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...
The processes by which nonlinear physical systems approach thermal equilibrium is of great importance in many areas of science. Central to this is the mechanism by which energy is transferred between the many degrees of freedom comprising these...
Thermodynamics, and the classic balance between entropy and enthalpy, provides a proverbial zoo of exotic phase behaviour that chemists can harness to create new materials out of simple liquids and polymers. The diversity of self-assembling...
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 identification and characterization of functional genetic variation is essential for future advances in molecular diagnostics, pharmacogenomics, and personalized medicine. Recent attempts at identifying nucleotide level variation (somatic...
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...
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...
Magnetic susceptibility imaging of magnetic nanoparticles (mNPs) has many potential applications in biomedicine such as contrast enhanced imaging and image guidance for magnetic hyperthermia therapy. This thesis describes three imaging methods...
Ultra-high molecular weight polyethylene (UHMWPE) remains the most common bearing material for total joint arthroplasty. Advances in radiation cross-linking and other post-consolidation treatments have led to a rapid differentiation of polyethylene...
Casimir effect. Zero-point field. Electric conductivity. Quantum electrodynamics.
The Casimir force arises from an alteration of boundary condition in vacuum and is often regarded as a manifestation of quantum zero point energy. Considerable progress has been made in the last decade with an impressive achievement of experimental...
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...
In this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
In Chapter 2 we look at the distribution of permutation statistics in the context of pattern-avoiding permutations. The first part of this chapter deals with a recursively defined bijection of Robertson [37] between 123- and 132-avoiding...
Mentally ill -- Care -- Decision making. Mental illness -- Treatment -- Decision making. Mental health services -- Decision making. Mental health -- Information services. Medical informatics. Mental Disorders -- drug therapy.
Objective. We explored preferences and perceptions about treatment decision-making roles among persons with severe mental illness and evaluated two computer-based medication values clarification tools. Methods. In this study we conducted a pilot...
This thesis comprises two separate but related studies, dealing with two strongly interacting nanoscale systems on the border between the quantum and classical domains. In Part 1, we use a Born-Markov approximated master equation approach to study...
For many scientific applications, the data set cannot entirely fit in main memory. The data must reside out-of-core, i.e., on parallel disks. For many basic data-movement operations such as permuting, if the programmer does not design efficient...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
The neurophysiological examination of auditory-object representations has focused on how early auditory cortical areas code for the spectral and temporal features of auditory objects. The goals of this dissertation was to investigate how auditory...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...