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Thesis

Nonlinear dynamics and neural systems: Synchronization and modeling

Authors: Kramer, Mark Alan (2005)

We study the electrical activity of the human cortex in two ways. First, we state seven coupling measures to analyze electroencephalogram and electrocortiogram time series. We apply these measures to simulated and observed data, and we use the measures to deduce changes in coupling induced by auditory stimuli and produced by dementia. Second, we define a mathematical model of the spatially averaged, mean-field cortical electrical activity recorded by the electroencephalograph and electrocortiograph. We compare the model results with ictal electrocortical data collected from four human subjects, and we show that the observed and simulated results agree in two important ways. We use the model to develop three methods for controlling seizures through electrical stimulation and to sugge...

Thesis

Ore revisited: An algorithmic investigation of the simple commutator promise problem (Oystein Ore)

Authors: Ulrich, James L (2005)

Motivated by a desire to test the security of the pubic key exchange protocol of I. Anshel, M. Anshel, and D. Goldfeld, (“An Algebraic Method for Public-Key Cryptography”, Mathematical Research Letters, vol. 6, pp. 1-5, 1999), we study algorithmic approaches to the simple commutator decision and promise problems (SCDP/SCPP) for the braid groups Bn. We take as our point of departure a seminal paper of O. Ore, (“Some Remarks on Commutators”, Proceedings of the American Mathematical Society, Vol. 2, No. 2, pp.307-314, 1951), which studies the SCPP for the symmetric groups. Our results build on the work of H. Cejtin and I. Rivin, (“A Property of Alternating Groups”, arXiv:math.GR/0303036). We extract, from their proof that any element of the alternating subgroup of Sn can be written as...

Thesis

Parallel Programming Using Thread-level Speculation

Authors: Prabhu, Manohar Karkal (2005)

As the performance increases of single-threaded processors diminish, consumer desktop processors are moving toward multi-core designs. Thread-level speculation (TLS) increases the space of applications that can benefit from these designs. With TLS, a sequential application is divided into fairly independent tasks that are speculatively executed in parallel, while the hardware dynamically enforces data dependencies to provide the appearance of sequential execution. This thesis demonstrates that support for TLS greatly eases the task of manual parallel programming. Because TLS provides a sequential programming interface to parallel hardware, it enables the programmer to focus only on issues of performance, rather than correctness. The dissertation starts by demonstrating the parall...

Thesis

Removal of copper(II) and lead(II) from soils by poly(amidoamine) dendrimers and reductive immobilization of chromium(VI) by stabilized zero-valent iron nanoparticles

Authors: Xu, Yinhui (2005)

This research investigated the feasibility of using poly(amidoamine) PAMAM dendrimers for removal of copper(II) and lead(II) from soils, and using a new class of stabilized zero-valent iron (ZVI) nanoparticles for reductive immobilization of chromium (VI) in contaminated soils. PAMAM dendrimers ranging from generation (G) 1.0 to 4.5 and with -NH2, -COO", and -OH" terminal groups were tested for extraction of copper(II) and lead(II) from a sandy loam soil, a clay soil, and a sandy clay loam. A series of fixed-bed column experiments were conducted to study the effects of dendrimer dosage, generation number, functional groups, pH, ionic strength, and soil type on the removal efficiency. It was found that more than 90% of the preloaded copper (II) was removed by -66-bed volumes a den...

Thesis

Structure and Properties of Electrospun Polymer Fibers and Applications in Biomedical Engineering

Authors: Casper, Cheryl L. (2005)

Increased interest in nanotechnology has revived a fiber processing technique invented back in the 1930’s. Electrospinning produces nanometer to micron size fibers that are not otherwise achievable using conventional fiber spinning methods. Due to small fiber diameters, high surface area, tailorable surface morphology, and the creation of an interconnected fibrous network, electrospun fibers have found use in a variety of applications. However, a multitude of parameters directly affect the electrospinning process thus requiring a fundamental understanding of how various parameters affect the process and resulting fiber properties. Accordingly, the focus of this dissertation is to provide insight on how solution characteristics and processing parameters directly affect the electrospi...

Thesis

The Numeraire Portfolio and Arbitrage in Semimartingale Models of Financial Markets

Authors: Kardaras, Konstantinos (2005)

We study the existence of the numeraire portfolio under predictable convex constraints in a general semimartingale financial model. The numeraire portfolio generates a wealth process which makes the relative wealth processes of all other portfolios with respect to it supermartingales. Necessary and sufficient conditions for the existence of the numeraire portfolio are obtained in terms of the triplet of predictable characteristics of the asset price process. This characterization is then used to obtain further necessary and sufficient conditions, in terms of an arbitrage-type notion. In particular, the full strength of the "No Free Lunch with Vanishing Risk" (NFLVR) is not needed, only the weaker "No Unbounded Profit with Bounded Risk" (NUPBR) condition that involves the boundedness...