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...
Access control is a core component of any information-security strategy. Researchers have spent tremendous energy over the past forty years defining abstract access-control models and proving various properties about them. However, surprisingly...
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...
Robustness to genetic perturbations is a fundamental property of all living things. The genetic code is degenerate, RNA secondary structure is robust to sequence changes, and protein structure is robust to amino acid substitutions. Complex systems...
The Euler '-function and Carmichael -function are extremely important in modern number theory, and much work has been devoted to studying the distribution and arithmetic properties of the values of each function. One interesting unresolved question...
Medical imaging methods have become increasingly important in diagnosing diseases and assisting therapeutic treatment. In particular, early detection of breast cancer is considered as a critical factor in reducing the mortality rate of women....
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...
In this thesis we study 1=k-geodesics, those closed geodesics that minimize on any subinterval of length L=k, where L is the length of the geodesic. These curves arise as critical points of the uniform energy, a function introduced in Morse theory...
We provide a theoretical model for a design involving a dc voltage biased Josephson junction (JJ) that strongly drives a high quality factor microwave cavity via the ac Josephson effect. We explore the rich classical dynamics of the resultant...
The main driving force behind the development of computers was the attempt to solve problems that would otherwise require a large amount of time to be solved. Despite the technological development that has made computers ubiquitous in daily lives,...
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)....
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...
Decompression sickness (DCS, or the "Bends") is a condition that afflicts hundreds of divers each year and is cause for concern for both the Navy, the Air Force, and NASA. Despite the fact that bubble formation is the purported cause of DCS...
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...
Nucleotide sequence -- Data processing. Linkage (Genetics) -- Data processing. Computer algorithms. Human population genetics. Medical Term Base Pairing -- genetics. Base Sequence -- genetics. Genome wide association studies.
This thesis investigates techniques for the discovery and use of phase information in genetic studies. ""Phase"" refers to the precise assignment of the members of a different base pairs at the same genomic locus to two possible candidate...
Little is known about the emergence of life from nonliving precursors. A key missing- piece is the origin of homochirality: nearly all life is characterized by exclusively dextrorotary sugars and levorotary amino acids. The research presented in...
Manifolds (Mathematics) Geodesics (Mathematics) Space and time.
We investigate weak and strong refocusing of light rays in a space-time and related concepts. A strongly causal space-time ( X^ n +1 , g ) is emphstrongly refocusing at x ∈ X if there is a point y ≠ x such that all null-geodesics through y pass...
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...
Sorting very large datasets is a key subroutine in almost any application that is built on top of a large database. Two ways to sort out-of-core data dominate the literature: merging-based algorithms and partitioning-based algorithms. Within these...
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...
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...