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Phytoöstrogene sind in den vergangenen Jahren zunehmend in den Fokus der Wissenschaft gerückt, weil sie eine potentielle Alternative zur klassischen Hormonersatztherapie darstellen. Diese ist aufgrund von zum Teil drastischen Nebenwirkungen für den Einsatz von klimakterischen Beschwerden umstritten. In dieser Arbeit wird die dosisabhängige Wirkung des Phytoöstrogens Genistein an ausgewählten östrogenselektiven Organen näher untersucht. Die Versuche wurden am Modell der langzeitovarektomierten Maus durchgeführt. Es wurden 70 ovarektomierte Tiere in sieben Gruppen aufgeteilt und untersucht. Fünf der sieben Gruppen erhielten genisteinhaltiges Futter in verschiedenen Konzentrationen. Die anderen beiden Gruppen erhielten Estradiol als Zusatz oder sojafreie Diät und dienten jeweils als Positiv- und Negativkontrollgruppe. Zusätzlich gab es eine nicht ovarektomierte intakte Kontrollgruppe, die ebenfalls sojafreies Futter erhielt. Während des dreimonatigen Versuchszeitraums wurden regelmäßig Gewicht und Futterverbrauch der Tiere gemessen. Nach Ende des Versuchs wurden die Feuchtgewichte von Uterus und Herz bestimmt sowie die Genexpression am linken Ventrikel von IGF-1, ERα und Myocardin mittels PCR analysiert. Darüber hinaus wurde am Tibia-Knochen per pQCT die Messung der Spongiosadichte, des polaren Widerstandsmoments und des prozentualen Anteils der Trabekel an der Spongiosaquerschnittsfläche durchgeführt. Die Ergebnisse zeigen, dass Genistein direkt am Herz wirkt, indem es das relative Herzgewicht und die Genexpression am Herz erhöht. Genistein beeinflusst auch das Körpergewicht und das relative Gewicht des Uterus und die untersuchten Knochenparameter dosisabhängig. Genistein kann in höherer Dosierung am Uterus proliferierend wirken, jedoch nach derzeitigem Kenntnisstand weniger stark als der klassische Hormonersatztherapie-Wirkstoff E2. Genistein kann zukünftig nur dann eine Therapiealternative zur klassischen Hormonersatztherapie darstellen, wenn es gelingt, eine Dosis zu finden, bei der Genistein die gewünschten Wirkungen entfaltet, gleichzeitig aber die unerwünschte proliferierende Wirkung an Brust und Uterus sicher ausgeschlossen werden kann. Im Modell der ovarektomierten Maus scheint eine Dosis von 1 g/kg Genistein im Futter ein vielversprechender Ansatzpunkt für weitere Untersuchungen zu sein.

L’objectif de cette thèse est d’étudier le comportement en temps long de certains processus de Markov déterministes par morceaux (PDMP) dont le flot suivi par la composante spatiale commute aléatoirement entre plusieurs flots possédant un unique équilibre attractif (éventuellement le même pour chaque flot). Nous donnerons dans un premier temps un exemple d’étude d’un tel processus construit dans le plan à partir de flots associés à des équations différentielles linéaires stables où il est déjà possible d’observer des comportements contre-intuitifs. La deuxième partie de ce manuscrit est dédiée à l’étude et la comparaison de deux modèles de compétition pour une ressource dans un environnement hétérogène. Le premier modèle est un modèle alétoire simulant l’hétérogénéité temporelle d’un environnement sur les espèces en compétition à l’aide d’un PDMP. Son étude utilise des outils maintenant classiques sur l’étude des PDMP. Le deuxième modèle est un modèle déterministe (présentant sous forme d’un système d’équations différentielles) modélisant l’impact de l’hétérogénéité spatiale d’un environnement sur ces mêmes espèces. Nous verrons que malgré leur nature très différente, le comportement en temps long de ces deux systèmes est relativement similaire et est essentiellement déterminé par le signe des taux d’invasion de chacune des espèces qui sont des quantités dépendant exclusivement des paramètres du système et modélisant la vitesse de croissance (ou de décroissance) de ces espèces lorsqu’elles sont au bord de l’extinction. / The objective of this thesis is to study the long time behaviour of some piecewise deterministic Markov processes (PDMP). The flow followed by the spatial component of these processes switches randomly between several flow converging towards an equilibrium point (not necessarily the same for each flow). We will first give an example of such a process built in the plan from two linear stable differential equations and we will see that its stability depends strongly on the switching times. The second part of this thesis is dedicated to the study and comparison of two competition models in a heterogeneous environment. The first model is a probabilistic model where we build a PDMP simulating the effect of the temporal heterogeneity of an environment over the species in competition. Its study uses classical tools in this field. The second model is a deterministic model simulating the effect of the spatial heterogeneity of an environment over the same species. Despite the fact that the nature of the two models is very different, we will see that their long time behavior is very similar. We define for both model several quantities called invasion rates modelizing the growth (or decreasing) rate speed of a species when it is near to extinction and we will see that the signs of these invasion rates fully describes the long time behavior for both systems.

<div>Uncertainty quantification techniques based on the spectral approach have been studied extensively in the literature to characterize and quantify, at low computational cost, the impact that uncertainties may have on large-scale engineering problems. One such technique is the <i>generalized polynomial chaos</i> (gPC) which utilizes a time-independent orthogonal basis to expand a stochastic process in the space of random functions. The method uses a specific Askey-chaos system that is concordant with the measure defined in the probability space in order to ensure exponential convergence to the solution. For nearly two decades, this technique has been used widely by several researchers in the area of uncertainty quantification to solve stochastic problems using the spectral approach. However, a major drawback of the gPC method is that it cannot be used in the resolution of problems that feature strong nonlinear dependencies over the probability space as time progresses. Such downside arises due to the time-independent nature of the random basis, which has the undesirable property to lose unavoidably its optimality as soon as the probability distribution of the system's state starts to evolve dynamically in time.</div><div><br></div><div>Another technique is the <i>time-dependent generalized polynomial chaos</i> (TD-gPC) which utilizes a time-dependent orthogonal basis to better represent the stochastic part of the solution space (aka random function space or RFS) in time. The development of this technique was motivated by the fact that the probability distribution of the solution changes with time, which in turn requires that the random basis is frequently updated during the simulation to ensure that the mean-square error is kept orthogonal to the discretized RFS. Though this technique works well for problems that feature strong nonlinear dependencies over the probability space, the TD-gPC method possesses a serious issue: it suffers from the curse of dimensionality at the RFS level. This is because in all gPC-based methods the RFS is constructed using a tensor product of vector spaces with each of these representing a single RFS over one of the dimensions of the probability space. As a result, the higher the dimensionality of the probability space, the more vector spaces needed in the construction of a suitable RFS. To reduce the dimensionality of the RFS (and thus, its associated computational cost), gPC-based methods require the use of versatile sparse tensor products within their numerical schemes to alleviate to some extent the curse of dimensionality at the RFS level. Therefore, this curse of dimensionality in the TD-gPC method alludes to the need of developing a more compelling spectral method that can quantify uncertainties in long-time response of dynamical systems at much lower computational cost.</div><div><br></div><div>In this work, a novel numerical method based on the spectral approach is proposed to resolve the curse-of-dimensionality issue mentioned above. The method has been called the <i>flow-driven spectral chaos</i> (FSC) because it uses a novel concept called <i>enriched stochastic flow maps</i> to track the evolution of a finite-dimensional RFS efficiently in time. The enriched stochastic flow map does not only push the system's state forward in time (as would a traditional stochastic flow map) but also its first few time derivatives. The push is performed this way to allow the random basis to be constructed using the system's enriched state as a germ during the simulation and so as to guarantee exponential convergence to the solution. It is worth noting that this exponential convergence is achieved in the FSC method by using only a few number of random basis vectors, even when the dimensionality of the probability space is considerably high. This is for two reasons: (1) the cardinality of the random basis does not depend upon the dimensionality of the probability space, and (2) the cardinality is bounded from above by <i>M+n+1</i>, where <i>M</i> is the order of the stochastic flow map and <i>n</i> is the order of the governing stochastic ODE. The boundedness of the random basis from above is what makes the FSC method be curse-of-dimensionality free at the RFS level. For instance, for a dynamical system that is governed by a second-order stochastic ODE (<i>n=2</i>) and driven by a stochastic flow map of fourth-order (<i>M=4</i>), the maximum number of random basis vectors to consider within the FSC scheme is just 7, independent whether the dimensionality of the probability space is as low as 1 or as high as 10,000.</div><div><br></div><div>With the aim of reducing the complexity of the presentation, this dissertation includes three levels of abstraction for the FSC method, namely: a <i>specialized version</i> of the FSC method for dealing with structural dynamical systems subjected to uncertainties (Chapter 2), a <i>generalized version</i> of the FSC method for dealing with dynamical systems governed by (nonlinear) stochastic ODEs of arbitrary order (Chapter 3), and a <i>multi-element version</i> of the FSC method for dealing with dynamical systems that exhibit discontinuities over the probability space (Chapter 4). This dissertation also includes an implementation of the FSC method to address the dynamics of large-scale stochastic structural systems more effectively (Chapter 5). The implementation is done via a modal decomposition of the spatial function space as a means to reduce the number of degrees of freedom in the system substantially, and thus, save computational runtime.</div>

Os objetivos deste trabalho vão da apresentação do andamento das pesquisas relacionadas à análise de distúrbios associados à qualidade da energia elétrica (QEE), até a proposta de um algoritmo baseado em diversas ferramentas para a detecção e localização no tempo, bem como a classificação automática destes distúrbios. Nesta pesquisa é proposta uma detecção não somente do início e fim de um único evento, mas também, de n possíveis desconformidades na forma de onda que possam vir a ocorrer ou existir em determinados registros e/ou arquivos de dados em análise. Como diferencial deste trabalho, tem-se que da determinação da localização das alterações/descontinuidades na forma de onda, foi possível obter janelas de dados com tamanhos flexíveis. Desta maneira, vários eventos sobre o sinal em análise puderam ser avaliados, bem como as durações associadas. Para isso, a Transformada Wavelet (TW) foi utilizada para realizar a detecção e também a localização destas alterações no tempo. Já para a classificação da ocorrência, ou das ocorrências, a TW, a Transformada de Fourier (TF) e o valor RMS foram empregados. A flexibilidade das janelas de dados permitiu uma adequada escolha de qual ferramenta poderia ser mais bem utilizada na classificação. Conforme implementado, cada uma destas ferramentas apresenta uma resposta e através de um módulo de decisão lógica é determinada a resposta final do algoritmo. Para validar o estudo, várias situações de distúrbios foram caracterizadas referentes a um sistema elétrico de distribuição real, implementado e simulado pela aplicação do software ATP (Alternative Transients Program). Os resultados obtidos foram excelentes tanto para a detecção e localização no tempo, como para a classificação e estimação da amplitude e duração dos eventos. / The objectives of this work are going since the presentation of the researches related to the analyses of power quality (PQ) disturbances through the proposal of an algorithm based on several tools for detection and location in time, as well as the automatic classification of these phenomena. It is proposed to determine not only the initial and the end of a unique event, but all the n possible disconformities in the waveform that can exist or occur in the data file registered data in analyses. As the differential of this research, from the location in time of the alteration/discontinuities in the waveforms, it was possible to obtain data windows with flexible sizes. So, several events on the signal were evaluated, as well as their specific timeduration. For this purpose, the Wavelet transform (WT) was used to reach the detection and localization in time of the waveform alterations. For the event classification, the TW, the Fourier transform (FT) and the Root Mean Square (RMS) value were used. The data window flexibility allowed an appropriate choice of which tool could be better used in the classification task. As implemented, each one of these tools presented an answer, and the final answer was obtained by using a logic decision module. To validate the study, some situations of disturbances were characterized using a real distribution system, implemented and simulated applying the ATP (Alternative Transients Program) software. The results were excellent in such a way for detection and localization in time, as well as for the automatic classification and estimation of the magnitude and the event duration.

Os objetivos deste trabalho vão da apresentação do andamento das pesquisas relacionadas à análise de distúrbios associados à qualidade da energia elétrica (QEE), até a proposta de um algoritmo baseado em diversas ferramentas para a detecção e localização no tempo, bem como a classificação automática destes distúrbios. Nesta pesquisa é proposta uma detecção não somente do início e fim de um único evento, mas também, de n possíveis desconformidades na forma de onda que possam vir a ocorrer ou existir em determinados registros e/ou arquivos de dados em análise. Como diferencial deste trabalho, tem-se que da determinação da localização das alterações/descontinuidades na forma de onda, foi possível obter janelas de dados com tamanhos flexíveis. Desta maneira, vários eventos sobre o sinal em análise puderam ser avaliados, bem como as durações associadas. Para isso, a Transformada Wavelet (TW) foi utilizada para realizar a detecção e também a localização destas alterações no tempo. Já para a classificação da ocorrência, ou das ocorrências, a TW, a Transformada de Fourier (TF) e o valor RMS foram empregados. A flexibilidade das janelas de dados permitiu uma adequada escolha de qual ferramenta poderia ser mais bem utilizada na classificação. Conforme implementado, cada uma destas ferramentas apresenta uma resposta e através de um módulo de decisão lógica é determinada a resposta final do algoritmo. Para validar o estudo, várias situações de distúrbios foram caracterizadas referentes a um sistema elétrico de distribuição real, implementado e simulado pela aplicação do software ATP (Alternative Transients Program). Os resultados obtidos foram excelentes tanto para a detecção e localização no tempo, como para a classificação e estimação da amplitude e duração dos eventos. / The objectives of this work are going since the presentation of the researches related to the analyses of power quality (PQ) disturbances through the proposal of an algorithm based on several tools for detection and location in time, as well as the automatic classification of these phenomena. It is proposed to determine not only the initial and the end of a unique event, but all the n possible disconformities in the waveform that can exist or occur in the data file registered data in analyses. As the differential of this research, from the location in time of the alteration/discontinuities in the waveforms, it was possible to obtain data windows with flexible sizes. So, several events on the signal were evaluated, as well as their specific timeduration. For this purpose, the Wavelet transform (WT) was used to reach the detection and localization in time of the waveform alterations. For the event classification, the TW, the Fourier transform (FT) and the Root Mean Square (RMS) value were used. The data window flexibility allowed an appropriate choice of which tool could be better used in the classification task. As implemented, each one of these tools presented an answer, and the final answer was obtained by using a logic decision module. To validate the study, some situations of disturbances were characterized using a real distribution system, implemented and simulated applying the ATP (Alternative Transients Program) software. The results were excellent in such a way for detection and localization in time, as well as for the automatic classification and estimation of the magnitude and the event duration.

This thesis consists of three parts: The first and second parts focus on long-time asymptotics of macroscopic and kinetic models respectively, while in the third part we connect these regimes using different scaling approaches. (1) Keller–Segel-type aggregation-diffusion equations: We study a Keller–Segel-type model with non-linear power-law diffusion and non-local particle interaction: Does the system admit equilibria? If yes, are they unique? Which solutions converge to them? Can we determine an explicit rate of convergence? To answer these questions, we make use of the special gradient flow structure of the equation and its associated free energy functional for which the overall convexity properties are not known. Special cases of this family of models have been investigated in previous works, and this part of the thesis represents a contribution towards a complete characterisation of the asymptotic behaviour of solutions. (2) Hypocoercivity techniques for a fibre lay-down model: We show existence and uniqueness of a stationary state for a kinetic Fokker-Planck equation modelling the fibre lay-down process in non-woven textile production. Further, we prove convergence to equilibrium with an explicit rate. This part of the thesis is an extension of previous work which considered the case of a stationary conveyor belt. Adding the movement of the belt, the global equilibrium state is not known explicitly and a more general hypocoercivity estimate is needed. Although we focus here on a particular application, this approach can be used for any equation with a similar structure as long as it can be understood as a certain perturbation of a system for which the global Gibbs state is known. (3) Scaling approaches for collective animal behaviour models: We study the multi-scale aspects of self-organised biological aggregations using various scaling techniques. Not many previous studies investigate how the dynamics of the initial models are preserved via these scalings. Firstly, we consider two scaling approaches (parabolic and grazing collision limits) that can be used to reduce a class of non-local kinetic 1D and 2D models to simpler models existing in the literature. Secondly, we investigate how some of the kinetic spatio-temporal patterns are preserved via these scalings using asymptotic preserving numerical methods.

L'attraction d'ondes dans des systèmes contra-propagatifs est un phénomène général, établi initialement en Physique dans le contexte de l'attraction de polarisation entre deux ondes contra-propagatives se propageant dans des fibres optiques. Ce phénomène a été observé expérimentalement, et ses propriétés étudiées via des simulations numériques. Les modèles qui s'y rattachent sont des systèmes hyperboliques d'équations aux dérivées partielles, avec des conditions aux bords dépendant du temps sur un intervalle fini. Le mécanisme sous-jacent peut être expliqué par l'existence de tores singuliers dans les équations stationnaires correspondantes. Le but de cette thèse est d'analyser en détail l'exemple le plus simple dans cette famille de modèles. Nous montrons que la plupart des phénomènes de processus d'attraction d'ondes sont en fait existants dans un modèle linéaire avec intéraction résonnante. Nous établissons l'existence et la régularité des solutions et analysons la relaxation vers la solution stationnaire qui caractérise les propriétés de l'attraction d'ondes. / Wave attraction in counter-propagating waves systems is a general phenomenon that was first established in Physics in the context of the attraction of the polarization between two counter-propagating waves in optical fibers. This phenomenon has been observed experimentally, and its properties were studied through numerical simulations. The models are Hamiltonian hyperbolic systems of partial differential equations, with time-dependent boundary conditions on a finite interval. The underlying mechanism can be traced back to the existence of singular tori in the corresponding stationary equations. In this work we analyze in detail the simplest example in this family of models. We show that most of the phenomena of the wave attraction process are already present in a linear model with resonant interaction. We establish the existence and regularity of the solutions and analyze the relaxation towards a stationary solution that features the wave attraction properties.

Lorsqu’un médecin diagnostique une pathologie chronique tel un diabète ou une artérite, pathologies choisies dans cette recherche, le patient entame, de fait, un processus d’apprentissage de la pathologie et de sa nouvelle vie avec ce diagnostic.Pourtant, ce processus diffère d’un patient à un autre et aboutit à des conduites diverses malgré des recommandations médicales consensuelles. Les professionnels de santé, en effet, ont des objectifs communs pour ces pathologies chroniques qui sont que les patients arrivent à avoir une alimentation équilibrée, pratiquent une activité physique quotidienne, s’abstiennent de tout comportement tabagique et prennent le traitement médicamenteux prescrit. Dans ce but, un certain nombre d’actions sont mises en place,de la campagne de santé publique au travail médical dans un cabinet libéral en passant par des programmes construits d’éducation. Ce que le patient fait grâce (ou malgré)cette éducation est l’objet de cette recherche.À la croisée des domaines de la santé et de l’éducation, nous avons choisi une méthodologie variée pour rendre compte à la fois de l’aspect anthropologique de cet apprentissage en considérant ce qui ne dépend pas du patient et à la fois de l’aspect didactique en observant le résultat des différentes situations sollicitées pour faire changer les patients. La première partie, centrée sur les aspects théoriques, montre la nécessité de considérer le corps dans l’éducation lorsqu’elle est dite thérapeutique.Pour comprendre ce qui est généralement peu ou pas interrogé par les acteurs de l’éducation thérapeutique, nous avons examiné l’ancrage historique des rapports entre le corps, la santé et l’éducation pour mieux étudier le « devenir malade » des patients considérés dans notre étude. Après un approfondissement historique du soin, de l’éducation puis du corps, les rapports actuels entre le corps et la santé ont été observés à l’aide des proverbes usuels, des livres en sciences humaines et sociales, de l’image publicitaire ainsi que des articles de presse. Les processus de transformation des corps malades pouvaient alors être compris selon cet ancrage et l’environnement éducatif dans lequel se situent actuellement les patients. Dans la troisième partie nous avons utilisé les récits des patients rencontrés. La mise en récit de la maladie est le dernier temps méthodologique. Grâce à l’histoire, à la compréhension du monde environnant les patients et à leur récit de vie, nous avons pu dégager des styles de discours. Trois grands styles sont repérés : celui des « experts » qui présentent une centration sur les savoirs,celui des « actifs » avec une centration sur l’activité physique et celui des « mangeurs »avec une centration sur l’alimentation. La compréhension de ces différents styles de discours est à mettre en lien avec les changements de conduites considérés sur le temps long de la pathologie chronique, dans le cadre de la dernière partie de ce travail. Ces modes de changements, tout au long du reste de la vie des patients, prennent différentes formes caractéristiques que nous avons pu dégager selon certains chemin explicatifs.L’ensemble des résultats permet de montrer l’intérêt d’interroger l’éducation thérapeutique actuelle et ses programmes ainsi que les concepts qui y sont attachés en utilisant le corps comme entrée. / As soon as a doctor diagnoses a chronic disease such as diabetes or arteritis, pathologies on which we shall focus in our research, patient begins a learning process of the pathology and their new life with this diagnosis. However this process differs from one patient to another and leads to diverse behaviours despite consistent medical recommendations. In fact, health professionals do seek common objectives: a balanced diet, daily physical activities, tobacco abstinence and a treatment medical that is followed. To reach this goal, various actions are put in place such as public health campaigns, work in the doctor’s office or Therapeutic Patient Education (TPE) programs. Our research focuses on how patients may react to (and benefit), from such education. At the junction of the health and education domains, we choose a diverse methodology to account for both the anthropological side of this learning experience, considering what does not depend on the patient, as well as its, the didactic side, thus observing the outcome of different pedagogical activities. The first part, focused on theory, demonstrates how considering the body is essential in education, especially in therapeutic education. To understand what is typically rarely considered, if not at all by TPE’s actors, we explore the historical roots of relationships between body, health and education to then better understand “becoming ill” as it relates to patients considered as part of our studies. After a historical investigation of cure, education and then the body, actual relationships between body and health are examined with using usual saying, books of Human and social sciences, advertisement pictures and newspaper articles. The transformation processes of sick bodies can then be understood from this viewpoint as well as through the patient’s educational environment. In the third part we used disease narratives from patients we have met. The disease storytelling within life stories is the last methodology step. In light of history, and through the patients’ environment and life stories, we could extract different speech styles that make sense when body speech is analysed in light of various anthropological data. Three major style types are identified: “experts” with centration on knowledge, “actives” with centration on physical activities and “eater” with centration on food. Understanding these style types requires considering behaviour changes in the long time of chronic pathologies, as done in the last part of our work. These different modes of change throughout the patients’ life present different characteristics, which we have been able to discern from various explanation paths. All results together allow us to demonstrate the value there is in questioning current TPE programs and its related concepts using the body as an input.

La motivation principale de cette thèse est l'étude du comportement en temps grand des solutions non-bornées d'équations de Hamilton-Jacobi visqueuses dans RN en présence d'un terme d'Ornstein-Uhlenbeck. Nous considérons la même question dans le cas d'une équation de Hamilton-Jacobi du premier ordre. Dans le premier cas, qui constitue le cœur de la thèse, nous généralisons les résultats de Fujita, Ishii et Loreti (2006) dans plusieurs directions. La première est de considérer des opérateurs de diffusion plus généraux en remplaçant le Laplacien par une matrice de diffusion quelconque. Nous considérons ensuite des opérateurs non-locaux intégro-différentiels de type Laplacien fractionnaire. Le second type d'extension concerne le Hamiltonien qui peut dépendre de x et est seulement supposé sous-linéaire par rapport au gradient. / The main aim of this thesis is to study large time behavior of unbounded solutions of viscous Hamilton-Jacobi equations in RN in presence of an Ornstein-Uhlenbeck drift. We also consider the same issue for a first order Hamilton-Jacobi equation. In the first case, which is the core of the thesis, we generalize the results obtained by Fujita, Ishii and Loreti (2006) in several directions. The first one is to consider more general operators. We first replace the Laplacian by a general diffusion matrix and then consider a non-local integro-differential operator of fractional Laplacian type. The second kind of extension is to deal with more general Hamiltonians which are merely sublinear.