This thesis describes the statistical methodology behind a variety of industrial screening experiments. The primary focus of the thesis is on supersaturated designs that have more parameters to be investigated than runs available. Such designs are particularly useful when experi…
The objects of interest in this thesis are classifying spaces EFG for discrete groups G with stabilisers in a given family F of subgroups of G. The main focus of this thesis lies in the family Fvc(G) of virtually cyclic subgroups of G. A classifying space for this specific famil…
This thesis presents and applies methods for the design and analysis of experiments for a family of coefficient shrinkage methods, known collectively as bridge regression, with emphasis on the two special cases of ridge regression and the lasso. The application is the problem of…
In this thesis we study the interactions between light and matter in photorefractive liquid crystal cells. To model the liquid crystal alignment we develop a fast and accurate approximation of the normally stiff equations which minimise the Landau-deGennes free energy of a nemat…
Graphical models provide a very promising avenue for making sense of large, complex datasets. The most popular graphical models in use at the moment are Bayesian networks (BNs). This thesis shows, however, they are not always ideal factorisations of a system. Instead, I advocate…
In this thesis, we consider the problem of solving two player infinite games, such as parity games, mean-payoff games, and discounted games, the problem of solving Markov decision processes. We study a specific type of algorithm for solving these problems that we call strategy i…
The general subject area of research considered in this thesis is population level epidemic modelling of infectious diseases, with specific application to the problems of model indeterminacy and systems that include processes associated with maternally acquired immunity. The wor…
In electronic devices solder joints form a mechanical as well as an electrical connection between the circuit board and the component (e.g. a chip or a resistor). Temperature variations occurring during field use cause crack initiation and crack growth inside the joints. Accurat…
We consider a series of problems from the field of biological fluid mechanics, in particular the properties and optimisation of human sperm motility, and the fluid flow in the oviduct. As an initial approach, we consider and refine a sinusoidal planar model by introducing a new …
This thesis is mainly concerned with solving a new type of periodic homogenization problem. A solution of removing the Diophantine hypothesis on the homogenization problem where the interface sits at an irrational angle to the period is attempted but is not yet complete. As an a…
We investigate one-dimensional (1D) wave turbulence (WT) systems that are characterised by six-wave interactions. We begin by presenting a brief introduction to WT theory - the study of the non-equilibrium statistical mechanics of nonlinear random waves, by giving a short histor…
Consider an analytic two-degrees of freedom Hamiltonian system with an equilibrium point that undergoes a Hamiltonian-Hopf bifurcation, i.e., the eigenvalues of the linearized system at the equilibrium change from complex ±β ±iα (α,β > 0) for ε > 0 to pure imaginary ±iω1 and ±iω…
We define a universal Fréchet set S of a Banach space Y as a subset containing a point of Fréchet differentiability of every Lipschitz function g : Y -> R. We prove a sufficient condition for S to be a universal Fréchet set and use this to construct new examples of such sets. Th…
Meshless Local Petrov-Galerkin method based on Rankine source solution (MLPG_R) has been developed by Dr. Qingwei Ma (Ma, 2005b) and has been used to simulate the nonlinear water wave problems in 2D cases without the occurrence of the breaking waves. In this thesis, MLPG_R metho…
In this thesis we consider several questions on harmonic and analytic functions spaces and some of their operators. These questions deal with Carleson-type measures in the unit ball, bi-parameter paraproducts and multipliers problem on the bitorus, boundedness of the Bergman pro…
Temporal representation and reasoning plays a fundamental and increasingly important role in some areas of Computer Science and Artificial Intelligence. A natural approach to represent and reason about time-dependent knowledge is to associate them with instantaneous time points …
This thesis presents novel Markov chain Monte Carlo methodology that exploits the natural representation of a statistical model as a Riemannian manifold. The methods developed provide generalisations of the Metropolis-adjusted Langevin algorithm and the Hybrid Monte Carlo algori…