As the visual effect and movie industries are striving for realism and high fidelity images, physically based lighting, global illumination, realistic materials, and highly tessellated geometry are gradually accepted and used in movie and game...
We present new appearance editing algorithms that allow artists to perform complex editing operations on spatially-varying appearance datasets such as images and measured materials, in an intuitive and efficient manner. The goal is to develop...
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...
A polynomial is a product of distinct cyclotomic polynomials if and only if it is a divisor over [Special characters omitted.] [x ] of xn - 1 for some positive integer n. In this thesis, we will examine two natural questions concerning the divisors...
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)...
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 large and complex networks such as the Internet and road networks, traffic routing is typically decentralized. Users in the network choose their routes independently to minimize their own delay, leading to complicated and nonintuitive outcomes...
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...
For a local field K, we study the affine buildings Ξ n and Δ n naturally associated to SL n ( K ) and Sp n ( K ), respectively. Since Sp n ( K ) is a subgroup of SL 2 n ( K ), we investigate properties of a natural embedding of Δ n in Ξ 2 n ....
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
This thesis focuses on the emergence of universal dynamical scaling in quantum critical spin systems driven out of equilibrium, with emphasis on quench dynamics which involves isolated standard critical points, multi-critical points, and...
Bayesian nonparametric methods have become increasingly popular in machine learning for their ability to allow the data to determine model complexity. In particular, Bayesian nonparametric versions of common latent variable models can learn as...
Multiresolution image transformations have become commonplace tools for analyzing images for a number of applications, including enhancement and restoration. Powerful models for these applications have been developed in the transform domain of...
Breast cancer is the most common cancer in women. The discovery of breast tumor subtypes and the subsequent development of treatments aimed at them has allowed a reduction in the mortality of breast cancer. However, tumors with similar...
Epilepsy is associated with cognitive impairments which often manifest as a higher prevalence of memory impairments. Memory impairments in patients with epilepsy may persist even with sufficient control of seizures, suggesting other factors may...
The overarching goal of this thesis was two-fold. First, to determine if the effects of chronic anabolic androgenic steroid (AAS) treatment on anxiety-like behaviors are sex-specific and second to determine how different environmental modulators...
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 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...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.