Durant cette thèse, une méthode d'analyse statistique sur la gerbe d'éclats d’une bombe, en particulier sur leurs masses, a été mise au point. Nous avions à disposition trois échantillons partiels de données expérimentales et un modèle mécanique simulant l'explosion d'un anneau. Dans un premier temps, un modèle statistique a été créé à partir du modèle mécanique fourni, pour générer des données pouvant être similaires à celles d'une expérience. Après cela, la distribution des masses a pu être étudiée. Les méthodes d'analyse classiques ne donnant pas de résultats suffisamment précis, une nouvelle méthode a été mise au point. Elle consiste à représenter la masse par une variable aléatoire construite à partir d'une base de polynômes chaos. Cette méthode donne de bons résultats mais ne permet pas de prendre en compte le lien entre les éclats d'une même charge. Il a donc été décidé ensuite de modéliser la masse par un processus stochastique, et non par une variable aléatoire. La portée des éclats, qui dépend en partie de la masse, a elle aussi été modélisée par un processus. Pour finir, une analyse de sensibilité a été effectuée sur cette portée avec les indices de Sobol. Ces derniers s'appliquant aux variables aléatoires, nous les avons adaptés aux processus stochastiques de manière à prendre en compte les liens entre les éclats. Dans la suite, les résultats de cette dernière analyse pourront être améliorés. Notamment, grâce à des indices présentés en dernière partie qui seraient adaptés aux variables dépendantes, et permettraient l'utilisation de processus stochastiques à accroissements non indépendants. / During this thesis, a method of statistical analysis on sheaf of bomb fragments, in particular on their masses, has been developed. Three samples of incomplete experimental data and a mechanical model which simulate the explosion of a ring were availables. First, a statistical model based on the mechanical model has been designed, to generate data similar to those of an experience. Then, the distribution of the masses has been studied. The classical methods of analysis being not accurate enough, a new method has been developed. It consists in representing the mass by a random variable built from a basis of chaos polynomials. This method gives good results however it doesn't allow to take into account the link between slivers. Therefore, we decided to model the masses by a stochastic process, and not a random variable. The range of fragments, which depends of the masses, has also been modeled by a process. Last, a sensibility analysis has been carried out on this range with Sobol indices. Since these indices are applied to random variables, it was necessary to adapt them to stochastic process in a way that take into account the links between the fragments. In the last part, it is shown how the results of this analysis could be improved. Specifically, the indices presented in the last part are adapted to dependent variables and therefore, they could be suitable to processes with non independent increases.

The Moran process is a model for simulating evolutionary dynamics. In that model, one mutant with higher fitness is introduced to a structured population. Evolution is simulated in rounds. In one round, individual is selected proportio- nally to its fitness and spreads to the place of a random neighbour. In this thesis, we motivate the Moran process, present basic results, and define our variant. We work in a vertex dependent model; every individual has fitness according to its type and occupied vertex. In the vertex dependent model we prove two theorems about the number of steps the process has to make to get to the stable state. We show that on the complete graph, the process takes only polynomially many steps and we find a graph where the process take exponentially many steps, but in the normal settings the number of steps is the same as on the complete graph. 1

One of the characteristics that distinguishes living things from non-living things is motility. On the cellular level, the motility or non-motility of different types of cells can be life building, life-saving or life-threatening. A thorough study of cell motion is needed to help understand the underlying mechanisms that enhance or prohibit cell motion. We introduce a discrete centroid model of cell motion in the context of a generalized random walk. We find an approximation for the theoretical mean square displacement (MSD) that uses a subset of the state space to estimate the MSD for the entire space. We give some intuition as to why this is an unexpectedly good estimate. A lower and upper bound for the MSD is also given. We extend the centroid model to an ODE model and use it to analyze the distribution of focal adhesion (FA) lifetimes gathered from experimental data. We found that in all but one case a unimodal, non-symmetric gamma distribution is a good match for the experimental data. We use a detach-rate function in the ODE model to determine how long a FA will persist before it detaches. A detach-rate function that is dependent on both force and time produces distributions with a best fit gamma curve that closely matches the data. Using the data gathered from the matching simulations, we calculate both the cell speed and mean FA lifetime and compare them. Where available, we also compare this relationship to that of the experimental data and find that the simulation reasonably matches it in most cases. In both the simulations and experimental data, the cell speed and mean FA lifetime are related, with longer mean lifetimes being indicative of slower speeds. We suspect that one of the main predictors of cell speed for migrating cells is the distribution of the FA lifetimes.

One of the characteristics that distinguishes living things from non-living things is motility. On the cellular level, the motility or non-motility of different types of cells can be life building, life-saving or life-threatening. A thorough study of cell motion is needed to help understand the underlying mechanisms that enhance or prohibit cell motion. We introduce a discrete centroid model of cell motion in the context of a generalized random walk. We find an approximation for the theoretical mean square displacement (MSD) that uses a subset of the state space to estimate the MSD for the entire space. We give some intuition as to why this is an unexpectedly good estimate. A lower and upper bound for the MSD is also given. We extend the centroid model to an ODE model and use it to analyze the distribution of focal adhesion (FA) lifetimes gathered from experimental data. We found that in all but one case a unimodal, non-symmetric gamma distribution is a good match for the experimental data. We use a detach-rate function in the ODE model to determine how long a FA will persist before it detaches. A detach-rate function that is dependent on both force and time produces distributions with a best fit gamma curve that closely matches the data. Using the data gathered from the matching simulations, we calculate both the cell speed and mean FA lifetime and compare them. Where available, we also compare this relationship to that of the experimental data and find that the simulation reasonably matches it in most cases. In both the simulations and experimental data, the cell speed and mean FA lifetime are related, with longer mean lifetimes being indicative of slower speeds. We suspect that one of the main predictors of cell speed for migrating cells is the distribution of the FA lifetimes.

京都大学 / 0048 / 新制・課程博士 / 博士(工学) / 甲第21747号 / 工博第4564号 / 新制||工||1711(附属図書館) / 京都大学大学院工学研究科都市社会工学専攻 / (主査)教授 山田 忠史, 准教授 SCHMOECKER Jan-Dirk, 教授 宇野 伸宏 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

Complex mathematical models are often built to describe a physical process that would otherwise be extremely difficult, too costly or sometimes impossible to analyze. Generally, these models require solutions to many partial differential equations. As a result, the computer codes may take a considerable amount of time to complete a single evaluation. A time tested method of analysis for such models is Monte Carlo simulation. These simulations, however, often require many model evaluations, making this approach too computationally expensive. To limit the number of experimental runs, it is common practice to model the departure as a Gaussian stochastic process (GaSP) to develop an emulator of the computer model. One advantage for using an emulator is that once a GaSP is fit to realized outcomes, the computer model is easy to predict in unsampled regions of the input space. This is an attempt to 'characterize' the overall model of the computer code. Most of the historical work on design and analysis of computer experiments focus on the characterization of the computer model over a large region of interest. However, many practitioners seek other objectives, such as input screening (Welch et al., 1992), mapping a response surface, or optimization (Jones et al., 1998). Only recently have researchers begun to consider these topics in the design and analysis of computer experiments. In this dissertation, we explore a more traditional response surface approach (Myers, Montgomery and Anderson-Cook, 2009) in conjunction with traditional computer experiment methods to search for the optimum response of a process. For global optimization, Jones, Schonlau, and Welch's (1998) Efficient Global Optimization (EGO) algorithm remains a benchmark for subsequent research of computer experiments. We compare the proposed method in this paper to this leading benchmark. Our goal is to show that response surface methods can be effective means towards estimating an optimum response in the computer experiment framework. / Ph. D.

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In this thesis, we are concerned with the modifications of the stochastic processes and the random probability measures. First chapter is devoted to modifications of the stochastic process to the space of continuous functions, modifications of submartingale to the set of right-continuous with finite left-hand limits functions and separable modifications of stochastic process. In the second chapter is the attention on the regularization of random probability measure in Markov kernel focused. In particular, we work with random probability measures on the Borel subset of the Polish space, or Radon separable topological space.

O ambiente aquático tem notória importância para a pesquisa, pela biodiversidade e vastidão, e também do ponto de vista comercial, para a indústria militar e de óleo&gás por exemplo. Entretanto, a sua exploração é prejudicada por diversos fatores, entre eles devido à dificuldade de navegação. Infelizmente, carece-se de sinal GPS (Global Positioning System) embaixo d\'água, o que exige outras técnicas de localização. Assim, este trabalho analisa um sistema de navegação para um veículo submarino autônomo. Graças a sensores de velocidade, girômetros, bússola, entre outros, aplica-se o princípio de dead reckoning para calcular a posição atual do veículo a partir da última posição conhecida. Para tal, é feito inicialmente um estudo dos sensores a serem utilizados e um algoritmo de navegação é proposto, cujos resultados são expressos em coordenadas geodésicas (latitude e longitude), permitindo a visualização da trajetória do veículo em mapas geo-referenciados. Além disso, problemas práticos de medição são tratados. Em seguida, é feito um estudo sobre o ruído dos sensores, utilizando a curva de variância de Allan para caracterização dos sinais dos girômetros e do DVL (Doppler Velocity Logger). Por meio de equações de propagação de erro, os ruídos são recuperados em simulação, permitindo a estimação do erro de posição e de atitude (posição angular) acumulados para uma dada manobra. Finalmente, discute-se um critério de emersão a partir das estimativas de erro de posição. / The main part of our planet is filled with water, so the aquatic environment has notorious research and commercial importance. However, its exploration faces many difficulties. In navigation, the lack of GPS signal (Global Positioning System) during underwater missions requires different techniques, so this document focus on analyzing a navigation system for autonomous underwater vehicles. Thanks to different embedded sensors, like DVL (Doppler Velocity Logger), compass, gyrometers and others, the processes of dead reckoning is applied, witch calculates vehicle\'s current position by using the previously determined position. To do so, a navigation algorithm is implemented, providing geodesic coordinates to plot vehicle\'s trajectories on geo-referenced maps. Also, practical difficulties are discussed and treated. To improve the quality of the results, girometer\'s and DVL\'s errors are analyzed using Allan\'s variance and the navigation errors are estimated using first order time derivative equations in an augmented state space. Lastly, it is discussed a criterion to emerge and correct the vehicle\'s position using GPS signal.

Nesta tese propomos um modelo estocástico multimodal para regulação da expressão gênica em nível de transcrição. A definição de um espaço de parâmetros que contém o conteúdo biológico do sistema aliada à escolha apropriada de uma base para construir a matriz de acoplamento entre os estados do sistema levaram à obtenção de soluções exatas do modelo. Tais soluções são obtidas transformando as equações mestras em equações diferenciais parciais usando a técnica das funções geradoras e escrevendo os coeficientes das equações parciais em termos dos parâmetros biológicos do modelo. No regime estacionário obtivemos uma relação de recorrência para os coeficientes das séries de potências que definem as funções geradoras e a especificação das configurações de equilíbrio do sistema permite que estas séries sejam calculadas exatamente. Com as soluções exatas calculadas não só as distribuições de probabilidade foram obtidas como os momentos das distribuições. As distribuições de probabilidade de equilíbrio apresentam estruturas multimodais com vários picos e a análise do ruído (flutuação) mostra que a existência de um estado intermediário de eficiência transcricional leva a redução do ruído global do sistema. A inspeção dos autovalores da matriz de acoplamento mostrou que existem regiões onde a dinâmica dos momentos é de caráter oscilatória com amortecimento. Diferentes esquemas de acoplamento levam à diferentes regimes transientes, tal característica revela que o sistema multimodal apresentam maior flexibilidade adaptativa quando comparado com sistemas de um ou dois estados. / In this thesis we propose a stochastic model for multimodal regulation of gene expression at the transcriptional level. The definition of a parameter space that contains the contents of the biological system coupled with the appropriate choice of a base to build the coupling matrix between the states of the system led to the exact solutions of the model. Such solutions are obtained by transforming master equations in partial differential equations using the technique of generating functions and writing the coefficients of partial equations in terms of biological parameters of the model. In the steady a recurrence relation for the coefficients of power series defining the generating functions was obtained and specification of the equilibrium configurations of the system allows the exact calculation of these series. With the exact solutions calculated not only the probability distributions were obtained but also the moments of the distributions. The equilibrium distributions probability is multimodal and presents several peaks. Analysis of the noise (fluctuation) shows that the existence of an state with intermediate transcriptional efficiency leads to a reduction of the overall system noise. Inspection of the eigenvalues of the coupling matrix showed that there are regions where the dynamics of the moments is damped oscillating. Different coupling schemes lead to different transient regimes, this feature reveals that the multimodal system have greater adaptive flexibility when compared to systems of one or two states.