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#### A Mathematical Discussion of Corotational Finite Element Modeling

(2011-03-31)

This thesis discusses the mathematics of the Element Independent Corotational (EICR) Method and the more general Unified Small-Strain Corotational Formulation. The former was developed by Rankin, Brogan and Nour-Omid [106]. ...

#### Statistical Methods for Testing Treatment-Covariate Interactions in Cancer Clinical Trials

(2011-09-27)

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 ...

#### On the Reduced Operator Algebras of Free Quantum Groups

(2012-08-03)

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 trace-preserving ...

#### Stability of Agreement in State-dependent Interaction Environments

(2013-07-02)

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, ...

#### Distributed Online Optimization on time-varying networks

(2015-09-01)

This thesis introduces two classes of discrete-time distributed online optimization algorithms, with a group of agents which communicate over a network. At each time, a private convex objective function is revealed to ...

#### Inclusive Fitness on Evolutionary Graphs

(2012-10-04)

The evolution of cooperative behaviours has received a large amount of attention in the literature. A recurrent result is that a spatial population structure often aids the evolution of cooperation. One such possible ...

#### On the Optimality of the Hamming Metric for Decoding Block Codes over Binary Additive Noise Channels

(2013-07-12)

Most of the basic concepts of algebraic coding theory are derived for the memoryless binary symmetric channel. These concepts do not necessarily hold for time-varying channels or for channels with memory. However, errors ...

#### 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 ...

#### Local controllability of affine distributions

(2010-01-12)

In this thesis, we develop a feedback-invariant theory of local controllability for affine distributions. We begin by developing an unexplored notion in control theory that we call proper small-time local controllability ...

#### Embeddings of flag manifolds and cohomological components of modules

(2011-08-23)

This thesis is a study in Representation Theory and Geometry. These two branches of mathematics have a fruitful interaction, with many applications to Physics and other sciences. Central objects of interest are homogeneous ...