties is calculated when the wavelength is much longer than the defining lengthscale of the microstructure. The method developed allows the determination of the elastic properties in the most general (monoclinic) fibre reinforced media and the resulting expressions for the effective moduli are concise. The method is therefore both more general and provides neater closed form solutions than extant methods. Results are shown to be excellent even for very high volume fractions of fibres.
2005-07-01
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/185/1/Dynamic_Homogenization.pdf
Parnell, William J and Abrahams, I David (2005) Dynamic homogenization in periodic fibre reinforced media. Quasi-static limit for SH waves. Wave Motion, 43 (6). pp. 474-498. ISSN 0165-2125 (In Press)
http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%235553%232006%23999569993%23624815%23FLA%23&_cdi=5553&_pubType=J&_auth=y&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=929ebf84f462f09b0171708643e8a113
10.1016/j.wavemoti.2006.03.003
10.1016/j.wavemoti.2006.03.003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:201
2017-10-20T14:12:05Z
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7375626A656374733D4D5343:4D53435F3230
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/201/
Standard tableaux and Klyachko's Theorem on Lie representations
Johnson, Marianne
05 Combinatorics
17 Nonassociative rings and algebras
20 Group theory and generalizations
We show that for all but two partitions $\lambda$ of $n >6$ there exists a standard tableau of shape $\lambda$ with major index coprime to $n$. In conjunction with a deep result of Kra{\'s}kiewicz and Weyman this provides a new purely combinatorial proof of Klyachko's famous theorem on Lie representations of the general linear group.
Manchester Institute for the Mathematical Sciences
2005-10-10
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/201/1/Preprint.pdf
Johnson, Marianne (2005) Standard tableaux and Klyachko's Theorem on Lie representations. Journal of Combinatorial Theory, Series A. ISSN 1749-9097 (In Press)
http://www.sciencedirect.com/science/journal/00973165
10.1016/j.jcta.2006.02.002
10.1016/j.jcta.2006.02.002
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:233
2017-10-20T14:12:06Z
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https://eprints.maths.manchester.ac.uk/233/
Review of Bridges from Classical to Nonmonotonic Logic by David Makinson
Hosni, Hykel
03 Mathematical logic and foundations
2006-09
Article
PeerReviewed
application/postscript
en
https://eprints.maths.manchester.ac.uk/233/1/makinson.ps
Hosni, Hykel (2006) Review of Bridges from Classical to Nonmonotonic Logic by David Makinson. Bulletin of Symbolic Logic, 12 (03). ISSN 1079-8986 (In Press)
http://www.math.ucla.edu/~asl/bsl/1203/1203-004.ps
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:292
2017-10-20T14:12:08Z
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https://eprints.maths.manchester.ac.uk/292/
Krull-Gabriel dimension of 1-domestic string algebras
Prest, Mike
Puninski, Gena
03 Mathematical logic and foundations
16 Associative rings and algebras
We classify indecomposable pure injective modules over a wide class of 1-domestic string algebras and calculate the Krull–Gabriel dimension of these algebras.
2002
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/292/1/prepunkgg.pdf
Prest, Mike and Puninski, Gena (2002) Krull-Gabriel dimension of 1-domestic string algebras. Algebras and Representation Theory. ISSN 1386-923X (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:306
2017-10-20T14:12:08Z
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7375626A656374733D50414353:504143535F3430:504143535F3436
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/306/
Coupled thermoelasticity in a composite half-space
Parnell, William J
74 Mechanics of deformable solids
46 Continuum mechanics of solids
The problem of fully coupled thermoelasticity in a composite half-space is considered where the composite has variations in its physical properties in one direction only. The resulting one-dimensional problem thus depends on the so-called microscale of the composite. Homogenization of the fully coupled theory provides the leading order system of coupled equations (independent of the microscale) together with the effective physical properties of the thermoelastic medium. In particular the effective coupling parameter δ is found and it is shown to exhibit rather interesting properties; for a range of volume fractions in two-phase composites it is shown that δ lies below the corresponding coupling parameter for a homogeneous material made up of either phase. Transient boundary value problems of the homogenized system are then solved and compared with the classical problem of a homogeneous half-space. The magnitude of resulting discontinuities in field variables and their derivatives are found and their dependence on the effective coupling parameter is exhibited.
2005-10-03
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/306/1/therm.pdf
Parnell, William J (2005) Coupled thermoelasticity in a composite half-space. Journal of Engineering Mathematics. ISSN 0022-0833 (In Press)
http://dx.doi.org/10.1007/s10665-006-9038-1
10.1007/s10665-006-9038-1
10.1007/s10665-006-9038-1
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:594
2017-10-20T14:12:19Z
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7375626A656374733D4D5343:4D53435F3635
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/594/
Computed eigenmodes of planar regions
Trefethen, Lloyd N.
Betcke, Timo
35 Partial differential equations
65 Numerical analysis
Recently developed numerical methods make possible the high-accuracy computation of eigenmodes of the Laplacian for a variety of "drums" in two dimensions. A number of computed examples are presented together with a discussion of their implications concerning bound and continuum states, isospectrality, symmetry and degeneracy, eigenvalue avoidance, resonance, localization, eigenvalue optimization, perturbation of eigenvalues and eigenvectors, and other matters.
2005
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/594/1/trefethen_updated.pdf
Trefethen, Lloyd N. and Betcke, Timo (2005) Computed eigenmodes of planar regions. AMS Contemporary Mathematics. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:645
2017-10-20T14:12:20Z
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74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/645/
Convolution roots and embedding of probability measures on Lie groups
Dani, S. G.
McCrudden, M.
22 Topological groups, Lie groups
We show that for a large class of connected Lie groups $G$, viz. from \emph{class} $\mathcal{C}$ described below, given a probability measure μ on $G$ and a natural number $n$, for any sequence $\{\nu_i\}$ of $n$th convolution roots of μ there exists a sequence $\{z_i\}$ of elements of G, centralising the support of μ, and such that $\{z_i \nu_i \z_i^{-1}\} is relatively compact; thus the set of roots is relatively compact ‘modulo’ the conjugation action of the centraliser of supp μ. We also analyse the dependence of the sequence $\{z_i\}$ on $n$. The results yield a simpler and more transparent proof of the embedding theorem for infinitely divisible probability measures on the Lie groups as above, proved in [S.G. Dani, M. McCrudden, Embeddability of infinitely divisible distributions on linear Lie groups, Invent. Math. 110 (1992) 237–261].
2006
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/645/1/Convolution_Roots.pdf
Dani, S. G. and McCrudden, M. (2006) Convolution roots and embedding of probability measures on Lie groups. Advances in Mathematics. ISSN 0001-8708 (In Press)
http://www.sciencedirect.com/science?_ob=PublicationURL&_tockey=%23TOC%236681%239999%23999999999%2399999%23FLP%23&_cdi=6681&_pubType=J&view=c&_auth=y&_acct=C000010021&_version=1&_urlVersion=0&_userid=121749&md5=119094a9cbbd012135a7d4215a95e1f9
10.1016/j.aim.2006.05.002
10.1016/j.aim.2006.05.002
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:697
2017-10-20T14:12:22Z
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https://eprints.maths.manchester.ac.uk/697/
Antigenicity and immunogenicity of HIV-1 consensus subtype B
envelope glycoproteins
Kothe, Denise L.
Decker, Julie M.
Li, Yingying
Weng, Zhiping
Bibollet-Ruche, Frederic
Zammit, Kenneth P.
Slazar, Maraia G.
Chen, Yalu
Salazar-Gonzalez, Jesus F.
Moldoveanu, Zina
Mestecky, Jiri
Gao, Feng
Haynes, Barton F.
Shaw, George M.
Muldoon, Mark
Korber, Bette T. M.
Hahn, Beatrice H.
62 Statistics
92 Biology and other natural sciences
“Centralized” (ancestral and consensus) HIV-1 envelope immunogens induce broadly cross-reactive T cell responses in laboratory animals; however, their potential to elicit cross-reactive neutralizing antibodies has not been fully explored. Here, we report the construction of a panel of consensus subtype B (ConB) envelopes and compare their biologic, antigenic, and immunogenic properties to those of two wild-type Env controls from individuals with early and acute HIV-1 infection. Glycoprotein expressed from full-length (gp160), uncleaved (gp160-UNC), truncated (gp145), and N-linked glycosylation site deleted (gp160-201N/S) versions of the ConB env gene were packaged into virions and, except for the fusion defective gp160-UNC, mediated infection via the CCR5 co-receptor. Pseudovirions containing ConB Envs were sensitive to neutralization by patient plasma and monoclonal antibodies, indicating the preservation of neutralizing epitopes found in contemporary subtype B viruses. When used as DNA vaccines in guinea pigs, ConB and wild-type env immunogens induced appreciable binding, but overall only low level neutralizing antibodies. However, all four ConB immunogens were significantly more potent than one wild-type vaccine at eliciting neutralizing antibodies against a panel of tier 1 and tier 2 viruses, and ConB gp145 and gp160 were significantly more potent than both wild-type vaccines at inducing neutralizing antibodies against tier 1 viruses. Thus, consensus subtype B env immunogens appear to be at least as good as, and in some instances better than, wild-type B env immunogens at inducing a neutralizing antibody response, and are amenable to further improvement by specific gene modifications.
2007-03-30
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/697/2/Kothe_Virology360.pdf
Kothe, Denise L. and Decker, Julie M. and Li, Yingying and Weng, Zhiping and Bibollet-Ruche, Frederic and Zammit, Kenneth P. and Slazar, Maraia G. and Chen, Yalu and Salazar-Gonzalez, Jesus F. and Moldoveanu, Zina and Mestecky, Jiri and Gao, Feng and Haynes, Barton F. and Shaw, George M. and Muldoon, Mark and Korber, Bette T. M. and Hahn, Beatrice H. (2007) Antigenicity and immunogenicity of HIV-1 consensus subtype B envelope glycoproteins. Virology, 360 (1). pp. 218-234. ISSN 0042-6822 (In Press)
10.1016/j.virol.2006.10.017
10.1016/j.virol.2006.10.017
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:829
2017-10-20T14:12:27Z
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https://eprints.maths.manchester.ac.uk/829/
A Note on Binary Inductive Logic
Nix, C. J.
Paris, J. B.
03 Mathematical logic and foundations
We consider the problem of induction over languages containing binary
relations and outline a way of interpreting and constructing a class of
probability functions on the sentences of such a language. Some principles
of inductive reasoning satisfied by these probability functions are discussed,
leading in turn to a representation theorem for a more general class of
probability functions satisfying these principles.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/829/1/A_Note_on_Binary_Inductive_Logic.pdf
Nix, C. J. and Paris, J. B. (2007) A Note on Binary Inductive Logic. Journal of Philosophical Logic. xxx-xxx. ISSN 1573-0433 (In Press)
http://www.springerlink.com/content/100295/
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:848
2017-10-20T14:12:28Z
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https://eprints.maths.manchester.ac.uk/848/
Linear groups of finite Morley rank
Borovik, Alexandre
20 Group theory and generalizations
This paper is a brief survey of recent results and some open
problems related to linear groups of finite Morley rank, an area of research where Bruno Poizat's impact is very prominent. As a sign of respect to his strongly expressed views that mathematics has to be done, written and published only in the native tongue of the immediate author---the scribe, in effect---of the text, I insist on writing my paper in Russian, even if the results presented belong to a small but multilingual community of researchers of American, British, French, German, Kazakh, Russian, Turkish origin. To emphasise even further the linguistic subtleties involved, I use British spelling in the English fragments of my text.
2008
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/848/1/AVB-LugdunensisK.pdf
Borovik, Alexandre (2008) Linear groups of finite Morley rank. Journal of the Institute of Mathematics of Jussieu, 7. ISSN 1474-7480 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:867
2017-10-20T14:12:28Z
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https://eprints.maths.manchester.ac.uk/867/
A weak embedding property of probability measures on Lie groups
Dani, S.G.
McCrudden, M.
22 Topological groups, Lie groups
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/867/1/New_Weak_Embedding.pdf
Dani, S.G. and McCrudden, M. (2007) A weak embedding property of probability measures on Lie groups. Mathematical Research Letters. (In Press)
http://www.mrlonline.org/mrl/
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:955
2017-10-20T14:12:32Z
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7375626A656374733D4D5343:4D53435F3335
7375626A656374733D4D5343:4D53435F3734
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https://eprints.maths.manchester.ac.uk/955/
A brief historical perspective of the Wiener-Hopf technique
Lawrie, Jane B.
Abrahams, I. David
35 Partial differential equations
74 Mechanics of deformable solids
It is a little over 75 years since two of the most important mathematicians of the 20th century collaborated on finding the exact solution of a particular equation with semi-infinite convolution type integral operator. The elegance and analytical sophistication of the method, now called the Wiener–Hopf technique, impress all who use it. Its applicability to almost all branches of engineering, mathematical physics and applied mathematics is borne out by the many thousands of papers published on the subject since its conception. The Wiener–Hopf technique remains an extremely important tool for modern scientists, and the areas of application continue to broaden. This special issue of the Journal of Engineering Mathematics is dedicated to the work of Wiener and Hopf, and includes a number of articles which demonstrate the relevance of the technique to a representative range of model problems.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/955/1/A_Brief_Historical.pdf
Lawrie, Jane B. and Abrahams, I. David (2007) A brief historical perspective of the Wiener-Hopf technique. Journal of Engineering Mathematics, 59 (4). pp. 351-358. ISSN 1573-2703 (In Press)
http://www.springerlink.com/content/u8837j172320/?p=0b5ab3705e5648048776604ef36102af&pi=0
10.1007/s10665-007-9195-x
10.1007/s10665-007-9195-x
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:961
2017-10-20T14:12:32Z
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7375626A656374733D4D5343:4D53435F3335
7375626A656374733D4D5343:4D53435F3734
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/961/
Pricing financial claims contingent upon an underlying asset monitored at discrete times
Green, Ross
Abrahams, I. David
Fusai, Gianluca
35 Partial differential equations
74 Mechanics of deformable solids
Exotic option contracts typically specify a contingency upon an underlying asset price monitored at a discrete set of times. Yet, techniques used to price such options routinely assume continuous monitoring leading to often substantial price discrepancies. A brief review of relevant option-pricing methods is presented. The pricing problem is transformed into one of Wiener–Hopf type using a z-transform in time and a Fourier transform in the logarithm of asset prices. The Wiener–Hopf technique is used to obtain probabilistic identities for the related random walks killed by an absorbing boundary. An accurate and efficient approximation is obtained using Padé approximants and an approximate inverse z-transform based on the trapezoidal rule. For simplicity, European barrier options in a Gaussian Black–Scholes framework are used to exemplify the technique (for which exact analytic expressions are obtained). Extensions to different option contracts and options driven by other Lévy processes are discussed.
2007
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/961/1/Pricing_Financial_Claims.pdf
Green, Ross and Abrahams, I. David and Fusai, Gianluca (2007) Pricing financial claims contingent upon an underlying asset monitored at discrete times. Journal of Engineering Mathematics, 59 (4). pp. 373-384. ISSN 1573-2703 (In Press)
http://www.springerlink.com/content/v538723v5r5u0240/?p=ef2781caf0894896be4f3b3e6367c08e&pi=2
10.1007/s10665-007-9176-0
10.1007/s10665-007-9176-0
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:962
2017-10-20T14:12:32Z
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7375626A656374733D4D5343:4D53435F3335
7375626A656374733D4D5343:4D53435F3734
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/962/
The effect of surface tension on trapped modes in water-wave problems
Harter, R.
Abrahams, I. David
Simon, M. J.
35 Partial differential equations
74 Mechanics of deformable solids
In this paper the effect of surface tension is considered on two two-dimensional water-wave problems involving pairs of immersed bodies. Both models, having fluid of infinite depth, support localized oscillations, or trapped modes, when capillary effects are excluded. The first pair of bodies is surface-piercing whereas the second pair is fully submerged. In the former case it is shown that the qualitative nature of the streamline shape is unaffected by the addition of surface tension in the free surface condition, no matter how large this parameter becomes. The main objective of this paper, however, is to study the submerged body problem. For this case it is found, by contrast, that there exists a critical value of the surface tension above which it is no longer possible to produce a completely submerged pair of bodies which support trapped modes. This critical value varies as a function of the separation of the two bodies. It can be inferred from this that surface tension does not always play a qualitatively irrelevant role in the linear water-wave problem.
2007-12-08
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/962/1/The_Effect_of_Surface_Tension.pdf
Harter, R. and Abrahams, I. David and Simon, M. J. (2007) The effect of surface tension on trapped modes in water-wave problems. Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences, 463 (2088). pp. 3131-3149. ISSN 1471-2946 (In Press)
http://www.journals.royalsoc.ac.uk/content/w620428x23135x48/?p=aaa9be72d7e84db996c2b67bfd962d7c&pi=51
10.1098/rspa.2007.0063
10.1098/rspa.2007.0063
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:971
2017-10-20T14:12:33Z
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74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/971/
Complex dynamics of shear banded flows
Fielding, S.M.
74 Mechanics of deformable solids
Many complex fluids undergo a flow induced transition to a state of coexisting bands of differing viscosities and internal structuring. This effect, which is called shear banding, is widely observed in wormlike micellar surfactants, onion surfactants, colloidal suspensions and polymer solutions. According to a rapidly accumulating body of experimental evidence, shear bands often exhibit complex dynamics, which can be either oscillatory or chaotic in nature. This can be seen in the unsteady response of the bulk rheological signals, and in the motion of the interface between the bands. After giving a brief overview of this experimental evidence, we review in some detail recent efforts to address it theoretically.
2007
Article
PeerReviewed
application/pdf
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https://eprints.maths.manchester.ac.uk/971/1/Fielding_SoftMatter3.pdf
Fielding, S.M. (2007) Complex dynamics of shear banded flows. Soft Matter, 3. 1262 -1279. ISSN 1744-683X (In Press)
http://www.rsc.org/publishing/journals/SM/article.asp?doi=b707980j
10.1039/b707980j
10.1039/b707980j
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Lie powers and Witt vectors
Bryant, R. M.
Johnson, Marianne
11 Number theory
17 Nonassociative rings and algebras
20 Group theory and generalizations
In the study of Lie powers of a module $V$ in prime characteristic $p$, a basic role is played by certain modules $B_n$ introduced by Bryant and Schocker. The isomorphism types of the $B_n$ are not fully understood, but these modules fall into infinite families $\{ B_k, B_{pk}, B_{p^2 k}, \dots \}$, one family $B(k)$ for each positive integer $k$ not divisible by $p$, and there is a recursive formula for the modules within $B(k)$. Here we use combinatorial methods and Witt vectors to show that each module in $B(k)$ is isomorphic to a direct sum of tensor products of direct summands of the $k$th tensor power $V^{\otimes k}$.
2008-01-10
Article
PeerReviewed
application/pdf
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https://eprints.maths.manchester.ac.uk/1004/1/Lie_powers_and_Witt_vectors_%28Bryant_and_Johnson%29.pdf
Bryant, R. M. and Johnson, Marianne (2008) Lie powers and Witt vectors. Journal of Algebraic Combinatorics. ISSN 0925-9899 (In Press)
http://www.springerlink.com/
10.1007/s10801-007-0117-9
10.1007/s10801-007-0117-9
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1009
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Geometric Brownian Motion with delay: mean square characterisation
Appleby, J.A.D.
Mao, X.
Riedle, M.
60 Probability theory and stochastic processes
A geometric Brownian motion with delay is the solution of a stochastic differential equation where the drift
and diffusion coefficient depend linearly on the past of the solution, i.e. a linear stochastic functional
differential equation. In this work the asymptotic behavior in mean square of a geometric Brownian motion
with delay is completely characterized by a sufficient and necessary condition in terms of the drift and
diffusion coefficients.
2007-11-15
Article
PeerReviewed
application/pdf
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https://eprints.maths.manchester.ac.uk/1009/1/geo_brown_SFDE-2.pdf
Appleby, J.A.D. and Mao, X. and Riedle, M. (2007) Geometric Brownian Motion with delay: mean square characterisation. Proceedings of the AMS. ISSN 0002-9939 (In Press)
http://www.ams.org/proc/
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An Invitation to Toric Topology: Vertex Four of a Remarkable Tetrahedron.
Buchstaber, Victor M
Ray, Nigel
55 Algebraic topology
57 Manifolds and cell complexes
2008-02-18
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1055/1/tortoptet6.pdf
Buchstaber, Victor M and Ray, Nigel (2008) An Invitation to Toric Topology: Vertex Four of a Remarkable Tetrahedron. Proceedings of the International Conference in Toric Topology: Osaka 2006. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1107
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https://eprints.maths.manchester.ac.uk/1107/
Information Geometry: Near Randomness and Near Independence
Arwini, Khadiga
Dodson, CTJ
53 Differential geometry
60 Probability theory and stochastic processes
The main motivation for this book lies in the breadth of applications
in which a statistical model is used to represent small departures
from, for example, a Poisson process. Our approach uses information geometry to provide
a common context but we need only rather elementary material from differential geometry, information theory and mathematical statistics. Introductory
sections serve together to help those
interested from the applications side in making use of our methods
and results.
Reported in this monograph is a body of results, and
computer-algebraic methods that seem to have quite general
applicability to statistical models admitting representation
through parametric families of probability density functions. Some
illustrations are given from a variety of contexts for geometric
characterization of statistical states near to the three important standard
basic reference states: (Poisson) randomness, uniformity, independence. The
individual applications are somewhat heuristic
models from various fields and we incline more to terminology and notation
from the applications rather than from formal statistics. However, a
common thread is a geometrical representation for statistical perturbations of the
basic standard states, and hence results gain qualitative stability.
Moreover, the geometry is controlled by a metric structure that
owes its heritage through maximum likelihood to information theory
so the quantitative features---lengths of curves, geodesics,
scalar curvatures etc.---have some respectable authority. We
see in the applications simple models for galactic
void distributions and galaxy clustering, amino acid clustering
along protein chains, cryptographic protection, stochastic fibre
networks, coupled geometric features in hydrology and quantum chaotic behaviour.
Springer-Verlag
2008-08-13
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1107/1/CoverArwiniDodsonLNM1953.pdf
Arwini, Khadiga and Dodson, CTJ (2008) Information Geometry: Near Randomness and Near Independence. Lecture Notes in Mathematics, 1953 . Springer-Verlag, Berlin, Heidelberg, Germany. ISBN 978-3-540-69391-8 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1109
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Numerical methods for palindromic eigenvalue problems:
Computing the anti-triangular Schur form
Mackey, D. Steven
Mackey, Niloufer
Mehl, Christian
Mehrmann, Volker
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
We present structure-preserving numerical methods
for the eigenvalue problem of complex palindromic pencils.
Such problems arise in control theory,
as well as from palindromic linearizations
of higher degree palindromic matrix polynomials.
A key ingredient of these methods
is the development of an appropriate condensed form ---
the anti-triangular Schur form.
Ill-conditioned problems with eigenvalues near the unit circle,
in particular near $\pm 1$, are discussed.
We show how a combination of unstructured methods
followed by a structured refinement
can be used to solve such problems accurately.
2007-08
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1109/1/MacMMM08_final.pdf
Mackey, D. Steven and Mackey, Niloufer and Mehl, Christian and Mehrmann, Volker (2007) Numerical methods for palindromic eigenvalue problems: Computing the anti-triangular Schur form. Numerical Linear Algebra with Applications. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1116
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https://eprints.maths.manchester.ac.uk/1116/
Conjugate connections and differential equations on infinite dimensional manifolds
Aghasi, M.
Dodson, C.T.J.
Galanis, G.N.
Suri, A.
53 Differential geometry
58 Global analysis, analysis on manifolds
On a smooth manifold M, the vector bundle structures of the second order
tangent bundle, T^2M bijectively correspond to linear connections. In this
paper we classify such structures for those Frechet manifolds which can
be considered as projective limits of Banach manifolds. We investigate also
the relation between ordinary differential equations on Frechet spaces
and the linear connections on their trivial bundle; the methodology extends
to solve differential equations on those Frechet manifolds which are
obtained as projective limits of Banach manifolds. Such equations arise in
theoretical physics. We indicate an extension of the Earle and Eells foliation theorem
to the Frechet case.
2008-07-08
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1116/1/Santiago2008_v2.pdf
Aghasi, M. and Dodson, C.T.J. and Galanis, G.N. and Suri, A. (2008) Conjugate connections and differential equations on infinite dimensional manifolds. In: VIII International Colloquium on Differential Geometry, 7-11 July 2008, Santiago de Compostela, Spain. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1235
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https://eprints.maths.manchester.ac.uk/1235/
A Formal Framework for User-centric Control of Multi-Agent Cyber-physical Systems
Bujorianu, Marius
Bujorianu, Manuela
Barringer, Howard
03 Mathematical logic and foundations
60 Probability theory and stochastic processes
Cyber physical systems are examples of a new emerging modelling paradigm that can be defined as multi-dimensional system co-engineering (MScE). In MScE, different aspects of complex systems are considered altogether, producing emergent properties, or loosing some useful ones. This holistic approach requires interdisciplinary methods that result from formal mathematical and AI co-engineering. In this paper, we propose a formal framework consisting of a reference model for multi-agent cyber physical systems, and a formal logic for expressing safety properties. The agents we consider are enabled with continuous physical mobility and evolve in an uncertain physical environment. Moreover, the model is user centric, by defining a complex control that considers the output of a runtime verification process, and possible commands of a human controller. The
formal logic, called safety analysis logic (SafAL), combines probabilities with epistemic operators. In SafAL, one can specify the reachability
properties of one agent, as well as prescriptive commands to the user. We define symmetry reduction semantics and a new concept of bisimulation for agents. A full abstraction theorem is presented, and it is proved that SafAL represents a logical characterization of bisimulation. A foundational study is carried out for model checking SafAL formulae against Markov models. A fundamental result states that the bisimulation preserves the probabilities of the reachable state sets.
Springer Verlag
Fisher, Michael
Sadri, Fariba
Thielscher, Michael
2009-02-19
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1235/1/clima.pdf
Bujorianu, Marius and Bujorianu, Manuela and Barringer, Howard (2009) A Formal Framework for User-centric Control of Multi-Agent Cyber-physical Systems. In: Proceeding of the 9th CLIMA workshop. Lecture Notes in Computer Science . Springer Verlag, Berlin, Germany. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1243
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Flux balance analysis: A geometric perspective
Smallbone, Kieran
Simeonidis, Evangelos
92 Biology and other natural sciences
Advances in the field of bioinformatics have led to reconstruction of genome-scale networks for a number of key organisms. The application of physicochemical constraints to these stoichiometric networks allows researchers, through methods such as flux balance analysis, to highlight key sets of reactions necessary to achieve particular objectives. The key benefits of constraint-based analysis lie in the minimal knowledge required to infer systemic properties. However, network degeneracy leads to a large number of flux distributions that satisfy any objective; moreover, these distributions may be dominated by biologically irrelevant internal cycles. By examining the geometry underlying the problem, we define two methods for finding a unique solution within the space of all possible flux distributions; such a solution contains no internal cycles, and is representative of the space as a whole. The first method draws on typical geometric knowledge, but cannot be applied to large networks because of the high computational complexity of the problem. Thus a second method, an iteration of linear programs which scales easily to the genome scale, is defined. The algorithm is run on four recent genome-scale models, and unique flux solutions are found. The algorithm set out here will allow researchers in flux balance analysis to exchange typical solutions to their models in a reproducible format. Moreover, having found a single solution, statistical analyses such as correlations may be performed.
2008-10-20
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1243/1/smallbone09.pdf
Smallbone, Kieran and Simeonidis, Evangelos (2008) Flux balance analysis: A geometric perspective. Journal of Theoretical Biology. ISSN 0022-5193 (In Press)
10.1016/j.jtbi.2009.01.027
10.1016/j.jtbi.2009.01.027
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1271
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On the entropy flows to disorder
Dodson, CTJ
60 Probability theory and stochastic processes
Gamma distributions, which contain the exponential as a
special case, have a distinguished place in the representation of
near-Poisson randomness for statistical processes; typically, they represent
distributions of spacings between events or voids among objects.
Here we look at the properties of the
Shannon entropy function and calculate its corresponding flow curves, relating
them to examples of constrained degeneration from ordered processes.
We consider also univariate and bivariate gamma, as well as Weibull distributions
since these include exponential distributions.
2008
Conference or Workshop Item
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1271/1/GammaEntropyFlows.pdf
Dodson, CTJ (2008) On the entropy flows to disorder. In: The 2nd Chaotic Modeling and Simulation International Conference, 1-5 June 2009, Charnia, Crete. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1280
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Capturing the essence of a metabolic network: A flux balance analysis approach
Murabito, Ettore
Simeonidis, Evangelos
Smallbone, Kieran
Swinton, Jonathan
92 Biology and other natural sciences
As genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux Balance Analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.
Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of a FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.
Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined.
2009
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1280/1/murabito09.pdf
Murabito, Ettore and Simeonidis, Evangelos and Smallbone, Kieran and Swinton, Jonathan (2009) Capturing the essence of a metabolic network: A flux balance analysis approach. Journal of Theoretical Biology. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1294
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Capturing the essence of a metabolic network: A flux balance analysis approach
Murabito, Ettore
Simeonidis, Evangelos
Smallbone, Kieran
Swinton, Jonathan
92 Biology and other natural sciences
As genome-scale metabolic reconstructions emerge, tools to manage their size and complexity will be increasingly important. Flux Balance Analysis (FBA) is a constraint-based approach widely used to study the metabolic capabilities of cellular or subcellular systems. FBA problems are highly underdetermined and many different phenotypes can satisfy any set of constraints through which the metabolic system is represented.
Two of the main concerns in FBA are exploring the space of solutions for a given metabolic network and finding a specific phenotype which is representative for a given task such as maximal growth rate. Here we introduce a recursive algorithm suitable for overcoming both of these concerns. The method proposed is able to find the alternate optimal patterns of active reactions of a FBA problem and identify the minimal subnetwork able to perform a specific task as optimally as the whole.
Our method represents an alternative to and an extension of other approaches conceived for exploring the space of solutions of an FBA problem. It may also be particularly helpful in defining a scaffold of reactions upon which to build up a dynamic model, when the important pathways of the system have not yet been well-defined.
2009-06-21
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1294/1/murabito09.pdf
Murabito, Ettore and Simeonidis, Evangelos and Smallbone, Kieran and Swinton, Jonathan (2009) Capturing the essence of a metabolic network: A flux balance analysis approach. Journal of Theoretical Biology. ISSN 0022-5193 (In Press)
10.1016/j.jtbi.2009.06.013
10.1016/j.jtbi.2009.06.013
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1323
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Nilpotent blocks of quasisimple groups for odd primes
An, Jianbei
Eaton, Charles W.
20 Group theory and generalizations
We investigate the nilpotent blocks of positive defect of the quasisimple groups for odd primes. In particular, it is shown that every nilpotent block of a quasisimple group has abelian defect groups. A conjecture of Puig concerning the recognition of nilpotent blocks is also shown for these groups.
2009-07
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1323/1/nilblkodd09final.pdf
An, Jianbei and Eaton, Charles W. (2009) Nilpotent blocks of quasisimple groups for odd primes. Journal für die reine und angewandte Mathematik (2009.6). ISSN 1749-9097 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1355
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On Davis-Januszkiewicz Homotopy Types II; completion and globalisation
Notbohm, Dietrich
Ray, Nigel
55 Algebraic topology
For any finite simplicial complex K, Davis and Januszkiewicz
have defined a family of homotopy equivalent CW-complexes whose integral cohomology rings are isomorphic to the Stanley-Reisner algebra of K. Subsequently, Buchstaber and Panov gave an alternative construction, which they showed to be homotopy equivalent to the original examples. It is therefore natural to investigate the extent to which the homotopy type of a space X is determined by such a cohomology ring. Having analysed this problem
rationally in Part I, we here consider it prime by prime, and utilise Lannes' T functor and Bousfield-Kan type obstruction theory to study the p-completion of X. We find the situation to be more subtle than for rationalisation, and confirm the uniqueness of the completion whenever K is a join of skeleta of simplices. We apply our results to the global problem by appealing to Sullivan's arithmetic square, and deduce integral uniqueness whenever the
Stanley-Reisner algebra is a complete intersection.
2008-12
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1355/1/djhtIIfinal.pdf
Notbohm, Dietrich and Ray, Nigel (2008) On Davis-Januszkiewicz Homotopy Types II; completion and globalisation. Algebraic and Geometric Topology, To app. ISSN 1472-2747 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1398
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Genetic analysis of wheat landraces enables the location of the first agricultural sites in Italy to be identified
Isaac, Andrew D.
Muldoon, Mark
Brown, Keri A.
Brown, Terence A.
92 Biology and other natural sciences
We typed five microsatellite loci in 52 landraces of Italian emmer wheat to determine if genetic analysis of cereals can provide information relevant to the spread of agriculture. Each of the five loci was polymorphic with 43 allele combinations identified in the 52 landraces. The allele combinations fell into two groups. Group 1 comprised 27 genotypes found in 42 landraces and Group 2 comprised 15 genotypes found in 10 landraces. The landraces with Group 1 genotypes showed a strong correlation between geographical and genetic distances (r = 0.601, p < 0.001) but those with Group 2 genotypes did not (r = 0.116, p = 0.244). We inferred that the Group 1 landraces might therefore retain a phylogeographical structure that reflects ancient events. We present a phylogeographical model for the spread of agriculture that enables the point of origin of crop cultivation to be predicted by comparison between the genetic and geographical distances between landraces. We applied this model to the Group 1 landraces by positioning 131 hypothetical points of origin around the coastline and northern border of Italy. The highest correlation coefficients between genetic and geographical distances were seen for hypothetical points of origin located on the coast of northern Puglia. We repeated the analysis with 1040 hypothetical points of origin located within the Italian peninsula. Again, the highest correlation coefficients were located in northern Puglia. These predicted points of origin correspond with the location of the earliest agricultural sites in Italy. The results show that plant genetics can be used to study the spread of agriculture.
2010-05-05
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1398/1/IsaacMuldoonBrownBrown_JArcheoSci.pdf
Isaac, Andrew D. and Muldoon, Mark and Brown, Keri A. and Brown, Terence A. (2010) Genetic analysis of wheat landraces enables the location of the first agricultural sites in Italy to be identified. Journal of Archaeological Science, 37 (5). pp. 950-956. ISSN 0305-4403 (In Press)
10.1016/j.jas.2009.11.028
10.1016/j.jas.2009.11.028
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1414
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A new bound for the smallest x with \pi(x) > \li(x)
Chao, Kuok Fai
Plymen, Roger
11 Number theory
We reduce the leading term in Lehman's theorem. This improved estimate allows us to refine the main theorem of Bays & Hudson[2]. Entering 2,000,000 zeta zeros, we prove that there exists x in the interval [exp(727.951858), exp(727.952178)] for which \pi(x) - li(x) > 3.2 \times 10^151. There are at least 10^154 successive integers x in this interval for which \pi(x) > li(x). This interval is strictly a sub-interval of the interval in Bays & Hudson, and is narrower by a factor of about 12.
2009
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1414/1/CP60.pdf
Chao, Kuok Fai and Plymen, Roger (2009) A new bound for the smallest x with \pi(x) > \li(x). International Journal of Number Theory. pp. 1-12. (In Press)
http://arxiv.org/abs/math.NT/0509312
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1466
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https://eprints.maths.manchester.ac.uk/1466/
Modelling Aspects of Tumour Metabolism
Maini, Philip K
Gatenby, Robert A
Smallbone, Kieran
92 Biology and other natural sciences
2010-03-10
Conference or Workshop Item
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1466/1/maini10.pdf
Maini, Philip K and Gatenby, Robert A and Smallbone, Kieran (2010) Modelling Aspects of Tumour Metabolism. In: International Congress of Mathematicians, 19-27 August 2010, Hyderabad, India. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1488
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https://eprints.maths.manchester.ac.uk/1488/
A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations
Liao, Qifeng
Silvester, David
65 Numerical analysis
76 Fluid mechanics
The implementation of quadratic velocity, linear pressure finite element approximation methods for the steady-state incompressible (Navier-)
Stokes equations is addressed in this work. Three types of a posteriori error indicator are introduced and are shown to give global error estimates that are equivalent to the true discretisation error. Computational results suggest that the solution of local Poisson problems provides a cost-effective error estimation strategy, both from the perspective of accurate estimation of the global error and for the purpose of selecting elements for refinement within a contemporary self-adaptive refinement algorithm.
2010-05-04
Article
PeerReviewed
application/pdf
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https://eprints.maths.manchester.ac.uk/1488/1/sdarticle.pdf
Liao, Qifeng and Silvester, David (2010) A simple yet effective a posteriori estimator for classical mixed approximation of Stokes equations. Applied Numerical Mathematics. ISSN 0168-9274 (In Press)
http://dx.doi.org/10.1016/j.apnum.2010.05.003
10.1016/j.apnum.2010.05.003
10.1016/j.apnum.2010.05.003
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Geometric structure in the principal series of the p-adic group G_2
Aubert, Anne-Marie
Baum, Paul
Plymen, Roger
20 Group theory and generalizations
22 Topological groups, Lie groups
In the representation theory of reductive $p$-adic groups
$G$, the issue of reducibility of induced representations is an
issue of great intricacy. It is our contention, expressed as a
conjecture in [3], that there exists a simple geometric structure
underlying this intricate theory.
We will illustrate here the conjecture with some detailed
computations in the principal series of $G_2$.
A feature of this article is the role played by cocharacters
$h_c$ attached to two-sided cells $c$ in certain extended
affine Weyl groups.
The quotient varieties which occur in the Bernstein programme are
replaced by extended quotients. We form the disjoint union
$A(G)$ of all these extended quotient varieties. We conjecture
that, after a simple algebraic correction, the space $A(G)$ is
a model of the smooth dual $Irr(G)$. In this respect, our
programme is a conjectural refinement of the Bernstein programme.
The algebraic correction is controlled by the cocharacters
$h_c$. The cocharacters themselves appear to be closely
related to Langlands parameters.
2010-07-30
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1505/1/principalG2_5.pdf
Aubert, Anne-Marie and Baum, Paul and Plymen, Roger (2010) Geometric structure in the principal series of the p-adic group G_2. Representation Theory. (In Press)
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Why does yeast ferment? A flux balance analysis study
Simeonidis, Evangelos
Murabito, Ettore
Smallbone, Kieran
Westerhoff, Hans V.
92 Biology and other natural sciences
Advances in biological techniques have led to the availability of genome-scale metabolic reconstructions for yeast. The size and complexity of such networks impose limits on what types of analyses one can perform. Constraint-based modelling overcomes some of these restrictions by using physicochemical constraints to describe the potential behaviour of an organism. FBA (flux balance analysis) highlights flux patterns through a network that serves to achieve a particular objective and requires a minimal amount of data to make quantitative inferences about network behaviour. Even though FBA is a powerful tool for system predictions, its general formulation sometimes results in unrealistic flux patterns. A typical example is fermentation in yeast: ethanol is produced during aerobic growth in excess glucose, but this pattern is not present in a typical FBA solution. In the present paper, we examine the issue of yeast fermentation against respiration during growth. We have studied a number of hypotheses from the modelling perspective, and novel formulations of the FBA approach have been tested. By making the observation that more respiration requires the synthesis of more mitochondria, an energy cost related to mitochondrial synthesis is added to the FBA formulation. Results, although still approximate, are closer to experimental observations than earlier FBA analyses, at least on the issue of fermentation.
2010-10-01
Article
PeerReviewed
application/pdf
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https://eprints.maths.manchester.ac.uk/1527/1/simeonidis10.pdf
Simeonidis, Evangelos and Murabito, Ettore and Smallbone, Kieran and Westerhoff, Hans V. (2010) Why does yeast ferment? A flux balance analysis study. Biochemical Society Transactions, 38. pp. 1225-1229. (In Press)
10.1042/BST0381225
10.1042/BST0381225
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Isomonodromic deformations and twisted Yangians
arising in Teichmüller theory
Chekhov, Leonid
Mazzocco, Marta
14 Algebraic geometry
In this paper we build a link between the Teichmüller theory of hyperbolic Riemann surfaces and isomonodromic
deformations of linear systems whose monodromy group is the Fuchsian group associated to the
given hyperbolic Riemann surface by the Poincaré uniformization. In the case of a one-sheeted hyperboloid
with n orbifold points we show that the Poisson algebra Dn of geodesic length functions is the semiclassical
limit of the twisted q-Yangian Y
q (on) for the orthogonal Lie algebra on defined by Molev, Ragoucy and
Sorba. We give a representation of the braid-group action on Dn in terms of an adjoint matrix action. We
characterize two types of finite-dimensional Poissonian reductions and give an explicit expression for the
generating function of their central elements. Finally, we interpret the algebra Dn as the Poisson algebra of
monodromy data of a Frobenius manifold in the vicinity of a non-semi-simple point.
2011-01-03
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1562/1/advances.pdf
Chekhov, Leonid and Mazzocco, Marta (2011) Isomonodromic deformations and twisted Yangians arising in Teichmüller theory. Advances in Mathematics. ISSN 0001-8708 (In Press)
10.1016/j.aim.2010.12.017
10.1016/j.aim.2010.12.017
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Reachability in one-dimensional controlled polynomial dynamical systems
Korovina, Margarita
Vorobjov, Nicolai
37 Dynamical systems and ergodic theory
68 Computer science
In this paper we address the reachability problem in controlled o-minimal dynamical systems.
This problem can be formulated as follows.
Given a controlled o-minimal dynamical system and
a target set, starting at an initial point, is there a
finite choice of time points and control parameters applied at
these points such that the target set is reachable.
We prove the existence of a finite control stategy and construct an algorithm which provides finite control
strategies for one-dimensional controlled polynomial dynamical systems.We also provide a complexity result which shows upper bounds on the numbers of switches in finite control strategies.
In Proc. The Ershov Informatics Conference, Institute Informaic Systems Press
2011
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1627/1/dynamical_final.pdf
Korovina, Margarita and Vorobjov, Nicolai (2011) Reachability in one-dimensional controlled polynomial dynamical systems. In Proc. The Ershov Informatics Conference, Institute Informaic Systems Press, Russian. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1634
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Algorithmic Properties of Sigma--definability over Positive Predicate Structures
Korovina, Margarita
Kudinov, Oleg
68 Computer science
In this paper we propose a generalisation of the authors p results on semantical characterisation of $\Sigma$--definability.
We prove that over every positive predicate structure a set is $\Sigma$-definable if and only if it is definable by a disjunction of a recursively enumerable set of
existential formulas.
Speinger-Verlag
Löwe, Benedikt
Normann, Dag
Soskov, Ivan
Soskova, Alexandra
2011
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1634/1/posit_pred_str.pdf
Korovina, Margarita and Kudinov, Oleg (2011) Algorithmic Properties of Sigma--definability over Positive Predicate Structures. In: Models of Computation in Context, Proc. 7th Conference on Computability in Europe, CiE 2011. Springer Lecture Notes in Computer Science (6735). Speinger-Verlag, Heidelberg. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1643
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On the decidability of the real field with a
generic power function
Jones, Gareth
Servi, Tamara
03 Mathematical logic and foundations
We show that the theory of the real eld with a generic real power
function is decidable, relative to an oracle for the rational cut of the
exponent of the power function. We show the existence of generic
computable real numbers, hence providing an example of a decidable
o-minimal proper expansion of the real eld by an analytic function.
2010
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1643/1/JonesServi.pdf
Jones, Gareth and Servi, Tamara (2010) On the decidability of the real field with a generic power function. Journal of Symbolic Logic. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1644
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The density of algebraic points on certain Pfaffian surfaces
Jones, G. O.
Thomas, M. E. M.
03 Mathematical logic and foundations
11 Number theory
We prove some instances of Wilkie's conjecture on the density of rational points on sets definable in the real exponential field. In particular, we prove that this conjecture is true for surfaces defined using restricted exponentiation, and that it is true for a general Pfaffian surface provided that the surface admits a certain kind of parameterization.
2011
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1644/1/JonesThomasQJM.pdf
Jones, G. O. and Thomas, M. E. M. (2011) The density of algebraic points on certain Pfaffian surfaces. The Quarterly Journal of Mathematics. (In Press)
http://qjmath.oxfordjournals.org/content/early/2011/06/01/qmath.har011.abstract
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Some illustrations of information geometry in biology and physics
Dodson, CTJ
53 Differential geometry
60 Probability theory and stochastic processes
Many real processes have stochastic features which
seem to be representable in some intuitive sense as `close to Poisson', `nearly random', `nearly uniform'
or with binary variables `nearly independent'. Each of those particular reference states,
defined by an equation, is unstable in the formal sense,
but it is passed through or hovered
about by the observed process. Information geometry gives
precise meaning for nearness and neighbourhood in a state space of processes, naturally quantifying
proximity of a process to a particular state via an information
theoretic metric structure on smoothly parametrized families of
probability density functions. We illustrate some aspects of the
methodology through case studies: inhomogeneous statistical evolutionary rate processes
for epidemics, amino acid spacings along protein chains,
constrained disordering of crystals, distinguishing nearby signal distributions and testing pseudorandom number generators.
IGI-Global
2011
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1662/1/DodsonCSE.pdf
Dodson, CTJ (2011) Some illustrations of information geometry in biology and physics. In: Handbook of Research on Computational Science and Engineering: Theory and Practice. IGI-Global, Hershey, USA, pp. 1-27. ISBN 9781613501160 (In Press)
10.4018/978-1-61350-116-0
10.4018/978-1-61350-116-0
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1702
2017-11-07T22:38:46Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1703
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Characterisation of multiple substrate-specific (d)ITP/(d)XTPase and modelling of deaminated purine nucleotide metabolism
Davies, Oluwafemi
Mendes, Pedro
Smallbone, Kieran
Malys, Naglis
92 Biology and other natural sciences
Accumulation of modified nucleotides is defective to various cellular processes, especially those involving DNA and RNA. To be viable, organisms possess a number of (deoxy)nucleotide phosphohydrolases, which hydrolyze these nucleotides removing them from the active NTP and dNTP pools. Deamination of purine bases can result in accumulation of such nucleotides as ITP, dITP, XTP and dXTP. E. coli RdgB has been characterised as a deoxyribonucleoside triphosphate pyrophosphohydrolase that can act on these nucleotides. S. cerevisiae homologue encoded by YJR069C was purified and its (d)NTPase activity was assayed using fifteen nucleotide substrates. ITP, dITP, and XTP were identified as major substrates and kinetic parameters measured. Inhibition by ATP, dATP and GTP were established. On the basis of experimental and published data, modelling and simulation of ITP, dITP, XTP and dXTP metabolism was performed. (d)ITP/ (d)XTPase is a new example of enzyme with multiple substrate-specificity demonstrating that multispecificity is not a rare phenomenon.
2011
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1703/1/davies.pdf
Davies, Oluwafemi and Mendes, Pedro and Smallbone, Kieran and Malys, Naglis (2011) Characterisation of multiple substrate-specific (d)ITP/(d)XTPase and modelling of deaminated purine nucleotide metabolism. BMB Reports, 44 (11). (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1715
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Modelling acidosis and the cell cycle in multicellular tumour spheroids
Tindall, Marcus J.
Dyson, Louise
Smallbone, Kieran
Maini, Philip K.
35 Partial differential equations
92 Biology and other natural sciences
A partial differential equation model is developed to understand the effect that nutrient and acidosis have on the distribution of proliferating and quiescent cells and dead cell material (necrotic and apopotic) within a multicellular tumour spheroid. The rates of cell quiescence and necrosis depend upon the local nutrient and acid concentrations and quiescent cells are assumed to consume less nutrient and produce less acid than proliferating cells. Analysis of the differences in nutrient consumption and acid production by quiescent and proliferating cells shows low nutrient levels do not necessarily lead to increased acid concentration via anaerobic metabolism. Rather, it is the balance between proliferating and quiescent cells within the tumour which is important; decreased nutrient levels lead to more quiescent cells, which produce less acid than proliferating cells. We examine this effect via a sensitivity analysis which also includes a quantification of the effect that nutrient and acid concentrations have on the rates of cell quiescence and necrosis.
2011-10
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1715/1/MIMS_ep2011_95.pdf
Tindall, Marcus J. and Dyson, Louise and Smallbone, Kieran and Maini, Philip K. (2011) Modelling acidosis and the cell cycle in multicellular tumour spheroids. Journal of Theoretical Biology. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1784
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Backward stability of iterations for computing the polar decomposition
Nakatsukasa, Yuji
Higham, Nicholas J.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
Among the many iterations available for computing the polar decomposition
the most practically useful are the scaled Newton iteration and
the recently proposed dynamically weighted Halley iteration.
Effective ways to scale these and other iterations are known,
but their numerical stability is much less well understood.
In this work we show that a general iteration
$X_{k+1} = f(X_k)$ for computing the unitary polar factor
is backward stable under two conditions.
The first condition requires that the iteration is implemented in a mixed
backward--forward stable manner
and the second requires that the mapping $f$
does not significantly decrease the size of any singular value relative to the
largest singular value.
Using this result we show that the
dynamically weighted Halley iteration
is backward stable when it is
implemented using Householder QR factorization
with column pivoting and either row pivoting or row sorting.
We also prove the backward stability of the scaled Newton iteration under
the assumption that matrix inverses are computed in a mixed
backward-forward stable fashion;
our proof is much shorter than a previous one of
Kielbasinski and Zietak.
We also use our analysis to explain the instability of
the inverse Newton iteration and to show that the Newton-Schulz iteration
is only conditionally stable.
This work shows that by carefully blending perturbation analysis with
rounding error analysis it is possible to produce a general result that can
prove the backward stability or
predict or explain the instability (as the case may be)
of a wide range of practically interesting iterations for the polar decomposition.
2011-12-02
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1784/1/41803_1_art_2_lzptd9_sc.pdf
Nakatsukasa, Yuji and Higham, Nicholas J. (2011) Backward stability of iterations for computing the polar decomposition. SIAM Journal On Matrix Analysis and Applications. ISSN 1749-9097 (In Press)
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Homogenization Methods to Approximate the
Effective Response of Random
Fibre-reinforced Composites
Willoughby, Natasha
Parnell, William J.
Hazel, Andrew L.
Abrahams, I David
74 Mechanics of deformable solids
46 Continuum mechanics of solids
In this article a fibre-reinforced composite material is modelled via an approach employing a Representative Volume Element with periodic boundary conditions. The effective elastic moduli of the material are thus derived. In particular, the method of asymptotic homogenization is used where a finite number of fibres are randomly distributed within the representative periodic cell. The study focuses on the efficacy of such an approach in representing a macroscopically random (hence transversely isotropic) material. Of particular importance is the sensitivity of the method to cell shape, and how this choice affects the resulting (configurationally averaged) elastic moduli. The averaging method is shown to yield results that lie within the Hashin-Shtrikman variational bounds for fibre-reinforced media and compares well with the multiple scattering and (classical) self-consistent approximations with a deviation from the latter in the larger volume fraction cases. Results also compare favourably with well-known experimental data from the literature.
2011
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1788/1/RVE_Willoughby_et_al_eprints.pdf
Willoughby, Natasha and Parnell, William J. and Hazel, Andrew L. and Abrahams, I David (2011) Homogenization Methods to Approximate the Effective Response of Random Fibre-reinforced Composites. International Journal of Solids and Structures. (In Press)
10.1016/j.ijsolstr.2012.02.010
10.1016/j.ijsolstr.2012.02.010
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1789
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https://eprints.maths.manchester.ac.uk/1789/
Employing pre-stress to generate finite cloaks for antiplane elastic waves
Parnell, William J.
Norris, Andrew N.
Shearer, Tom
74 Mechanics of deformable solids
46 Continuum mechanics of solids
It is shown that nonlinear elastic pre-stress of neo-Hookean hyperelastic materials can be used as a mechanism to generate finite cloaks and thus render objects near-invisible to incoming antiplane elastic waves. This approach appears to negate the requirement for special cloaking metamaterials with inhomogeneous and anisotropic material properties in this case. These properties are induced naturally by virtue of the pre-stress. The size of the cloaking region can be altered at will by modification of the applied pre-stress.
2012-01-09
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1789/1/finite_cloak_SH_re_submitted_APL.pdf
Parnell, William J. and Norris, Andrew N. and Shearer, Tom (2012) Employing pre-stress to generate finite cloaks for antiplane elastic waves. Applied Physics Letters. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1822
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Yeast 5 � an Expanded Reconstruction of the Saccharomyces Cerevisiae Metabolic Network
Heavner, Benjamin D
Smallbone, Kieran
Barker, Brandon
Mendes, Pedro
Walker, Larry P
92 Biology and other natural sciences
Background: Efforts to improve the computational reconstruction of the Saccharomyces cerevisiae biochemical reaction network and to refine the stoichiometrically constrained metabolic models that can be derived from such a reconstruction have continued since the first stoichiometrically constrained yeast genome scale metabolic model was published in 2003. Continuing this ongoing process, we have constructed an update to the Yeast Consensus Reconstruction, Yeast 5. The Yeast Consensus Reconstruction is a product of efforts to forge a community-based reconstruction emphasizing standards compliance and biochemical accuracy via evidence-based selection of reactions. It draws upon models published by a variety of independent research groups as well as information obtained from biochemical databases and primary literature.
Results: Yeast 5 refines the biochemical reactions included in the reconstruction, particularly reactions involved in sphingolipid metabolism; updates gene-reaction annotations; and emphasizes the distinction between reconstruction and stoichiometrically constrained model. Although it was not a primary goal, this update also improves the accuracy of model prediction of viability and auxotrophy phenotypes and increases the number of epistatic interactions. This update maintains an emphasis on standards compliance, unambiguous metabolite naming, and computer-readable annotations available through a structured document format. Additionally, we have developed MATLAB scripts to evaluate the model�s predictive accuracy and to demonstrate basic model applications, such as simulating aerobic and anaerobic growth. These scripts, which provide an independent tool for evaluating the performance of various
stoichiometrically constrained yeast metabolic models using flux balance analysis, are included as additional files.
Conclusions: Yeast 5 expands and refines the computational reconstruction of yeast metabolism and improves the predictive accuracy of a stoichiometrically constrained yeast metabolic model. It differs from previous reconstructions and models by emphasizing the distinction between the yeast metabolic reconstruction and the stoichiometrically constrained model, and makes both available as additional files and at http://yeast.sf.net/ as separate systems biology markup language (SBML) files. Through this separation, we intend to make the modeling process more accessible, explicit, transparent, and reproducible.
2012
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1822/1/heavner12.pdf
Heavner, Benjamin D and Smallbone, Kieran and Barker, Brandon and Mendes, Pedro and Walker, Larry P (2012) Yeast 5 � an Expanded Reconstruction of the Saccharomyces Cerevisiae Metabolic Network. BMC Systems Biology. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1825
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An Assessment of sustainable housing affordability using a multiple criteria decision making method
Mulliner, Emma
Smallbone, Kieran
Maliene, Vida
91 Game theory, economics, social and behavioral sciences
Housing affordability is a complex issue that must not only be assessed in terms economic viability. In order to increase quality of life and community sustainability the environmental and social sustainability of housing must also be taken into consideration.
The paper considers the application of a methodology that can be applied to assess the affordability of different housing locations in a sustainable manner, taking into account a range of economic, environmental and social criteria. The COPRAS method of multi-criteria decision making (MCDM) is selected and applied to three residential areas as an example of how sustainable housing affordability can be assessed using a MCDM method. The outcome of the study reveals that considering a range of social and environmental criteria can greatly affect the calculation of an areas affordability, in comparison to focusing solely on financial attributes. COPRAS was found to be an effective method for the assessment and could be applied in other regions or internationally.
2012
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1825/1/mulliner12.pdf
Mulliner, Emma and Smallbone, Kieran and Maliene, Vida (2012) An Assessment of sustainable housing affordability using a multiple criteria decision making method. Omega. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1830
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Kinetic modelling of metabolic pathways: Application to serine biosynthesis
Smallbone, Kieran
Stanford, Natalie J.
92 Biology and other natural sciences
In this chapter, we describe the steps needed to create a kinetic model of a metabolic pathway using kinetic data from both experimental measurements and literature review. Our methodology is presented by using the example of serine biosynthesis in E. coli.
Humana Press
Alper, Hal S.
2012-05-01
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1830/1/smallbone_stanford.pdf
Smallbone, Kieran and Stanford, Natalie J. (2012) Kinetic modelling of metabolic pathways: Application to serine biosynthesis. In: Systems Metabolic Engineering: Methods and Protocols. Methods in Molecular Biology . Humana Press. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1840
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Improving metabolic flux predictions using absolute gene expression data
Lee, Dave
Smallbone, Kieran
Dunn, Warwick B.
Murabito, Ettore
Winder, Catherine L.
Kell, Douglas B.
Mendes, Pedro
Swainston, Neil
92 Biology and other natural sciences
Background:
Constraint-based analysis of genome-scale metabolic models typically relies upon maximisation of a cellular objective function such as the rate or efficiency of biomass production. Whilst this assumption may be valid in the case of microorganisms growing under certain conditions, it is likely invalid in general, and especially for multicellular organisms, where cellular objectives differ greatly both between and within cell types. Moreover, for the purposes of biotechnological applications, it is normally the flux to a specific metabolite or product that is of interest rather than the rate of production of biomass per se.
Results:
An alternative objective function is presented, that is based upon maximising the correlation between experimentally measured absolute gene expression data and predicted internal reaction fluxes. Using quantitative transcriptomics data acquired from Saccharomyces cerevisiae cultures under two growth conditions, the method outperforms traditional approaches for predicting experimentally measured exometabolic flux that are reliant upon maximisation of the rate of biomass production.
Conclusion:
Due to its improved prediction of experimentally measured metabolic fluxes, and of its lack of a requirement for knowledge of the biomass composition of the organism under the conditions of interest, the approach is likely to be of rather general utility. The method has been shown to predict fluxes reliably in single cellular systems. Subsequent work will investigate the method�s ability to generate condition- and tissue-specific flux predictions in multicellular organisms.
2012-05-30
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1840/1/lee12.pdf
Lee, Dave and Smallbone, Kieran and Dunn, Warwick B. and Murabito, Ettore and Winder, Catherine L. and Kell, Douglas B. and Mendes, Pedro and Swainston, Neil (2012) Improving metabolic flux predictions using absolute gene expression data. BMC Systems Biology. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1891
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https://eprints.maths.manchester.ac.uk/1891/
Frobenius groups of automorphisms and their fixed points
Khukhro, E. I.
Makarenko, N. Yu.
Shumyatsky, P.
17 Nonassociative rings and algebras
20 Group theory and generalizations
Suppose that a finite group $G$ admits a Frobenius group of
automorphisms $FH$ with kernel $F$ and complement $H$ such that
the fixed-point subgroup of $F$ is trivial: $C_G(F)=1$. In this
situation various properties of $G$ are shown to be close to the
corresponding properties of $C_G(H)$. By using Clifford's theorem
it is proved that the order $|G|$ is bounded in terms
of $|H|$ and $|C_G(H)|$, the rank of $G$ is bounded in terms
of $|H|$ and the rank of $C_G(H)$, and
that $G$ is nilpotent if $C_G(H)$ is nilpotent. Lie ring methods
are used for bounding the exponent
and the nilpotency class
of $G$ in the case of metacyclic $FH$. The exponent of $G$ is
bounded in terms of $|FH|$ and the exponent of $C_G(H)$ by using Lazard's
Lie algebra associated with the Jennings--Zassenhaus
filtration and its connection with powerful subgroups. The
nilpotency class of $G$ is bounded in terms of $|H|$ and the
nilpotency class of $C_G(H)$ by considering Lie rings with a
finite cyclic grading satisfying a certain `selective nilpotency'
condition. The latter technique also yields similar results
bounding the nilpotency class of Lie rings and algebras with a
metacyclic Frobenius group of automorphisms, with corollaries for
connected Lie groups and torsion-free locally nilpotent groups
with such groups of automorphisms. Examples show that such nilpotency results
are no longer true for non-metacyclic Frobenius groups of automorphisms.
2011
Article
NonPeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1891/1/eart104.pdf
Khukhro, E. I. and Makarenko, N. Yu. and Shumyatsky, P. (2011) Frobenius groups of automorphisms and their fixed points. Forum Mathematicum, to app. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1910
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https://eprints.maths.manchester.ac.uk/1910/
Local Fusion Graphs for Symmetric Groups
Ballantyne, John J
Greer, Nicholas M
Rowley, Peter J
20 Group theory and generalizations
For a group $G$, $\pi$ a set of odd positive integers and $X$ a set of involutions of $G$ we define a graph $\mathcal{F}_\pi(G,X)$. This graph, called a $\pi$-local fusion graph, has vertex set $X$ with $x,y \in X$ joined by an edge provided $x \neq y$ and the order of $xy$ is in $\pi$. In this paper we investigate $\mathcal{F}_\pi(G,X)$ when $G$ is a finite symmetric group for various choices of $X$ and $\pi$.
2012
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1910/1/LocalFusionGraphSymJGT.pdf
Ballantyne, John J and Greer, Nicholas M and Rowley, Peter J (2012) Local Fusion Graphs for Symmetric Groups. Journal of Group Theory. (In Press)
10.1515/jgt-2012-0027
10.1515/jgt-2012-0027
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1988
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https://eprints.maths.manchester.ac.uk/1988/
Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations
Bethune, Iain
Bull, J. Mark
Dingle, Nicholas J.
Higham, Nicholas J.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
68 Computer science
Ever-increasing core counts create the need to develop parallel algorithms that avoid closely-coupled execution across cores. In this paper we present two case studies investigating the performance of several parallel asynchronous implementations of Jacobi's method for solving systems of linear equations. Although conditions for the convergence of asynchronous Jacobi are well known, what drives its rate of convergence is less well understood. The first case study investigates the algorithm's performance when executed on large numbers of processors on a Cray XE6, while the second explores the effect of varying the number of synchronous and asynchronous processors. We observe that the performance of parallel asynchronous Jacobi is highly implementation, problem and architecture-dependent.
2011-10-18
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1988/1/paper.pdf
Bethune, Iain and Bull, J. Mark and Dingle, Nicholas J. and Higham, Nicholas J. (2011) Investigating the Performance of Asynchronous Jacobi's Method for Solving Systems of Linear Equations. To appear in International Journal of High Performance Computing Applications. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:1996
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https://eprints.maths.manchester.ac.uk/1996/
Dimensionality reduction for classification of stochastic fibre radiographs
Dodson, CTJ
Sampson, WW
53 Differential geometry
60 Probability theory and stochastic processes
Dimensionality reduction helps to identify small numbers of essential features
of stochastic fibre networks for classification of image pixel density
datasets from experimental radiographic measurements of commercial samples and simulations.
Typical commercial macro-fibre networks use finite length fibres suspended in a fluid from which
they are continuously deposited onto a moving bed to make a continuous web;
the fibres can cluster to differing degrees,
primarily depending on the fluid turbulence, fibre dimensions and flexibility.
Here we use information geometry of trivariate Gaussian spatial distributions of pixel density among
first and second neighbours to reveal features related to sizes and density of fibre clusters.
Springer
Nielsen, F
Barbaresco, F
2013-08
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/1996/1/DodsonSampsonGSI2013.pdf
Dodson, CTJ and Sampson, WW (2013) Dimensionality reduction for classification of stochastic fibre radiographs. In: Geometric Science of Information GSI2013. Lecture Notes in Computer Science, 8085 (8085). Springer, Heidelberg, pp. 158-165. ISBN ISBN 978-3-642-40020-9 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2006
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https://eprints.maths.manchester.ac.uk/2006/
The Irrelevant Information Principle for Collective Probabilistic Reasoning
Adamcik, Martin
Wilmers, George
03 Mathematical logic and foundations
68 Computer science
Within the framework of discrete probabilistic uncertain reasoning a large literature exists justifying the maximum entropy inference process, ME, as being optimal in the context of a single agent whose subjective probabilistic knowledge base is consistent. In particular Paris and Vencovska completely characterised the ME inference process by means of an attractive set of axioms which an inference process should satisfy.
More recently the second author extended the Paris-Vencovska axiomatic approach to inference processes in the context of several agents whose subjective probabilistic knowledge bases, while individually consistent, may be collectively inconsistent. In particular he defined a natural multi--agent extension of the inference process ME called the social entropy process, SEP. However, while SEP has been shown to possess many attractive properties, those which are known are almost certainly insufficient to uniquely characterise it. It is therefore of particular interest to study those Paris-Vencovska principles valid for ME whose immediate generalisations to the multi-agent case are not satisfied by SEP. One of these principles is the Irrelevant Information Principle, a powerful and appealing principle which very few inference processes satisfy even in the single agent context. In this paper we will investigate whether SEP can satisfy an interesting modified generalisation of this principle.
2013-02
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2006/1/irrel_adamcik_wilmers.pdf
Adamcik, Martin and Wilmers, George (2013) The Irrelevant Information Principle for Collective Probabilistic Reasoning. Kybernetika. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2063
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https://eprints.maths.manchester.ac.uk/2063/
Classification of symmetry groups for planar n-body choreographies
Montaldi, James
Steckles, Katrina
37 Dynamical systems and ergodic theory
58 Global analysis, analysis on manifolds
70 Mechanics of particles and systems
Since the foundational work of Chenciner and Montgomery in 2000 there has been a great deal of interest in choreographic solutions of the n-body problem: periodic motions where the n bodies all follow one another at regular intervals along a closed path. The principal approach combines variational methods with symmetry properties. In this paper, we give a systematic treatment of the symmetry aspect. In the first part we classify all possible symmetry groups of planar n-body, collision-free choreographies. These symmetry groups fall in to 2 infinite families and, if n is odd, three exceptional groups. In the second part we develop the equivariant fundamental group and use it to determine the topology of the space of loops with a given symmetry, which we show is related to certain cosets of the pure braid group in the full braid group, and to centralizers of elements of the corresponding coset. In particular, we refine the symmetry classification by classifying the connected components of the set of loops with any given symmetry. This leads to the existence of many new choreographies in n-body systems governed by a strong force potential.
2013-11
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2063/1/choreographies.pdf
Montaldi, James and Steckles, Katrina (2013) Classification of symmetry groups for planar n-body choreographies. Forum of Mathematics, Sigma, 1. ISSN 2050-5094 (In Press)
10.1017/fms.2013.5
10.1017/fms.2013.5
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2116
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https://eprints.maths.manchester.ac.uk/2116/
Implementing QR Factorization Updating Algorithms on GPUs
Andrew, Robert
Dingle, Nicholas J.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
68 Computer science
Linear least squares problems are commonly solved by QR factorization. When multiple solutions need to be computed with only minor changes in the underlying data, knowledge of the difference between the old data set and the new can be used to update an existing factorization at reduced computational cost. We investigate the viability of implementing QR updating algorithms on GPUs and demonstrate that GPU-based updating for removing columns achieves speed-ups of up to 13.5x compared with full GPU QR factorization. We characterize the conditions under which other types of updates also achieve speed-ups.
2014-03-26
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2116/1/paper.pdf
Andrew, Robert and Dingle, Nicholas J. (2014) Implementing QR Factorization Updating Algorithms on GPUs. Parallel Computing. ISSN 0167-8191 (In Press)
http://www.sciencedirect.com/science/article/pii/S0167819114000337?_rdoc=1&_fmt=high&_origin=gateway&_docanchor=&md5=b8429449ccfc9c30159a5f9aeaa92ffb
10.1016/j.parco.2014.03.003
10.1016/j.parco.2014.03.003
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2164
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https://eprints.maths.manchester.ac.uk/2164/
Point vortices on the hyperbolic plane
Montaldi, James
Nava-Gaxiola, Citlalitl
37 Dynamical systems and ergodic theory
70 Mechanics of particles and systems
We investigate the dynamical system of point vortices on the hyperboloid. This system has noncompact
symmetry SL(2,R) and a coadjoint equivariant momentum map. The relative equilibrium
conditions are found and the trajectories of relative equilibria with non-zero momentum
value are described. We also provide the classification of relative equilibria and the stability criteria
for a number of cases, focusing on 2 and 3 vortices. Unlike the systemon the sphere, this system
has relative equilibria with non-compact momentum isotropy subgroup, and these are used to illustrate
the different stability types of relative equilibria.
2014-10-07
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2164/1/hyperbolicvortex.pdf
Montaldi, James and Nava-Gaxiola, Citlalitl (2014) Point vortices on the hyperbolic plane. J. Mathematical Physics, 55 (102702). pp. 1-14. (In Press)
10.1063/1.4897210
10.1063/1.4897210
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2269
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https://eprints.maths.manchester.ac.uk/2269/
Existence of symmetric central configurations
Montaldi, James
70 Mechanics of particles and systems
Central configurations have been of great interest over many years, with the earliest examples due to Euler and Lagrange. There are numerous results in the literature demonstrating the existence of central configurations with specific symmetry properties, using slightly different techniques in each. The aim here is to describe a uniform approach by adapting to the symmetric case the well-known variational argument showing the existence of central configurations. The principal conclusion is that there is a central configuration for every possible symmetry type, and for any symmetric choice of masses. Finally the same argument is applied to the class of balanced configurations introduced by Albouy and Chenciner.
2015-06
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2269/1/centralConfigurations.pdf
Montaldi, James (2015) Existence of symmetric central configurations. Celestial Mechanics and Dynamical Astronomy. ISSN 0923-2958 (In Press)
10.1007/s10569-015-9625-4
10.1007/s10569-015-9625-4
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2300
2017-10-20T14:13:19Z
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https://eprints.maths.manchester.ac.uk/2300/
Rational values of Weierstrass zeta functions
Jones, Gareth O.
Thomas, Margaret E.M.
03 Mathematical logic and foundations
11 Number theory
2014-01-30
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2300/1/JonesThomas-WeierstrassZeta_update_2015_05_23-1.pdf
Jones, Gareth O. and Thomas, Margaret E.M. (2014) Rational values of Weierstrass zeta functions. Proceedings of the Edinburgh Mathematical Society. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2345
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https://eprints.maths.manchester.ac.uk/2345/
The equivariant K-theory and cobordism rings of divisive weighted projective spaces
Harada, Megumi
Holm, Tara
Ray, Nigel
Williams, Gareth
14 Algebraic geometry
55 Algebraic topology
57 Manifolds and cell complexes
We apply results of Harada, Holm and Henriques to prove that the Atiyah-Segal equivariant
complex K-theory ring of a divisive weighted projective space (which is singular for nontrivial
weights) is isomorphic to the ring of integral piecewise Laurent polynomials on the associated
fan. Analogues of this description hold for other complex-oriented equivariant cohomology theories,
as we conrm in the case of homotopical complex cobordism, which is the universal example.
We also prove that the Borel versions of the equivariant K-theory and complex cobordism rings
of more general singular toric varieties, namely those whose integral cohomology is concentrated
in even dimensions, are isomorphic to rings of appropriate piecewise formal power series. Finally,
we conrm the corresponding descriptions for any smooth, compact, projective toric variety, and
rewrite them in a face ring context. In many cases our results agree with those of Vezzosi and
Vistoli for algebraic K-theory, Anderson and Payne for operational K-theory, Krishna and Uma
for algebraic cobordism, and Gonzalez and Karu for operational cobordism; as we proceed, we
summarize the details of these coincidences.
2013-09-25
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2345/1/tmj2-accepted-hhrw.pdf
Harada, Megumi and Holm, Tara and Ray, Nigel and Williams, Gareth (2013) The equivariant K-theory and cobordism rings of divisive weighted projective spaces. Tohoku Mathematical Journal. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2368
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https://eprints.maths.manchester.ac.uk/2368/
A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils
Shearer, Tom
74 Mechanics of deformable solids
92 Biology and other natural sciences
46 Continuum mechanics of solids
A new strain energy function for the hyperelastic modelling of ligaments and tendons whose fascicles have a helical arrangement of fibrils is derived. The stress-strain response of a single fascicle whose fibrils exhibit varying levels of crimp throughout its radius is calculated and used to determine the form of the strain energy function. The new constitutive law is used to model uniaxial extension test data for human patellar tendon and is shown to provide an excellent fit, with the average relative error being 9.8%. It is then used to model shear and predicts that the stresses required to shear a tendon are much smaller than those required to uniaxially stretch it to the same strain level. Finally, the strain energy function is used to model ligaments and tendons whose fascicles are helical, and the relative effects of the fibril helix angle, the fascicle helix angle and the fibril crimp variable are compared. It is shown that they all have a significant effect; the fibril crimp variable governs the non-linearity of the stress-strain curve, whereas the helix angles primarily affect its stiffness. Smaller values of the helix angles lead to stiffer tendons; therefore, the model predicts that one would expect to see fewer helical sub-structures in stiff positional tendons, and more in those that are required to be more flexible.
2015-08-08
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2368/1/A_new_strain_energy_function_for_modelling_ligaments_and_tendons_whose_fascicles_have_a_helical_arrangement_of_fibrils.pdf
Shearer, Tom (2015) A new strain energy function for modelling ligaments and tendons whose fascicles have a helical arrangement of fibrils. Journal of Biomechanics. ISSN 0021-9290 (In Press)
http://www.sciencedirect.com/science/article/pii/S002192901500425X
10.1016/j.jbiomech.2015.07.032
10.1016/j.jbiomech.2015.07.032
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2416
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https://eprints.maths.manchester.ac.uk/2416/
Geometry in a Fréchet Context
A Projective Limit Approach
Dodson, CTJ
Galanis, G
Vassiliou, E
53 Differential geometry
58 Global analysis, analysis on manifolds
Many geometrical features of manifolds and fibre bundles modelled on Fréchet spaces either cannot be defined or are difficult to handle directly. This is due to the inherent deficiencies of Fréchet spaces; for example, the lack of a general solvability theory for differential equations, the non-existence of a reasonable Lie group structure on the general linear group of a Fréchet space, and the non-existence of an exponential map in a Fréchet-Lie group. In this book, the authors describe in detail a new approach that overcomes many of these limitations by using projective limits of geometrical objects modelled on Banach spaces. It will appeal to researchers and graduate students from a variety of backgrounds with an interest in infinite-dimensional geometry. The book concludes with an appendix outlining potential applications and motivating future research.
Features:
Proposes a new approach that overcomes many complications of the geometric theory.
Self-contained chapters and detailed proofs help the reader progress systematically through the book.
Includes an extensive introduction to the geometry of Banach manifolds and bundles.
Provides a number of suggestions for further research in the geometry and for applications, notably in physical field theory.
Cambridge University Press
2015-12
Book
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2416/1/fr.pdf
Dodson, CTJ and Galanis, G and Vassiliou, E (2015) Geometry in a Fréchet Context A Projective Limit Approach. LMS Lecture Notes in Mathematics, 428 . Cambridge University Press, Cambridge, UK. ISBN 9781316601952 (In Press)
http://www.cambridge.org/gb/academic/subjects/mathematics/geometry-and-topology/geometry-frechet-context-projective-limit-approach?format=PB
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2449
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https://eprints.maths.manchester.ac.uk/2449/
Rigid orbits and sheets in reductive Lie algebras over fields of prime characteristic.
Premet, Alexander
Stewart, David
17 Nonassociative rings and algebras
20 Group theory and generalizations
We classify the sheets and the rigid nilpotent orbits in reductive Lie algebras over fields of good characteristic and show that the distribution of nilpotent orbits amongst the sheets remains the same as in the characteristic zero case. We use GAP to determine the reachable and strongly reachable nilpotent orbits in all characteristics and provide some information on derived subalgebras of centralisers.
2016
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2449/1/nilporbcalcs4.pdf
Premet, Alexander and Stewart, David (2016) Rigid orbits and sheets in reductive Lie algebras over fields of prime characteristic. Journal of the Institute of Mathematics of Jussieu. ISSN 1749-9097 (In Press)
doi:10.1017/S1474748016000086
doi:10.1017/S1474748016000086
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2488
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https://eprints.maths.manchester.ac.uk/2488/
Characterization of objects by electrosensing fish
based on the first order polarization tensor
Ahmad Khairuddin, Taufiq K
Lionheart, William R B
41 Electromagnetism; electron and ion optics
87 Biological and medical physics
Weakly electric fish generate electric current and use hundreds of voltage
sensors on the surface of their body to navigate and locate food. Experiments [G.
von der Emde and S. Fetz, J. Exp Biol, 210, 3082�3095, 2007] show that they can
discriminate between differently shaped conducting or insulating objects by using
electrosensing. One approach to electrically identify and characterize the object with a
lower computational cost rather than full shape reconstruction is to use the first order
Polarization Tensor (PT) of the object.
In this paper, by considering experimental work on Peters� elephantnose fish
Gnathonemus petersii, we investigate the possible role of the first order PT in the
ability of the fish to discriminate between objects of different shape. We also suggest
some experiments that might be performed to further investigate the role of the first
order PT in electrosensing fish. Finally, we speculate on the possibility of electrical
cloaking or camouflage in prey of electrosensing fish and what might be learnt from
the fish in human remote sensing.
2016
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2488/1/fishpaper-taufiqlionheart-v3.pdf
Ahmad Khairuddin, Taufiq K and Lionheart, William R B (2016) Characterization of objects by electrosensing fish based on the first order polarization tensor. Bioinspiration & Biomimetics. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2523
2017-10-20T14:13:28Z
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https://eprints.maths.manchester.ac.uk/2523/
On some information geometric approaches to cyber security
Dodson, CTJ
53 Differential geometry
62 Statistics
Various contexts of relevance to cyber security involve the analysis of data
that has a statistical character and in some cases the extraction of particular
features from datasets of fitted distributions or empirical frequency distributions.
Such statistics, for example,
may be collected in the automated monitoring of IP-related data
during accessing or attempted accessing of web-based resources, or may be
triggered through an alert for suspected cyber attacks.
Information geometry provides a Riemannian geometric framework in which to
study smoothly parametrized families of probability density functions, thereby
allowing the use of geometric tools to study statistical features of processes
and possibly the representation of features that are associated with attacks.
In particular, we can obtain mutual distances among members of the family
from a collection of datasets, allowing for example measures of departures
from Poisson random or uniformity, and discrimination between nearby distributions.
Moreover, this allows the representation of large numbers of datasets
in a way that respects any topological features in the frequency data
and reveals subgroupings in the datasets using dimensionality reduction.
Here some results are reported on statistical and information geometric studies
concerning pseudorandom sequences, encryption-decryption timing analyses,
comparisons of nearby signal distributions and departure from uniformity for
evaluating obscuring techniques.
Springer
Daras, Nicholas J
Rassias, Thermistocles M
2017-03
Book Section
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2523/1/DodsonCyberSecurityFinal.pdf
Dodson, CTJ (2017) On some information geometric approaches to cyber security. In: Operations Research, Engineering, and Cyber Security. Springer Optimization and Its Applications (113). Springer, Germany. (In Press)
http://www.springer.com/gb/book/9783319514987
http://www.springer.com/gb/book/9783319514987
http://www.springer.com/gb/book/9783319514987
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2544
2017-10-20T14:13:29Z
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https://eprints.maths.manchester.ac.uk/2544/
A formula for the Frechet derivative of a
generalized matrix function
Noferini, Vanni
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
We state and prove an extension of the Daleckii-Krein theorem, thus obtaining an
explicit formula for the Frechet derivative of generalized matrix functions. Moreover,
we prove the differentiability of generalized matrix functions of real matrices under very
mild assumptions. For complex matrices, we argue that generalized matrix functions
are real differentiable but generally not complex differentiable. Finally, we discuss the
application of our result to the study of the condition number of generalized matrix
functions. Along our way, we also derive generalized matrix functional analogues of
a few classical theorems on polynomial interpolation of classical matrix functions and
their derivatives.
2016-04-15
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2544/1/gendk_SIMAX_rev2c.pdf
Noferini, Vanni (2016) A formula for the Frechet derivative of a generalized matrix function. SIAM Journal of Matrix Analysis and Applications (2016.2). ISSN 1749-9097 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2568
2017-11-22T09:37:12Z
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2601
2017-11-22T09:42:41Z
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https://eprints.maths.manchester.ac.uk/2601/
A new restriction for initially stressed elastic solids
Gower, A.L.
Shearer, T.
Ciarletta, P.
46 Continuum mechanics of solids
We introduce a fundamental restriction on the strain energy function and stress tensor for initially stressed elastic solids. The restriction applies to strain energy functions W that are explicit functions of the elastic deformation gradient F and initial stress tau, that is W := W (F, tau). The restriction is a consequence of energy conservation and ensures that the predicted stress and strain energy do not
depend upon an arbitrary choice of reference configuration. We call this restriction initial stress reference independence (ISRI). It transpires that most strain energy functions found in the literature do not satisfy ISRI, and may therefore lead to unphysical behaviour, which we illustrate through a simple example. To remedy this shortcoming, we derive three strain energy functions that do
satisfy the restriction. We also show that using initial strain (often from a virtual configuration) to model initial stress leads to strain energy functions that automatically satisfy ISRI. Finally, we reach the following important result: ISRI reduces the number of unknowns in the linear stress tensor for initially stressed solids. This new way of reducing the linear stress may open new
pathways for the non-destructive determination of initial stresses through ultrasonic experiments, among others.
2017-08-17
Article
PeerReviewed
application/pdf
en
https://eprints.maths.manchester.ac.uk/2601/1/A_new_restriction_for_initially_stressed_elastic_solids.pdf
Gower, A.L. and Shearer, T. and Ciarletta, P. (2017) A new restriction for initially stressed elastic solids. Quarterly Journal of Mechanics and Applied Mathematics, 70. pp. 455-478. (In Press)
https://academic.oup.com/qjmam/article/doi/10.1093/qjmam/hbx020/4083567/A-New-Restriction-for-Initially-Stressed-Elastic
10.1093/qjmam/hbx020
10.1093/qjmam/hbx020
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2618
2018-01-30T09:14:32Z
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https://eprints.maths.manchester.ac.uk/2618/
Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers
Anzt, Hartwig
Dongarra, Jack
Flegar, Goran
Higham, Nicholas J.
Quintana-Orti, Enrique S.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
We propose an adaptive scheme to reduce communication overhead caused by data movement by selectively storing the diagonal blocks of a block Jacobi preconditioner in different precision formats (half, single, or double). This specialized preconditioner can then be combined with any Krylov subspace method for the solution of sparse linear systems to perform all arithmetic in double precision. We assess the effects of the adaptive-precision preconditioner on the iteration count and data transfer cost of a preconditioned conjugate gradient solver. A preconditioned conjugate gradient method is, in general, a memory-bound algorithm, and therefore its execution time and energy consumption are largely dominated by the costs of accessing the problem's data in memory. Given this observation, we propose a model that quantifies the time and energy savings of our approach based on the assumption that these two costs depend linearly on the bit length of a floating point number. Furthermore, we use a number of test problems from the SuiteSparse matrix collection to estimate the potential benefits of the adaptive block-Jacobi preconditioning scheme.
2017-09-22
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2618/5/paper_eprint.pdf
Anzt, Hartwig and Dongarra, Jack and Flegar, Goran and Higham, Nicholas J. and Quintana-Orti, Enrique S. (2017) Adaptive Precision in Block-Jacobi Preconditioning for Iterative Sparse Linear System Solvers. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2664
2018-10-02T08:39:57Z
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https://eprints.maths.manchester.ac.uk/2664/
Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers
Haidar, Azzam
Tomov, Stanimire
Dongarra, Jack
Higham, Nicholas J.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
Low-precision floating-point arithmetic is a powerful tool for accelerating scientific computing applications, especially those in artificial intelligence. Here, we present an investigation showing that other high-performance computing (HPC) applications can also harness this power. Specifically, we use the general HPC problem, $Ax = b$, where $A$ is a large dense matrix, and a double precision (FP64) solution is needed for accuracy. Our approach is based on mixed-precision (FP16 -> FP64) iterative refinement, and we generalize and extend prior advances into a framework, for which we develop architecture-specific algorithms and highly tuned implementations. These new methods show how using half-precision Tensor Cores (FP16-TC) for the arithmetic can provide up to 4 times speedup. This is due to the performance boost that the FP16-TC provide as well as to the improved accuracy over the classical FP16 arithmetic that is obtained because the GEMM accumulation occurs in FP32 arithmetic.
Conference or Workshop Item
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2664/1/International%20ACM%20Conference.pdf
Haidar, Azzam and Tomov, Stanimire and Dongarra, Jack and Higham, Nicholas J. Harnessing GPU Tensor Cores for Fast FP16 Arithmetic to Speed up Mixed-Precision Iterative Refinement Solvers. In: International Conference on Supercomputing, New York, NY, USA, 2018. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2665
2018-10-04T10:49:19Z
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https://eprints.maths.manchester.ac.uk/2665/
Conversions between barycentric, RKFUN, and Newton representations of rational interpolants
Elsworth, Steven
Güttel, Stefan
65 Numerical analysis
We derive explicit formulas for converting between rational interpolants in barycentric, rational Krylov (RKFUN), and Newton form. We show applications of these conversions when working with rational approximants produced by the AAA algorithm [Y. Nakatsukasa, O. Sete, L. N. Trefethen, SIAM J. Sci. Comput. 40(3), 2018] within the Rational Krylov Toolbox and for the solution of nonlinear eigenvalue problems.
2017-11-22
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2665/3/document-laa-rev2.pdf
Elsworth, Steven and Güttel, Stefan (2017) Conversions between barycentric, RKFUN, and Newton representations of rational interpolants. Linear Algebra and its Applications (2017.40). ISSN 0024-3795 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2675
2018-11-21T13:53:45Z
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https://eprints.maths.manchester.ac.uk/2675/
Evolving Graphs and Similarity-based Graphs with Applications
Weijian, Zhang
05 Combinatorics
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
68 Computer science
A graph is a mathematical structure for modelling the pairwise relations between objects. This thesis studies two types of graphs, namely, similarity-based graphs and evolving graphs.
We look at ways to traverse an evolving graph. In particular, we examine the influence of temporal information on node centrality. In the process, we develop EvolvingGraphs.jl, a software package for analyzing time-dependent networks.
We develop Etymo, a search system for discovering interesting research papers. Etymo utilizes both similarity-based graphs and evolving graphs to build a knowledge graph of research articles in order to help users to track the development of ideas. We construct content similarity-based graphs using the full text of research papers. And we extract key concepts from research papers and exploit the temporal information in research papers to construct a concepts evolving graph.
2018-10-17
Thesis
NonPeerReviewed
text
en
cc_by_nc
https://eprints.maths.manchester.ac.uk/2675/1/getpdfwithcoverpage
Weijian, Zhang (2018) Evolving Graphs and Similarity-based Graphs with Applications. Doctoral thesis, University of Manchester.
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2694
2019-03-21T18:09:07Z
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https://eprints.maths.manchester.ac.uk/2694/
Bridging the gap between flat and hierarchical low-rank
matrix formats: the multilevel BLR format
Amestoy, Patrick
Buttari, Alfredo
L'Excellent, Jean-Yves
Mary, Theo
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
2018-05-05
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2694/1/main.pdf
Amestoy, Patrick and Buttari, Alfredo and L'Excellent, Jean-Yves and Mary, Theo (2018) Bridging the gap between flat and hierarchical low-rank matrix formats: the multilevel BLR format. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2701
2019-04-07T08:30:14Z
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https://eprints.maths.manchester.ac.uk/2701/
Filtering Frequencies in a Shift-and-invert Lanczos Algorithm
for the Dynamic Analysis of Structures
Zemaityte, Mante
Tisseur, Francoise
Kannan, Ramaseshan
65 Numerical analysis
The shift-and-invert Lanczos algorithm is a commonly used solution procedure to compute the eigenpairs of large, sparse eigenvalue problems that arise when approximating the elastic dynamic response of large structures under the influence of seismic forces. Not all eigenvectors are equally important to the response when the structure is exposed to a mass-dependent external force of the form $g(t) Mb$, where $M$ is the mass matrix of the system and $b$ the rigid body vector. Structural engineers select eigenvectors $x_j$, $j=1,\ldots,\ell$, such that their cumulative mass participation, measured as $\sum_{j=1}^\ell (x_j^T Mb)^2/(b^TMb)$,is above a target threshold $\xi$. We show that when the starting vector for the unshifted Lanczos
algorithm is the spatial distribution vector $b$, the Lanczos procedure can be used to provide an estimate of the cumulative mass participation. This allows us to identify intervals containing eigenvalues whose eigenvectors have a large contribution to the cumulative mass participation and filter out intervals containing eigenvalues whose eigenvectors have a negligible contribution. We use this information to devise a sequence of shifts $\sigma_1, \ldots,\sigma_p$ for the shift-and-invert Lanczos algorithm as well as a stopping criterion for the iteration with shift $\sigma_i$ so that the cumulative mass participation of the computed eigenvectors reaches the required level $\xi$.
Numerical experiments on real engineering problems show that
our approach computes up to $70\%$ fewer eigenvectors and requires fewer shifts, on average, than the more general shifting strategy proposed by Ericsson and Ruhe (Math. Comp., 35 (1980)) together with its modification presented in Grimes et al. (SIAM J. Matrix Anal. and Appl. 40(4), 1994).
2018-05-25
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2701/1/ztk19.pdf
Zemaityte, Mante and Tisseur, Francoise and Kannan, Ramaseshan (2018) Filtering Frequencies in a Shift-and-invert Lanczos Algorithm for the Dynamic Analysis of Structures. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2718
2019-06-17T20:51:43Z
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https://eprints.maths.manchester.ac.uk/2718/
Non-Abelian momentum polytopes for products of CP^2
Montaldi, James
Shaddad, Amna
53 Differential geometry
This is the first of two companion papers. The joint aim is to study a generalization to higher dimension of the point vortex systems familiar in 2-D. In this paper we classify the momentum polytopes for the action of the Lie group SU(3) on products of copies of complex projective 4-space. For 2 copies, the momentum polytope is simply a line segment, which can sit in the positive Weyl chamber in a number of ways. For a product of 3 copies there are 8 different types of generic momentum polytope for the product of 3 copies, and numerous transition polytopes, all of which are classified here. The different polytopes depend on the weights of the symplectic form on each copy of projective space. In the second paper we use reduction techniques to study the possible dynamics of interacting point vortices.
The results are also applied to determine the inequalities satisfied by the sum of up to three 3x3 Hermitian matrices with double eigenvalues.
AIMS
2019-06-17
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2718/3/CP2Polytopes2.pdf
Montaldi, James and Shaddad, Amna (2019) Non-Abelian momentum polytopes for products of CP^2. J. Geometric Mechanics. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2719
2019-06-17T20:52:27Z
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https://eprints.maths.manchester.ac.uk/2719/
Generalized point vortex dynamics on CP^2
Montaldi, James
Shaddad, Amna
37 Dynamical systems and ergodic theory
53 Differential geometry
This is the second of two companion papers.
We describe a generalization of the point vortex system on surfaces to a Hamiltonian dynamical system consisting of two or three points on complex projective space $\CP ^2$ interacting via a Hamiltonian function depending only on the distance between the points. The system has symmetry group SU(3). The first paper describes all possible momentum values for such systems, and here we apply methods of symplectic reduction and geometric mechanics to analyze the possible relative equilibria of such interacting generalized vortices.
The different types of polytope depend on the values of the `vortex strengths', which are manifested as coefficients of the symplectic forms on the copies of $\CP ^2$. We show that the reduced space for this Hamiltonian action for 3 vortices is generically a 2-sphere, and proceed to describe the reduced dynamics under simple hypotheses on the type of Hamiltonian interaction. The other non-trivial reduced spaces are topological spheres with isolated singular points.
For 2 generalized vortices, the reduced spaces are just points, and the motion is governed by a collective Hamiltonian, whereas for 3 the reduced spaces are of dimension at most 2. In both cases the system will be completely integrable in the non-abelian sense.
AIMS
2019-07-17
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2719/3/CP2Vortices2.pdf
Montaldi, James and Shaddad, Amna (2019) Generalized point vortex dynamics on CP^2. J. Geometric Mechanics. (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2721
2019-06-19T14:28:57Z
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https://eprints.maths.manchester.ac.uk/2721/
An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential
Fasi, Massimiliano
Higham, Nicholas J.
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
The most popular algorithms for computing the matrix exponential are those based on the scaling and squaring technique. For optimal efficiency these are usually tuned to a particular precision of floating-point arithmetic. We design a new scaling and squaring algorithm that takes the unit roundoff of the arithmetic as input and chooses the algorithmic parameters in order to keep the forward error in the underlying Padé approximation below the unit roundoff. To do so, we derive an explicit expression for all the coefficients in an error expansion for Padé approximants to the exponential and use it to obtain a new bound for the truncation error. We also derive a new technique for selecting the internal parameters used by the algorithm, which at each step decides whether to scale or to increase the degree of the approximant. The algorithm can employ diagonal Padé approximants or Taylor approximants and can be used with a Schur decomposition or in transformation-free form. Our numerical experiments show that the new algorithm performs in a forward stable way for a wide range of precisions and that the most accurate of our implementations, the Taylor-based transformation-free variant, is superior to existing alternatives.
2018-11-25
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2721/1/fahi19.pdf
Fasi, Massimiliano and Higham, Nicholas J. (2018) An Arbitrary Precision Scaling and Squaring Algorithm for the Matrix Exponential. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2734
2019-10-16T23:23:56Z
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https://eprints.maths.manchester.ac.uk/2734/
Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic
Jeannerod, Claude-Pierre
Mary, Theo
Pernet, Clément
Roche, Daniel
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
We consider the LU factorization of an $n\times n$ matrix $A$ represented as a block low-rank (BLR) matrix: most of its off-diagonal blocks are approximated by matrices of small rank $r$, which reduces the asymptoticcomplexity of computing the LU factorization of $A$ down to $\O(n^2r)$. In this article, our aim is to further reduce this complexity by exploiting fast matrix arithmetic, that is, the ability to multiply two $n\times n$ full-rank matrices together for $\O(n^\w)$ flops, where $\w<3$. This is not straightforward: simply accelerating the intermediate operations performed in the standard BLR factorization algorithm does not suffice to reduce the quadratic complexity in $n$, because these operations are performed on matrices whose size is too small. To overcome this obstacle, we devise a new BLR factorization algorithm that, by recasting the operations so as to work on intermediate matrices of larger size, can exploit more efficiently fast matrix arithmetic. This new algorithm achieves an asymptotic complexity of $\O(n^{(\w+1)/2}r^{(\w-1)/2})$, which represents an asymptotic improvement compared to the standard BLR factorization as soon as $\w<3$. In particular, for Strassen's algorithm, $\w\approx2.81$ yields a complexity of $\O(n^{1.904}r^{0.904})$. Our numerical experiments are in good agreement with this theoretical result.
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2734/1/main.pdf
Jeannerod, Claude-Pierre and Mary, Theo and Pernet, Clément and Roche, Daniel Improving the Complexity of Block Low-Rank Factorizations with Fast Matrix Arithmetic. SIAM Journal On Matrix Analysis And Applications. ISSN 1095-7162 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2748
2020-02-22T14:15:53Z
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https://eprints.maths.manchester.ac.uk/2748/
A Class of Fast and Accurate Summation Algorithms
Blanchard, Pierre
Higham, Nicholas J.
Mary, Theo
65 Numerical analysis
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2748/1/paper.pdf
Blanchard, Pierre and Higham, Nicholas J. and Mary, Theo A Class of Fast and Accurate Summation Algorithms. SIAM Journal on Scientific Computing. ISSN 1095-7197 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2750
2020-02-27T11:32:54Z
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https://eprints.maths.manchester.ac.uk/2750/
Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores
Blanchard, Pierre
Higham, Nicholas J.
Lopez, Florent
Mary, Theo
Pranesh, Srikara
65 Numerical analysis
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2750/1/paper.pdf
Blanchard, Pierre and Higham, Nicholas J. and Lopez, Florent and Mary, Theo and Pranesh, Srikara Mixed Precision Block Fused Multiply-Add: Error Analysis and Application to GPU Tensor Cores. SIAM Journal on Scientific Computing. ISSN 1095-7197 (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2791
2020-11-12T21:21:40Z
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https://eprints.maths.manchester.ac.uk/2791/
Numerical Behavior of NVIDIA Tensor Cores
Fasi, Massimiliano
Higham, Nicholas J.
Mikaitis, Mantas
Pranesh, Srikara
65 Numerical analysis
68 Computer science
We explore the floating-point arithmetic implemented in the NVIDIA tensor cores, which are hardware accelerators for mixed-precision matrix multiplication available on the Volta, Turing, and Ampere microarchitectures. Using Volta V100, Turing T4 and Ampere A100 graphics cards, we determine what precision is used for the intermediate results, whether subnormal numbers are supported, what rounding mode is used, in which order the operations underlying the matrix multiplication are performed, and whether partial sums are normalized. These aspects are not documented by NVIDIA, and we gain insight by running carefully designed numerical experiments on these hardware units. Knowing the answers to these questions is important if one wishes to: 1) accurately simulate NVIDIA tensor cores on conventional hardware; 2) understand the differences between results produced by code that utilizes tensor cores and code that uses only IEEE 754-compliant arithmetic operations; and 3) build custom hardware whose behavior matches that of NVIDIA tensor cores. As part of this work we provide a test suite that can be easily adapted to test newer versions of the NVIDIA tensor cores as well as similar accelerators from other vendors, as they become available. Moreover, we identify a non-monotonicity issue affecting floating point multi-operand adders if the intermediate results are not normalized after each step.
2020-04-23
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2791/1/fhmp20.pdf
Fasi, Massimiliano and Higham, Nicholas J. and Mikaitis, Mantas and Pranesh, Srikara (2020) Numerical Behavior of NVIDIA Tensor Cores. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2828
2021-07-14T07:32:21Z
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https://eprints.maths.manchester.ac.uk/2828/
Diffraction tomography inversion and the transverse ray transform
Lionheart, William R.B.
Korsunsky, Alexander M.
45 Integral equations
61 Structure of solids and liquids; crystallography
81 Materials science
87 Biological and medical physics
We show that a reciprocal space squared intensity map of a material can be recovered, for each characteristic length scale, from diffraction tomography data by a simple slice-by-slice reconstruction method. Moreover if the reciprocal space map can be represented by a finite sum of spherical harmonic components for each length scale then the coefficients of that expansion can be recovered from inverting the transverse ray transform (TRT), where the data are polynomial coefficients of the azimuthal diffraction pattern for each length scale.
2021-07
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2828/1/fully3d_LionheartKorsunsky_v2.pdf
Lionheart, William R.B. and Korsunsky, Alexander M. (2021) Diffraction tomography inversion and the transverse ray transform. Proceedings of 16th International Meeting on Fully Three-Dimensional Image Reconstruction in Radiology and Nuclear Medicine. (In Press)
https://kuleuvencongres.be/fully3d-2021
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2847
2022-02-12T19:33:01Z
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7375626A656374733D4D5343:4D53435F3533
7375626A656374733D4D5343:4D53435F3630
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2847/
Information geometry for control of some stochastic processes
Dodson, CTJ
53 Differential geometry
60 Probability theory and stochastic processes
A basic requirement in control systems is a metric that measures discrepancies between actual and desired states.
For statistically influenced systems information geometric methods provide natural
Riemannian metrics on smooth spaces of states; such manifolds arise in minimum-phase
linear systems and multi-input systems with known stochastic noise.
Commonly recurring practical situations
are `nearly' Poisson or `nearly' Uniform with
a complementarity in the geometry of these two; another involves multivariate Gaussians
and their mixtures.
Similarly we
encounter `nearly' independent Poisson, and `nearly' independent Gaussian processes. For such cases we have information geometric results and examples.
Some of these methods are applicable to control systems for statistically influenced processes, such as monitoring essential features in continuous
production of threads, films, foils and
fibre networks, and batch processing of stochastic textures.
Springer
Article
PeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2847/1/DodsonBrasovJMSfinal.pdf
text
en
https://eprints.maths.manchester.ac.uk/2847/3/DodsonBrasovJMSfinal.pdf
Dodson, CTJ Information geometry for control of some stochastic processes. J. Math. Sciences. (In Press)
https://link-springer-com.manchester.idm.oclc.org/journal/10958/volumes-and-issues
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2849
2022-02-18T18:33:52Z
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7375626A656374733D4D5343:4D53435F3635
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2849/
Mixed Precision Algorithms in Numerical Linear Algebra
Higham, Nicholas J.
Mary, Theo
15 Linear and multilinear algebra; matrix theory
65 Numerical analysis
Today's floating-point arithmetic landscape is broader than ever. While scientific computing has traditionally used single precision and double precision floating-point arithmetics, half precision is increasingly available in hardware and quadruple precision is supported in software. Lower precision arithmetic brings increased speed and reduced communication and energy costs, but it produces results of correspondingly low accuracy. Higher precisions are more expensive but can potentially provide great benefits, even if used sparingly. A variety of mixed precision algorithms have been developed that combine the superior performance of lower precisions with the better accuracy of higher precisions. Some of these algorithms aim to provide results of the same quality as algorithms running in a fixed precision but at a much lower cost; others use a little higher precision to improve the accuracy of an algorithm. This survey treats a broad range of mixed precision algorithms in numerical linear algebra, both direct and iterative, for problems including matrix multiplication, matrix factorization, linear systems, least squares, eigenvalue decomposition, and singular value decomposition. We identify key algorithmic ideas, such as iterative refinement, adapting the precision to the data, and exploiting mixed precision block fused multiply--add operations. We also describe the possible performance benefits and explain what is known about the numerical stability of the algorithms. This survey should be useful to a wide community of researchers and practitioners who wish to develop or benefit from mixed precision numerical linear algebra algorithms.
2021-12-29
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2849/1/paper_eprint.pdf
Higham, Nicholas J. and Mary, Theo (2021) Mixed Precision Algorithms in Numerical Linear Algebra. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2869
2022-09-30T09:03:02Z
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7375626A656374733D4D5343:4D53435F3638
74797065733D4D494D535F7072657072696E74
https://eprints.maths.manchester.ac.uk/2869/
Mixed Precision LU Factorization on GPU Tensor Cores: Reducing Data Movement and Memory Footprint
Lopez, Florent
Mary, Theo
65 Numerical analysis
68 Computer science
2020-09-13
MIMS Preprint
NonPeerReviewed
text
en
https://eprints.maths.manchester.ac.uk/2869/1/paper.pdf
Lopez, Florent and Mary, Theo (2020) Mixed Precision LU Factorization on GPU Tensor Cores: Reducing Data Movement and Memory Footprint. [MIMS Preprint] (In Press)
oai:eprints.maths.manchester.ac.uk.MIMS.EPrints:2884
2023-03-29T17:22:57Z
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7375626A656374733D4D5343:4D53435F3632
7375626A656374733D4D5343:4D53435F3932
74797065733D61727469636C65
https://eprints.maths.manchester.ac.uk/2884/
Modelling and classifying joint trajectories of self-reported mood and pain in a large cohort study
Das, Rajenki
Muldoon, Mark
Lunt, Mark
McBeth, John
Yimer, Belay Birlie
House, Thomas
62 Statistics
92 Biology and other natural sciences
It is well-known that mood and pain interact with each other, however individual-level variability in this relationship has been less well quantified than overall associations between low mood and pain. Here, we leverage the possibilities presented by mobile health data, in particular the “Cloudy with a Chance of Pain” study, which collected longitudinal data from the residents of the UK with chronic pain conditions. Participants used an App to record self-reported measures of factors including mood, pain and sleep quality. The richness of these data allows us to perform model-based clustering of the data as a mixture of Markov processes. Through this analysis we discover four endotypes with distinct patterns of co-evolution of mood and pain over time. The differences between endotypes are sufficiently large to play a role in clinical hypothesis generation for personalised treatments of comorbid pain and low mood.
2023-03-30
Article
PeerReviewed
text
en
cc_by_4
https://eprints.maths.manchester.ac.uk/2884/1/pdig.0000204.pdf
Das, Rajenki and Muldoon, Mark and Lunt, Mark and McBeth, John and Yimer, Belay Birlie and House, Thomas (2023) Modelling and classifying joint trajectories of self-reported mood and pain in a large cohort study. PLOS Digital Health, 2 (3). e0000204. ISSN 2767-3170 (In Press)
10.1371/journal.pdig.0000204
10.1371/journal.pdig.0000204