Browsing Mathematics and Statistics, Department of by Title
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Arithmetic problems around the ABC conjecture and connections with logic
(20140428)The main theme in this thesis is the ABC conjecture. We prove some partial results towards it and we find new applications of this conjecture, mainly in the context of B\"uchi's n squares problem (which has consequences ... 
Aspects of Geometric Mechanics and Control of Mechanical Systems
(1995)Many interesting control systems are mechanical control systems. In spite of this, there has not been much effort to develop methods which use the special structure of mechanical systems to obtain analysis tools which ... 
Asymmetric matching allele models: imperfect matching, stability and the impact of mutation
Asymmetric matching alleles models assume that each parasite genotype specializes on a matching host genotype to a different degree. We study system behavior of a single locus diallelic asymmetric matching alleles model. ... 
Betti numbers and regularity of projective monomial curves
(20080925)In this thesis we describe how the balancing of the $\operatorname{Tor}$ functor can be used to compute the minimal free resolution of a graded module $M$ over the polynomial ring $B=\mathbb{K}[X_0,\dots,X_m]$ ($\mathbb{K}$ ... 
Bifurcations of Periodic Solutions of Functional Differential Equations with SpatioTemporal Symmetries
(20120430)We study bifurcations of periodic solutions with spatiotemporal symmetries of functional differential equations (FDEs). The two main results are: (1) a centre manifold reduction around a periodic solution of FDEs with ... 
Channel Capacity in the Presence of Feedback and Side Information
(20130712)This thesis deals with the Shannontheoretic fundamental limits of channel coding for singleuser channels with memory and feedback and for multiuser channels with side information. We first consider the feedback capacity ... 
Channel Optimized Scalar Quantization over Orthogonal Multiple Access Channels with Memory
In this thesis, the joint sourcechannel coding method, channel optimized scalar quantization, is applied to realvalued, correlated data. The data is sent over the orthogonal multiple access channel, with nonbinary noisy ... 
Channel Optimized Vector Quantization: Iterative Design Algorithms
(20080904)Joint sourcechannel coding (JSCC) has emerged to be a major field of research recently. Channel optimized vector quantization (COVQ) is a simple feasible JSCC scheme introduced for communication over practical channels. In ... 
The circular law: Proof of the replacement principle
(20090713)It was conjectured in the early 1950¡¯s that the empirical spectral distribution (ESD) of an $n \times n$ matrix whose entries are independent and identically distributed with mean zero and variance one, normalized by ... 
Codomain Rigidity of the Dirichlet to Neumann Operator for the Riemannian Wave Equation
(20160823)We study the Dirichlet to Neumann operator for the Riemannian wave equation on a compact Riemannian manifold. If the Riemannian manifold is modelled as an elastic medium, this operator represents the data available to an ... 
Coinfection and the Evolution of Resistance: A Mathematical Analysis
(20110506)This thesis investigates the effect of coinfection on the emergence of resistant pathogens. Firstly, a multiple infection model with treatment is derived and the conditions for invasion are established. The invasion ... 
Computationally Intensive Methods for Spectrum Estimation
(20160427)Spectrum estimation is an essential technique for analyzing time series data. A leading method in the field of spectrum estimation is the multitaper method. The multitaper method has been applied to many scientific fields ... 
Configuration controllability of simple mechanical control systems
(Society for Industrial and Applied Mathematics, 1995)In this paper we present a definition of "configuration controllability" for mechanical systems whose Lagrangian is kinetic energy with respect to a Riemannian metric minus potential energy. A computable test for this ... 
Constructing pairingfriendly algebraic curves of genus 2 curves with small rhovalue
(20111109)For pairingbased cryptographic protocols to be both efficient and secure, the underlying genus 2 curves defined over finite fields used must satisfy pairingfriendly conditions, and have small rhovalue, which are not ... 
Control of nonholonomic mechanical systems using virtual surfaces
In this report we study the modelling of simple mechanical systems evolving on trivial principal bundles, specifically \emph{locomotion} systems with nonholonomic constraints. We show how we can model motion via group ... 
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
(IEEE, 2000)In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater ... 
Controllability of a hovercraft model (and two general results)
(2003)Modelling and controllability studies of a hovercraft system are undertaken. The system studied is a little more complicated than some in the literature in that the inertial dynamics of the thrust fan are taken into ... 
Controllability of Underactuated Coupled Parabolic Systems
This thesis studies the null controllability of a system of coupled parabolic PDEs. Moreover, our work specializes to an important subclass of these control problems, where systems are underactuated and are coupled by first ... 
Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
(2001)This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model ... 
Curves of low genus on surfaces and applications to Diophantine problems
(20150831)We describe in detail a technique due to Vojta for finding the explicit set of curves of low genus on certain algebraic surfaces of general type, and refine some of its aspects. We then provide applications of this method ...