Browsing Department of Pure Mathematics and Mathematical Statistics (DPMMS) by Issue Date
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Cliques in graphs
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20101012)The main focus of this thesis is to evaluate $k_r(n,\delta)$, the minimal number of $r$cliques in graphs with $n$ vertices and minimum degree~$\delta$. A fundamental result in Graph Theory states that a trianglefree graph ...

Response to: DNA identification by pedigree likelihood ratio accommodating population substructure and mutations
(20110325)Abstract Mutation models are important in many areas of genetics including forensics. This letter criticizes the model of the paper 'DNA identification by pedigree likelihood ratio accommodating population substructure and ...

Problems of optimal choice on posets and generalizations of acyclic colourings
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 201106)NOTE : The mathematical symbols in the abstract do not always display correctly in this text field. Please see the abstract in the thesis for the definitive abstract. ABSTRACT: This dissertation is in two parts, each ...

On Villani's conjecture concerning entropy production for the Kac Master equation
(America Institute of Mathematical SciencesKinetic and Related Models, 20110601)In this paper we take an idea presented in recent paper by Carlen, Carvalho, Le Roux, Loss, and Villani ([3]) and push it one step forward to find an exact estimation on the entropy production. The new estimation essentially ...

Witt groups of complex varieties
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsTrinity Hall, 20110712)The thesis Witt Groups of Complex Varieties studies and compares two related cohomology theories that arise in the areas of algebraic geometry and topology: the algebraic theory of Witt groups, and real topological Ktheory. ...

Unipotent elements in algebraic groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120110)This thesis is concerned with three distinct, but closely related, research topics focusing on the unipotent elements of a connected reductive algebraic group G, over an algebraically closed field k, and nilpotent elements ...

Statistical issues in Mendelian randomization: use of genetic instrumental variables for assessing causal associations
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 20120306)Mendelian randomization is an epidemiological method for using genetic variation to estimate the causal effect of the change in a modifiable phenotype on an outcome from observational data. A genetic variant satisfying ...

Hyper and structural Markov laws for graphical models
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120306)My thesis focuses on the parameterisation and estimation of graphical models, based on the concept of hyper and meta Markov properties. These state that the parameters should exhibit conditional independencies, similar to ...

Ample subvarieties and qample divisors
(ElsevierAdvances in Mathematics, 20120320)We introduce a notion of ampleness for subschemes of any codimension using the theory of qample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...

Sharp trace inequalities for fractional Laplacians
(American Mathematical SocietyProceedings of the American Mathematical Society, 20120405)The sharp trace inequality of José Escobar is extended to traces for the fractional Laplacian on Rⁿ and a complete characterization of cases of equality is discussed. The proof proceeds via Fourier transform and uses Lieb’s ...

The Fukaya category, exotic forms and exotic autoequivalences
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120410)A symplectic manifold is a smooth manifold M together with a choice of a closed nondegenerate twoform. Recent years have seen the importance of associating an A∞category to M, called its Fukaya category, in helping ...

Linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20120703)I study linear waves on higher dimensional Schwarzschild black holes and Schwarzschild de Sitter spacetimes. In the first part of this thesis two decay results are proven for general finite energy solutions to the linear ...

A Counter Example to Cercignani’s Conjecture for the d Dimensional Kac Model
(SpringerJournal of Statistical Physics, 20120821)Kac’s d dimensional model gives a linear, many particle, binary collision model from which, under suitable conditions, the celebrated Boltzmann equation, in its spatially homogeneous form, arise as a mean field limit. The ...

Modelling nonlinear exposuredisease relationships in a large individual participant metaanalysis allowing for the effects of exposure measurement error
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsMRC Biostatistics Unit, 20121009)This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a large individual participant data (IPD) metaanalysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...

Collaborating queues: large service network and a limit order book
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsEmmanuel CollegeStatistics Laboratory, 20121009)We analyse the steadystate behaviour of two different models with collaborating queues: that is, models in which "customers" can be served by many types of "servers", and "servers" can process many types of "customers". The ...

Algebraic boundaries of Hilbert's SOS cones
(Cambridge University PressCompositio Mathematica, 20121015)We study the geometry underlying the difference between nonnegative polynomials and sums of squares. The hypersurfaces that discriminate these two cones for ternary sextics and quaternary quartics are shown to be ...

Automorphisms of free products of groups
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20130205)The symmetric automorphism group of a free product is a group rich in algebraic structure and with strong links to geometric configuration spaces. In this thesis I describe in detail and for the first time the (co)homology ...

Maximum likelihood parameter estimation in time series models using sequential Monte Carlo
(University of CambridgeDepartment of Pure Mathematics and Mathematical StatisticsStatistical LaboratoryDarwin College, 20130611)Time series models are used to characterise uncertainty in many realworld dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...

Chaos and Entropic Chaos in Kac's Model Without High Moments
(Institute of Mathematical StatisticsElectronic Journal of Probability, 20130827)In this paper we present a new local Lévy Central Limit Theorem, showing convergence to stable states that are not necessarily the Gaussian, and use it to find new and intuitive entropically chaotic families with underlying ...

Extremal and probabilistic bootstrap percolation
(University of CambridgeDepartment of Pure Mathematics and Mathematical Statistics, 20131112)In this dissertation we consider several extremal and probabilistic problems in bootstrap percolation on various families of graphs, including grids, hypercubes and trees. Bootstrap percolation is one of the simplest ...