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Kyoto University (京都大学) / 0048 / 新制・課程博士 / 博士(工学) / 甲第17234号 / 工博第3661号 / 新制||工||1556(附属図書館) / 29980 / 京都大学大学院工学研究科原子核工学専攻 / (主査)教授 中島 健, 教授 福山 淳, 准教授 山本 俊弘 / 学位規則第4条第1項該当

Ce travail se propose d'étudier deux problèmes complémentaires concernant des systèmes différentiels à coefficients aléatoires étudiés au moyen de simulations de Monte Carlo. Le premier problème consiste à calculer la loi à un instant t* de la solution d'une équation différentielle à coefficients aléatoires. Comme on ne peut pas, en général, exprimer cette loi de probabilité au moyen d'une fonction connue, il est nécessaire d'avoir recours à une approche par simulation pour se faire une idée de cette loi. Mais cette approche ne peut pas toujours être utilisée à cause du phénomène d'explosion des solutions en temps fini. Ce problème peut être surmonté grâce à une compactification de l'ensemble des solutions. Une approximation de la loi au moyen d'un développement de chaos polynomial fournit un outil d'étude alternatif. La deuxième partie considère le problème d'estimer les coefficients d'un système différentiel quand une trajectoire du système est connue en un petit nombre d'instants. On utilise pour cela une méthode de Monté Carlo très simple, la méthode de rejet, qui ne fournit pas directement une estimation ponctuelle des coefficients mais plutôt un ensemble de valeurs compatibles avec les données. L'examen des propriétés de cette méthode permet de comprendre non seulement comment choisir les différents paramètres de la méthode mais aussi d'introduire quelques options plus efficaces. Celles-ci incluent une nouvelle méthode, que nous appelons la méthode de rejet séquentiel, ainsi que deux méthodes classiques, la méthode de Monte-Carlo par chaînes de Markov et la méthode de Monte-Carlo séquentielle dont nous examinons les performances sur différents exemples. / This work addresses two complementary problems when studying differential systems with random coefficients using a simulation approach. In the first part, we look at the problem of computing the law of the solution at time t* of a differential equation with random coefficients. It is shown that even in simplest cases, one will usually obtain a random variable where the pdf cannot be computed explicitly, and for which we need to rely on Monte Carlo simulation. As this simulation may not always be possible due to the explosion of the solution, several workarounds are presented. This includes displaying the histogram on a compact manifold using two charts and approximating the distribution using a polynomial chaos expansion. The second part considers the problem of estimating the coefficients in a system of differential equations when a trajectory of the system is known at a set of times. To do this, we use a simple Monte Carlo sampling method, known as the rejection sampling algorithm. Unlike deterministic methods, it does not provide a point estimate of the coefficients directly, but rather a collection of values that “fits” the known data well. An examination of the properties of the method allows us not only to better understand how to choose the different parameters when implementing the method, but also to introduce more efficient methods. This includes a new approach which we call sequential rejection sampling and methods based on the Markov Chain Monte Carlo and Sequential Monte Carlo algorithms. Several examples are presented to illustrate the performance of all these methods.

We introduce computationally efficient Monte Carlo methods for studying the statistics of stochastic differential equations in two distinct settings. In the first, we derive importance sampling methods for data assimilation when the noise in the model and observations are small. The methods are formulated in discrete time, where the "posterior" distribution we want to sample from can be analyzed in an accessible small noise expansion. We show that a "symmetrization" procedure akin to antithetic coupling can improve the order of accuracy of the sampling methods, which is illustrated with numerical examples. In the second setting, we develop "stochastic continuation" methods to estimate level sets for statistics of stochastic differential equations with respect to their parameters. We adapt Keller's Pseudo-Arclength continuation method to this setting using stochastic approximation, and generalized least squares regression. Furthermore, we show that the methods can be improved through the use of coupling methods to reduce the variance of the derivative estimates that are involved.

O filtro cuno faz parte do circuito de tratamento de água do reator IEA-R1 que , quando saturado, é substituído, se tornando um rejeito radioativo que deve ser gerenciado. Neste trabalho foi realizada a caracterização primária do filtro cuno do reator nuclear IEA-R1 do IPEN utilizando-se espectrometria gama associada ao método de Monte Carlo. A espectrometria gama foi realizada utilizando-se um detector de germânio hiperpuro (HPGe). O cristal de germânio representa o volume ativo de detecção do detector HPGe, que possui uma região denominada camada morta ou camada inativa. Na literatura tem sido reportada uma diferença entre os valores experimentais e teóricos na obtenção da curva de eficiência desses detectores. Neste trabalho foi utilizado o código MCNP-4C para a obtenção da calibração em eficiência do detector para a geometria do filtro cuno, onde foram estudadas as influências da camada morta e do efeito de soma em cascata no detector HPGe. As correções dos valores de camada morta foram realizadas variando-se a espessura e o raio do cristal de germânio. O detector possui 75,83 cm3 de volume ativo de detecção, segundo informações fornecidas pelo fabricante. Entretanto os resultados encontrados mostraram que o valor de volume ativo real é menor do que o especificado, onde a camada morta representa 16% do volume total do cristal. A análise do filtro cuno por meio da espectrometria gama, permitiu a identificação de picos de energia. Por meio desses picos foram identificados três radionuclídeos no filtro: 108mAg, 110mAg e 60Co. A partir da calibração em eficiência obtida pelo método de Monte Carlo, o valor de atividade estimado para esses radionuclídeos está na ordem de MBq. / The Cuno filter is part of the water processing circuit of the IEA-R1 reactor and, when saturated, it is replaced and becomes a radioactive waste, which must be managed. In this work, the primary characterization of the Cuno filter of the IEA-R1 nuclear reactor at IPEN was carried out using gamma spectrometry associated with the Monte Carlo method. The gamma spectrometry was performed using a hyperpure germanium detector (HPGe). The germanium crystal represents the detection active volume of the HPGe detector, which has a region called dead layer or inactive layer. It has been reported in the literature a difference between the theoretical and experimental values when obtaining the efficiency curve of these detectors. In this study we used the MCNP-4C code to obtain the detector calibration efficiency for the geometry of the Cuno filter, and the influence of the dead layer and the effect of sum in cascade at the HPGe detector were studied. The correction of the dead layer values were made by varying the thickness and the radius of the germanium crystal. The detector has 75.83 cm3 of active volume of detection, according to information provided by the manufacturer. Nevertheless, the results showed that the actual value of active volume is less than the one specified, where the dead layer represents 16% of the total volume of the crystal. A Cuno filter analysis by gamma spectrometry has enabled identifying energy peaks. Using these peaks, three radionuclides were identified in the filter: 108mAg, 110mAg and 60Co. From the calibration efficiency obtained by the Monte Carlo method, the value of activity estimated for these radionuclides is in the order of MBq.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

The purpose of this research is to investigate properties of diffusion processes in porous media. Porous media are modelled by random Sierpinski carpets, each carpet is constructed by mixing two different generators with the same linear size. Diffusion on porous media is studied by performing random walks on random Sierpinski carpets and is characterized by the random walk dimension $d_w$. In the first part of this work we study $d_w$ as a function of the ratio of constituents in a mixture. The simulation results show that the resulting $d_w$ can be the same as, higher or lower than $d_w$ of carpets made by a single constituent generator. In the second part, we discuss the influence of static external fields on the behavior of diffusion. The biased random walk is used to model these phenomena and we report on many simulations with different field strengths and field directions. The results show that one structural feature of Sierpinski carpets called traps can have a strong influence on the observed diffusion properties. In the third part, we investigate the effect of diffusion under the influence of external fields which change direction back and forth after a certain duration. The results show a strong dependence on the period of oscillation, the field strength and structural properties of the carpet.

Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.Computational methods for predicting the binding affinity of small organic molecules tobiological macromolecules cover a vast range of theoretical and physical complexity. Generally, as the required accuracy increases so does the computational cost, thereby making the user choose a method that suits their needs within the parameters of the project. We present how WScore, a rigid-receptor docking program normally consigned to structure-based hit discovery in drug design projects, is systematically ameliorated to perform accurately enough for lead optimization with a set of ROCK1 complexes and congeneric ligands from a structure-activity relationship study. Initial WScore results from the Schrödinger 2019-3 release show poor correlation (R² ∼0.0), large errors in predicted binding affinity (RMSE = 2.30 kcal/mol), and bad native pose prediction (two RMSD > 4Å) for the six ROCK1 crystal structures and associated active congeneric ligands. Improvements to WScore’s treatment of desolvation, myriad code fixes, and a simple ensemble consensus scoring protocol improved the correlation (R² = 0.613), the predicted affinity accuracy (RMSE = 1.34 kcal/mol), and native pose prediction (one RMSD > 1.5Å). Then we evaluate a physically and thermodynamically rigorous free energy perturbation (FEP) method, FEP+, against CryoEM structures of the Machilis hrabei olfactory receptor, MhOR5, and associated dose-response assays of a panel of small molecules with the wild-type and mutants. Augmented with an induced-fit docking method, IFD-MD, FEP+ performs well for ligand mutating relative binding FEP (RBFEP) calculations which correlate with experimental log(EC50)with an R² = 0.551. Ligand absolute binding FEP (ABFEP) on a set of disparate ligands from the MhOR5 panel has poor correlation (R² = 0.106) for ligands with log(EC50) within the assay range. But qualitative predictions correctly identify the ligands with the lowest potency. Protein mutation calculations have no log(EC50) correlation and consistently fail to predict the loss of potency for a majority of MhOR5 single point mutations. Prediction of ligand efficacy (the magnitude of receptor response) is also an unsolved problem as the canonical active and inactive conformations of the receptor are absent in the FEP simulations. We believe that structural insights of the mutants for both bound and unbound (apo) states are required to better understand the shortcomings of the current FEP+ methods for protein mutation RBFEP. Finally, improvements to GPU-accelerated linear algebra functions in an Auxiliary-Field Quantum Monte Carlo (AFQMC) program effect an average 50-fold reduction in GPU kernel compute time using optimized GPU library routines instead of custom made GPU kernels. Also MPI parallelization of the population control algorithm that destroys low-weight walkers has a bottleneck removed in large, multi-node AFQMC calculations.

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No / Nonadiabatic Monte Carlo transition-state theory is used to explore competing C¿Cl and C¿Br bond fission processes in a simple model of 1[n,pi*(CO)] photoexcited bromoacetyl chloride. Morse potentials are used to represent bond stretching coordinates, and the positions and magnitudes of nonadiabatic coupling between excited state potentials are modeled using ab initio data. The main effect of nonadiabaticity is to favor C¿Cl fission over C¿Br, despite a larger barrier to C¿Cl dissociation. The absolute values of the rate constants are smaller than observed experimentally, but the calculated branching ratios are close to the experimental value. For C¿Cl fission, it is shown that the minimum energy crossing point is not sufficient to describe the rate constant, suggesting that care must be taken when using alternative models which make this assumption.