Browsing Mathematics and Statistics, Department of by Title
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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 ... 
Irreducibility of Random Hilbert Schemes
(20160913)We prove that a random Hilbert scheme that parametrizes the closed subschemes with a fixed Hilbert polynomial in some projective space is irreducible and nonsingular with probability greater than $0.5$. To consider the ... 
Jacobian linearisation in a geometric setting
(IEEE, 2003)Linearisation is a common technique in control applications, putting useful analysis and design methodologies at the disposal of the control engineer. In this paper, linearisation is studied from a differential ... 
Joint Modelling of Longitudinal Quality of Life Measurements and Survival Data in Cancer Clinical Trials
(20130123)In cancer clinical trials, longitudinal Quality of Life (QoL) measurements on a patient may be analyzed by classical linear mixed models but some patients may drop out of study due to recurrence or death, which causes ... 
Joint SourceChannel Coding Reliability Function for Single and MultiTerminal Communication Systems
(20080515)Traditionally, source coding (data compression) and channel coding (error protection) are performed separately and sequentially, resulting in what we call a tandem (separate) coding system. In practical implementations, ... 
Kinematic controllability and motion planning for the snakeboard
(IEEE, 2003)The snakeboard is shown to be kinematically controllable. Associated with the two decoupling vector fields for the problem, a constrained static nonlinear programming problem is posed whose solutions provide a solution to ... 
Lagrangian submanifolds and an application to the reduced Schrödinger equation in central force problems
(D. Reidel, 1992)In this Letter, a Lagrangian foliation of the zero energy level is constructed for a family of planar central force problems. The dynamics on the leaves are explicitly computed and these dynamics are given a simple ... 
Lifting distributions to tangent and jet bundles
(1998)We provide two natural ways to lift a distribution from a manifold to its tangent bundle, and show that they agree if and only if the original distribution is integrable. The case when the manifold is the total space ... 
Linear Programming Decoding for NonUniform Sources and for Binary Channels With Memory
(20081209)Linear programming (LP) decoding of lowdensity paritycheck codes was introduced by Feldman et al. in [1]. In his formulation it is assumed that communication takes place over a memoryless channel and that the source is ... 
The linearisation of a simple mechanical control system
(2002)A geometric interpretation is given for the linearisation of a mechanical control system with a kinetic minus potential energy Lagrangian. 
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 ... 
Lossless Coding of Markov Random Fields with Complex Cliques
(20130814)The topic of Markov Random Fields (MRFs) has been well studied in the past, and has found practical use in various image processing, and machine learning applications. Where coding is concerned, MRF specific schemes have ... 
Loworder controllability and kinematic reductions for affine connection control systems
(2002)Controllability and kinematic modeling notions are investigated for a class of mechanical control systems. First, loworder controllability results are given for a class of mechanical control systems. Second, a ... 
Management and Sensing of Spectrum in Cognitive Radio
(20130604)Under the contemporary spectrum usage regulations, radio frequency bands are allocated statically to licensed users in a large geographical area and over a long period of time. Recent investigations have revealed that such ... 
Marginal Models for Modeling Clustered Failure Time Data
(20130201)Clustered failure time data often arise in biomedical and clinical studies where potential correlation among survival times is induced in a cluster. In this thesis, we develop a class of marginal models for right censored ... 
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]. ... 
Mathematics Problems and Thinking Mathematically in Undergraduate Mathematics
(20150501)Mathematics is much more than a formal system of procedures and formulae; it is also a way of thinking built on creativity, precision, reasoning, and representation. I present a model for framing the process of doing ... 
Measuring Dependence via Mutual Information
(20111003)Considerable research has been done on measuring dependence between random variables. The correlation coefficient is the most widely studied linear measure of dependence. However, the limitation of linearity limits its ... 
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 ... 
The Minimum Witt Index of a Graph
(20070917)An independent set in a graph G is a set of pairwise nonadjacent vertices, and the maximum size, alpha(G), of an independent set in G is called the independence number. Given a graph G and weight matrix A of G with entries ...