This thesis investigates a notion of Turing reducibility introduced by Winkler [8] that is total on all computably enumerable oracles. Groszek and Weber show in [7] that this is a new notion of reducibility and it is not transitive. They give su...
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...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Ζ[subscript n]). We then consider the isoperimetric numbers of these graphs. In chapter three we determine upper bounds for the isoperimetric number by a detailed...
Part 1 . A computational study targeting the lowest energy structure, electronic state and physical properties of small carbon clusters containing one or two heteroatoms has been done. The structural properties sought included whether the most...
The study of twin primes gives rise to several famously difficult problems in number theory--in fact, we still cannot definitively say whether there are infinitely many twin primes. In this work, we consider a related problem, namely: What is the...
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,...
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...
In this thesis, we consider several problems relating to cyclic subgroups of the group [mathematical equation]. Each element of [mathematical equation] has a unique representative in one of the two intervals [mathematical equation] and...
How is concrete conceptual information represented in the brain? Little is known about the neural organization for details of concrete objects when presented as words. The goal of the first two studies was to investigate this. In the third study,...
Digital integrated circuits -- Testing. Digital integrated circuits -- Testing -- Mathematical models. Digital integrated circuits -- Design and construction.
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...
Perceptual-motor learning -- Physiological aspects. ; Language acquisition -- Physiological aspects. ; Motor ability -- Physiological aspects. ; Knots and splices.
The studies presented in this dissertation explore several points of intersection between action perception and production within the human brain. One's ability to use perceptual information about another individual's actions to guide and inform...
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 look at several problems that lie in the intersection between combinatorial and multiplicative number theory. A common theme of many of these problems are estimates for and properties of the smooth numbers, those integers not...
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...
CD4+ T cells are critical for the control of virus infections, memory cell formation and immune surveillance. Epstein-Barr virus and Kaposi’s sarcoma-associated herpesvirus are two γ-herpesviruses identified in humans and are strongly associated...
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)....
Most current multiprocessor file systems are designed to use multiple disks in parallel, using the high aggregate bandwidth to meet the growing I/O requirements of parallel scientific applications. Most multiprocessor file systems provide...
Space perception. ; Motion perception (Vision). ; Vestibular apparatus.
Head Direction (HD) cells are neurons located primarily in the limbic system that fire as a function of directional heading in the horizontal, or yaw, plane in the freely moving animal. Our hypothesis is that the HD signal is the result of two...
Self-reconfiguring (SR) robots are modular systems that can autonomously change shape, or reconfigure , for increased versatility and adaptability in unknown environments. In this thesis, we investigate planning and control for systems of...