We consider the task of computing reliable numerical approximations of the solutions of elliptic equations and systems where the coefficients vary discontinuously, rapidly, and by large orders of magnitude. Such problems, which occur in diffusion and in linear elastic deformation of composite materials, have solutions with low regularity with the result that reliable numerical approximations can be found only in approximating spaces, invariably with high dimension, that can accurately represent the large and rapid changes occurring in the solution. The use of the Galerkin approach with such high dimensional approximating spaces often leads to very large scale discrete problems which at best can only be solved using efficient solvers. However, even then, their scale is sometimes so large that the Galerkin approach becomes impractical and alternative methods of approximation must be sought. In this thesis we adopt two approaches. We propose a new asymptotic method of approximation for problems of diffusion in materials with periodic structure. This approach uses Fourier series expansions and enables one to perform all computations on a periodic cell; this overcomes the difficulty caused by the rapid variation of the coefficients. In the one dimensional case we have constructed problems with discontinuous coefficients and computed the analytical expressions for their solutions and the proposed asymptotic approximations. The rates at which the given asymptotic approximations converge, as the period of the material decreases, are obtained through extensive computational tests which show that these rates are fundamentally dependent on the level of regularity of the right hand sides of the equations. In the two dimensional case we show how one can use the Galerkin method to approximate the solutions of the problems associated with the periodic cell. We construct problems with discontinuous coefficients and perform extensive computational tests which show that the asymptotic properties of the approximations are identical to those observed in the one dimensional case. However, the computational results show that the application of the Galerkin method of approximation introduces a discretization error which can obscure the precise asymptotic rate of convergence for low regularity right hand sides. For problems of two dimensional linear elasticity we are forced to consider an alternative approach. We use domain decomposition techniques that interface the subdomains with conjugate gradient methods and obtain algorithms which can be efficiently implemented on computers with parallel architectures. We construct the balancing preconditioner, M,, and show that it has the optimal conditioning property k(Mh(^-1)Sh) =< C(1 + log(H/h))^2 where Sh is the discretized Steklov—Poincaré operator, C> 0 is a constant which is independent of the magnitude of the material discontinuities, H is the maximum subdomain diameter, and h is the maximum finite element diameter. These properties of the preconditioning operator Mh allow one to use the computational power of a parallel computer to overcome the difficulties caused by the changing form of the solution of the problem. We have implemented this approach for a variety of problems of planar linear elasticity and, using different domain decompositions, approximating spaces, and materials, find that the algorithm is robust and scales with the dimension of the approximating space and the number of subdomains according to the condition number bound above and is unaffected by material discontinuities. In this we have proposed and implemented new inner product expressions which we use to modify the bilinear forms associated with problems over subdomains that have pure traction boundary conditions.

ROCHA NETO, Odílio Coimbra da. Estimativa da condutividade elétrica por meio de dados hiperespectrais em solos afetados por sais. 2016. 117 f. : Tese (doutorado) - Universidade Federal do Ceará, Centro de Ciências Agrárias, Departamento de Engenharia Agrícola, Programa de Pós-Graduação em Engenharia Agrícola, Fortaleza-CE, 2016. / Submitted by guaracy araujo (guaraa3355@gmail.com) on 2016-08-08T16:15:17Z No. of bitstreams: 1 2016_tese_ocrochaneto.pdf: 3643209 bytes, checksum: f3daa9dd6a70b91cd6315eea748ed3c8 (MD5) / Approved for entry into archive by guaracy araujo (guaraa3355@gmail.com) on 2016-08-08T16:18:45Z (GMT) No. of bitstreams: 1 2016_tese_ocrochaneto.pdf: 3643209 bytes, checksum: f3daa9dd6a70b91cd6315eea748ed3c8 (MD5) / Made available in DSpace on 2016-08-08T16:18:45Z (GMT). No. of bitstreams: 1 2016_tese_ocrochaneto.pdf: 3643209 bytes, checksum: f3daa9dd6a70b91cd6315eea748ed3c8 (MD5) Previous issue date: 2016 / Remote sensing data interpretation is based primarily on the spectral reflectance analysis of materials for wavelength ranging from visible to short wave infrared (400 to 2500nm). For this, one can use reflectance spectroscopy which is a technique capable of measuring, at different wavelengths, the electromagnetic energy reflected from the surface of materials and represent it in the form of a graph called spectral reflectance curve. The analytical power of this technique derives from the spectral information being correlated directly with the chemical composition and physical characteristics of the substances that makes the target. However, the large volume of information contained in a spectral signature increases the difficulty of analyzing it, especially if the dataset is made of images. Thus, computational models are expected to be a viable means of analyzing these spectral curves. The refore, the objective of this thesis is to evaluate the performance of different computational models, such as least squares (LS), multilayer perceptron (MLP) and extreme learning machine (ELM) artificial neural networks, trained on laboratory data to estimate the electrical conductivity of salty soils, and to apply them to a hyperspectral image of the field . This thesis was organized in three parts: first, the ability of computer models to estimate the electrical conductivity of saturation extract (ECse) based on electrical conductivity data from a 1:1 dilution (EC 1:1) is assessed; second, computing strategy for best estimating the electrical conductivity of soil samples using their spectral readings under laboratory conditions are evaluated; and finally, the performance of the best found model applied to an airborne SpecTIR sensor hyperspectral image collected at the Irrigated District of the Morada Nova was evaluated. To evaluate the proposed algorithms, soil samples were collected in the Morada Nova Irrigation District with a history of salinity. These samples were used for model calibration and validation. Spectral data were obtained using the spectroradiometer FieldSpec® 3Hi-Res, from 350 to 2500nm. In an attempt to improve the performance of the models, data transformation was applied using either principal component analysis or derivative analysis. The results show the best performance was produced by the linear model fitted by least squares algorithm applied to the raw data (no transformation), and the spectral bands selected to estimate the electrical conductivity were 395, 1642 and 1717 nm. To estimate the soil's electrical conductivity from SpecTIR's image sensor data, the model calibrated in the laboratory has proved to be feasible, generating a value o f 1.46 for RPD, and 0.80 for the Pearson correlation coefficient. Therefore, one can conclude that the calibrated models using samples in the laboratory are satisfactory for estimating EC based on hyperspectral images. / A interpretação de dados do sensoriamento remoto fundamenta-se, basicamente, na análise do comportamento da reflectância espectral dos materiais no intervalo de comprimento de onda do visível ao infravermelho de ondas curtas (400 a 2500 nm). Para isso, pode-se usar a espectrorradiometria de reflectância, que é uma técnica capaz de medir, em diferentes comprimentos de ondas, a energia eletromagnética refletida da superfície dos materiais e representá-la na forma de um gráfico denominado curva de reflectância espectral. O poder analítico desta técnica advém do fato da informação espectral se correlacionar diretamente com a composição química e com as características físicas das substâncias contidas no alvo. No entanto, o grande volume de informações contidas em uma assinatura espectral aumenta a dificuldade de analisá-la, principalmente quando se trabalha com imagens. Com isso, o emprego de modelos computacionais se mostra como uma saída viável para a análise de curvas espectrais. Dessa forma, o objetivo desta tese é avaliar o desempenho de diferentes modelos computacionais como: mínimos quadrados (MQ), rede neural artificial do tipo perceptron de múltiplas camadas (MLP) e máquina de aprendizagem extrema (ELM), treinados em laboratório para estimar a condutividade elétrica do solo, e aplicá-los em imagens de alta resolução espectral. Esta tese foi separada em três etapas onde foram avaliados: a capacidade dos modelos computacionais em estimar a condutividade elétrica do extrato de saturação (CEes) a partir de amostra de condutividade elétrica 1:1 (CE1:1); as estratégias computacionais que melhor estimam a condutividade elétrica de amostras de solo a partir de leituras espectrais de solos obtidas em laboratório; e testar desempenho da melhor estratégia obtida no passo anterior, aplicando-a em uma imagem do sensor aerotransportado SpecTIR, coletado na região do Perímetro Irrigado de Morada Nova. Para avaliação dos algoritmos, foram coletadas amostras de solos na região de Morada Nova com histórico de áreas afetadas por sais. Estas amostras foram utilizadas para a calibração e validação dos modelos. Dados espectrais foram obtidos utilizando o espectrorradiômetro FieldSpec® 4 Hi-Res, entre 350 a 2500 nm. Foi avaliado o ganho de performance dos modelos matemáticos pela transformação dos dados através da análise por componente principal e pela análise derivativa. Com os resultados obtidos, pôde-se observar que as melhores respostas foram alcançadas pelo modelo linear dos mínimos quadrados aplicados aos dados puros, onde as bandas selecionadas para estimar a condutividade elétrica foram de 395, 1642 e 1717 nm. Para estimar a condutividade elétrica do solo na imagem do sensor SpecTIR sobre a área de estudo, o modelo calibrado em laboratório se mostrou interessante, produzindo um RPD de 1,46 e um coeficiente de correlação de Pearson de 0,80. Com isso, conclui-se que os modelos calibrados utilizando amostras em laboratório são satisfatórios para estimar a CE de imagens hiperespectrais.

The thesis of this study is that modern optimization theory is a natural extension of classical optimization theory. As such, modern optimization theory will be applied to administrative problems only after interpretive studies are made that provide (1) an explanation of the general theoretical development of the techniques of modern optimization theory, (2) computational algorithms for implementing the techniques of modern optimization theory, (3) detailed demonstrations of the computational aspects of each technique and its corresponding algorithm, and (4) an identification of the types of problems to which these techniques are applicable.

Submitted by Maria Beatriz Vieira (mbeatriz.vieira@gmail.com) on 2017-08-30T14:07:13Z No. of bitstreams: 2 license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) dissertacao_julia_labonde.pdf: 678599 bytes, checksum: d233ff13ddb416df716b9ee25c98978d (MD5) / Approved for entry into archive by Aline Batista (alinehb.ufpel@gmail.com) on 2017-09-01T19:13:34Z (GMT) No. of bitstreams: 2 dissertacao_julia_labonde.pdf: 678599 bytes, checksum: d233ff13ddb416df716b9ee25c98978d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Approved for entry into archive by Aline Batista (alinehb.ufpel@gmail.com) on 2017-09-01T19:14:34Z (GMT) No. of bitstreams: 2 dissertacao_julia_labonde.pdf: 678599 bytes, checksum: d233ff13ddb416df716b9ee25c98978d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) / Made available in DSpace on 2017-09-01T19:14:45Z (GMT). No. of bitstreams: 2 dissertacao_julia_labonde.pdf: 678599 bytes, checksum: d233ff13ddb416df716b9ee25c98978d (MD5) license_rdf: 0 bytes, checksum: d41d8cd98f00b204e9800998ecf8427e (MD5) Previous issue date: 2016-02-19 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior - CAPES / A leptospirose é uma doença infecciosa de importância mundial, que afeta humanos e animais, causada por espiroquetas patogênicas pertencentes ao gênero Leptospira. Para a área epidemiológica e clínica é fundamental que os laboratórios tenham a capacidade de identificar e classificar com precisão as espécies de Leptospira que causam doença, para que sejam tomadas decisões coerentes com relação à saúde pública. Neste estudo, nós relatamos pela primeira vez a utilização de ferramentas de mineração de dados para fins de classificação de cepas do gênero Leptospira. Vinte e cinco loci referentes a 15 genes foram selecionadas e analisados em 600 genomas rascunho de Leptospira, com o propósito de buscar polimorfismos que pudessem ser utilizados na classificação de cada espécie. Para isso, foram utilizados os algoritmos baseados em mineração de dados C4.5, Naive Bayes e Support Vector Machine. Todos os algoritmos computacionais de mineração de dados utilizados neste trabalho apresentaram valores de acurácia acima de 93% para classificação de Leptospira a nível de espécie, no entanto, o algoritmo C4.5, além de atingir a melhor acurácia de classificação (95.6%), também apresentou os genes que contribuíram para o resultado final da análise. O mesmo banco de dados genômicos utilizado pelos algoritmos computacionais foi submetido a testes com a metodologia MLST – técnica mais utilizada para classificação molecular de espécies deste gênero – no entanto, nenhum dos testes apresentou acurácia superior a 80%. Visto o algoritmo de mineração de dados C4.5 atingir uma acurácia superior aos outros algoritmos, pode-se concluir que C4.5 é uma ferramenta de mineração de dados bastante promissora para classificar espécies de Leptospira. / Leptospirosis is an infectious disease of global importance that affects humans and animals caused by pathogenic spirochetes belonging to the genus Leptospira. For epidemiological and clinical areas, it is essential that laboratories have the ability to identify and classify accurately species of Leptospira that cause disease, to take decisions consistent with respect to public health. In this study, we report for the first time the use of data mining tools for the purposes of strain classification of the genus Leptospira. Twenty-five loci related to 15 genes were selected and analyzed in 600 Leptospira draft genomes in order to search polymorphisms that could be used for the classification of each species. For this, data mining-based algorithms - C4.5, Naive Bayes and SVM - were used. All data mining computational algorithms used in this study showed accuracy levels above 93% for Leptospira classification species, however, the C4.5 algorithm achieve the best accuracy rating (95.6%) and presented the genes that contributed to the final result of the analysis. The same genomic database used by computer algorithms has been tested with the MLST methodology – most used technique for molecular classification of species of this genus - however, none of the tests show accuracy higher to 80%. Because data mining algorithm C4.5 achieve better accuracy than other algorithms, it can be concluded that C4.5 is a very promising data mining tool to classify species of Leptospira.

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CoordenaÃÃo de AperfeÃoamento de Pessoal de NÃvel Superior / A interpretaÃÃo de dados do sensoriamento remoto fundamenta-se, basicamente, na anÃlise do comportamento da reflectÃncia espectral dos materiais no intervalo de comprimento de onda do visÃvel ao infravermelho de ondas curtas (400 a 2500 nm). Para isso, pode-se usar a espectrorradiometria de reflectÃncia, que à uma tÃcnica capaz de medir, em diferentes comprimentos de ondas, a energia eletromagnÃtica refletida da superfÃcie dos materiais e representÃ-la na forma de um grÃfico denominado curva de reflectÃncia espectral. O poder analÃtico desta tÃcnica advÃm do fato da informaÃÃo espectral se correlacionar diretamente com a composiÃÃo quÃmica e com as caracterÃsticas fÃsicas das substÃncias contidas no alvo. No entanto, o grande volume de informaÃÃes contidas em uma assinatura espectral aumenta a dificuldade de analisÃ-la, principalmente quando se trabalha com imagens. Com isso, o emprego de modelos computacionais se mostra como uma saÃda viÃvel para a anÃlise de curvas espectrais. Dessa forma, o objetivo desta tese à avaliar o desempenho de diferentes modelos computacionais como: mÃnimos quadrados (MQ), rede neural artificial do tipo perceptron de mÃltiplas camadas (MLP) e mÃquina de aprendizagem extrema (ELM), treinados em laboratÃrio para estimar a condutividade elÃtrica do solo, e aplicÃ-los em imagens de alta resoluÃÃo espectral. Esta tese foi separada em trÃs etapas onde foram avaliados: a capacidade dos modelos computacionais em estimar a condutividade elÃtrica do extrato de saturaÃÃo (CEes) a partir de amostra de condutividade elÃtrica 1:1 (CE1:1); as estratÃgias computacionais que melhor estimam a condutividade elÃtrica de amostras de solo a partir de leituras espectrais de solos obtidas em laboratÃrio; e testar desempenho da melhor estratÃgia obtida no passo anterior, aplicando-a em uma imagem do sensor aerotransportado SpecTIR, coletado na regiÃo do PerÃmetro Irrigado de Morada Nova. Para avaliaÃÃo dos algoritmos, foram coletadas amostras de solos na regiÃo de Morada Nova com histÃrico de Ãreas afetadas por sais. Estas amostras foram utilizadas para a calibraÃÃo e validaÃÃo dos modelos. Dados espectrais foram obtidos utilizando o espectrorradiÃmetro FieldSpec 4 Hi-Res, entre 350 a 2500 nm. Foi avaliado o ganho de performance dos modelos matemÃticos pela transformaÃÃo dos dados atravÃs da anÃlise por componente principal e pela anÃlise derivativa. Com os resultados obtidos, pÃde-se observar que as melhores respostas foram alcanÃadas pelo modelo linear dos mÃnimos quadrados aplicados aos dados puros, onde as bandas selecionadas para estimar a condutividade elÃtrica foram de 395, 1642 e 1717 nm. Para estimar a condutividade elÃtrica do solo na imagem do sensor SpecTIR sobre a Ãrea de estudo, o modelo calibrado em laboratÃrio se mostrou interessante, produzindo um RPD de 1,46 e um coeficiente de correlaÃÃo de Pearson de 0,80. Com isso, conclui-se que os modelos calibrados utilizando amostras em laboratÃrio sÃo satisfatÃrios para estimar a CE de imagens hiperespectrais. / Remote sensing data interpretation is based primarily on the spectral reflectance analysis of materials for wavelength ranging from visible to short wave infrared (400 to 2500nm). For this, one can use reflectance spectroscopy which is a technique capable of measuring, at different wavelengths, the electromagnetic energy reflected from the surface of materials and represent it in the form of a graph called spectral reflectance curve. The analytical power of this technique derives from the spectral information being correlated directly with the chemical composition and physical characteristics of the substances that makes the target. However, the large volume of information contained in a spectral signature increases the difficulty of analyzing it, especially if the dataset is made of images. Thus, computational models are expected to be a viable means of analyzing these spectral curves. The refore, the objective of this thesis is to evaluate the performance of different computational models, such as least squares (LS), multilayer perceptron (MLP) and extreme learning machine (ELM) artificial neural networks, trained on laboratory data to estimate the electrical conductivity of salty soils, and to apply them to a hyperspectral image of the field . This thesis was organized in three parts: first, the ability of computer models to estimate the electrical conductivity of saturation extract (ECse) based on electrical conductivity data from a 1:1 dilution (EC 1:1) is assessed; second, computing strategy for best estimating the electrical conductivity of soil samples using their spectral readings under laboratory conditions are evaluated; and finally, the performance of the best found model applied to an airborne SpecTIR sensor hyperspectral image collected at the Irrigated District of the Morada Nova was evaluated. To evaluate the proposed algorithms, soil samples were collected in the Morada Nova Irrigation District with a history of salinity. These samples were used for model calibration and validation. Spectral data were obtained using the spectroradiometer FieldSpec 3Hi-Res, from 350 to 2500nm. In an attempt to improve the performance of the models, data transformation was applied using either principal component analysis or derivative analysis. The results show the best performance was produced by the linear model fitted by least squares algorithm applied to the raw data (no transformation), and the spectral bands selected to estimate the electrical conductivity were 395, 1642 and 1717 nm. To estimate the soil's electrical conductivity from SpecTIR's image sensor data, the model calibrated in the laboratory has proved to be feasible, generating a value o f 1.46 for RPD, and 0.80 for the Pearson correlation coefficient. Therefore, one can conclude that the calibrated models using samples in the laboratory are satisfactory for estimating EC based on hyperspectral images.

Orientador: João Frederico da Costa Azevedo Meyer / Dissertação (mestrado profissional) - Universidade Estadual de Campinas, Instituto de Matematica, Estatistica e Computação Cientifica / Made available in DSpace on 2018-08-12T23:09:37Z (GMT). No. of bitstreams: 1 Alves_LourimaraFariasBarros_M.pdf: 3434748 bytes, checksum: 47ffff091840f19264eeb59a290d59d5 (MD5) Previous issue date: 2009 / Resumo: Em todo mundo, a preocupação com problemas ambientais vem crescendo de maneira muito rápida, com especial destaque aos recursos hídricos, pois a humanidade parecia acreditar que tais recursos seriam inesgotáveis, e hoje se depara com uma realidade totalmente diferente. Neste contexto, este trabalho buscou por meio de dois sistemas: um de Equações de Diferenças e o outro de Equações Diferenciais obter em primeira aproximação a modelagem matemática do comportamento evolutivo de manchas de materiais poluentes de superfície no Rio Balsas ao sul do estado do Maranhão. Com estudo e análise dessa modelagem, construímos algoritmos computacionais (em ambiente MATLAB) que permitem a criação de instrumental para simulação de acidentes, de estratégias de prevenção, de contenção além de também servir de apoio no combate a práticas que possam levar à presença de materiais tóxicos prejudiciais à biota fuvial / Abstract: Worldwide, the growing concern with environmental problems has happened quite rapidly, with special emphasis, in many cases, as regards sweet water resources; humanity has acted as if such resources were endless, and today the situation has changed into a very diferent reality. In this general picture, this work proposes the modelling of the evolutive behavior of pollutants on the water surface of rivers, focusing upon the Rio Balsas, in southern Maranhão State. A analysis of the chosen modelling process, led to the defnition computational algorithms, obtained in a MATLAB environment creating numerical tools for the simulation of accidents and processes, for theoretically testing prevention and protection strategies, as well as serving a general purpose of challenging choices and procedures that may lead to the presence of toxic material at levels which negatively affect local biota / Mestrado / Biomatematica / Mestre em Matemática

The process of quantifying the robustness of a given nonlinear system is not necessarily trivial. If the dynamics of the system in question are not sufficiently involved, then a tight estimate of a bound on system performance may be obtained. As the dynamics of the system concerned become more and more involved, it is often found that using the results existing in the literature provides a very conservative bound on system performance. Therefore, the motivation for this work is to develop a general method to obtain a less conservative estimate of a bound on system performance, compared to the results already available in literature. The scope of this work is limited to two dimensions at present. Note that working in a two dimensional space does not necessarily make the objective easily achievable. This is because quantifying the robustness of a general nonlinear system perturbed by disturbances can very easily become intractable, even on a space with dimension as low as two. The primary contribution of this work is a computational algorithm, the points generated by which are conjectured to lie on the boundary of the smallest robust forward invariant set for a given nonlinear system. A well known path-planning algorithm, available in existing literature, is leveraged to make the algorithm developed computationally efficient. If the system dynamics are not accurately known, then the above computed approximation of an invariant set may cease to be invariant over the given finite time interval for which the computed set is expected to be invariant. Therefore, the secondary contribution of this work is an algorithm monitoring a computed approximation of an invariant set. It is shown that for a certain type of systems, this secondary monitoring algorithm can be used to detect that a computed approximation of an invariant set is about to cease to be invariant, even if the primary algorithm computed the set based on an unsophisticated dynamical model of a system under consideration. The work related to computing approximations of invariant sets is tested mainly with the curve tracking problem in two dimensions. The algorithm monitoring whether a computed approximation of an invariant set is about to cease to be invariant is inspired by work related to detecting Lithium-ion (Li-ion) battery terminal voltage collapse detection.

Σκοπός της παρούσας διπλωματικής εργασίας είναι η μελέτη της μεθόδου bootstrap και η ανάπτυξη ενός αλγορίθμου bootstrap στη γλώσσα προγραμματισμού Matlab με σκοπό την επιλογή MPSS σε περιπτώσεις ανάλυσης της αποτελεσματικότητας όταν υπάρχει τεχνολογική ετερογένεια. Εκτός από τις τιμές της τεχνικής αποτελεσματικότητας με τη μέθοδο DEA που έχουν υλοποιηθεί και βρεθεί σε προηγούμενη εργασία, της οποίας συνέχεια είναι η παρούσα, βρίσκονται οι bootstrapped τιμές της αποτελεσματικότητας, δηλαδή οι τιμές χωρίς την παρουσία του θορύβου που μπορεί να αλλοιώσει τα αποτελέσματα καθώς και το διάστημα εμπιστοσύνης των τιμών. Δημιουργείται έτσι ένα ολοκληρωμένο πακέτο ώστε ο χρήστης να μπορεί να υπολογίζει τις παραπάνω τιμές των δεδομένων που θα εισάγει και οι οποίες θα αποθηκεύονται σε μορφή κατάλληλη για περαιτέρω επεξεργασία. / The purpose of this thesis is to study the bootstrap method and develop a bootstrap algorithm in Matlab programming language to select the MPSS analysis in cases of technical efficiency where there is technological heterogeneity.Besides the values of technical efficiency with DEA method that have been implemented and found in a previous work, we compute the bootstrapped values of efficiency, ie the values without the presence of noise that can affect the results and the confidence interval values. This creates a complete package so the user can calculate the above values of the data entered and will be stored in a form suitable for further processing.