The development of sequential analysis has led to the proposal of tests that are more economical in that the Average Sample Number (A. S. N.) of the sequential test is smaller than the sample size of the fixed sample test. Although these tests usually have a smaller A. S. N. than the equivelent fixed sample procedure, there still remains the possibility that an extremely large sample size will be necessary to make a decision. To remedy this, truncated sequential tests have been developed. A method of truncation for testing a composite hypotheses is studied. This method is formed by mixing a fixed sample test and a sequential test and is applied to the exponential distribution and normal distribution to establish its usefulness. It is proved that our truncation method can give a similar Operating Characteristic (O. C.) curve to that of corresponding fixed sample test if the test parameters are properly chosen. The average sample size required by our truncation method as compared with other existing truncation methods gives us a satisfactory result. Though the truncation method we suggested in this study is not an optimum truncation, it is still worthwhile, especially, when we are interested in the testing of a composite hypotheses.

For various reasons it might be required to scan an object that partially lies outside the field of view(FOV) of a CT scanner. The parts of the object that lie outside the FOV will not contribute to the line integrals measured by the detector which will cause image artifacts that affect the final image quality. In this paper, I suggest a novel reconstruction approach that estimates the attenuation by the object outside the FOV using a priori knowledge about the outline of the object. It is shown that, knowing the object’s outline, it is possible to determine whether the attenuation along a given line is truncated. The total attenuation for a truncated projection is then estimated by interpolating the data between the consistent projections. The method therefore requires some of the projections to be consistent. This estimate, along with the knowledge of the distance traversed by the X-Ray inside the object is then used to determine the average attenuation. The method was tested on both numerical and physical phantoms. The results are satisfactory even when up to 80% of the projections are truncated. Structural Similarity Index (SSIM) was compared for the complete reconstructed images,and regions of truncations before and after the algorithm was applied. Reconstructed images from completely consistent projections served as ground truth. The results indicate that the algorithm can be used to reconstruct partially truncated CT data, which was tested on numerical and physical phantoms (of semicircular cross section). There is scope for further testing of the algorithm on irregularly shaped objects. / Technology

京都大学 / 新制・課程博士 / 博士(生命科学) / 甲第24985号 / 生博第514号 / 新制||生||68(附属図書館) / 京都大学大学院生命科学研究科高次生命科学専攻 / (主査)教授 北島 智也, 教授 見学 美根子, 教授 今吉 格 / 学位規則第4条第1項該当 / Doctor of Philosophy in Life Sciences / Kyoto University / DFAM

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A numerical analysis based on the finite element method is developed to simulate the mechanical response of a typical sixteen-ounce plastic drink cup subjected to a lateral compressive load. The aim of the analysis is to simulate a test in which the cup is supported horizontally in a fixture on a testing machine platen, and a loading nose attached to the actuator is displaced downward into the cup. The numerical model is developed using the software packages MSC.Patran, ABAQUS/CAE, and ABAQUS/Standard. The high impact polystyrene material of the cup is modeled as linear elastic, considering isotropic and orthotropic material behavior. The structural model of the cup is a truncated conical shell including a ring at the open end of the cup and circumferential stiffening ribs. The analysis is based on small strain, large rotation shell kinematics, and the loading apparatus of the test is simulated with a rigid, circular cylinder contacting the cup. Coupons cut from the wall of a cup are subjected to tension to determine the ranges of the meridional and circumferential moduli of elasticity. Rings cut from the open end of the cup were tested in diametrical tension to aid in validating the finite element modeling. Reasonable correlation of the simulation to available cup compression test data is achieved. Parametric studies are conducted for several meridional thickness distributions of the cup wall, and for a range of orthotropic material properties. / Master of Science

A simulação pluriGaussiana truncada é usada para simulação de dados categóricos, tais como fácies em um contexto geológico. Esse método é uma extensão da Gaussiana truncada, mas que permite a simulação de feições geológicas complexas. Nessa dissertação, a simulação pluriGaussiana truncada foi baseada nas curvas de proporção obtidas da interpolação multiquádrica. Esse método foi testado com uma amostra composta por 24 sondagens obtidas de um modelo geológico sintético. As realizações da simulação pluriGuassiana truncada foram pós-processadas para obter o modelo médio, bem como as incertezas associadas. Os resultados mostraram que as incertezas estão associadas com os contatos litológicos. / The truncated pluriGaussian simulation is used for categorical data simulation, such as facies in a geological context. This method is an extension of the Gaussian truncated, but it allows simulation of complex geological features. In this dissertation, the method of truncated pluriGaussian simulation was based on proportion curves computed form multiquadric interpolation. This method was tested with a sample composed of 24 drill holes drawn from a synthetic geologic model. Realizations of truncated pluriGaussian simulation are post-processed to get the average model and associated uncertainty as well. Result showed that uncertainties are always associated with geological contacts.

No presente trabalho apresentamos o algoritmo de simulacão perfeita CFTP, proposto em Propp & Wilson (1996). Seguindo o trabalho de Philippe & Robert (2003) implementamos o CFTP gerando amostras da distribuicão normal bivariada truncada no quadrante positivo. O algoritmo proposto e comparado com o amostrador de Gibbs e o método de rejeição. Finalmente, apresentamos sugestões para a implementação do CFTP para gerar amostras da distribuição normal truncada em dimensões maiores que dois e a geração de amostras em conjuntos diferente do quadrante positivo. / This project will display the CFTP perfect simulation algorithm presented at Propp & Wilson (1996). According to Philippe & Robert (2003) will be implemented the CFTP providing samples of the bivariate normal distribution truncated at the positive quadrant. The proposed algorithm is compared to the samples generated by Gibbs Sampler and by the rejection sampling ( or acceptance rejection method or \"accept-reject algorithm\"). Finally, suggestions to the implementation of CFTP in order to produce truncated normal distribution samples at bigger dimensions than two and the provide a diferent set of samples from the positive quadrant.

A simulação pluriGaussiana truncada é usada para simulação de dados categóricos, tais como fácies em um contexto geológico. Esse método é uma extensão da Gaussiana truncada, mas que permite a simulação de feições geológicas complexas. Nessa dissertação, a simulação pluriGaussiana truncada foi baseada nas curvas de proporção obtidas da interpolação multiquádrica. Esse método foi testado com uma amostra composta por 24 sondagens obtidas de um modelo geológico sintético. As realizações da simulação pluriGuassiana truncada foram pós-processadas para obter o modelo médio, bem como as incertezas associadas. Os resultados mostraram que as incertezas estão associadas com os contatos litológicos. / The truncated pluriGaussian simulation is used for categorical data simulation, such as facies in a geological context. This method is an extension of the Gaussian truncated, but it allows simulation of complex geological features. In this dissertation, the method of truncated pluriGaussian simulation was based on proportion curves computed form multiquadric interpolation. This method was tested with a sample composed of 24 drill holes drawn from a synthetic geologic model. Realizations of truncated pluriGaussian simulation are post-processed to get the average model and associated uncertainty as well. Result showed that uncertainties are always associated with geological contacts.

Reconstructing sparse signals from undersampled measurements is a challenging problem that arises in many areas of data science, such as signal processing, circuit design, optical engineering and image processing. The most natural way to formulate such problems is by searching for sparse, or parsimonious, solutions in which the underlying phenomena can be represented using just a few parameters. Accordingly, a natural way to phrase such problems revolves around L0 minimization in which the sparsity of the desired solution is controlled by directly counting the number of non-zero parameters. However, due to the nonconvexity and discontinuity of the L0 norm such optimization problems can be quite difficult. One modern tactic to treat such problems is to leverage convex relaxations, such as exchanging the L0 norm for its convex analog, the L1 norm. However, to guarantee accurate reconstructions for L1 minimization, additional conditions must be imposed, such as the restricted isometry property. Accordingly, in this thesis, we propose a novel extension to current approaches revolving around truncated L1 minimization and demonstrate that such approach can, in important cases, provide a better approximation of L0 minimization. Considering that the nonconvexity of the truncated L1 norm makes truncated l1 minimization unreliable in practice, we further generalize our method to partial L1 minimization to combine the convexity of L1 minimization and the robustness of L0 minimization. In addition, we provide a tractable iterative scheme via the augmented Lagrangian method to solve both optimization problems. Our empirical study on synthetic data and image data shows encouraging results of the proposed partial L1 minimization in comparison to L1 minimization.

No presente trabalho apresentamos o algoritmo de simulacão perfeita CFTP, proposto em Propp & Wilson (1996). Seguindo o trabalho de Philippe & Robert (2003) implementamos o CFTP gerando amostras da distribuicão normal bivariada truncada no quadrante positivo. O algoritmo proposto e comparado com o amostrador de Gibbs e o método de rejeição. Finalmente, apresentamos sugestões para a implementação do CFTP para gerar amostras da distribuição normal truncada em dimensões maiores que dois e a geração de amostras em conjuntos diferente do quadrante positivo. / This project will display the CFTP perfect simulation algorithm presented at Propp & Wilson (1996). According to Philippe & Robert (2003) will be implemented the CFTP providing samples of the bivariate normal distribution truncated at the positive quadrant. The proposed algorithm is compared to the samples generated by Gibbs Sampler and by the rejection sampling ( or acceptance rejection method or \"accept-reject algorithm\"). Finally, suggestions to the implementation of CFTP in order to produce truncated normal distribution samples at bigger dimensions than two and the provide a diferent set of samples from the positive quadrant.