Browsing Department of Mathematics and Statistics Graduate Theses by Publish Date
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Minimal Presentations of Sofic Shifts and Properties of PeriodicFiniteType Shifts
(20090812)Constrained codes have been used in data storage systems, such as magnetic tapes, CD’s and DVD’s, in order to reduce the likelihood of errors by predictable noise. The study of constrained codes is based on the study of ... 
ErrorResilient Tile Sets for DNA SelfAssembly
(20090825)Experiments have demonstrated that DNA molecules can compute like a machine to solve mathematical problems, which is significant because of their parallel computation ability. However, due to the nature of biochemical ... 
A Geometric Approach to Energy Shaping
(20090902)In this thesis is initiated a more systematic geometric exploration of energy shaping. Most of the previous results have been dealt wih particular cases and neither the existence nor the space of solutions has been discussed ... 
Topics in Combinatorics and Random Matrix Theory
(20090927)Motivated by the longest increasing subsequence problem, we examine sundry topics at the interface of enumerative/algebraic combinatorics and random matrix theory. We begin with an expository account of the increasing ... 
Invariants of Modular TwoRow Groups
(20091006)It is known that the ring of invariants of any tworow group is CohenMacaulay. This result inspired the conjecture that the ring of invariants of any tworow group is a complete intersection. In this thesis, we study ... 
Pairwise Optimization of Modulation Constellations for NonUniform Sources
(20091007)The design of twodimensional signal constellations for the transmission of binary nonuniform memoryless sources over additive white Gaussian noise channels is investigated. The main application of this problem is the ... 
Transcendence of Various Infinite Series and Applications of Baker's Theorem
(20091113)We consider various infinite series and examine their arithmetic nature. Series of interest are of the form $$\sum_{n =0}^{\infty} \frac{f(n)A(n)}{B(n)}, \;\;\;\; \sum_{n \in \mathbb{Z}}\frac{f(n)A(n)}{B(n)}, \;\;\;\; ... 
Local controllability of affine distributions
(20100112)In this thesis, we develop a feedbackinvariant theory of local controllability for affine distributions. We begin by developing an unexplored notion in control theory that we call proper smalltime local controllability ... 
A New Approach in Survival Analysis with Longitudinal Covariates
(20100427)In this study we look at the problem of analysing survival data in the presence of longitudinally collected covariates. New methodology for analysing such data has been developed through the use of hidden Markov modeling. ... 
Modelling Pathogen Evolution with Branching Processes
(20100728)Pathogen evolution poses a significant challenge to public health, as efforts to control the spread of infectious diseases struggle to keep up with a shifting target. To better understand this adaptive process, we turn ... 
Sobolev Gradient Flows and Image Processing
(20100825)In this thesis we study Sobolev gradient flows for PeronaMalik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. ... 
Symmetry Transforms, Global Plasma Equilibria and Homotopy Analysis Method
(20100825)Magnetohydrodynamics (MHD) flows and equations have been the focus of a large number of researchers. Here a study of such flows and equations is presented. The first chapter contains a brief introduction to Homotopy ... 
Hamiltonian Systems of Hydrodynamic Type
(20101223)We study the Hamiltonian structure of an important class of nonlinear partial differential equations: the socalled systems of hydrodynamic type, which are firstorder in tempospatial variables, and quasilinear. Chapters ... 
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 ... 
A Mathematical Discussion of Corotational Finite Element Modeling
(20110331)This thesis discusses the mathematics of the Element Independent Corotational (EICR) Method and the more general Unified SmallStrain Corotational Formulation. The former was developed by Rankin, Brogan and NourOmid [106]. ... 
The evolution of mimicry in parasites
(20110406)Parasites may express proteins that mimic host proteins such that the host immune system cannot discriminate between host and parasite. An immune response to host proteins results in autoimmunity, and therefore, mechanisms ... 
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 ... 
Statistical Inference for the Treatment Effect in Cancer Clinical Trials
(20110525)Randomized clinical trials provide the best evidence on the effect of treatment studied. There are different types of measures on the treatment effect, depending on the endpoints of the trials. For a given measure, based ... 
Variations on Artin's Primitive Root Conjecture
(20110811)Let $a \in \mathbb{Z}$ be a nonzero integer. Let $p$ be a prime such that $p \nmid a$. Define the index of $a$ modulo $p$, denoted $i_{a}(p)$, to be the integer $i_{a}(p) := [(\mathbb{Z}/p\mathbb{Z})^{\ast}:\langle a ... 
Moduli Spaces of K3 Surfaces with Large Picard Number
(20110815)Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces ...