Browsing Mathematics and Statistics, Department of by Title
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The geometry of the maximum principle for affine connection control systems
(2000)The maximum principle of Pontryagin is applied to systems where the drift vector field is the geodesic spray corresponding to an affine connection. The result is a secondorder differential equation whose righthand side ... 
Global Fluctuations of Random Matrices and the SecondOrder Cauchy Transform
In this thesis we study the global fluctuations of random matrices (i.e., the covariance of two traces) from a secondorder free probability perspective, putting a particular emphasis on block Gaussian matrices. Our main ... 
Group structures in a class of control systems
(1992)We investigate two classes of control systems, one of Brockett and one of Murray and Sastry. We are able to show that these two systems may be formulated in the language of principle fibre bundles. Controllability of ... 
Hall conditions for edgeweighted bipartite graphs
(20100728)A weighted variant of Hall's condition for the existence of matchings is shown to be equivalent to the existence of a matching in a lexicographic product. This is used to introduce characterizations of those bipartite ... 
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 ... 
Highorder variations for families of vector fields
(2002)Sufficient conditions involving Lie brackets of arbitrarily highorder are obtained for local controllability of families of vector fields. After providing a general framework for the generation of highorder ... 
HighQ Spectral Peaks and Nonstationarity in the Deep Ocean Infragravity Wave Band: Tidal Harmonics and Solar Normal Modes
(Wiley, 20190220)Infragravity waves have received the least study of any class of waves in the deep ocean. This paper analyzes a 389daylong deep ocean pressure record from the Hawaii Ocean Mixing Experiment for the presence of narrowband ... 
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 ...