Open Access Repositories: Recent submissions
Now showing items 41-60 of 4204
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Quantifying separability in virtually special groups
(Mathematical Society PublishingPacific Journal of Mathematics, 2016)We give a new, effective proof of the separability of cubically convex-cocompact subgroups of special groups. As a consequence, we show that if G is a virtually compact special hyperbolic group, and Q ≤ G is a K-quasiconvex ...
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Cubulating hyperbolic free-by-cyclic groups: the irreducible case
(Duke University PressDuke Mathematical Journal, 2016)Let V be a fi nite graph and let ∅ : V → V be an irreducible train track map whose mapping torus has word-hyperbolic fundamental group G. Then G acts freely and cocompactly on a CAT(0) cube complex. Hence, if F is a ...
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The 1-2 model
(American Mathematical SocietyIn the Tradition of Ahlfors–Bers, VII, 2017)The current paper is a short review of rigorous results for the 1-2 model. The 1-2 model on the hexagonal lattice is a model of statistical mechanics in which each vertex is constrained to have degree either 1 or 2. It was ...
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Detecting and Localizing Differences in Functional Time Series Dynamics: A Case Study in Molecular Biophysics
(Taylor & FrancisJournal of the American Statistical Association, 2016-03-22)Motivated by the problem of inferring the molecular dynamics of DNA in solution, and linking them with its base-pair composition, we consider the problem of comparing the dynamics of functional time series (FTS), and of ...
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Free groups and the axiom of choice
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2016-01-05)The Nielsen–Schreier theorem states that subgroups of free groups are free. As all of its proofs use the Axiom of Choice, it is natural to ask whether the theorem is equivalent to the Axiom of Choice. Other questions arise ...
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Effectivity of Iitaka fibrations and pluricanonical systems of polarized pairs
(SpringerPublications mathématiques de l'IHÉS, 2016-01-18)For every smooth complex projective variety W of dimension d and nonnegative Kodaira dimension, we show the existence of a universal constant m depending only on d and two natural invariants of the very general fibres of ...
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Proof of a conjecture of Batyrev and Nill
(Johns Hopkins University PressAmerican Journal of Mathematics, 2016)We prove equivalences of derived categories for the various mirrors in the Batyrev-Borisov construction. In particular, we obtain a positive answer to a conjecture of Batyrev and Nill. The proof involves passing to an ...
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Kriging prediction for manifold-valued random fields
(ElsevierJournal of Multivariate Analysis, 2015-12-25)The statistical analysis of data belonging to Riemannian manifolds is becoming increasingly important in many applications, such as shape analysis, diffusion tensor imaging and the analysis of covariance matrices. In many ...
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Turán-type results for complete h-partite graphs in comparability and incomparability graphs
(SpringerOrder, 2015-01-05)We consider an h-partite version of Dilworth's theorem with multiple partial orders. Let P be a fi nite set, and let <₁, ..., <ᵣ be partial orders on P. Let G(P, <₁, ..., <ᵣ) be the graph whose vertices are the elements ...
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Problems in Ramsey theory, probabilistic combinatorics and extremal graph theory
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)In this dissertation, we treat several problems in Ramsey theory, probabilistic combinatorics and extremal graph theory.
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A More General Pandora Rule?
(ElsevierJournal of Economic Theory, 2015-11-02)In a model introduced by Weitzman an agent called Pandora opens boxes sequentially, in whatever order she likes, discovers prizes within, and optimally stops. Her aim is to maximize the expected value of the greatest ...
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Computing the Cassels-Tate pairing
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)
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Symmetric structures in Banach spaces
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity College, 1990-02-20)
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Stability and bifurcation for the Kuramoto model
(ElsevierJournal de Mathématiques Pures et Appliquées, 2015-11-11)We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we ...
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New approaches to modern statistical classification problems
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 2015-11-10)This thesis concerns the development and mathematical analysis of statistical procedures for classification problems. In supervised classification, the practitioner is presented with the task of assigning an object to ...
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Critical behaviour in charging of electric vehicles
(IOP PublishingNew Journal of Physics, 2015-09-02)The increasing penetration of electric vehicles over the coming decades, taken together with the high cost to upgrade local distribution networks and consumer demand for home charging, suggest that managing congestion on ...
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The X-ray transform for connections in negative curvature
(SpringerCommunications in Mathematical Physics, 2015-11-23)We consider integral geometry inverse problems for unitary connections and skew-Hermitian Higgs fields on manifolds with negative sectional curvature. The results apply to manifolds in any dimension, with or without boundary, ...
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Optimal impartial selection
(Society for Industrial and Applied MathematicsSIAM Journal on Computing, 2015-10-20)We study a fundamental problem in social choice theory, the selection of a member of a set of agents based on impartial nominations by agents from that set. Studied previously by Alon et al. [Proceedings of TARK, 2011, pp. ...
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Remarks on motives of abelian type
(Tohoku Mathematical Journal, 2015-08-11)A motive over a field k is of abelian type if it belongs to the thick and rigid subcategory of Chow motives spanned by the motives of abelian varieties over k. This paper contains three sections of independent interest. ...