Browsing Mathematics and Statistics, Department of by Title
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Embeddings of flag manifolds and cohomological components of modules
(20110823)This thesis is a study in Representation Theory and Geometry. These two branches of mathematics have a fruitful interaction, with many applications to Physics and other sciences. Central objects of interest are homogeneous ... 
Energypreserving affine connections
(1997)A Riemannian affine connection on a Riemannian manifold has the property that is preserves the ``kinetic energy'' associated with the metric. However, there are other affine connections which have this property, and ... 
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 ... 
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 ... 
Evolutionarily Stable Learning and Foraging Strategies
(20120201)This thesis examines a series of problems with the goal of better understanding the fundamental dilemma of whether to invest effort in obtaining information that may lead to better opportunities in the future versus ... 
Evolvability and Pleiotropic Constraint
Evolvability is a population's ability to change its underlying genetic makeup through natural selection, to evolve. Most measures of shortterm evolvability relate genetic change to the abundance and geometry of standing ... 
An example with interesting controllability and stabilisation properties
(2005)A simple threestate system with two inputs is considered. The system's controllability is determined using properties of vectorvalued quadratic forms. The quadratic structure is then used as the basis for the design of ... 
Exploring the Evolutionary Relationship Between Virulence and Drug Resistance
One of the many possible negative outcomes of pathogen evolution is the emergence of a virulent drug resistant strain. A pathogen may exploit plasmidmediated gene transfer to gain drug resistance and virulence genes in ... 
Feedback Stabilisation of Locally Controllable Systems
(20120925)Controllability and stabilisability are two fundamental properties of control systems and it is intuitively appealing to conjecture that the former should imply the latter; especially so when the state of a control system ... 
Filter Stability, Observability and Robustness for Partially Observed Stochastic Dynamical Systems
Filter stability refers to the correction of an incorrectly initialized filter for a partially observed stochastic dynamical system with increasing measurements. In this thesis, we study the filter stability problem, develop ... 
Forecasting and NonStationarity of Surgical Demand Time Series
(20140204)Surgical scheduling is complicated by naturally occurring, and humaninduced variability in the demand for surgical services. We used time series methods to detect, model and forecast these behaviors in surgical demand ... 
A Framework for the MetaAnalysis of Survey Data
(20111206)The research outlined in this thesis covers various different statistical issues relating to metaanalysis of survey data. These issues include the creation of an original comprehensive methodological framework for combining ... 
Generalization of Ruderman's Problem to Imaginary Quadratic Fields
(20120413)In 1974, H. Ruderman posed the following question: If $(2^m2^n)(3^m3^n)$, then does it follow that $(2^m2^n)(x^mx^n)$ for every integer $x$? This problem is still open. However, in 2011, M. R. Murty and V. K. Murty ... 
Geodesic reduction via frame bundle geometry
(20070725)Reduction theory for systems with symmetry deals with the problem of understanding dynamics on a manifold with an action of a Lie group. In geometric mechanics, this problem can be formulated in the Lagrangian, Hamiltonian ... 
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 ... 
Geometric Jacobian Linearization
(20071221)For control systems that evolve on Euclidean spaces, Jacobian linearization is a common technique in many control applications, analysis, and controller design methodologies. However, the standard linearization method ... 
Geometric local controllability: secondorder conditions
(2002)In a geometric point of view, a nonlinear control system, affine in the controls, is thought of as an affine subbundle of the tangent bundle of the state space. In deriving conditions for local controllability from ... 
Geometric sliding mode control: The linear and linearised theory
(2002)The idea of sliding mode control for stabilisation is investigated to determine its geometric features. A geometric definition is provided for a sliding submanifold, and for various properties of a sliding submanifold. Sliding ... 
Geometry of Dirac Operators
(20160705)Let $M$ be a compact, oriented, even dimensional Riemannian manifold and let $S$ be a Clifford bundle over $M$ with Dirac operator $D$. Then \[ \textsc{Atiyah Singer: } \quad \text{Ind } \mathsf{D}= \int_M ... 
The geometry of the GibbsAppell equations and Gauss's Principle of Least Constraint
(1995)We present a generalisation of the GibbsAppell equations which is valid for general Lagrangians. The general form of the GibbsAppell equations is shown to be valid in the case when constraints and external forces ...