This work presents the development, validation and application of a novel deconvolution method based on B-splines for analyzing variable-rate reservoir performance data. Variable-rate deconvolution is a mathematically unstable problem which has been under investigation by many researchers over the last 35 years. While many deconvolution methods have been developed, few of these methods perform well in practice - and the importance of variable-rate deconvolution is increasing due to applications of permanent downhole gauges and large-scale processing/analysis of production data. Under these circumstances, our objective is to create a robust and practical tool which can tolerate reasonable variability and relatively large errors in rate and pressure data without generating instability in the deconvolution process. We propose representing the derivative of unknown unit rate drawdown pressure as a weighted sum of Bsplines (with logarithmically distributed knots). We then apply the convolution theorem in the Laplace domain with the input rate and obtain the sensitivities of the pressure response with respect to individual B-splines after numerical inversion of the Laplace transform. The sensitivity matrix is then used in a regularized least-squares procedure to obtain the unknown coefficients of the B-spline representation of the unit rate response or the well testing pressure derivative function. We have also implemented a physically sound regularization scheme into our deconvolution procedure for handling higher levels of noise and systematic errors. We validate our method with synthetic examples generated with and without errors. The new method can recover the unit rate drawdown pressure response and its derivative to a considerable extent, even when high levels of noise are present in both the rate and pressure observations. We also demonstrate the use of regularization and provide examples of under and over-regularization, and we discuss procedures for ensuring proper regularization. Upon validation, we then demonstrate our deconvolution method using a variety of field cases. Ultimately, the results of our new variable-rate deconvolution technique suggest that this technique has a broad applicability in pressure transient/production data analysis. The goal of this thesis is to demonstrate that the combined approach of B-splines, Laplace domain convolution, least-squares error reduction, and regularization are innovative and robust; therefore, the proposed technique has potential utility in the analysis and interpretation of reservoir performance data.

O uso de imagens é crucial na medicina, e seu uso no diagnóstico de doenças é uma das principais ferramentas clínicas da atualidade. Porém, frequentemente necessitam de pós-processamento para serem úteis. Embora ferramentas clássicas sejam utilizadas para esse fim, elas não dão tratamento específico a certas características de imagens fractais, como as provindas de sistemas biológicos. Nesse enfoque, este trabalho objetivou a criação de novas bases de interpolação utilizando a Q-Estatística para verificar se seriam estas seriam adequadas à representação de objetos com características fractais que as bases clássicas. Foram criados dois tipos de splines: uma unidimensional e outra bidimensional, que permitiram um tipo diferente de interpolação, fundamentado na q-Estatística. Os testes demonstraram a potencialidade dessas ferramentas para uso em sinais e imagens médicas, com acentuada redução do erro de interpolação no caso unidimensional (em até 351,876%) e uma redução sutil no caso bidimensional (0,3%). Como resultado adicional, foram criados filtros de imagens e avaliados seus resultados em imagens médicas, que resultaram em melhorias de até 1.340% de ganho efetivo na remoção de ruídos de natureza fractal (marrom). Os resultados sugerem que as q-bases desenvolvidas foram capazes de representar melhor imagens e sinais médicos, bem como é interessante o uso dos filtros desenvolvidos na remoção de diversos tipos de ruído do tipo 1/f^b. / The use of images is crucial in modern medicine, and diagnostic imaging is a major clinical tools used in detecting, monitoring and completion of many treatments. However, often the images need to be post-processed for display to health professionals or automated analysis, searching for signs of abnormalities. Although classical tools are used for that purpose, they do not give special treatment to certain characteristics of fractal images, such as those coming from biological systems. These characteristics are produced, in general, by complex dynamic systems as a result of internal interactions of sub-system components, giving the system a fractal character. In this context, the main objective of this work was to propose interpolation bases using the Q-statistic, creating bases of Q-interpolation, and verify if such bases would be best suited to the representation of objects with fractal characteristics than classical bases, assumed the premise that such a theory model best this kind of phenomenon than classical theory. Based on this hypothesis, we created two types of splines: one-dimensional and one-dimensional, called Q-splines, which allow a different type of interpolation and they can capture behaviors as super-additive or sub-additive among the constituents of a spline. These models have demonstrated numerically the potential use of this type of interpolation for use in signals and medical images, reducing the interpolation error by up to 351.876 % in the one-dimensional case and 0.3 % in two dimensional. As secondary results, were defined two families of image filters, called anisotropic Q-filters and isotropic Q-filters, and their results were evaluated in real medical images. In virtually all analyzes it was possible to obtain the best results from conventional approaches, sometimes with improvements of 1.340 % in some filters, in removing noise fractal nature (brown). The results were more modest for the interpolation of two-dimensional images, however, generally proved exciting and encouraging, clearly showing that these new approaches are not only viable, but also can produce better results compared to classical approaches. Based on these results, we concluded that the Q-bases developed are best able to represent not only signs but medical imaging (1D and 2D) although its use can be improved by the adoption of approaches adapted to the vector representation of information, that favor the use of splines. Similarly, the Q-filters were more suitable for the processing of medical signals when compared to conventional approaches.

L'un des défis fondamentaux de la robotique d'aujourd'hui est d'obtenir des cartes robustes en utilisant des mécanismes efficaces pour l'exploration et la modélisation des environnements toujours plus complexes. Ce problème est connu comme celui de la planification, de la localisation et de la cartographie simultanée (SPLAM).Dans cette thèse nous avons développé des outils pour obtenir une stratégie de SPLAM. D'abord, l'exploration est faite par le graphe d'exploration aléatoire (REG) basé sur la création d'une structure de graphe et sur un contrôle de frontières. Ensuite, le problème de localisation et de cartographie simultanée (SLAM) est résolu avec une stratégie topologique basée sur des B-Splines. Pour valider notre stratégie, nous avons créé une autre approche de SPLAM basée sur des outils connus comme le Filtre de Kalman étendu pour le SLAM et sur l'arbre aléatoire (SRT) pour l'exploration. Ces résultats sont comparés avec les résultats de notre stratégie. / One of the fundamental challenges of today's robotics is to obtain robust maps using efficient mechanisms for exploring and modeling increasingly complex environments. This is known as simultaneous planning, localization and mapping (SPLAM) problem.Considering this problem, in this thesis we have developed some tools to obtain a SPLAM strategy. First, the exploration is made by the Random Exploration Graph approach (REG) which is based on the creation of a graph structure and on a frontier control. Next, the simultaneous localization and mapping (SLAM) problem is solved using a B-Spline based topologic strategy. To validate our strategy, we have created another SPLAM approach based on well known tools as the Extended Kalman Filter for SLAM and on the Sensor based Random tree (SRT) for the exploration problem. Its results are confronted with the results obtained by our strategy.

O uso de imagens é crucial na medicina, e seu uso no diagnóstico de doenças é uma das principais ferramentas clínicas da atualidade. Porém, frequentemente necessitam de pós-processamento para serem úteis. Embora ferramentas clássicas sejam utilizadas para esse fim, elas não dão tratamento específico a certas características de imagens fractais, como as provindas de sistemas biológicos. Nesse enfoque, este trabalho objetivou a criação de novas bases de interpolação utilizando a Q-Estatística para verificar se seriam estas seriam adequadas à representação de objetos com características fractais que as bases clássicas. Foram criados dois tipos de splines: uma unidimensional e outra bidimensional, que permitiram um tipo diferente de interpolação, fundamentado na q-Estatística. Os testes demonstraram a potencialidade dessas ferramentas para uso em sinais e imagens médicas, com acentuada redução do erro de interpolação no caso unidimensional (em até 351,876%) e uma redução sutil no caso bidimensional (0,3%). Como resultado adicional, foram criados filtros de imagens e avaliados seus resultados em imagens médicas, que resultaram em melhorias de até 1.340% de ganho efetivo na remoção de ruídos de natureza fractal (marrom). Os resultados sugerem que as q-bases desenvolvidas foram capazes de representar melhor imagens e sinais médicos, bem como é interessante o uso dos filtros desenvolvidos na remoção de diversos tipos de ruído do tipo 1/f^b. / The use of images is crucial in modern medicine, and diagnostic imaging is a major clinical tools used in detecting, monitoring and completion of many treatments. However, often the images need to be post-processed for display to health professionals or automated analysis, searching for signs of abnormalities. Although classical tools are used for that purpose, they do not give special treatment to certain characteristics of fractal images, such as those coming from biological systems. These characteristics are produced, in general, by complex dynamic systems as a result of internal interactions of sub-system components, giving the system a fractal character. In this context, the main objective of this work was to propose interpolation bases using the Q-statistic, creating bases of Q-interpolation, and verify if such bases would be best suited to the representation of objects with fractal characteristics than classical bases, assumed the premise that such a theory model best this kind of phenomenon than classical theory. Based on this hypothesis, we created two types of splines: one-dimensional and one-dimensional, called Q-splines, which allow a different type of interpolation and they can capture behaviors as super-additive or sub-additive among the constituents of a spline. These models have demonstrated numerically the potential use of this type of interpolation for use in signals and medical images, reducing the interpolation error by up to 351.876 % in the one-dimensional case and 0.3 % in two dimensional. As secondary results, were defined two families of image filters, called anisotropic Q-filters and isotropic Q-filters, and their results were evaluated in real medical images. In virtually all analyzes it was possible to obtain the best results from conventional approaches, sometimes with improvements of 1.340 % in some filters, in removing noise fractal nature (brown). The results were more modest for the interpolation of two-dimensional images, however, generally proved exciting and encouraging, clearly showing that these new approaches are not only viable, but also can produce better results compared to classical approaches. Based on these results, we concluded that the Q-bases developed are best able to represent not only signs but medical imaging (1D and 2D) although its use can be improved by the adoption of approaches adapted to the vector representation of information, that favor the use of splines. Similarly, the Q-filters were more suitable for the processing of medical signals when compared to conventional approaches.

Previous healthcare-based studies have reported increasing herpes zoster (HZ) incidence over time; however, this could be an artifact of increased healthcare utilization. This study is a cross-sectional analysis of 15,103 respondents in the 2008 wave of the Health and Retirement Study (HRS) to evaluate changes in HZ incidence from 1940 to 2008. Negative binomial regression is used to model the effect of calendar year, age of onset of HZ, gender and race/ethnicity on HZ incidence. A nonparametric method based on B-spline basis expansion is used to model the effect of calendar year to avoid imposing a predetermined functional form and produce flexible and accurate estimates. This study demonstrates increasing HZ incidence from 1940 to 2008 using self-reported HZ. Although the reason for this increase remains unknown, this study supports the assertion that this trend is real and not an artifact of increasing healthcare utilization for HZ over time.

No description available.

The incompressible Navier-Stokes equations are among the most important partial differential systems arising from classical physics. They are utilized to model a wide range of fluids, from water moving around a naval vessel to blood flowing through the arteries of the cardiovascular system. Furthermore, the secrets of turbulence are widely believed to be locked within the Navier-Stokes equations. Despite the enormous applicability of the Navier-Stokes equations, the underlying behavior of solutions to the partial differential system remains little understood. Indeed, one of the Clay Mathematics Institute's famed Millenium Prize Problems involves the establishment of existence and smoothness results for Navier-Stokes solutions, and turbulence is considered, in the words of famous physicist Richard Feynman, to be "the last great unsolved problem of classical physics." Numerical simulation has proven to be a very useful tool in the analysis of the Navier-Stokes equations. Simulation of incompressible flows now plays a major role in the industrial design of automobiles and naval ships, and simulation has even been utilized to study the Navier-Stokes existence and smoothness problem. In spite of these successes, state-of-the-art incompressible flow solvers are not without their drawbacks. For example, standard turbulence models which rely on the existence of an energy spectrum often fail in non-trivial settings such as rotating flows. More concerning is the fact that most numerical methods do not respect the fundamental geometric properties of the Navier-Stokes equations. These methods only satisfy the incompressibility constraint in an approximate sense. While this may seem practically harmless, conservative semi-discretizations are typically guaranteed to balance energy if and only if incompressibility is satisfied pointwise. This is especially alarming as both momentum conservation and energy balance play a critical role in flow structure development. Moreover, energy balance is inherently linked to the numerical stability of a method. In this dissertation, novel B-spline discretizations for the generalized Stokes and Navier-Stokes equations are developed. The cornerstone of this development is the construction of smooth generalizations of Raviart-Thomas-Nedelec elements based on the new theory of isogeometric discrete differential forms. The discretizations are (at least) patch-wise continuous and hence can be directly utilized in the Galerkin solution of viscous flows for single-patch configurations. When applied to incompressible flows, the discretizations produce pointwise divergence-free velocity fields. This results in methods which properly balance both momentum and energy at the semi-discrete level. In the presence of multi-patch geometries or no-slip walls, the discontinuous Galerkin framework can be invoked to enforce tangential continuity without upsetting the conservation and stability properties of the method across patch boundaries. This also allows our method to default to a compatible discretization of Darcy or Euler flow in the limit of vanishing viscosity. These attributes in conjunction with the local stability properties and resolution power of B-splines make these discretizations an attractive candidate for reliable numerical simulation of viscous incompressible flows. / text

Made available in DSpace on 2014-06-12T23:14:42Z (GMT). No. of bitstreams: 2 arquivo2690_1.pdf: 6789118 bytes, checksum: 05cc3d356f57a760866a4fc16453b6e0 (MD5) license.txt: 1748 bytes, checksum: 8a4605be74aa9ea9d79846c1fba20a33 (MD5) Previous issue date: 2011 / Coordenação de Aperfeiçoamento de Pessoal de Nível Superior / Vários estudos têm indicado que, das várias classes de algoritmos de reconstrução aplicáveis para dados limitados, os baseados na técnica de reconstrução algébrica são mais flexíveis e precisos. Infelizmente, estas técnicas, geralmente, sofrem de ruídos ocasionados por processos de correção durante a reconstrução e também por inconsistências nos dados adquiridos pelos tomógrafos. O pós - processamento da imagem reconstruída com a aplicação de filtros pode ser feito para atenuar a presença de ruídos, mas geralmente atenuam também as descontinuidades presentes em bordas que distinguem objetos ou falhas. O presente trabalho propõe a redução de ruídos assegurando a continuidade (das derivadas) da superfície antes da reconstrução, representando cada incógnita por uma combinação linear de pontos de controle e suas bases B-splines. São aplicadas três bases Bsplines: B1 , B2 e B3, assegurando as continuidade C0, C1 e C2, respectivamente. Para validação da técnica, foram utilizadas simulações de modelos propostos na literatura e medidas experimentais por tomografia gama. Os resultados foram comparados com as técnicas algébricas ART, SIRT, MART e SMART, sendo validada satisfatoriamente para todos os phantoms propostos. Todas as bases B-splines aplicadas obtiveram erros menores que as técnicas de correção ART e SIRT, sendo a B3, a de melhor desempenho. Este resultado pode ser explicado pelas restrições de suavidade impostas à superfície reconstruída pelas bases Bsplines e a inclinação das técnicas aditivas a ruídos, principalmente para um número limitado de dados (5 e 10 vistas). A performance das técnicas multiplicativas para essa situação é a melhor, mostrando uma imagem sem artefatos e com pouco ruído. Devido a esse fato, a técnica b-spline não tem bons resultados, apresentando na maioria dos casos, erros maiores. Para todos os testes realizados, as técnicas de representação B-splines superaram os filtros de mesma natureza aplicados no pós-processamento, sugerindo que a técnica seja utilizada no lugar da filtragem pós-processamento

Os P-splines de Eilers e Marx (1996) são métodos de suavização que é uma combinação de bases B-splines e uma penalização discreta sobre os coeficientes das bases utilizados para suavizar dados normais e não normais em uma ou mais dimensões, no caso de várias dimensões utiliza-se como suavização o produto tensor dos P-splines. Também os P-splines são utilizados como representação de modelos mistos Currie et al. (2006) pela presença de características tais como: efeitos fixos, efeitos aleatórios, correlação espacial ou temporal e utilizados em modelos mais generalizados tais como os modelos mistos lineares generalizados e modelos mistos aditivos generalizados. Neste trabalho apresentou-se toda a abordagem, metodologia e descrição dos P-splines como modelos mistos e como componentes das estruturas suavizadoras de variáveis unidimensionais e bidimensionais dos modelos mistos aditivos generalizados, mostrando essa abordagem e propondo seu uso em uma aplicação no comportamento dos níveis médios da produção de cana-de-açúcar sob a influência das alterações das variáveis climáticas como temperatura e precipitação, que foram medidos ao longo de 10 anos em cada mesorregião do Estado de São Paulo. O motivo de usar essa abordagem como método de suavização é que muitas vezes não é conhecido a tendência dessas covariáveis climáticas mas sabe-se que elas influenciam diretamente sobre a variável resposta. Além de permitir essa abordagem inclusão de efeitos fixos e aleatórios nos modelos a serem propostos, permitirá a inclusão do processo autoregressivo AR(1) como estrutura de correlação nos resíduos. / P-splines of Eilers e Marx (1996) are methods of smoothing that is a combination of B-splines bases and penalty the coefficients of the bases used to smooth normal and non-normal data in one or more dimensions; in the case of several dimensions it is used as smoothing the tensor product of the P-splines. Also the P-splines are used as representation of mixed models Currie et al. (2006) by the presence of characteristics such as: fixed effects, random effects, spatial or temporal correlation and used in more generalized models such as generalized linear mixed models and generalized additive mixed models. In this work the whole approach, methodology and description of the P-splines as mixed models and as components of the smoothing structures of one-dimensional and two-dimensional variables of generalized additive mixed models were presented, showing this approach and proposing its application in the behavior of the average levels of sugarcane production, which is influenced by changes in climatic variables such as temperature and precipitation , which were measured over 10 years in each mesoregion of the state of São Paulo. The reason for using this approach as a smoothing method is that the tendency of these climate covariables is not know for the most part, but is known that they influence directly the response variable, besides allowing this approach to include fixed and random effects in the models to be proposed, will allow the inclusion of the autoregressive process AR(1) as a correlation structure in the residuos.

Os P-splines de Eilers e Marx (1996) são métodos de suavização que é uma combinação de bases B-splines e uma penalização discreta sobre os coeficientes das bases utilizados para suavizar dados normais e não normais em uma ou mais dimensões, no caso de várias dimensões utiliza-se como suavização o produto tensor dos P-splines. Também os P-splines são utilizados como representação de modelos mistos Currie et al. (2006) pela presença de características tais como: efeitos fixos, efeitos aleatórios, correlação espacial ou temporal e utilizados em modelos mais generalizados tais como os modelos mistos lineares generalizados e modelos mistos aditivos generalizados. Neste trabalho apresentou-se toda a abordagem, metodologia e descrição dos P-splines como modelos mistos e como componentes das estruturas suavizadoras de variáveis unidimensionais e bidimensionais dos modelos mistos aditivos generalizados, mostrando essa abordagem e propondo seu uso em uma aplicação no comportamento dos níveis médios da produção de cana-de-açúcar sob a influência das alterações das variáveis climáticas como temperatura e precipitação, que foram medidos ao longo de 10 anos em cada mesorregião do Estado de São Paulo. O motivo de usar essa abordagem como método de suavização é que muitas vezes não é conhecido a tendência dessas covariáveis climáticas mas sabe-se que elas influenciam diretamente sobre a variável resposta. Além de permitir essa abordagem inclusão de efeitos fixos e aleatórios nos modelos a serem propostos, permitirá a inclusão do processo autoregressivo AR(1) como estrutura de correlação nos resíduos. / P-splines of Eilers e Marx (1996) are methods of smoothing that is a combination of B-splines bases and penalty the coefficients of the bases used to smooth normal and non-normal data in one or more dimensions; in the case of several dimensions it is used as smoothing the tensor product of the P-splines. Also the P-splines are used as representation of mixed models Currie et al. (2006) by the presence of characteristics such as: fixed effects, random effects, spatial or temporal correlation and used in more generalized models such as generalized linear mixed models and generalized additive mixed models. In this work the whole approach, methodology and description of the P-splines as mixed models and as components of the smoothing structures of one-dimensional and two-dimensional variables of generalized additive mixed models were presented, showing this approach and proposing its application in the behavior of the average levels of sugarcane production, which is influenced by changes in climatic variables such as temperature and precipitation , which were measured over 10 years in each mesoregion of the state of São Paulo. The reason for using this approach as a smoothing method is that the tendency of these climate covariables is not know for the most part, but is known that they influence directly the response variable, besides allowing this approach to include fixed and random effects in the models to be proposed, will allow the inclusion of the autoregressive process AR(1) as a correlation structure in the residuos.