Continual improvements to clinical breast imaging technologies have led to ever earlier detections and increasingly accurate localizations of female breast cancers. While these advancements have certainly improved the prognoses of many patients,...
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...
Annual screening mammograms are recommended for all women above 40 years of age for early detection of breast cancer, and are known to improve cancer mortality rates. However, mammography is hampered by low sensitivity and a high rate of false...
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...
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...
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...
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...
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...
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.
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
We prove the existence of nontrivial multiparameter isospectral deformations of metrics on the classical compact simple Lie groups SO (n) (n = 9, n ≥11), Spin(n) (n = 9, n ≥11), SU (n) (n ≥7), and Sp (n) (n ≥5). The proof breaks into three...
The problem of moving rigid bodies efficiently is of particular interest in robotics because the simplest model of a mobile robot or of a manipulated object is often a rigid body. Path planning, controller design and robot design may all benefit...
This thesis explores practical and theoretical aspects of several privacy-providing technologies, including tools for anonymous web-browsing, verifiable electronic voting schemes, and private information retrieval from databases. State-of-art...