A sign pattern is a matrix whose entries are from the set $\{+, -, 0\}$. This thesis contains problems about refined inertias and minimum ranks of sign patterns. The refined inertia of a square real matrix $B$, denoted $\ri(B)$, is the ordered $4$-tuple $(n_+(B), \ n_-(B), \ n_z(B), \ 2n_p(B))$, where $n_+(B)$ (resp., $n_-(B)$) is the number of eigenvalues of $B$ with positive (resp., negative) real part, $n_z(B)$ is the number of zero eigenvalues of $B$, and $2n_p(B)$ is the number of pure imaginary eigenvalues of $B$. The minimum rank (resp., rational minimum rank) of a sign pattern matrix $\cal A$ is the minimum of the ranks of the real (resp., rational) matrices whose entries have signs equal to the corresponding entries of $\cal A$. First, we identify all minimal critical sets of inertias and refined inertias for full sign patterns of order 3. Then we characterize the star sign patterns of order $n\ge 5$ that require the set of refined inertias $\mathbb{H}_n=\{(0, n, 0, 0), (0, n-2, 0, 2), (2, n-2, 0, 0)\}$, which is an important set for the onset of Hopf bifurcation in dynamical systems. Finally, we establish a direct connection between condensed $m \times n $ sign patterns and zero-nonzero patterns with minimum rank $r$ and $m$ point-$n$ hyperplane configurations in ${\mathbb R}^{r-1}$. Some results about the rational realizability of the minimum ranks of sign patterns or zero-nonzero patterns are obtained.

Grande parte do sucesso do Google provêm do algoritmo Page Rank, que avalia quantitativamente a importância de cada página na web. Esta ordenação é obtida através do vetor estacionário de uma matriz estocástica específica, utilizando o Método das Potências. A velocidade de convergência deste método será avaliada em detalhe, já que se trata de uma resposta imediata da pesquisa do usuário. Afim de entender as diferentes situações que o modelo pode enfrentar, diversas simulações são apresentadas neste trabalho. Em particular, estamos interessados nos fatores que influenciam a velocidade de convergência. Para tanto, o número de páginas total e de cada conjunto fechado, bem como o número de conjuntos fechados e de nós pendentes foram estudados. / Great part of Google\'s success comes from the Page Rank algorithm, wich quantitatively evaluates the importance of each page on the web. This sort is achieved through a specific stochastic matrix stationary vector, using the Power Method. The convergency speed of this method will be evaluated in details, since this is a imediate response for the user search. In order to understand the diferent situations the model can confront, several simulations are shown in this work. In particular, we are interested in the factors which influences the convergency speed. For that, the total and inside each closed set number of pages and also the closed sets and dangling nodes numbers were studied.

Le développement de méthodes de décomposition de tableaux multi-dimensionnels suscite toujours autant d'attention, notamment d'un point de vue applicatif. La plupart des algorithmes, de décompositions tensorielles, existants requièrent une estimation du rang du tenseur et sont sensibles à une surestimation de ce dernier. Toutefois, une telle estimation peut être difficile par exemple pour des rapports signal à bruit faibles. D'un autre côté, estimer simultanément le rang et les matrices de facteurs du tenseur ou du tenseur cœur n'est pas tâche facile tant les problèmes de minimisation de rang sont généralement NP-difficiles. Plusieurs travaux existants proposent d'utiliser la norme nucléaire afin de servir d'enveloppe convexe de la fonction de rang. Cependant, la minimisation de la norme nucléaire engendre généralement un coût de calcul prohibitif pour l'analyse de données de grande taille. Dans cette thèse, nous nous sommes donc intéressés à l'approximation d'un tenseur bruité par un tenseur de rang faible. Plus précisément, nous avons étudié trois modèles de décomposition tensorielle, le modèle CPD (Canonical Polyadic Decomposition), le modèle BTD (Block Term Decomposition) et le modèle MTD (Multilinear Tensor Decomposition). Pour chacun de ces modèles, nous avons proposé une nouvelle méthode d'estimation de rang utilisant une métrique moins coûteuse exploitant la parcimonie de groupe. Ces méthodes de décomposition comportent toutes deux étapes : une étape d'estimation de rang, et une étape d'estimation des matrices de facteurs exploitant le rang estimé. Des simulations sur données simulées et sur données réelles montrent que nos méthodes présentent toutes une plus grande robustesse à la présence de bruit que les approches classiques. / Last decades, tensor decompositions have gained in popularity in several application domains. Most of the existing tensor decomposition methods require an estimating of the tensor rank in a preprocessing step to guarantee an outstanding decomposition results. Unfortunately, learning the exact rank of the tensor can be difficult in some particular cases, such as for low signal to noise ratio values. The objective of this thesis is to compute the best low-rank tensor approximation by a joint estimation of the rank and the loading matrices from the noisy tensor. Based on the low-rank property and an over estimation of the loading matrices or the core tensor, this joint estimation problem is solved by promoting group sparsity of over-estimated loading matrices and/or the core tensor. More particularly, three new methods are proposed to achieve efficient low rank estimation for three different tensors decomposition models, namely Canonical Polyadic Decomposition (CPD), Block Term Decomposition (BTD) and Multilinear Tensor Decomposition (MTD). All the proposed methods consist of two steps: the first step is designed to estimate the rank, and the second step uses the estimated rank to compute accurately the loading matrices. Numerical simulations with noisy tensor and results on real data the show effectiveness of the proposed methods compared to the state-of-the-art methods.

Grande parte do sucesso do Google provêm do algoritmo Page Rank, que avalia quantitativamente a importância de cada página na web. Esta ordenação é obtida através do vetor estacionário de uma matriz estocástica específica, utilizando o Método das Potências. A velocidade de convergência deste método será avaliada em detalhe, já que se trata de uma resposta imediata da pesquisa do usuário. Afim de entender as diferentes situações que o modelo pode enfrentar, diversas simulações são apresentadas neste trabalho. Em particular, estamos interessados nos fatores que influenciam a velocidade de convergência. Para tanto, o número de páginas total e de cada conjunto fechado, bem como o número de conjuntos fechados e de nós pendentes foram estudados. / Great part of Google\'s success comes from the Page Rank algorithm, wich quantitatively evaluates the importance of each page on the web. This sort is achieved through a specific stochastic matrix stationary vector, using the Power Method. The convergency speed of this method will be evaluated in details, since this is a imediate response for the user search. In order to understand the diferent situations the model can confront, several simulations are shown in this work. In particular, we are interested in the factors which influences the convergency speed. For that, the total and inside each closed set number of pages and also the closed sets and dangling nodes numbers were studied.

Non-invasively reosolving spatial distribution of tissue metabolites serves as a diagnostic tool to in-vivo metabolism thus making magnetic resonance spectroscopic imaging (MRSI) a very useful application. The tissue concentrations of various metabolites reveal disease state and pseudo-progression of tumors. Also, bio-chemical changes manifest much earlier than structural changes that are achieved using standard magnetic resonance imaging(MRI). However, MRSI has not achieved its potential due to several technical challenges that are specic to it. Several technical advances in the eld of MRI does not translate to MRSI. The specic limitations which make MRSI challenging include long scan times, poor spatial resolution, extremely low signal to noise ratio (SNR). In the last few decades, research in MRSI has focused on advanced data acquisition and reconstruction methods, however they cannot achieve high resolution and feasible scan time. Moreover there are several artifacts that lead to increase of spatial resolution not to mention starved SNR. Existing methods cannot deal with these limitations which considerably impacts applications of MRSI. This thesis work we revisit these problems and introduce data acquisition and reconstruction techniques to address several such challenges. In the first part of the thesis we introduce a variable density spiral acquisition technique which achieves high SNR corresponding to metabolites of interest while reducing truncation artifacts. Along with that we develop a novel compartmentalized reconstruction framework to recover high resolution data from lipid unsuppressed data. Avoiding lipid suppression not only reduces scan time and reliability but also improves SNR which is otherwise reduced even further with existing lipid suppression methods. The proposed algorithm exploits the idea that the lipid and metabolite compartment reside in low-dimensional subspace and we use orthogonality priors to reduce overlap of subspaces. We also look at spectral artifacts like Nyquist ghosting which is a common problem with spectral interleaving. Especially in echo-planar spectroscopic imaging (EPSI), one of the most popular MRSI techniques, maintaining a spatial and spectral resolution requires interleaving. Due to scanner inconsistencies spurious peaks arise which makes quantication inecient. In this thesis a novel structural low-rank prior is used to reduce and denoise spectra and achieve high resolution ESPI data. Finally we look at accelerating multi-dimensional spectroscopic problems. Resolving spectra in two dimensions can help study overlapping spectra and achieve more insight. However with an increased dimension the scan time increases. We developed an algorithm for accelerating this method by recovering data from undersampled measurements. We demonstrate the performance in two applications, 2D infra red spectroscopy and 2D MR spectroscopy . The aim of the thesis is to solve these challenges in MRSI from a signal processing perspective and be able to achieve higher resolution data in practical scan time to ultimately help MRSI reach its potential.

Most American universities and colleges require students to provide faculty evaluation at end of each academic term, as a way of measuring faculty teaching performance. Although some analysts think that this kind of evaluation does not necessarily provide a good measurement of teaching effectiveness, there is a growing agreement in the academic world about its reliability. This study attempts to find any strong statistical evidence supporting faculty evaluation by students as a measure of faculty teaching effectiveness. Emphasis will be on analyzing relationships between instructor ratings by students and corresponding students’ grades. Various statistical methods are applied to analyze a sample of real data and derive conclusions. Methods considered include multivariate statistical analysis, principal component analysis, Pearson's correlation coefficient, Spearman's and Kendall’s rank correlation coefficients, linear and logistic regression analysis.

O crescente volume de informações disponíveis na rede mundial de computadores, gera a necessidade do uso de ferramentas que sejam capazes de localizá-las e ordenálas, de forma cada vez mais precisa e que demandem cada vez menos recursos computacionais. Esta necessidade tem motivado pesquisadores a estudar e desenvolver modelos e técnicas que atendam esta demanda. Estudos recentes têm sinalizado que utilizar vários ordenamentos (rankings) previamente montados possibilita o retorno e ordenação de objetos de qualquer natureza com mais eficiência, principalmente pelo fato de haver uma redução no custo da busca pela informação. Este processo, conhecido como fusão de rankings, permite que se obtenha um ordenamento com base na opinião de diversos juízes (critérios), o que possibilita considerar um grande número de fontes, tanto geradas automaticamente como por especialistas. Entretanto os modelos propostos até então tem apresentado várias limitações na sua aplicação: desde a quantidade de rankings envolvidos até, principalmente, a utilização de rankings parciais. A proposta desta dissertação é apresentar um modelo de fusão de rankings que busca estabelecer um consenso entre as opiniões (rankings) dos diferentes juízes envolvidos, considerando distintos graus de relevância ou importância entre eles. A base desta proposta está na Análise de Preferência, um conjunto de técnicas que permite o tratamento da multidimensionalidade dos dados envolvidos. Ao ser testado em uma aplicação real, o modelo mostrou conseguir suprir algumas limitações apresentadas em outras abordagens, bem como apresentou resultados similares aos das aplicações originais. Esta pesquisa, ainda contribui, com a especificação de um sistema Web baseado em tecnologias open source, o qual permite que qualquer pessoa possa realizar a fusão de rankings. / The growing volume of available information on the web creates the need to use tools that are capable of retrieve and ordering this information, ever more precise and using less computer resources. This need has motivated researchers to study and develop models and techniques that solve this problem. Recent studies have indicated that use multiple rankings previously mounted makes possible the return and sorting of the objects of any kind with more efficiency, mainly because there is a reduction in the cost of searching for information. This process, called ranking fusion, provide a ranking based on the opinion of several judges (criteria), considering a large number of sources, both generated automatically and also by specialists. However the proposed models have shown severe limitations in its application: from the amount involved rankings to the use of partial rankings. The proposal of this dissertation is to show a model of ranking fusion that seeks to establish a consensus between the judgement (rankings) of the various judges involved, considering different degrees of relevance or importance among them. The baseline of this proposal is the Preference Analysis, a set of techniques that allows the treatment of multidimensional data handling. During tests in a real application, the model supplied some limitations presented by other approaches, and presented results similar to the original applications. Additionally, this research contributes with the specification of a web system based on open-sources technologies, enabling the realization of fusion rankings by anyone.

O crescente volume de informações disponíveis na rede mundial de computadores, gera a necessidade do uso de ferramentas que sejam capazes de localizá-las e ordenálas, de forma cada vez mais precisa e que demandem cada vez menos recursos computacionais. Esta necessidade tem motivado pesquisadores a estudar e desenvolver modelos e técnicas que atendam esta demanda. Estudos recentes têm sinalizado que utilizar vários ordenamentos (rankings) previamente montados possibilita o retorno e ordenação de objetos de qualquer natureza com mais eficiência, principalmente pelo fato de haver uma redução no custo da busca pela informação. Este processo, conhecido como fusão de rankings, permite que se obtenha um ordenamento com base na opinião de diversos juízes (critérios), o que possibilita considerar um grande número de fontes, tanto geradas automaticamente como por especialistas. Entretanto os modelos propostos até então tem apresentado várias limitações na sua aplicação: desde a quantidade de rankings envolvidos até, principalmente, a utilização de rankings parciais. A proposta desta dissertação é apresentar um modelo de fusão de rankings que busca estabelecer um consenso entre as opiniões (rankings) dos diferentes juízes envolvidos, considerando distintos graus de relevância ou importância entre eles. A base desta proposta está na Análise de Preferência, um conjunto de técnicas que permite o tratamento da multidimensionalidade dos dados envolvidos. Ao ser testado em uma aplicação real, o modelo mostrou conseguir suprir algumas limitações apresentadas em outras abordagens, bem como apresentou resultados similares aos das aplicações originais. Esta pesquisa, ainda contribui, com a especificação de um sistema Web baseado em tecnologias open source, o qual permite que qualquer pessoa possa realizar a fusão de rankings. / The growing volume of available information on the web creates the need to use tools that are capable of retrieve and ordering this information, ever more precise and using less computer resources. This need has motivated researchers to study and develop models and techniques that solve this problem. Recent studies have indicated that use multiple rankings previously mounted makes possible the return and sorting of the objects of any kind with more efficiency, mainly because there is a reduction in the cost of searching for information. This process, called ranking fusion, provide a ranking based on the opinion of several judges (criteria), considering a large number of sources, both generated automatically and also by specialists. However the proposed models have shown severe limitations in its application: from the amount involved rankings to the use of partial rankings. The proposal of this dissertation is to show a model of ranking fusion that seeks to establish a consensus between the judgement (rankings) of the various judges involved, considering different degrees of relevance or importance among them. The baseline of this proposal is the Preference Analysis, a set of techniques that allows the treatment of multidimensional data handling. During tests in a real application, the model supplied some limitations presented by other approaches, and presented results similar to the original applications. Additionally, this research contributes with the specification of a web system based on open-sources technologies, enabling the realization of fusion rankings by anyone.

Made available in DSpace on 2014-06-11T19:28:02Z (GMT). No. of bitstreams: 0 Previous issue date: 2010-03-02Bitstream added on 2014-06-13T20:57:35Z : No. of bitstreams: 1 gualbertojunior_ec_me_araca_parcial.pdf: 636906 bytes, checksum: 30b5eac1385afd759fc12c6f7102d1ac (MD5) Bitstreams deleted on 2015-01-16T10:37:52Z: gualbertojunior_ec_me_araca_parcial.pdf,Bitstream added on 2015-01-16T10:38:36Z : No. of bitstreams: 1 000620078.pdf: 2149145 bytes, checksum: f1633139b567f0389855aac6984d0cbc (MD5) / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES) / Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP) / O objetivo deste estudo foi avaliar histológica, histometrica e imunoistoquimicamente os efeitos do laser (LLLT) e da terapia fotodinâmica (PDT) no tratamento periodontal de ratas ovariectomizadas com ou sem reposição hormonal. Duzentas e setenta ratas foram divididas em 3 grupos de 90 animais: (A) SHAM; (B) Ovariectomizadas; (C) Ovariectomizadas tratadas com reposição hormonal. Nos primeiros molares inferiores esquerdos, de todos os animais, a doença periodontal foi induzida por ligadura. Após 7 dias, esta foi removida e nestes dentes procedeu-se a raspagem e alisamento corono-radicular (RAR). A seguir foram dividos em subgrupos de acordo com os tratamentos locais: I (n = 90) - Irrigação com 1 ml de soro fisiológico (RAR); II (n = 90) - Irrigação com 1 ml de soro fisiológico associado a aplicação de laser de baixa intensidade (LLLT) e III (n = 90) - Irrigação com 1 ml de azul de toluidina-O e, após 1 minuto, aplicação de laser em baixa intensidade (PDT). Dez animais de cada subgrupo foram sacrificados aos 7, 15 e 30 dias. Os animais do grupo A apresentaram perda óssea (PO) significativamente maior (p<0,01) no tratamento com RAR (1.11±0.26; 0.84±0.47) comparado à PDT (0.70±0.30; 0.42±0.20) nos períodos de 7 e 15 dias respectivamente. Os espécimes tratados com LLLT aos 30 dias demonstraram PO significativamente menor (p<0,01) no grupo A (0.35±0.18) comparado aos grupos B (0.82±0.21) e C (0.83±0.19). No tratamento com PDT, observou-se PO significativamente menor (p<0,01) no grupo A (0.42±0.20) comparado aos grupos B (0.95±0.20) e C (0.81±0.32) aos 15 dias. No entanto, no grupo C aos 30 dias a PDT demonstrou PO (0.52±0.23) em nível próximo ao observado nos espécimes do grupo A, no mesmo período (0.50±0.26). Na análise entre períodos, no mesmo grupo e tratamento, observou-se no grupo A, que o tratamento I apresentou PO significativamente maior... / The aim of this study was to evaluate histological, histometrically and immunohistochemistry the influence of laser and photodynamic therapy (PDT) as an adjuvant treatment on the experimentally induced periodontitis in ovariectomy rats with or without replacement hormone. Two hundred and seventy females rats were divided into 3 groups of 90 animals. (A) Normal female rats; (B) Control - Ovarectomy; (C) Ovarectomy treated with replacement hormone. The periodontal disease was induced by ligation and after 7 days was removed and the animals divided into subgroups who received the treatments: I - scaling and root planing (SRP) and irrigation with saline; II – SRP and irrigation with saline solution and LLLT (Laser -AsGaAl - 685 nm); III - SRP, irrigation with 1ml of Toluidine Blue (TBO) and, after 1 minute, application of laser (685 nm), performing photodynamic therapy (PDT). Ten animals of each subgroup were sacrificed at 7, 15 and 30 days. The animals of the group A presented bony loss (BL) significantly larger (p <0,01) in the treatment with RAR (1.11±0.26; 0.84±0.47) compared to PDT (0.70±0.30; 0.42±0.20) at 7 and 15 days respectively. In the specimens treated with LLLT at 30 days showed BL significantly less (p <0,01) in the group A (0.35±0.18) compared at groups B (0.82±0.21) and C (0.83±0.19). In the treatment with PDT, it was observed BL significantly less (p <0,01) in the group A (0.42±0.20) than groups B (0.95±0.20) and C (0.81±0.32) at 15 days. However, in the group C at 30 days PDT showed BL (0.52±0.23) in close level that observed in the specimens of the group A, in the same period (0.50±0.26). In the analysis among periods, in the same group and treatment, it was observed in the group A, that the treatment I presented BL significantly larger (p <0,01) at 7 days (1.11±0.26); that the treatment II showed larger BL (p <0,01) in the period of 7 days (0.90±0.29)... (Complete abstract click electronic access below)

O crescente volume de informações disponíveis na rede mundial de computadores, gera a necessidade do uso de ferramentas que sejam capazes de localizá-las e ordenálas, de forma cada vez mais precisa e que demandem cada vez menos recursos computacionais. Esta necessidade tem motivado pesquisadores a estudar e desenvolver modelos e técnicas que atendam esta demanda. Estudos recentes têm sinalizado que utilizar vários ordenamentos (rankings) previamente montados possibilita o retorno e ordenação de objetos de qualquer natureza com mais eficiência, principalmente pelo fato de haver uma redução no custo da busca pela informação. Este processo, conhecido como fusão de rankings, permite que se obtenha um ordenamento com base na opinião de diversos juízes (critérios), o que possibilita considerar um grande número de fontes, tanto geradas automaticamente como por especialistas. Entretanto os modelos propostos até então tem apresentado várias limitações na sua aplicação: desde a quantidade de rankings envolvidos até, principalmente, a utilização de rankings parciais. A proposta desta dissertação é apresentar um modelo de fusão de rankings que busca estabelecer um consenso entre as opiniões (rankings) dos diferentes juízes envolvidos, considerando distintos graus de relevância ou importância entre eles. A base desta proposta está na Análise de Preferência, um conjunto de técnicas que permite o tratamento da multidimensionalidade dos dados envolvidos. Ao ser testado em uma aplicação real, o modelo mostrou conseguir suprir algumas limitações apresentadas em outras abordagens, bem como apresentou resultados similares aos das aplicações originais. Esta pesquisa, ainda contribui, com a especificação de um sistema Web baseado em tecnologias open source, o qual permite que qualquer pessoa possa realizar a fusão de rankings. / The growing volume of available information on the web creates the need to use tools that are capable of retrieve and ordering this information, ever more precise and using less computer resources. This need has motivated researchers to study and develop models and techniques that solve this problem. Recent studies have indicated that use multiple rankings previously mounted makes possible the return and sorting of the objects of any kind with more efficiency, mainly because there is a reduction in the cost of searching for information. This process, called ranking fusion, provide a ranking based on the opinion of several judges (criteria), considering a large number of sources, both generated automatically and also by specialists. However the proposed models have shown severe limitations in its application: from the amount involved rankings to the use of partial rankings. The proposal of this dissertation is to show a model of ranking fusion that seeks to establish a consensus between the judgement (rankings) of the various judges involved, considering different degrees of relevance or importance among them. The baseline of this proposal is the Preference Analysis, a set of techniques that allows the treatment of multidimensional data handling. During tests in a real application, the model supplied some limitations presented by other approaches, and presented results similar to the original applications. Additionally, this research contributes with the specification of a web system based on open-sources technologies, enabling the realization of fusion rankings by anyone.