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...
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...
Space and time in language. ; Space perception. ; Figure-ground perception. ; Psycholinguistics.
Across languages, there exists a relatively small number of spatial prepositions. These terms are used to express the infinite number of possible spatial locations of an unlimited number of different entities in the environment. Previous research...
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...
'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...
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...
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...
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...
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...
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...
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...
Riemannian manifolds. Singularities (Mathematics). Laplacian operator. Spectral theory (Mathematics). Riemann surfaces. Curves on surfaces. Geometry
Historically, inverse spectral theory has been concerned with the relationship between the geometry and the spectrum of compact Riemannian manifolds, where spectrum means the eigenvalue spectrum of the Laplace operator as it acts on smooth...
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...
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...
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...
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,...
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 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...
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...
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...
There is a renewed interest in the study of the radiation belts with the recent launch of the Van Allen Probes satellites. The mechanisms that drive the global response of the radiation belts to geomagnetic storms are not yet well understood....
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 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...
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...
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...
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...
Metal powders -- Extrusion. Metal powders -- Microstructure. Shear flow.
The manufacture of bulk parts from metastable powder materials requires new approaches to cold consolidation. One potential technique is equal-channel angular extrusion (ECAE), a simple shear process. This thesis describes an investigation into the...
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)...
The discovery of the Van Allen radiation belts in the 1958 was the first major discovery of the Space Age. There are two belts of energetic particles. The inner belt is very stable, but the outer belt is extremely variable, especially during...
We describe a set of natural image statistics that are built upon two multi-scale image decompositions, the quadrature mirror filter pyramid decomposition and the local angular harmonic decomposition. These image statistics consist of first- and...