Chapter 1: Munchnones and mesoionic heterocycles The reactivity, regioselectivity, and synthetic applications of munchnones (1,3-oxazolium-5-olates) is a common theme which runs through Chapters 2-5. The definition, structure, and reactivity of...
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...
Traumatic brain injury (TBI) is the leading cause of acquired disability in children, yet innate repair mechanisms are incompletely understood. A possible innate mechanism to repair injury after insult is neurogenesis - the birth, migration,...
Si/SiGe quantum dots (QDs) are promising candidates for spin-based quantum bits (qubits) as a result of the reduced spin-orbit coupling as well as the Si isotopes with zero nuclear spin. Meanwhile qubit readout is a challenge related to...
We present new forensic tools that are capable of detecting traces of tampering in digital images without the use of watermarks or specialized hardware. These tools operate under the assumption that images contain natural properties from a variety...
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...
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...
Despite the array of targeted therapeutics that currently exist to combat breast cancer, disease progression leading to metastasis, and tumor recurrence still remains a significant clinical challenge. Efforts to identify novel pathways and...
The Mixed Lineage Leukemia (MLL1) gene was first cloned as a hot spot of chromosomal translocations in acute leukemia. More than 70 fusion proteins of MLL1 have been described in both lymphoid and myeloid leukemia and many are highly associated...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of the...
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...
Proteins are ubiquitous in cells and are essential to a wide range of biological processes. Since existing proteins occupy only a small portion of the space of possible amino acid composition, understanding their sequence-structure-function...
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...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
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.
Ice mechanics. Compressibility. Fracture mechanics. Strains and stresses. Brittleness.
This work describes the effect of triaxial compressive confinement on the strength of columnar S2 ice loaded under conditions leading to brittle failure. Cubes of columnar S2 ice were tested at -10 °C under triaxial (proportional) loading where...
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...
Fir waves are spatially and temporally repeating patterns of stand development and destruction in subalpine, balsam fir-dominated forests of the northeastern United States, perpetuated by downwind migration of strips of dying trees, "dieback...
Infrared imaging. Image reconstruction. Optical images -- Mathematical models. Breast -- Imaging. Infrared radiation in medicine.
Finite element based reconstruction algorithms for optical property profiling in biological tissues have been developed, implemented and evaluated using simulated data and laboratory measurements obtained with near infrared continuous wave (cw) and...
Acyl-CoA:Cholesterol Acyltransferases (ACATs) are key enzymes in cellular cholesterol metabolism. ACAT converts free cholesterol to cholesterol ester, which makes it more easily storable in lipid droplets. There are two ACAT genes encoding two...