Time series models are used to characterise uncertainty in many real-world dynamical phenomena. A time series model typically contains a static variable, called parameter, which parametrizes the joint law of the random ...

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 ...

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 ...

We analyse the steady-state 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 ...

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 symplectic manifold is a smooth manifold M together with a choice of a closed non-degenerate two-form. Recent years have seen the importance of associating an A∞-category to M, called its Fukaya category, in helping ...

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 ...

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 ...

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 ...

Abstract Background Genome-wide association studies (GWAS) are a widely used study design for detecting genetic causes of complex diseases. Current studies provide good coverage of common causal SNPs, but not rare ones. A ...

Density estimation is a fundamental statistical problem. Many methods are either sensitive to model misspecification (parametric models) or difficult to calibrate, especially for multivariate data (nonparametric smoothing ...

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 triangle-free graph ...

This dissertation deals with four problems concerning arithmetic structures in dense sets of integers. In Chapter 1 we give an exposition of the state-of-the-art technique due to Pintz, Steiger and Szemer edi which yields ...

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 K-theory. ...

This thesis is chiefly concerned with a classical conjecture of Littlewood's regarding the L^1-norm of the Fourier transform, and the closely related idempotent theorem. The vast majority of the results regarding these ...

On a complex variety X, two different approaches to K-theory are available: the algebraic K-theory of the variety, and the topological K-theory of the underlying topological space. In this context, the algebraic variant ...

Let E be an elliptic curve defined over the rationals Q, and p be a prime at least 5 where E has multiplicative reduction. This thesis studies the Iwasawa theory of E over certain false Tate curve extensions F[infinity], ...

The main theme of the thesis is to present and compare three different viewpoints on semi-abelian homology, resulting in three ways of defining and calculating homology objects. Any two of these three homology theories ...

Statistical physics seeks to explain macroscopic properties of matter in terms of microscopic interactions. Of particular interest is the phenomenon of phase transition: the sudden changes in macroscopic properties as ...

Let f=\sum a_nq^n be a normalised eigen-newform of weight k\ge2 and p an odd prime which does not divide the level of f. We study a reformulation of Kato's main conjecture for f over the Zp-cyclotomic extension of Q. In ...