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...
Oligomers -- Structure -- Mathematical models. Nuclear magnetic resonance spectroscopy.
Medical Term: Nuclear Magnetic Resonance, Biomolecular.
Protein complexes play vital roles in the fundamental processes of life. In particular, homo-oligomers are involved in cell signaling, regulation, and transport. To make detailed studies of these symmetric proteins, they need to be discovered, and...
An interval order is an ordered set whose elements are in correspondence with a collection of intervals in a linearly ordered set, with disjoint intervals ordered by their relative position. The order complex of an ordered set is the simplicial...
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...
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...
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...
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...
In a variety of applications spanning mobile devices, performance computing, and even renewable energy and automotive, power management and power delivery are an increasing bottleneck in reducing size and cost, improving reliability, and even...
Evolutionary Computation (EC) is one of the most advanced computational techniques. It has been frequently and successfully used to find good solutions to many complicated optimization problems with limited computational resources. EC is the...
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...
Magnetic Resonance Elastography (MRE) has emerged as a noninvasive, quantitative physical examination of the elastic properties of soft biological tissues including breast, liver, prostate, and brain. Implementation of constitutive relations that...
Electric generators -- Windings. Electric inductors -- Design and construction -- Mathematical models. Electric current converters -- Design and construction -- Mathematical models. Energy dissipation -- Mathematical models.
Magnetic components for high-frequency power conversion applications can have significant losses that compromise the performance of the converter. In particular, winding losses can be large due to high-frequency effects that are difficult to model...
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...
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...
Magnetic nanoparticles are promising candidates for use in biomedical applications as remote sensors of biophysical properties, thermal therapy agents, and detectors of specific biomolecules. Many approaches have been used to model magnetic...
We study motion planning problems, finding trajectories that connect two configurations of a system, from two different perspectives: optimality and survivability. For the problem of finding optimal trajectories, we provide a model in which the...
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...
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...
In the Firefighter Problem, a fire starts at a vertex of a graph, and in discrete time units, it spreads from burned vertices to their neighbors, unless they are protected by one of the f firefighters that are deployed every turn. Once burned or...
A novel synthetic route to the synthesis of 9-propyl-10-azacyclododecan-12-olide (1), a natural allomone isolated from the Mexican bean beetle pupa, is presented. The salient features of this synthetic route are a regioselective Beckmann...
Two localized spectroscopic imaging methods were investigated to detect and discriminate microscopic pathologies at the surface of excised breast tissues in order to improve resection completeness during breast conserving surgery. A scanning in...
Digital video -- Analysis. Forensic sciences. Image processing -- Digital techniques.
We present new forensic tools that are capable of detecting traces of tampering in digital video without the use of watermarks or specialized hardware. These tools operate under the assumption that video contain naturally occurring properties which...
In this work we investigate the quantum dynamics of three different configurations of nonlinear cavity systems. We begin by carrying out a quantum analysis of a dc superconducting quantum interference device (SQUID) mechanical displacement detector...
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 ....
We study the bijective combinatorics of reduced words. These are fundamental objects in the study of Coxeter groups. We restrict our focus to reduced words of permutations and signed permutations. Our results can all be situated within the context...
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...
We start by introducing avoidance coupling of Markov chains, with an overview of existing results. We then introduce and motivate a new notion, uniform coupling. We show that the only Markovian avoidance coupling on a cycle is of this type, and...
This research has established feasibility of surface temperature characterization using ruby fluorescence. Study was performed in pin-on-disk geometry, with balls made of different plastics sliding against the sapphire disk. Fluorescence signal was...
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...