Browsing Mathematics and Statistics, Department of by Title
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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 ... 
Modeling and Analysis of Dynamic Computer Experiments
Dynamic computer experiments which refer to computer experiments with time series outputs have increasingly gained popularity in both science and engineering. Analysis of dynamic computer experiments through statistical ... 
Modelling of Dynamic Computer Experiments with Both Qualitative and Quantitative Variables
Computer experiments are utilized as a popular tool of studying the relationship between responses and the factors that affect them. They are widely used in scientific researches and applications. Dynamic computer experiments ... 
Modelling Pathogen Evolution with Branching Processes
(20100728)Pathogen evolution poses a significant challenge to public health, as efforts to control the spread of infectious diseases struggle to keep up with a shifting target. To better understand this adaptive process, we turn ... 
Moduli Spaces of K3 Surfaces with Large Picard Number
(20110815)Morrison has constructed a geometric relationship between K3 surfaces with large Picard number and abelian surfaces. In particular, this establishes that the period spaces of certain families of lattice polarized K3 surfaces ... 
Moduli spaces of vector bundles on toric surfaces
The moduli spaces parametrizing isomorphism classes of vector bundles are poorly understood. For certain choices of the first Chern class and a suitable second Chern class, we show that there exists an ample line bundle ... 
Multitaper HigherOrder Spectral Analysis of Nonlinear Multivariate Random Processes
(20081104)In this work, I will describe a new statistical tool: the canonical bicoherence, which is a combination of the canonical coherence and the bicoherence. I will provide its definitions, properties, estimation by multitaper ...