Browsing Mathematics and Statistics, Department of by Title
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Accelerated Convergence of SaddlePoint Dynamics
In this thesis, a secondorder continuoustime saddlepoint dynamics is introduced that mimics Nesterov's accelerated gradient flow dynamics. We study the convergence properties of this dynamics using a family of timevarying ... 
Affine connection control systems
(1999)The affine connection formalism provides a useful framework for the investigation of a large class of mechanical systems. Mechanical systems with kinetic energy Lagrangians and possibly with nonholonomic constraints are ... 
Affine connections and distributions
(1996)We investigate various aspects of the interplay of an affine connection with a distribution. When the affine connection restricts to the distribution, we discuss torsion, curvature, and holonomy of the affine connection. ... 
Air Pollution and Health: Time Series Tools and Analysis
(20121029)This thesis is concerned, loosely, with time series analysis. It is also, loosely, concerned with smoothers and Generalized Additive Models. And, finally, it is also concerned with the estimation of health risk due to air ... 
Applications of Multitaper Spectral Analysis to Nonstationary Data
(20141015)This thesis is concerned with changes in the spectrum over time observed in Holocene climate data as recorded in the Burgundy grape harvest date series. These changes represent nonstationarities, and while spectral estimation ... 
Applications of Optimal Control Theory to Infectious Disease Modeling
(20110126)This thesis investigates the optimal use of intervention strategies to mitigate the spread of infectious diseases. Three main problems are addressed: (i) The optimal use vaccination and isolation resources under the ... 
Arithmetic and Intermediate Jacobians of CalabiYau threefolds
(20150910)This thesis is centered around particular CalabiYau threefolds. Borcea \cite{Borcea} and Voisin \cite{Voisin} construct CalabiYau threefolds using elliptic curves and K3 surfaces with nonsymplectic involutions. This ... 
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 ...