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Submitted by Thaís Saes Giuliani null (thais_saes@hotmail.com) on 2017-12-13T20:19:43Z No. of bitstreams: 1 Dissertação Thaís Saes Giuliani Ribeiro.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Submitted by Thaís Saes Giuliani Ribeiro (thais_saes@hotmail.com) on 2017-12-14T11:25:03Z No. of bitstreams: 1 Dissertação Thaís Saes Giuliani Ribeiro.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Approved for entry into archive by Elza Mitiko Sato null (elzasato@ibilce.unesp.br) on 2017-12-14T12:31:48Z (GMT) No. of bitstreams: 1 ribeiro_tsg_me_sjrp.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) / Made available in DSpace on 2017-12-14T12:31:48Z (GMT). No. of bitstreams: 1 ribeiro_tsg_me_sjrp.pdf: 1429513 bytes, checksum: 6145616464ae520fc8e8d6211d5e63d2 (MD5) Previous issue date: 2017-11-30 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Neste trabalho, mostramos como construir um processo estocástico de Markov e seu espaço de probabilidade a partir das probabilidades de transição e da distribuição inicial. Além disso, mostramos a convergência das matrizes de transição utilizando como ferramenta conhecimentos de Álgebra Linear. A aplicação das cadeias de Markov num contexto voltado para o Ensino Médio é mostrado no último capítulo, onde procuramos oferecer aos alunos a oportunidade de ter uma visão mais ampla de como a Matemática pode ser aplicada em outras áreas do conhecimento. / In this work, we show how to construct a stochastic Markov process and its probability space from the transition probabilities and the initial distribution. In addition, we show to investigate the convergence of the transition matrices using Linear Algebra knowledge as a tool. Application of Markov chains in a context focused on High School, it is shown in the last chapter, where we try to offer the students the opportunity to have a view of how mathematics can be applied in other areas of knowledge.

The thesis apply to reliability problems approach of Voronoi tessellation, typically used in the field of samples designs evaluation and for Monte Carlo samples reweighing. It is shown, this general technique estimation converges to that of Importance Sampling method despite it does not rely on Importance Sampling's auxiliary density. Consequently, reliability analysis could be divided into sampling itself and assessment of simulation results. As an extension of this idea, adaptive statistical sampling using QHull library was attempted.

Random sampling is a popular technique for providing fast approximate query answers, especially in data warehouse environments. Compared to other types of synopses, random sampling bears the advantage of retaining the dataset’s dimensionality; it also associates probabilistic error bounds with the query results. Most of the available sampling techniques focus on table-level sampling, that is, they produce a sample of only a single database table. Queries that contain joins over multiple tables cannot be answered with such samples because join results on random samples are often small and skewed. On the contrary, schema-level sampling techniques by design support queries containing joins. In this paper, we introduce Linked Bernoulli Synopses, a schema-level sampling scheme based upon the well-known Join Synopses. Both schemes rely on the idea of maintaining foreign-key integrity in the synopses; they are therefore suited to process queries containing arbitrary foreign-key joins. In contrast to Join Synopses, however, Linked Bernoulli Synopses correlate the sampling processes of the different tables in the database so as to minimize the space overhead, without destroying the uniformity of the individual samples. We also discuss how to compute Linked Bernoulli Synopses which maximize the effective sampling fraction for a given memory budget. The computation of the optimum solution is often computationally prohibitive so that approximate solutions are needed. We propose a simple heuristic approach which is fast and seems to produce close-to-optimum results in practice. We conclude the paper with an evaluation of our methods on both synthetic and real-world datasets.