Browsing Mathematics and Statistics, Department of by Title
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Constructing pairingfriendly algebraic curves of genus 2 curves with small rhovalue
(20111109)For pairingbased cryptographic protocols to be both efficient and secure, the underlying genus 2 curves defined over finite fields used must satisfy pairingfriendly conditions, and have small rhovalue, which are not ... 
Control of nonholonomic mechanical systems using virtual surfaces
In this report we study the modelling of simple mechanical systems evolving on trivial principal bundles, specifically \emph{locomotion} systems with nonholonomic constraints. We show how we can model motion via group ... 
Controllability and motion algorithms for underactuated Lagrangian systems on Lie groups
(IEEE, 2000)In this paper, we provide controllability tests and motion control algorithms for underactuated mechanical control systems on Lie groups with Lagrangian equal to kinetic energy. Examples include satellite and underwater ... 
Controllability of a hovercraft model (and two general results)
(2003)Modelling and controllability studies of a hovercraft system are undertaken. The system studied is a little more complicated than some in the literature in that the inertial dynamics of the thrust fan are taken into ... 
Controllability of Underactuated Coupled Parabolic Systems
This thesis studies the null controllability of a system of coupled parabolic PDEs. Moreover, our work specializes to an important subclass of these control problems, where systems are underactuated and are coupled by first ... 
Controllable kinematic reductions for mechanical systems: concepts, computational tools, and examples
(2001)This paper introduces the novel notion of kinematic reductions for mechanical systems and studies their controllability properties. We focus on the class of simple mechanical control systems with constraints and model ... 
Curves of low genus on surfaces and applications to Diophantine problems
(20150831)We describe in detail a technique due to Vojta for finding the explicit set of curves of low genus on certain algebraic surfaces of general type, and refine some of its aspects. We then provide applications of this method ... 
Datadriven estimation for Aalen's additive risk model
(20070802)The proportional hazards model developed by Cox (1972) is by far the most widely used method for regression analysis of censored survival data. Application of the Cox model to more general event history data has become ... 
Decompositions of control systems on manifolds with an affine connection
(NorthHolland, 1997)In this letter we present a decomposition for control systems whose drift vector field is the geodesic spray associated with an affine connection. With the geometric insight gained with this decomposition, we are able to ... 
Discussion on: ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty''
(Lavoisier, 2005)This is an invited discussion paper on the paper ``Dynamic Sliding Mode Control for a Class of Systems with Mismatched Uncertainty'' by XingGang Yan, Sarah K. Spurgeon, and Christopher Edwards, that will appear in the ... 
Disease, Sex and Evolution
This thesis focuses upon some evolutionary problems related to sexual reproduction and disease. We first consider whether we should expect a fundamental difference between the outcomes of pre and postcopulatory sexual ... 
Distributed Online Optimization on timevarying networks
(20150901)This thesis introduces two classes of discretetime distributed online optimization algorithms, with a group of agents which communicate over a network. At each time, a private convex objective function is revealed to ... 
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 ...