Browsing Mathematics and Statistics, Department of by Title
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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, ... 
Reduction, linearization, and stability of relative equilibria for mechanical systems on Riemannian manifolds
(2004)Consider a Riemannian manifold equipped with an infinitesimal isometry. For this setup, a unified treatment is provided, solely in the language of Riemannian geometry, of techniques in reduction, linearization, and stability ... 
Reinforcement Learning for Decentralized Stochastic Control
We consider decentralized optimization of a controlled stochastic system where a finite number of decision makers seek to arrive at optimal policies using only local measurements and cost realizations. For such a context, ... 
Rigid body mechanics in Galilean spacetimes
(2004)An observerindependent formulation of rigid body dynamics is provided in the general setting of a Galilean spacetime. The equations governing the motion of a rigid body undergoing a rigid motion in a Galilean spacetime ... 
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 ... 
Shorttime asymptotics of heat kernels of hypoelliptic Laplacians on Lie groups
(20111011)This thesis suggests an approach to compute the shorttime behaviour of the hypoelliptic heat kernel corresponding to subRiemannian structures on unimodular Lie groups of type I, without previously holding a closed form ... 
Simple mechanical control systems with constraints
(IEEE, 2000)We apply some recently developed control theoretic techniques to the analysis of a class of mechanical systems with constraints. Certain simple aspects of the theory of affine connections play an important part in our ... 
Smooth Complete Intersections with PositiveDefinite Intersection Form
(20121016)We classify the smooth complete intersections with positivedefinite intersection form on their middle cohomology. There are two families. The first family are quadric hypersurfaces in P(4k+1) with k a positive integer. ... 
Sobolev Gradient Flows and Image Processing
(20100825)In this thesis we study Sobolev gradient flows for PeronaMalik style energy functionals and generalizations thereof. We begin with first order isotropic flows which are shown to be regularizations of the heat equation. ... 
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 ... 
Special values of Lseries, periodic coefficients and related themes
This thesis is centered around the theme of special values of Lfunctions and other infinite series, which are often expected to be transcendental numbers. More specifically, we focus on the following two questions in ... 
Stability of Agreement in Statedependent Interaction Environments
(20130702)We study stochastic stability for a class of agreement dynamics and define two forms of agreement which we call stochastic agreement and stochastic absolute agreement. We identify conditions for a broad class of random, ... 
Statistical Inference for the Treatment Effect in Cancer Clinical Trials
(20110525)Randomized clinical trials provide the best evidence on the effect of treatment studied. There are different types of measures on the treatment effect, depending on the endpoints of the trials. For a given measure, based ... 
Statistical Inferences of TwoStage Phase II Cancer Clinical Trials with Two Coprimary Endpoints
In cancer research, twostage designs are usually used to assess the eﬀect of a new agent in phase II clinical trials. The optimal twostage designs with two coprimary endpoints have been proposed to assess the eﬀects ... 
Statistical Methods For Biomarker Threshold Models in Clinical Trials
In clinical trials, the main objective is to investigate the treatment effects on patients. However, many molecularly targeted drugs or treatments tend to benefit a subset of patients more, identified by a certain biomarker. ... 
Statistical Methods for Testing TreatmentCovariate Interactions in Cancer Clinical Trials
(20110927)Treatment–covariate interaction is often used in clinical trials to assess the homogeneity of treatment effects over these subgroups defined by a baseline covariate, which is frequently conducted after primary analysis ... 
Statistical Modeling and Analysis for Survival Data with a Cure Fraction
(20120126)The analysis of survival data with a possible cure fraction has attracted much interest in the last two decades. Various models and estimating methods have been proposed for such data and they have been applied in many ... 
Symmetric Gaussian Rearrangement with Applications to Gaussian Noise Stability
We introduce a new symmetric Gaussian rearrangement that applies to sets and functions which are invariant with respect to a given finite subgroup of the orthogonal group. The properties of this rearrangement are developed, ...