Browsing by Author "Jesus Rodriguez, Committee Member"

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Dynamical Behavior of a Discrete, One-island, Selection-migration Model with General Dominance.
(2010-07-28) Bostic, Kathryn Jordan; James Selgrade, Committee Chair; Ernest Stitzinger, Committee Member; Jesus Rodriguez, Committee Member; Alun Lloyd, Committee Member
Neural Networks for Pattern Classification and Universal Approximation
(2002-07-08) Liao, Yi; Shu-Cherng Fang, Committee Chair; Henry L. W. Nuttle, Committee Co-Chair; Yuan-Shin Lee, Committee Member; Jesus Rodriguez, Committee Member
This dissertation studies neural networks for pattern classification and universal approximation. The objective is to develope a new neural network model for pattern classification, and relax the conditions for Radial-Basis Function networks to be universal approximators. First, the problem of pattern classification is introduced, which is followed by a brief introduction of three popular nonlinear classification techniques, that is, Multi-Layer Perceptrons (MLP), Radial-Basis Function (RBF) networks, and Support Vector Machines (SVM). Then, based on the basic concepts of MLP, RBF and SVM, a new neural network model with bounded weights is proposed, and some experimental results are reported. Later, the problem of universal approximation by neural networks is introduced, and the researches on ridge activation functions and radial-basis activation functions are reviewed. Then, the relaxed conditions for RBF networks to be universal approximators are presented. We show that RVF networks can uniformly approximate any continuous function on a compact set provided that the radial basis activation function is continuous almost every where, locally essentially bounded, and not a polynomial. Some experimental results are reported to illustrate our findings. The dissertation ends with the conclusion and future research.
The Stone-Cech Compactification of the Plane
(2006-05-04) Cabbage, Brian William; Gary Faulkner, Committee Chair; Richard Chandler, Committee Member; Jesus Rodriguez, Committee Member; Ernie Stitzinger, Committee Member
The motivation for this dissertation came from Franco Obersnel's dissertation On Compactifications of the Set of Natural Numbers and the Half Line. In it he proves that any non-degenerate subcontinuum of the Stone Cech remainder of the half line will map onto any arbitrary continuum of weight ≤ ω₁. We are able to prove the same property for many (though not all) non-degenerate subcontinua of the Stone-Cech remainder of the plane, as well as investigating certain algebraic and topological structures on subsets of the remainder.