Browsing Mathematics and Statistics, Department of by Title
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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 ... 
Nonparametric Testing Methods for TreatmentBiomarker Interaction based on Local PartialLikelihood
(Wiley, 20150617)In clinical trials, patients with different biomarker features may respond differently to the new treatments or drugs. In personalized medicine, it is important to study the interaction between treatment and biomarkers in ... 
On Malliavin Calculus and Concentration Inequalities
(20140707)We prove new abstract results concerning concentration inequalities and density estimates for Malliavin differentiable random variables. The efficacy of these results are demonstrated by practical computations, such as the ... 
On Renyi Divergence Measures for Continuous Alphabet Sources
(20110830)The idea of `probabilistic distances' (also called divergences), which in some sense assess how `close' two probability distributions are from one another, has been widely employed in probability, statistics, information ... 
On the Convergence and Applications of Mean Shift Type Algorithms
(20131001)Mean shift (MS) and subspace constrained mean shift (SCMS) algorithms are nonparametric, iterative methods to find a representation of a high dimensional data set on a principal curve or surface embedded in a high ... 
On the Equivalence Between Maximum Likelihood and Minimum Distance Decoding for Binary Contagion and QueueBased Channels with Memory
(20160217)We study the optimal maximum likelihood (ML) block decoding of general binary codes sent over two classes of binary additive noise channels with memory. Specifically, we consider the infinite and finite memory Polya contagion ... 
On the homogeneity of the affine connection model for mechanical control systems
(IEEE, 2000)This work presents a review of a number of control results for mechanical systems. The key technical results derive mainly from the homogeneity properties of affine connection models for a large class of mechanical systems. ... 
On the Optimality of the Hamming Metric for Decoding Block Codes over Binary Additive Noise Channels
(20130712)Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for timevarying channels or for channels with memory. However, errors ... 
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 ... 
On the Reduced Operator Algebras of Free Quantum Groups
(20120803)In this thesis, we study the operator algebraic structure of various classes of unimodular free quantum groups, including thefree orthogonal quantum groups $O_n^+$, free unitary quantum groups $U_n^+$, and tracepreserving ... 
On the role of regularity in mathematical control theory
(20160408)In this thesis, we develop a coherent framework for studying timevarying vector fields of different regularity classes and their flows. This setting has the benefit of unifying all classes of regularity. In particular, ... 
Optimal control for a simplified hovercraft model
(2000)Timeoptimal and forceoptimal extremals are investigated for a planar rigid body with a single variable direction thruster. A complete and explicit characterisation of the singular extremals is possible for this problem. 
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 ... 
Optimal Quantization and Approximation in Source Coding and Stochastic Control
(20150623)This thesis deals with nonstandard optimal quantization and approximation problems in source coding and stochastic control. The first part of the thesis considers randomized quantization. Adapted from stochastic ... 
Optimality of WalrandVaraiya Type Policies and Approximation Results for ZeroDelay Coding of Markov Sources
(20150728)Optimal zerodelay coding of a finite state Markov source through quantization is considered. Building on previous literature, the existence and structure of optimal policies are studied using a stochastic control problem ... 
Pairwise Optimization of Modulation Constellations for NonUniform Sources
(20091007)The design of twodimensional signal constellations for the transmission of binary nonuniform memoryless sources over additive white Gaussian noise channels is investigated. The main application of this problem is 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 ... 
Prime divisors of sparse values of cyclotomic polynomials and Wieferich primes
(20190320)Bang (1886), Zsigmondy (1892) and Birkhoff and Vandiver (1904) initiated the study of the largest prime divisors of sequences of the form an−bn, denoted P(an−bn), by essentially proving that for integers a>b>0, P(an−bn)≥n+1 ... 
Pushsum Algorithm on Timevarying Random Graphs
In this thesis, we study the problem of achieving average consensus over a random timevarying sequence of directed graphs by extending the class of socalled push sum algorithms to such random scenarios. Provided that ... 
Real SecondOrder Freeness and Fluctuations of Random Matrices
(20110909)We introduce real secondorder freeness in secondorder noncommutative probability spaces. We demonstrate that under this definition, independent ensembles of the three real models of random matrices which we consider, ...