An important mode of stabilization of cations in biochemical reactions is interaction with the π systems-of aromatic residues. As part of an investigation of the interaction of carbocations with aromatic π systems, a study of various model...
This thesis is divided into 2 parts. In the first part of the thesis, we describe a software based approach to speeding up the Magnetic Resonance Imaging modality. In the second part of the thesis, we describe Significance Tree Quantization, which...
Motivated by quantum mechanics and geometric optics, it is a long-standing problem whether the length spectrum of a compact Riemannian manifold can be recovered from its Laplace spectrum. One route to proving that the length spectrum depends on the...
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
The performance of machine learning algorithms largely depends on data representation. As a critical step in machine learning, representation learning (feature learning) learns a transformation of training data to give a new representation that can...
Chlorinated ethenes are ubiquitous environmental pollutants of public concern due to their potential toxicity and carcinogenicity. Under appropriate conditions anaerobic bacteria mediate the dechlorination of perchloroethylene (a common dry...
Partially ordered sets and permutations are combinatorial structures having vast applications in theoretical computer science. In this thesis, we study various computational and algorithmic problems related to these structures. The first chapter of...
'Orthogonal modular forms are algebraic modular forms arising from lattices in quadratic spaces. In this thesis, we define orthogonal modular forms, establish their basic properties, and then apply them to a case of ternary quadratic spaces to...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
Robots -- Control systems. ; Robots -- Motion. ; Computer algorithms. ; Electronic data processing -- Distributed processing.
Self-reconfiguring robots are robots composed of many physically connected modules which can change their structural configuration to support multiple functionalities. We claim that self-reconfiguring robots are more versatile, extensible, and...
Two-phase flow -- Mathematical models. ; Gas dynamics -- Mathematical models. ; Kinetic theory of gases.
The kinetic theory based gas-dynamical computational method, due to (Prendergast and Xu, 1993: Xu and Prendergast, 1994) is generalized to two-phase flow computations. The Bhatnagar-Gross-Krook kinetic model is generalized to the case of two...
Forest ecology -- Northeastern States. ; Forest canopy ecology -- Northeastern States. ; Forest dynamics -- Northeastern States.
In closed-canopy forests, changes in the relative abundance of tree species due to major disturbance or to its absence are thought to be governed principally by differences among component species in the performance of juveniles. However, few...
'The control of waves using periodic structures is crucial for modern optical, electromagnetic and acoustic devices such as diffraction gratings, filters, photonic crystals, solar cells, sensors, and absorbers. We present a high-order accurate...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
Breast -- Cancer -- Tomography. ; Breast -- Cancer -- Imaging. ; Breast -- Cancer -- Diagnosis. ; Near infrared reflectance spectroscopy. ; Image processing -- Digital techniques.
Near-infrared (NIR) light has the potential to be used as a non-invasive means of diagnostic imaging within the human breast. Due to the diffusive nature of light in tissue, computational model-based methods are required for functional imaging...
The matrix metalloproteinases (MMPs) are family of enzymes with a common domain structure that degrade extracellular matrix proteins; these enzymes are overexpressed in numerous diseases including cancer and arthritis. Collagenase-1, 2, 3 (MMP-1,...
The septins are a class of GTP-binding cytoskeletal proteins conserved throughout eukaryotes. They were first described as a set of cell division cycle mutants in the budding yeast Saccharomyces cerevisiae, but since their initial discovery septins...
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...
This thesis investigates a notion of Turing reducibility introduced by Winkler [8] that is total on all computably enumerable oracles. Groszek and Weber show in [7] that this is a new notion of reducibility and it is not transitive. They give su...
A metric structure on a set gives a concept of distance between any two elements of that set, and it induces a topology. In this thesis, we provide several ways to put a metric structure on the collection of CW complexes. We accomplish this by...
We examine variations of cops and robbers games on graphs. Our goals are to introduce some randomness into their study, and to estimate (expected) capture time. We show that a cop chasing a random walker can capture him in expected time n + o(n)....
Siegel domains. Modular groups. Hecke algebras. Forms
In the 1960s Satake proved the existence of an isomorphism between the local Hecke algebra and the ring of polynomials invariant under the action of the signed permutation group W n (the Weyl group associated to Sp n over a local field)....
Estradiol is a key regulator of immune protection in the female reproductive tract (FRT). Its concentration varies during the menstrual cycle, leading to changes in innate immune protection. In this thesis, I demonstrate the multiple levels at...
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...
Protein complexes play vital roles in cellular processes within living organisms. They are formed by interactions between either different proteins (hetero-oligomers) or identical proteins (homo-oligomers). In order to understand the functions of...
Over the past decade, a pair of instructions called load-linked (LL) and store-conditional (SC) have emerged as the most suitable synchronization instructions for the design of lock-free algorithms. However, current architectures do not support...
Brain -- Localization of functions. Analogy. Frontal lobes. Neuropsychology.
This thesis represents a program of behavioral and brain-based research directed at elucidating the mechanisms of analogical reasoning. The studies that comprise this thesis took convergent experimental approaches to extend knowledge concerning two...
The fluxes of radiation belt electrons are highly variable, due to a competition between various acceleration, loss, and transport processes. Studies of any of the processes are equally important. My study focuses on electron-EMIC (electromagnetic...
The accelerated expansion of space in the Universe has been known for two decades. However, finding a plausible theory that describes this expansion is more difficult: Taking general relativity for granted requires us to stipulate the existence of...
Melanoma progresses as a multi-step process, where the thickness of the lesion and depth of tumor invasion are the best prognostic indicators of clinical outcome. Degradation of the interstitial collagens in the extracellular matrix is an integral...
GABA -- Receptors. Anabolic steroids -- Physiological effect. Androgens -- Physiological effect. Prosencephalon. Neurotransmitters -- Effect of drugs on. Psychoneuroendocrinology.
Anabolic androgenic steroids (AAS) are derivatives of testosterone originally designed for therapeutic applications to enhance anabolic potency (protein synthesis and muscle growth) while exerting low androgenic (masculinizing) effects. The...