Coding theory. Characters of groups. Error-correcting codes (Information theory). Polynomials.
We introduce vector-valued character theory, a higher dimensional generalization of character theory. We then use vector-valued characters to extend the MacWilliams equivalence theorem for linear codes to a class of additive codes, called...
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...
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,...
Loss processes greatly impact the dynamics of the Earth's radiation belts. In 1996, a balloon-borne germanium detector flown over Kiruna, Sweden detected the first terrestrial X-rays with energies on the order of 1 MeV. The spectrum for these...
This thesis investigates the embedding theory of orders in central simple algebras, placing a particular emphasis on the role that the phenomenon known as selectivity plays in the theory. Although the notion of selectivity is completely algebraic,...
This thesis approaches the problem of locating zero-day exploits used in network attacks. The hypothesis is that the advent of high-performance virtualization presents a unique opportunity to both discover these events and increase the attacker's...
We present a number of findings concerning groupoid dynamical systems and groupoid crossed products. The primary result is an identification of the spectrum of the groupoid crossed product when the groupoid has continuously varying abelian...
'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...
Van Allen radiation belts -- Mathematical models. Electrons -- Diffusion -- Mathematical models. Magnetohydrodynamic waves -- Mathematical models.
It is becoming increasingly important to understand the dynamics of radiation belt energetic particles given their potentially hazardous effects on satellites and our ever-increasing dependence on those satellites. There is a need to determine...
Goldman and Turaev constructed a Lie bialgebra structure on the free Z-module generated by free homotopy classes of loops on an oriented surface. Turaev conjectured that the cobracket of A is zero if and only if A is a power of a simple class. Chas...
We present designs, theory and the results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 μm × 60 μm × 7-20 μm in size, each robot consist of a...
A variety of forensic methods have been developed to identify falsified photos, each unified by the ability to estimate and detect properties of a photo that are perturbed by forgery. There exist, however, many photos in which the required...
Human locomotion -- Computer-assisted instruction. ; Real-time data processing. ; Human-computer interaction.
Teaching physical motions such as riding, exercising, swimming, etc. to human beings is hard. Coaches face difficulties in communicating their feedback verbally and cannot correct the student mid-action; teaching videos are two dimensional 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...
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...
Partially ordered sets. ; Convex polytopes. ; Representations of groups.
This thesis deals with geometric representations of ordered sets. In a geometric representation, each element of the ordered set is assigned a geometric object, with two elements incomparable in the ordered set if and only if the corresponding...
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...
Plasma instabilities. ; Ionospheric electron density. ; Ionosphere.
As a result of an unstable plasma stratification the nighttime equatorial ionosphere is subject to a variety of plasma instabilities known commonly as equatorial spread-F. In its fully developed form spread-F consists of large wedges of depleted...
At the heart of computer games and computer generated films lies 3D content creation. A student wanting to learn how to create and edit 3D meshes can quickly find thousands of videos explaining the workflow process. These videos are a popular...
This thesis centers around a generalization of the classical discrete Fourier transform. We first present a general diagrammatic approach to the construction of efficient algorithms for computing the Fourier transform of a function on a finite...
Electronic data processing -- Distributed processing. ; Computer network architectures. ; Programming languages (Electronic computers) -- Semantics. ; Database management.
I tackle the problem of naming and sharing resources across administrative boundaries. Conventional systems manifest the hierarchy of typical administrative structure in the structure of their own mechanism. While natural for communication that...
Lowest order charged particle motion in the Earth''s magnetosphere can be explained using simple adiabatic theory. However, nonadiabatic theory is required to explain particle behavior in cases such as when the particle's gyroradius is large...
Van Allen radiation belts -- Mathematical models. ; Magnetosphere -- Mathematical models. ; Magnetohydrodynamics -- Mathematical models.
The physics of geomagnetically-trapped radiation has been a topic of interest since the discovery of the Van Allen belts in 1958. As the energetic particles comprising these belts can pose a hazard to human activity in space, considerable effort...
Most theoretical and computational studies of turbulence in Navier-Stokes fluids and/or guiding-center plasmas have been carried out in the presence of spatially periodic boundary conditions. In view of the frequently-reproduced result that...
Through a series of case studies, signal processing and statistical tools, analyses of dynamic sea ice processes of drift, deformation, and ice pack expansion and decay are investigated for the Weddell Sea region during 1992. Cavitating fluid (CAV)...
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...
In this thesis, we present different approaches to tying knots using robots by enforcing different types of constraints. We attack the problem from three different directions; mechanical design, motion planning with simple control strategies, and...
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...