Browsing Department of Mathematics and Statistics Graduate Theses by Publish Date
Now showing items 120 of 158

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 ... 
Optimal design in regression and spline smoothing
(20070719)This thesis represents an attempt to generalize the classical Theory of Optimal Design to popular regression models, based on Rational and Spline approximations. The problem of finding optimal designs for such models can ... 
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 ... 
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 ... 
Nonparametric statistical procedures for therapeutic clinical trials with survival endpoints
(20070802)This thesis proposed two nonparametric statistical tests, based on the KolmogorovSmirnov distance and L2 mallows disatnce. To implement the proposed tests, nonparametric bootstrap method is employed to approximate the ... 
Performance analysis of linear block codes over the queuebased channel
(20070829)Most coding schemes used in today's communication systems are designed for memoryless channels. These codes break down when they are transmitted over channels with memory, which is in fact what realworld channels look ... 
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 ... 
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 ... 
On the Oscillations of Jupiter as Observed by Voyager 2
(20071218)Data recorded from Voyager 2 in 1979 during closest approach to Jupiter is prepared and analyzed for evidence of Jovian modal forcing. Comparisons are drawn between the data set in question and previously performed ... 
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 ... 
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, ... 
Channel Optimized Vector Quantization: Iterative Design Algorithms
(20080904)Joint sourcechannel coding (JSCC) has emerged to be a major field of research recently. Channel optimized vector quantization (COVQ) is a simple feasible JSCC scheme introduced for communication over practical channels. In ... 
Separating Invariants
(20080904)Roughly speaking, a separating algebra is a subalgebra of the ring of invariants whose elements distinguish between any two orbits that can be distinguished using invariants. In this thesis, we introduce the notion of a ... 
Tilting objects in derived categories of equivariant sheaves
(20080905)We construct classical tilting objects in derived categories of equivariant sheaves on quasiprojective varieties, which give equivalences with derived categories of modules over algebras. Our applications include a ... 
Betti numbers and regularity of projective monomial curves
(20080925)In this thesis we describe how the balancing of the $\operatorname{Tor}$ functor can be used to compute the minimal free resolution of a graded module $M$ over the polynomial ring $B=\mathbb{K}[X_0,\dots,X_m]$ ($\mathbb{K}$ ... 
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 ... 
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 ... 
Multitaper Methods for TimeFrequency Spectrum Estimation and Unaliasing of Harmonic Frequencies
(20090205)This thesis is concerned with various aspects of stationary and nonstationary time series analysis. In the nonstationary case, we study estimation of the WoldCram'er evolutionary spectrum, which is a timedependent ... 
Some Advances in the Multitaper Method of Spectrum Estimation
(20090209)Four contributions to the multitaper method of applied spectrum estimation are presented. These are a generalization of the multitaper method of spectrum estimation to timeseries possessing irregularly spaced ... 
The circular law: Proof of the replacement principle
(20090713)It was conjectured in the early 1950¡¯s that the empirical spectral distribution (ESD) of an $n \times n$ matrix whose entries are independent and identically distributed with mean zero and variance one, normalized by ...