The goal of Inductive Learning is to produce general rules from a set of seen examples, which can then be applied to other unseen examples. ID3 is an inductive learning algorithm that can be used for the classification task. The input to the algorithm is a set of tuples of description and class. The ID3 algorithm learns a decision tree from these input examples, which can then be used for classifying unseen examples given their descriptions. ID3 faces a problem called the replication problem. An algorithm called the Expert-Gate algorithm is presented in this thesis. The aim of the algorithm is to tackle the replication problem. We discuss the various issues involved with each step of the algorithm and present results corroborating our choices. The algorithm was tested on various artificially created problems as well as on a real life problem. The performance of the algorithm was compared with that of Fringe. The algorithm was found to give excellent results on the artificially created problems. The Expert-Gate algorithm gave satisfactory results on the NETtalk problem. Overall, we believe the algorithm is a good candidate for testing on other real life domains. / Graduation date: 1993

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 164-167). Also available on the Internet.

Thesis (Ph. D.)--University of Missouri-Columbia, 1997. / Typescript. Vita. Includes bibliographical references (leaves 164-167). Also available on the Internet.

Thesis (M.S. in Mechanical Engineering)--Naval Postgraduate School, June 1069. / Thesis Advisor(s): Marto, P. J. "June 1969." Description based on title screen as viewed on June 2, 2010. DTIC Descriptor(s): (Research Reactors, Reactor Reactivity), Reactor Cores, Fuel Burn Up, Fission Product Poisoning, Polyethylene Plastics, Perturbation Theory, Computer Programs, Theses. Author(s) subject terms: Perturbation, Polyethylene, Fermi Age, Extrapolation, Neutron Temperature, Samarium. Includes bibliographical references (p. 88). Also available in print.

Orientador: Suzete Maria Silva Afonso / Banca: Renata Zotin Gomes de Oliveira / Banca: Ligia Lais Femina / Resumo: Neste trabalho discutiremos alguns métodos clássicos para otimização irrestrita, a saber o Método de Cauchy e o Método de Newton, e analisaremos a convergência desses métodos. Veremos que o Método de Cauchy, que faz a cada iteração uma busca unidirecional na direção de máxima descida, ou seja, na direção oposta ao gradiente, tem convergência linear. O método de Newton, por outro lado, minimiza, em cada iteração, a aproximação quadrática da função objetivo. Nos métodos de busca unidirecional é preciso minimizar uma função a partir de um certo ponto, segundo uma direção dada, que é a direção de busca. Por essa razão, estudaremos o Método da Seção Áurea, que fornece uma minimização exata de uma função real de uma variável real / Abstract: In this work we will discuss some classic methods for unrestricted optimization, namely the Cauchy Method and Newton's Method, and we will analyze the convergence of those methods. We will see that the Cauchy Method, that realizes on each iteration a unidirectional search in the direction of maximum descent, that is, in the direction opposite to the gradient, has linear convergence. The Newton Method, on the other hand, minimizes, in each iteration, the quadratic approximation of the objective function. In unidirectional search methods, one must minimize a function from a certain point in a given direction, which is the search direction. For that reason, we will study the Golden Section Method, which provides the exact minimization of a real function of a real variable / Mestre

Children develop the ability to perceive symmetry very early in life; symmetry is abundant in the world around us, and it is a naturally occurring theme in children’s play and creative endeavors. Symmetry is a type of pattern structure and organization of visual information that has been found by psychologists to aid adults in the processing and recall of visual information. Symmetry plays an important role across branches of mathematics and at all levels, and it provides a link between mathematics and a variety of fields and areas of study. Despite this, symmetry does not figure prominently in early childhood mathematics curriculum in the United States. The purpose of this study is to develop, implement, and evaluate a computer program that expands young children’s innate perception and understanding of symmetry and its subtopics—reflection, translation, and rotation. Eighty-six first and second grade children were randomly assigned to one of two conditions: nine sessions using the symmetry computer program designed for this study, or nine sessions using a non-geometry-related computer program. Results showed that children assigned to the experimental condition were better able to identify symmetry subtypes, accurately complete translation tasks and symmetry tasks overall, and explain symmetric transformations. These findings suggest that children are capable of learning about symmetry and its subtypes, and the symmetry software program designed for this study has the potential to improve children’s understanding of symmetry beyond what is currently taught in the early elementary mathematics curriculum. Recommendations for other researchers, educators, and future research are discussed

The thesis presents a new approach to the decomposition of incompletely specified functions and its application to FPGA (Field Programmable Gate Array) mapping. Five methods: Variable Partitioning, Graph Coloring, Bond Set Encoding, CLB Reusing and Local Transformation are developed in order to efficiently perform decomposition and FPGA (Lookup-Table based FPGA) mapping. 1) Variable Partitioning is a high quality hemistic method used to find the "best" partitions, avoiding the very time consuming testing of all possible decomposition charts, which is impractical when there are many input variables in the input function. 2) Graph Coloring is another high quality heuristic\ used to perform the quasi-optimum don't care assignment, making the program possible to accept incompletely specified function and perform a quasi-optimum assignment to the unspecified part of the function. 3) Bond Set Encoding algorithm is used to simplify the decomposed blocks during the process of decomposition. 4) CLB Reusing algorithm is used to reduce the number of CLBs used in the final mapped circuit. 5) Local Transformation concept is introduced to transform nondecomposable functions into decomposable ones, thus making it possible to apply decomposition method to FPGA mapping. All the above developed methods are incorporated into a program named TRADE, which performs global optimization over the input functions. While most of the existing methods recursively perform local optimization over some kinds of network-like graphs, and few of them can handle incompletely specified functions. Cube calculus is used in the TRADE program, the operations are global and very fast. A short description of the TRADE program and the evaluation of the results are provided at the_ end of the thesis. For many benchmarks the TRADE program gives better results than any program published in the literature.