Made available in DSpace on 2016-06-02T20:28:27Z (GMT). No. of bitstreams: 1 4588.pdf: 701327 bytes, checksum: 07aaf91b8be59a3db7c6c5cf38e55c59 (MD5) Previous issue date: 2012-09-24 / Financiadora de Estudos e Projetos / We present an introductory study of smooth manifolds, bundles and Stiefel- Whitney classes (of real vector bundles). We explained that, given a certain smooth m-dimensional manifold, the Stiefel- Whitney classes of its tangent bundle can be used to ensure that such a manifold does not immerse (smoothly) in certain Euclidean spaces Rj . In this sense, we consider the Grassmann manifold G2;n of the 2-subspaces of Rn+2, and we carry out a detailed study of the following non-immersion theorem, proved by V. Oproiu [Proceedings of the Edinburgh Mathematical Society, 1977]: "Let n > 1 be a natural number and consider s = 2r such that s < ou = 2n < 2s. If n different s - 1, then G2;n does not immerse in R2s-3; if n = s - 1, then G2;n does not immerse in R3s-3." / Apresentamos um estudo introdutório de Variedades Suaves, Fibrados e Classes de Stiefel-Whitney (de fibrados vetorias reais). Explicamos que, dada uma certa variedade suave m-dimensional, as classes de Stiefel-Whitney do seu fibrado tangente podem ser usadas para garantir que tal variedade não imerge (suavemente) em certos espaços Euclidianos Rj . Nesse sentido, consideramos a variedade Grassmanniana G2;n, variedade dos 2-subespaços de Rn+2, e realizamos um estudo detalhado do seguinte teorema de não imersão, provado por V. Oproiu [Proceedings of the Edinburgh Mathematical Society, 1977]: "Seja n > 1 um natural e considere s = 2r tal que s < ou = 2n < 2s. Se n for diferente de s - 1, então G2;n não imerge em R2s-3; se n = s - 1, então G2;n não imerge em R3s-3."

Made available in DSpace on 2015-05-15T11:46:09Z (GMT). No. of bitstreams: 1 arquivototal.pdf: 403531 bytes, checksum: ecf0300b6ad75f58a9c2431f8679a8ca (MD5) Previous issue date: 2008-06-06 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Neste trabalho provamos o Teorema algebro-geométrico de Ganey, o qual caracteriza completamente as condições de Whitney de famílias de espaços analíticos complexos com singularidades arbitrárias em termos do fecho integral de módulos naturalmente associados a estas famílias. / Neste trabalho provamos o Teorema algebro-geométrico de Ganey, o qual caracteriza completamente as condições de Whitney de famílias de espaços analíticos complexos com singularidades arbitrárias em termos do fecho integral de módulos naturalmente associados a estas famílias.

The problem of embedding a manifold in Euclidean space is considered. Manifolds are introduced in Chapter I along with other basic definitions and examples. Chapter II contains a proof of the Regular Value Theorem along with the "Easy" Whitney Embedding Theorem. In Chapter III, vector bundles are introduced and some of their properties are discussed. Chapter IV introduces the Stiefel-Whitney classes and the four properties that characterize them. Finally, in Chapter V, the Stiefel-Whitney classes are used to produce a lower bound on the dimension of Euclidean space that is needed to embed real projective space.

The purpose of this thesis is to compare rank-based tests of bivariate stochastic order. Given two bivariate distributions $F$ and $G$, the general problem we are dealing with is to test $H_0: F=G$ against $H_1:F<G$, where $F$ and $G$ are independent continuous distributions on $\Re ^2$. (``$F<G$" means that $F(x)\leq G(x)~\forall x\in \Re^2$, and $\exists x\in \Re^2$ such that $F(x)< G(x)$.). In particular, we will analyze three analogues of the one-dimensional Mann-Whitney-Wilcoxon test in two dimensions. Two of the test statistics are new; we call them the Kendall and Spearman statistics. We will then show the asymptotic distributions and carry out empirical comparisons of the Kendall, Spearman and the third two-dimensional Mann-Whitney-Wilcoxon statistics.

No description available.

Syftet med denna studie är att undersöka om det utifrån det musikaliskainnehållet går att förstå och förklara viktiga aspekter som gör en låt till enlistetta. Valet av låtar, som utgör undersökningsmaterialet, baserades på att dessaskall ha legat etta på Billboard Hot-100, och att dessa skulle vara från olikatidsperioder: hela vägen från 80-talet och fram tills 2021. I denna studiebehandlas en tidsram på över 50 år. Från 80-talet valdes Olivia Newton-John -Physical, från 90-talet valdes Whitney Houston - I will always love you, från 00-talet valdes Kanye West- Golddigger, från 10-talet valdes Drake - God’s Planoch slutligen från 20-talet valdes BTS - Butter. En gemensam faktor dessa låtarhar, utöver att ha legat på första platsen på Billboard Hot-100, är att samtliga avlåtarna har legat etta på toppen i över tio veckor och de utvalda låtarna är fem avde endast 40 låtar som någonsin har åstadkommit det. Det finns otaliga analysersom kan utföras för att försöka att räkna ut framgången som låtarna har haft, menanalysen i denna studie fokuserar på de undersökta låtarnas uppbyggnad ochinnehåll. Studiens resultat visar att vissa övergripande mönster kan urskiljas. Entendens som iakttagits är att låtar som blir hits har någon säregen kvalitet somgör att de låter delvis likt tidigare låtar som har släppts men ändå jämförelsevisannorlunda. En annan viktig aspekt är att textinnehållet, för att en låt ska nåframgång och bli en listetta, bör fokusera på ämnet kärlek.

Recent inspections conducted on levee safety in the U.S. that participate in the United States Army Corps of Engineers (USACE) Levee Safety Program under Public-Law 84-99 have shown that the overwhelming majority (>95%) of these levees have at least some deficiency associated with them, and many being identified as having an unacceptable safety rating (≈30%). In the U.S., many levees were constructed using funding from the federal government, but the responsibility of operation and maintenance of the levees were turned over to local government bodies. Given the local funding of levee maintenance, the socioeconomic characteristics of these levee-protected communities may be useful in identifying which communities may not have the economic, social, and / or political capital to maintain their levees to an acceptable safety standard. Using the lens of socio-hydrology, this study examines the socioeconomic and demographic characteristics of levee-protected communities and their relationship to the safety rating of their levee system. Using GIS, socioeconomic data were compiled for each of the evaluated Illinois levee systems from the US Census and the USACE’s National Levee Database (NLD). In addition to socioeconomic data, the NLD contained information on a levee’s age, protection level, estimated value of structures within the levee-protected area, ownership, inspection status, safety rating, and other structural details. The value of levee-protected agricultural lands was also assessed using a soil productivity index used by the state of Illinois to assess taxes on farmland. This information was compiled to investigate the potential differences of socioeconomic characteristics of communities with unacceptable to those with an acceptable levee rating. To assess the differences between the compiled socioeconomic information, the Independent Samples U-Test was implemented to quantify differences between communities with an acceptable verse unacceptable safety rating. In this study, 71 levee systems were identified with a levee safety rating and socioeconomic data from which to perform the statistical comparison between levee systems with an acceptable versus unacceptable safety rating. Of these 71 levees systems, 28 had an unacceptable and 43 had an at least minimally acceptable safety rating. The results from the Independent Samples U-Test showed that five variables with substantial variance (α ≤ 0.2, 80% CI) between the levee safety ratings were, the age of the levee, property value per structure, the average soil productivity index, per capita income, and the percentage of population being black. Using these substantial variables, a binary logistic regression model was created to see if they could be used to realistically predict the levee system’s safety rating. The regression model was able to accurately predict 84% of the ‘acceptable’ group while only correctly predicting 25% of the ‘unacceptable’ group resulting in an overall accuracy of 61%. The inability of this model to predict a levee system’s safety rating underscores the complexities in trying to determine which socioeconomic factors are important for identifying a given levee system’s safety rating. This finding also suggests there are potentially other variables which may be more robust predictors of a community’s ability to adequately maintain their levee. Future research should investigate these complexities in identifying which communities can adequately maintain their levee system.

The approach to a theory of non-finitary matroids, as outlined by the author in [20], is here extended to the case in which the relevant closure operators are defined on arbitrary complete Boolean algebras, rather than on the power sets of sets. As a preliminary to this study, the theory of derivatives of operators on complete Boolean algebras is developed and the notion, having interest in its own right, of an analytic closure operator is introduced . The class of B-matroidal closure operators is singled out for especial attention and it is proved that this class is closed under Whitney duality. Also investigated is the class of those closure operators which are both matroidal and topological. / Thesis / Doctor of Philosophy (PhD)

Microarray technology enables simultaneous gene expression level monitoring for thousands of genes. While this technology has now been recognized as a powerful and cost-effective tool for large-scale analysis, the many systematic sources of experimental variations introduce inherent errors in the extracted data. Data is gathered by processing scanned images of microarray slides. Therefore robust image processing is particularly important and has a large impact on downstream analysis. The processing of the scanned images can be subdivided in three phases: gridding, segmentation and data extraction. To measure the gene expression levels, the processing of cDNA microarray images must overcome a large set of issues in these three phases that motivates this study. This study presents automatic gridding methods and compares their performances. Two segmentation techniques already used, the Seeded Region Growing Algorithm and the Mann-Whitney Test, are examined. We present limitations of these techniques. Finally, we studied the data extraction method used in MicroArray Suite (MS), a microarray analysis software, via synthetic images and explain its intricacies. / Master of Science

[pt] O objetivo desta pesquisa é estudar as propriedades geométricas e topológicas de curvas genéricas imersas no plano. Neste caso ser genérica significa que a curva só pode ter pontos duplos sem tangentes comuns nas duas passagens. Pode-se nomear as n singularidades da curva usando símbolos como a1, ... , an. Percorrendo a curva, produz-se uma palavra cíclica de tamanho 2n. Entretanto, nem toda palavra está relacionada a uma curva plana, há requisitos sobre a sua combinatória, o primeiro dos quais foi descoberto por Gauss. Avanços foram realizados no estudo de curvas localmente convexas no plano, na esfera e no plano projetivo. / [en] The aim of this work is to study the topological and geometric properties of closed generic immersed curves in the plane. In this case, generic means that the curve can only have double points without a common tangent. One can label the singularities using n symbols, such as a1, ... , an. Going around the curve, a cyclic word of length 2n is produced. However, not every word is related to a planar curve, there are requirements on its combinatorics, the first of which was found by Gauss. Advances were made in the study of locally convex curves on the plane, the sphere and the projective plane.