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Now showing items 1-10 of 102

#### On Upper Bounding Discrete Entropy

(2011-12-22)

Two upper bounds on the entropy of a discrete random variable are studied. The
standard upper bound is derived based on the differential entropy bound for a Gaus-
sian random variable. A tighter bound is proved using the ...

#### Networked Control Systems with Unbounded Noise under Information Constraints

(2012-12-06)

We investigate the stabilization of unstable multidimensional partially observed single-station, multi-sensor (single-controller) and multi-controller (single-sensor) linear systems controlled over discrete noiseless ...

#### On the Critical Points of Gaussian Mixtures

(2013-09-03)

This thesis is concerned with studying the question whether or not Gaussian mixtures have finitely many critical points. The relevance of this problem to the convergence of the mean-shift algorithm is discussed and an ...

#### Modelling Pathogen Evolution with Branching Processes

(2010-07-28)

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 ...

#### Real Second-Order Freeness and Fluctuations of Random Matrices

(2011-09-09)

We introduce real second-order freeness in second-order noncommutative probability spaces. We demonstrate that under this definition, independent ensembles of the three real models of random matrices which we consider, ...

#### The evolution of mimicry in parasites

(2011-04-06)

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 ...

#### Variations on Artin's Primitive Root Conjecture

(2011-08-11)

Let $a \in \mathbb{Z}$ be a non-zero integer. Let $p$ be a prime such that $p \nmid a$. Define the index of $a$ modulo $p$, denoted $i_{a}(p)$, to be the integer $i_{a}(p) := [(\mathbb{Z}/p\mathbb{Z})^{\ast}:\langle a ...

#### The Saddle Point Method and its Applications to Number Theory

(2015-09-15)

In this thesis, we study the classical procedures useful in obtaining asymptotic expansions of functions defined by integrals and their
applications to number theory. The final chapter in the thesis reports on a recent ...

#### Evolutionarily Stable Learning and Foraging Strategies

(2012-02-01)

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 ...

#### MEASURING DEPENDENCE VIA MUTUAL INFORMATION

(2011-10-03)

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 ...