For ordinary knots in R 3 , there are no degree one Vassiliev invariants. For virtual knots, however, the space of degree one Vassiliev invariants is infinite dimensional. We introduce a sequence of three degree one Vassiliev invariants of virtual...
In this thesis we develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
This thesis considers the two special sensor networks for future sensor network design: mobile sensor networks and hybrid network of sensors and robots. To investigate two types of networks, we abstract two most important aspects that are ingrained...
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...
Multisensor data fusion. Sensor networks. Plumes (Fluid dynamics). Automatic tracking. Signal processing -- Digital techniques -- Mathematics.
The work in this thesis deals with a novel approach for detecting and tracking chemical plumes in distributed sensor networks. The ultimate objective is solving the inverse location problem: given unknown sources released at unknown times, the...
Graph algorithms. Nuclear magnetic resonance spectroscopy -- Data processing. Proteins -- Structure -- Mathematical models. Proteins -- Crosslinking -- Mathematical models. Protein folding -- Mathematical models.
The study of three-dimensional protein structures produces insights into protein function at the molecular level. Graphs provide a natural representation of protein structures and associated experimental data, and enable the development of graph...
Investigations into alternative breast cancer (BC) imaging techniques have become increasingly popular based on the limitations of traditional imaging modalities: X-ray mammography uses ionizing radiation, has limited intrinsic contrast and is...
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...
This thesis presents data from ground camera observations of the aurora conducted from Alaska during the winters of 2005 through 2007. In conjunction with these camera observations, conjugate radar observations of the auroral ionosphere were...
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...
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...
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...
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...
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...
Multimodality imaging is becoming the standard of care for research and clinical studies. Such an approach is able to provide complementary information which can detect and characterize tumors. Advancing instrumentation for diffuse near-infrared...
There are no Vassiliev invariants of degree one for classical knots. A. Henrich proved the existence of a sequence of three Vassiliev invariants of degree one for virtual knots. The invariants get stronger and stronger, and the final invariant is...
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...
This dissertation explores the spatial and temporal distributions of impurities in natural ice. Using polarized light, ion chromatography (IC), synchrotron x-ray topography (SXT), scanning electron microscopy (SEM), and energy-dispersive...
Apoptosis is induced by chemicals and death receptor activation. Although the stimuli are different, common proteins are activated downstream. The Bcl-2 family of proteins plays an important role in mediating apoptotic signaling at the mitochondria...
Three-dimensional imaging in medicine -- Mathematical models. ; Stereoencephalotomy.
In the past, clinicians skilled at image-guided neurosurgery have relied solely on pre-operative scans for their navigational information. Often in the course of surgery, tissue is purposely retracted/resected or inadvertently moved resulting in a...