Thesis (Ph. D.)--University of Wisconsin--Madison, 1949. / Typescript. Vita. eContent provider-neutral record in process. Description based on print version record. Includes bibliographical references (leaves 25-26).

published_or_final_version / Mathematics / Doctoral / Doctor of Philosophy

Techniques from representation theory (Diaconis, 1988) and algebraic geometry (Drton et al., 2008) have been applied to the statistical analysis of discrete data with log-linear models. With these ideas in mind, we discuss the selection of sparse log-linear models, especially for binary data and data on other structured sample spaces. When a sample space and its symmetry group satisfy certain conditions, we construct a natural spanning set for the space of functions on the sample space which respects the isotypic decomposition; these vectors may be used in algorithms for model selection. The construction is explicitly carried out for the case of binary data.

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Thesis (doctoral)--Rheinische Friedrich-Wilhelms-Universität Bonn, 2005. / Includes vita. Includes bibliographical references (p. 90-93).

Orientador: Helio Vasconcelos Fagundes / Banca: José Geraldo Pereira / Banca: Maria Emília Xavier Guimarães / Resumo: No final do século XIX, L. Bianchi [1] fez a classificação das geometrias riemanianas em espaços tridimensionais, segundo seus possíveis grupos de isometrias. Parte de seus resultados foi adaptada, em uma linguagem mais moderna, por C. G. Behr [17] e outros, para o estudo de modelos cosmológicos espacialmente homogêneos mas não necessariamente isotrópicos. Esta dissertação expõe as idéias e resultados de Bianchi, e também os formalismos mais recentes no estudo desse problema. Por completeza, o espaço tridimensional do modelo de Kantowski-Sachs também é aqui incluído / Abstract: At the end of the 19th century, L. Bianchi [1] found a classification of the Riemannian geometries oni three-dimensional spaces, according to their possible isometry groups. A part of his results has been adapted, in a more modern language, by C. G. Behr [17] and others, for the study of cosmological models with homogeneous but not necessarily isotropic spatial sections. This dissertation presents Bianchi's ideas and results, and also more recent formalisms in the study of this problem. For completeness, the three-space of Kantowski-Sachs cosmological model is also here included / Mestre

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The representation theory of infinite dimensional groups is in its infancy. This paper is an attempt to apply the orbit method to a particular infinite dimensional group, the spin extension of the restricted unitary group. Our main contribution is in showing that various homogeneous spaces for this group admit measures which can be used to realize the unitary structure for the standard modules.

Thesis (Ph. D.)--University of Chicago, Dept. Mathematics, June 2000. / Includes bibliographical references. Also available on the Internet.