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...
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...
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...
Coherent states. Quantum field theory. Nonlinear theories.
In this thesis we study the properties of time-dependent, nontopological configurations and their effect on the macroscopic properties of a system described by a nonlinear field theory. These structures seem to be ubiquitous in relativistic field...
Multimodality imaging is becoming the standard of care for research and clinical studies. Such an approach is able to provide complementary information which can detect and characterize tumors. Advancing instrumentation for diffuse near-infrared...
Measurement of the ionospheric thermal particle population bridges the two different communities of ground-based radar and space-based rocket studies, which have the common goal of characterizing heavy ion transport in the cusp/cleft region. We...
In this thesis we review the methods for computation of cosmological correlations in the early universe known as the in-in formalism which are then applied to the problem of magnetogenesis from inflation. For this computation, a power-law single...
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...
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...
There is a growing demand for power-constrained sensors in many areas, particularly in emerging healthcare and next-generation biomedical applications. Such sensors have very limited power budget, among which interface circuits, including analog...
This thesis constitutes the first steps in the author's program to investigate the question of when a homotopy of 2-cocycles ω = {ω[subscript t]}[subscript t∊[0,1]] on a locally compact Hausdorff groupoid Ɠ induces an isomorphism of 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...
In order to most effectively investigate protein structure and improve protein function, it is necessary to carefully plan appropriate experiments. The combinatorial number of possible experiment plans demands effective criteria and efficient...
Prostate cancer (PCa) recurrences are often predicted by assessing the status of surgical margins (SM) – positive surgical margins (PSM) increase the chances of biochemical recurrence by 2-4 times which may lead to PCa recurrence. At present,...
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...