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...
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)....
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...
The brain is a vastly interconnected information processing network. In humans, this network supports the rich mental space at the root of the imagination and enables many flexible cognitive abilities such as scientific and artistic creativity. How...
Brain -- Physiology -- Mathematical models.
Brain stem -- Effect of chemicals on.
Basal ganglia -- Physiology.
Understanding how the brain works remains one of the toughest problems in science, despite the progress in scientific technology available for its study. The difficulty lies in the fact that the brain is a dynamic system, while the body of facts...
Loss of vascular smooth muscle cell function is a hallmark of vascular disease. Vascular smooth muscle cells become increasingly resistant to phenotypic modulation, apoptotic and senescent. Sirtuin 1 (SirT1) is a deactylase that regulates...
Proteins -- Structure -- Data processing. Proteins -- Analysis -- Data processing. Nuclear magnetic resonance spectroscopy. Oligomers -- Analysis -- Data processing.
Symmetric homo-oligomers (protein complexes with similar subunits arranged symmetrically) play pivotal roles in complex biological processes such as ion transport and cellular regulation. Structure determination of these complexes is necessary in...
In the past few years there has been a tremendous growth in the usage of digital images. Users can now access millions of photos, a fact that poses the need of having methods that can efficiently and effectively search the visual information of...
GABA -- Receptors. Anabolic steroids -- Physiological effect. Androgens -- Physiological effect. Prosencephalon. Neurotransmitters -- Effect of drugs on. Psychoneuroendocrinology.
Anabolic androgenic steroids (AAS) are derivatives of testosterone originally designed for therapeutic applications to enhance anabolic potency (protein synthesis and muscle growth) while exerting low androgenic (masculinizing) effects. The...
This thesis explores practical and theoretical aspects of several privacy-providing technologies, including tools for anonymous web-browsing, verifiable electronic voting schemes, and private information retrieval from databases. State-of-art...
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 develop a theory of Fourier analysis and fast Fourier transforms (FFTs) for finite inverse semigroups. Our results generalize results in the theory of Fourier analysis for finite groups. There is a general method for generating...
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...
Modern distributed systems scatter sensors, storage, and computation throughout the environment. Ideally these devices communicate and share resources, but there is seldom motivation for a device''s owner to yield control to another user. We...
Clinical medicine -- Decision making -- Mathematical models. ; Diagnosis Laboratory. ; Medical screening -- Mathematical models. ; Osteoporosis -- Diagnosis. ; Mycobacterial diseases -- Diagnosis.
This dissertation focuses on the use of decision analysis to study the optimal use of medical tests. The classic threshold model of clinical decision making provides methodological background and motivation for the dissertation. In this model,...
Three-dimensional imaging in medicine -- Mathematical models. ; Stereoencephalotomy.
In the past, clinicians skilled at image-guided neurosurgery have relied solely on pre-operative scans for their navigational information. Often in the course of surgery, tissue is purposely retracted/resected or inadvertently moved resulting in a...
We present designs, theory and the results of fabrication and testing for a novel parallel microrobotic assembly scheme using stress-engineered MEMS microrobots. The robots are 240-280 Î¼m Ã— 60 Î¼m Ã— 7-20 Î¼m in size, each robot consist of a...
The first chapter of this thesis encompasses progress towards the X-ray structure determination and drug design for the dihydrofolate reductase-thymidylate synthase (DHFR-TS) enzyme from the protozoa Toxoplasma gondii, along with another mutant...
This thesis contains some results concerning groupoid dynamical systems and crossed products. We introduce the notion of a proper groupoid dynamical system and of its generalized fixed point algebra. We show that our notion of proper groupoid...
For a long-lived metastable system, the decay of the survival probability is typically exponential. However, deviations are known to exist at short times (the quantum Zeno effect) and at long times (algebraic tails in classical hydrodynamic...
Patients -- Decision making. Patients -- Attitudes. Motivation (Psychology) -- Social aspects. Preferences (Philosophy) Medical care -- Evaluation. Medical care -- Research -- Methodology. Medical care -- Decision making.
Statement of Problem
Characterizing the public's preferential attitudes towards relatively more-/less-intense elective options in ""preference-sensitive"" health care situations is particularly relevant for the prioritization policies of...
Accurate chromosome segregation in human oocytes requires that meiotic sister chromatid cohesion remain intact for decades and work in model organisms indicates that deterioration of meiotic cohesion over time may be a major determinant of...
Lung cancer is the leading cause of cancer-related death in the USA and worldwide causing 160,000 and 1.5 million deaths per year, respectively. Due to the late stage of diagnosis, poor efficacy of chemotherapies (targeted and pleiotropic), and...
Production of fuel ethanol from cellulosic materials is a potentially attractive way to meet sustainability, energy security, and environmental goals. However, the high cost of processing using current technology has thus far prevented...
Purple sulfur bacteria (PSB) can dominate the nitrogen, carbon, and sulfur cycles in anoxic ecosystems via their anoxygenic photosynthetic metabolisms and are the only producers of the carotenoid, okenone, a biomarker targeted for photic zone...
Traumatic brain injury (TBI) is the leading cause of acquired disability in children, yet innate repair mechanisms are incompletely understood. A possible innate mechanism to repair injury after insult is neurogenesis - the birth, migration,...
Breast cancer is the most common cancer in women. The discovery of breast tumor subtypes and the subsequent development of treatments aimed at them has allowed a reduction in the mortality of breast cancer. However, tumors with similar...
Fluorescence molecular imaging will have an important clinical impact in the area of guided oncology surgery, where emerging technologies are poised to provide the surgeon with real-time molecular information to guide resection, using targeted...
PDZ protein-protein interaction domains recognize short linear motif (SLiM) sequences typically at the extreme C-terminus of a target protein. These domains often act as scaffolds, connecting target proteins to additional interaction and catalytic...