Browsing Mathematics and Statistics, Department of by Title
Now showing items 6079 of 151

Higher rank sieves and applications
(20160425)This thesis focuses on some of the key sieve theoretic ideas behind recent progress on bounded gaps between the primes. One such idea is the notion of higher rank sieve weights, first proposed by Atle Selberg and applied ... 
Homoclinic Points in the Composition of Two Reflections
(20130917)We examine a class of planar area preserving mappings and give a geometric condition that guarantees the existence of homoclinic points. To be more precise, let $f,g:R \to R$ be $C^1$ functions with domain all of $R$. ... 
Hybrid DigitalAnalog SourceChannel Coding and Information Hiding: InformationTheoretic Perspectives
(20071002)Joint sourcechannel coding (JSCC) has been acknowledged to have superior performance over separate sourcechannel coding in terms of coding efficiency, delay and complexity. In the first part of this thesis, we study ... 
An impulsive differential equation model for Marek's disease
(20160922)Many dynamical processes are subject to abrupt changes in state. Often these perturbations can be periodic and of short duration relative to the evolving process. These types of phenomena are described well by what are ... 
Inclusive Fitness on Evolutionary Graphs
(20121004)The evolution of cooperative behaviours has received a large amount of attention in the literature. A recurrent result is that a spatial population structure often aids the evolution of cooperation. One such possible ... 
Information and Estimation Theoretic Approaches to Data Privacy
Warner [145] in 1960s proposed a simple mechanism, now referred to as the randomized response model, as a remedy for what he termed “evasive answer bias” in survey sampling. The randomized response setting is as follows: ... 
Instability of Periodic Orbits of Some Rhombus and Parallelogram Four Body Problems
(20121127)The rhombus and parallelogram orbits are interesting families of periodic solutions, which come from celestial mechanics and the Nbody problem. Variational methods with finite order symmetry group are used to construct ... 
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 ...