Constructibility (Set theory). Trees (Graph theory).
This thesis investigates possible initial segments of the degrees of constructibility. Specifically, we completely characterize the structure of degrees in generic extensions of the constructible universe L via forcing with Souslin trees. Then we...
Computer input-output equipment. ; Computational grids (Computer systems). ; High performance computing. ; Electronic data processing -- Distributed processing.
High-performance computing increasingly occurs on computational grids composed of heterogeneous and geographically distributed systems of computers, networks, and storage devices that collectively act as a single virtual computer. A key challenge...
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...
There is a long history of attempts to explain why music is perceived as expressive of emotion. Many of the acoustic parameters that are used to communicate emotion in music are also used in human vocal expressions of emotion, suggesting that the...
We associate, to each positive integer n , a Cayley graph to the group PSL(2.Î–[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...
Nerve growth factor (NGF), the prototypic neurotrophin, is well characterized for its pro-survival and growth effects in sympathetic and sensory neurons. Acting as a target-derived factor, NGF regulates the maturation of innervating neurons, and...
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 this thesis, we characterize and enumerate the permutations which are realized by the orbits of signed shifts, a family of discrete dynamical systems on words. The permutations, which are called patterns of the signed shifts, are given by the...
Sponges are a historically ambiguous taxon, often considered primitively simple representatives of early Metazoa, living fossils from the era before the complex morphological features of the bilaterian phyla appeared in the Cambrian. Yet recent...
Boundary integral methods have long been used to solve boundary value problems for elliptic partial differential equations with piecewise constant coefficients, since they have several numerical advantages over conventional volume discretization....
In this thesis, we study the dynamics of magnetic flows on compact nilmanifolds. Magnetic flows are generalizations of geodesic flows. They model the motion of a particle of unit mass and unit charge in a smooth manifold M in the presence of a...
'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...
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...
In the late 1960s, Ihara began work that led to the Ihara zeta function, a zeta function which is defined on a finite graph. This function is an interesting graph invariant which gives information on expansion properties of the graph. It also...
We pose several adversarial variants of the multi-armed bandit scenario and propose new approaches for their play and analysis. Our casino patron seeks to discover information about an unknown system as a means to long-term payoff -- exploration...
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...
Cosmic acceleration could be an effect of a ""dark energy"" fluid pervading the Universe. It could also be an indication that general relativity is not the correct theory of gravity at cosmological length scales. Unfortunately, observations of the...
Many organisms recognize and respond to categories: predator, prey, rival, or juvenile. Organisms recognize these ecologically-important categories by assessing diverse sensory stimuli. A primary focus of my research has been understanding how...
During our fieldwork with real-world organizations---including those in Public Key Infrastructure (PKI), network configuration management, and the electrical power grid---we repeatedly noticed that security policies and related security artifacts...