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 ...

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 ...

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 ...

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 ...

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 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 ...

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 ...

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 ...

We introduce a notion of ampleness for subschemes of any codimension using the theory of q-ample line bundles. We also investigate certain geometric properties satisfied by ample subvarieties, e.g. the Lefschetz ...

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 ...

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 ...

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 ...

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 ...

This thesis was motivated by data from the Emerging Risk Factors Collaboration (ERFC), a large individual participant data (IPD) meta-analysis of risk factors for coronary heart disease(CHD). Cardiovascular disease is the ...

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 ...

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 ...

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 ...

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 ...

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 ...

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 ...