Browsing Mathematics and Statistics, Department of by Title
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Absolute risk estimation in a case cohort study of prostate cancer
(20130916)Background: Life expectancy calculations play a major role in the clinical management of prostate cancer with harms generally outweighing the benefits of screening and treatment if life expectancy is less than 10 years. ... 
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 ... 
Asymptotic Liberation in Free Probability
(20150126)Recently G. Anderson and B. Farrel presented the notion of asymptotic liberation on sequences of families of random unitary matrices. They showed that asymptotically liberating sequences of families of random unitary ... 
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 ... 
Bivariate Models for Mortality and Morbidity
(20141003)In this report, to assess the adverse effects of air pollution on health outcomes, gen eralized additive models (GAMs) were fitted to mortality and hospital admissions data for Toronto, Montreal, Ottawa and Vancouver. The ... 
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 Chowla Problem and its generalizations
(20150915)In this thesis, we study the vanishing of certain $L$series attached to periodic arithmetical functions. Throughout the writeup, we let $f$ be an algebraicvalued (at times even rationalvalued) arithmetical function, ... 
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 ...