Brain tissue mechanics are an important biomarker for neurological disorders, yet methods to obtain tissue information yield inconsistent conclusions. These techniques can be invasive or require excised tissue, where tissue function is altered from...
The purpose of this thesis is to describe methods for detecting hidden crevasses on glaciers in Polar regions. Crevasses form in ice sheets as a result of forces imposed upon the brittle ice. The crevasses are hidden from view by bridges of soft...
The processes affecting gas transport through the firn column are important to understand in order to accurately interpret climate records from ice cores. Historically, density measurements have been used to estimate open and closed porosity in the...
We begin with a result on the refocussing of null geodesics in space-times. We show that all oriented refocussing 2-dimensional Lorentz manifolds are also strongly refocussing. We also introduce a theory of virtual Legendrian knots. We show that...
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
This thesis contains material relating to two separate subjects. The first section determines when the C*-algebra affiliated to a directed graph has continuous trace. We use groupoid methods and the focus is on producing conditions on a graph that...
This project focuses on the development of research tools and methods that are used to study the relationship between neural activity and subsequent hemodynamic responses in the human brain. This relationship, referred to as neurovascular coupling,...
Opinion dynamics is a complex procedure that entails a cognitive process when it deals with how a person integrates influential opinions to form revised opinion. Early research on opinion formation and social influence can be traced back to the...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles Ï‰ = {Ï‰[subscript t]}[subscript tâˆŠ[0,1]] on a locally compact Hausdorff groupoid Æ“ induces an isomorphism of the...
The focus of this thesis is the study of nuclearity and exactness for groupoid crossed product C*-algebras. In particular, we present generalizations of two well-known facts from group dynamical systems and crossed products to the groupoid setting....
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
Increased fetal hemoglobin (HbF) expression is beneficial for [beta]-hemoglobinopathy patients; however, most inducing agents do not possess the ideal combination of efficacy, safety and availability. Better understanding the mechanisms involved in...
We present aligned hierarchies, a novel solution to the dimension reduction problem, representing high-dimensional and noisy sequential data as a low-dimensional object that encodes relevant information. In this thesis, we motivate our presentation...
Quantum wires and dots can be created by patterning inhomogeneous strain on semiconductor quantum wells. I have used laser spectroscopic methods to study the carrier transfer from the host quantum well to quantum wires and dots. For quantum dot...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
Robots -- Control systems -- Design and construction. Mobile robots. Robots -- Dynamics.
This thesis examines the issues of vehicle and information dynamics in the control of a multi-robot system using a radial-basis potential function controller. Distributed control of multi-robot systems requires each robot to communicate state...
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n â‰¥11), Spin(n) (n = 9, n â‰¥11), SU (n) (n â‰¥7), and Sp (n) (n â‰¥5). The proof breaks into three...
Breast -- Cancer -- Tomography. ; Breast -- Cancer -- Imaging. ; Microwave imaging in medicine. ; Breast -- Electric properties. ; Breast Neoplasms -- diagnosis. ; Diagnostic Imaging -- methods.
During an immune reaction to an invading pathogen, a population of lymphocytes with receptors that specifically recognize the pathogen are activated and become memory cells. Characteristically, memory lymphocytes persist for long periods of time...
Polynomials. Finite fields (Algebra). Algebraic functions. Number theory.
The ring of univariate polynomials over a finite field shares many foundational arithmetic properties with the ring of rational integers. This similarity makes it possible for many problems in elementary number theory to be translated 'through the...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
In this thesis we look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
The ubiquitous complexity of common diseases is one of the biggest challenges facing the field of personalized treatments and precision medicine. This complexity can be attributed to various sources such as the genetic make-up of an individual,...