The thesis explains the principle of optical conduction and describes its possible structures. It also deals with the automation of designing, projecting, constructing FTTH optical networks, processing RUIAN data, creating plugins into the QGIS geographic information system and implementing them using the Python programming language.

京都大学 / 0048 / 新制・課程博士 / 博士(農学) / 甲第20006号 / 農博第2190号 / 新制||農||1045(附属図書館) / 学位論文||H28||N5015(農学部図書室) / 33102 / 京都大学大学院農学研究科地域環境科学専攻 / (主査)教授 藤原 正幸, 教授 村上 章, 准教授 宇波 耕一 / 学位規則第4条第1項該当 / Doctor of Agricultural Science / Kyoto University / DFAM

Merton’s Optimal Investment-Consumption Problem is a classic optimization problem in finance. It aims to find the optimal controls for a portfolio with both risky and risk-less assets, inorder to maximize an investor’s utility function. One of the controls is the optimal allocationof wealth invested in a risky asset and the other control is the consumption rate. The problemis solved by using Dynamic Programming and the related Hamilton-Jacobi-Bellman equation.One of the disadvantages of the original problem is the consideration of constant volatility. Inthis thesis, we extend Merton’s problem considering the Grzelak-Oosterlee-Van Veeren modelthat describes the dynamics of a risky asset with stochastic volatility and stochastic interestrate. We derive the related Hamilton-Jacobi-Bellman for Merton’s problem considering theGrzelak-Oosterlee-Van Veeren model. We simulate the controls from Merton’s problem intwo different cases, one case where the volatility and interest rate are stochastic, following theGOVV-model. In the other case, the volatility and interest rate are assumed to be constant, asin Merton’s problem. The results obtained from simulations show that the case with stochasticvolatility and interest gave the same results as the case where the volatility and the interest ratewere assumed to be constant.

Denna studie ämnar att utreda hur det arv som Carl Michael Bellman lade grunden för levt vidare i efterföljande trubadurers diton. Förutom Bellman har Evert Taube, Cornelis Vreeswijk och Stefan Sundströms verk kartlagts. Med utgång från Bellman valdes fyra vanligt förekommande motiv: Vinet, Kärleken, Naturen samt Livet och döden. Genom att undersöka respektive trubadurers samlade verk kunde dessa sorteras in under de olika motiven. Bellman använde sig också av ett omfattande persongalleri, där olika karaktärer fick symbolisera dessa motiv. Således har trubadurernas persongallerier också inkluderats för analys. Studiens resultat visade att Bellmans vismodell återfinns i samtliga trubadurers verk. Denna modell har förvisso förändrats och förädlats för att passa respektive trubadurs egen stil, men de har alla en tydlig inspirationskälla. Slutligen presenterar denna studie ett antal didaktiska kopplingar. Bellman, Taube och Vreeswijk har blivit en del av Sveriges kulturella arv. Deras personporträtt går därmed att inkludera i svenskämnet på gymnasiet. Det är även möjligt att undersöka hur det svenska språket har förändrats genom att jämföra de olika visorna.

L'objectif de cette thèse est de développer la théorie du contrôle stochastique et ses applications en dynamique des populations. D'un point de vue théorique, nous présentons l'étude de problèmes de contrôle stochastique à horizon fini sur des processus de diffusion, de branchement non linéaire et de branchement-diffusion. Dans chacun des cas, nous raisonnons par la méthode de la programmation dynamique en veillant à démontrer soigneusement un argument de conditionnement analogue à la propriété de Markov forte pour les processus contrôlés. Le principe de la programmation dynamique nous permet alors de prouver que la fonction valeur est solution (régulière ou de viscosité) de l'équation de Hamilton-Jacobi-Bellman correspondante. Dans le cas régulier, nous identifions également un contrôle optimal markovien par un théorème de vérification. Du point de vue des applications, nous nous intéressons à la modélisation mathématique du cancer et de ses stratégies thérapeutiques. Plus précisément, nous construisons un modèle hybride de croissance de tumeur qui rend compte du rôle fondamental de l'acidité dans l'évolution de la maladie. Les cibles de la thérapie apparaissent explicitement comme paramètres du modèle afin de pouvoir l'utiliser comme support d'évaluation de stratégies thérapeutiques. / The main objective of this thesis is to develop stochastic control theory and applications to population dynamics. From a theoritical point of view, we study finite horizon stochastic control problems on diffusion processes, nonlinear branching processes and branching diffusion processes. In each case we establish a dynamic programmic principle by carefully proving a conditioning argument similar to the strong Markov property for controlled processes. Then we deduce that the value function is a (viscosity or regular) solution of the associated Hamilton-Jacobi-Bellman equation. In the regular case, we further identify an optimal control in the class of markovian strategies thanks to a verification theorem. From a pratical point of view, we are interested in mathematical modelling of cancer growth and treatment. More precisely, we build a hybrid model of tumor growth taking into account the essential role of acidity. Therapeutic targets appear explicitly as model parameters in order to be able to evaluate treatment strategies.

La simulation numérique est indissociable du calcul haute performance. Ces vingt dernières années,l'informatique a connu l'émergence d'architectures parallèles multi-niveaux. Exploiter efficacement lapuissance de calcul de ces machines peut s'avérer être une tâche délicate et requérir une expertise à la foistechnologique sur des notions avancées de parallélisme ainsi que scientifique de part la nature même desproblèmes traités.Le travail de cette thèse est pluri-disciplinaire s'appuyant sur la conception d'une librairie de calculparallèle réutilisable pour la résolution des équations Hamilton-Jacobi-Bellman. Ces équations peuventse retrouver dans des domaines diverses et variés tels qu'en biomédical, géophysique, ou encore robotiqueen l'occurence sur les applications de planification de mouvement et de reconstruction de formestri-dimensionnelles à partir d'images bi-dimensionnelles. Nous montrons que les principaux algorithmesnumériques amenant a résoudre ces équations telles que les méthodes de type fast marching, ne sont pasappropriés pour être efficaces dans un contexte parallèle. Nous proposons la méthode buffered fast iterativequi permet d'obtenir une scalabilité parallèle non obtenue jusqu'alors. Un des points sensibles relevésdans cette thèse est de parvenir à trouver une recette de compromis entre abstraction, performance etmaintenabilité afin de garantir non seulement une réutilisabilitédans le sens classique du domaine de génielogiciel mais également en terme de réutilisabilité séquentielle/parallèle / Numerical simulation is strongly bound with high performance computing. Programming scientificsoftwares requires at the same time good knowledge on the mathematical numerical models and alsoon the techniques to make them efficient on today's computers. Indeed, these last twenty years, wehave experienced the rising of multi-level parallel architectures. The work in this thesis dissertation ismultidisciplinary by designing a reusable parallel numerical library for solving Hamilton-Jacobi-Bellmanequations. Such equations are involved in various fields such as in biomedical, geophysics or robotics. Inparticular, we will show interests in path planning and shape from shading applications. We show thatthe methods to solve these equations such as the widely used fast marching method, are not designedto be used effciently in a parallel context. We propose a buffered fast iterative method which givesan interesting parallel scalability. This dissertation takes interest in the challenge to find compromisesbetween abstraction, performance and maintainability in order to combine both software reusability andalso sequential/parallel reusability. We propose code abstraction allowing algorithmic and data genericitywhile trying to keep a maintainable and performant code potentially parallelizable

Les problèmes de contrôle optimal se rencontrent dans l'industrie aérospatiale et dans la mécanique. Leur étude conduit à des difficultés mathématiques importantes. Dans cette thèse, nous nous intéressons aux conditions d'optimalité pour certains problèmes de contrôle avec des contraintes exprimées en termes d'inclusions différentielles. Nous considérons aussi des problèmes de contrôle associés aux modèles mathématiques issus de la Mécanique du Contact. Cette thèse est structurée en deux parties et six chapitres. La première partie, contenant les Chapitres 1, 2 et 3, représente un résumé de nos résultats, en Français. Nous y présentons les problèmes étudiés, les hypothèses sur les données, les notations utilisées ainsi que l’énoncé des principaux résultats. Les démonstrations sont omises. La deuxième partie du manuscrit représente la partie principale de la thèse. Elle contient les Chapitres 4, 5 and 6, chacun ayant fait l'objet d'une publication (parue ou soumise) dans une revue internationale avec comité de lecture.Nous y présentons nos principaux résultats, accompagnés des démonstrations et des références bibliographiques. / Optimal control problems arise in aerospace industry and in mechanics. They are challenging and involve important mathematical difficulties. In this thesis, we are interested to derive optimality conditions for optimal control problems with constraints under the form of differential inclusions. We also consider optimal control problems in the study of some boundary value problems arising in Contact Mechanics. The thesis is structured in two parts and six chapters. Part I represents an abstract of the main results, in French. It contains Chapters 1, 2 and 3. Here we present the problems we study together with the assumptions on the data, the notation and the statement of the main results. The proofs of these results are omitted, since them are presented in Part II of the manuscript.Part II represents the main part of the thesis. It contains Chapters 4, 5 and 6. Each of these chapters made the object of a paper published (or submitted) in an international journal. Here we present our main results, together with the corresponding proofs and bibliographical references.

Submitted by Maria Aparecida (cidazen@gmail.com) on 2017-09-04T13:42:58Z No. of bitstreams: 1 Watson Robert.pdf: 2699368 bytes, checksum: cf204eec3df50b251f4adbbbd380ffd0 (MD5) / Made available in DSpace on 2017-09-04T13:42:58Z (GMT). No. of bitstreams: 1 Watson Robert.pdf: 2699368 bytes, checksum: cf204eec3df50b251f4adbbbd380ffd0 (MD5) Previous issue date: 2014-08-21 / Due to the demand for high-performance equipments and the rising cost of energy, the industrial sector is developing equipments to attend minimization of the theirs operational costs. The implementation of these requirements generate a demand for projects and implementations of high-performance control systems. The optimal control theory is an alternative to solve this problem, because in its design considers the normative specifications of the system design, as well as those that are related to the operational costs. Motivated by these perspectives, it is presented the study of methods and the development of algorithms to the approximated solution of the Equation Hamilton-Jacobi-Bellman, in the form of discrete Riccati equation, model free and dependent of the dynamic system. The proposed solutions are developed in the context of adaptive dynamic programming that are based on the methods for online design of optimal control systems, Discrete Linear Quadratic Regulator type. The proposed approach is evaluated in multivariable models of the dynamic systems to evaluate the perspectives of the optimal control law for online implementations. / Devido a demanda por equipamentos de alto desempenho e o custo crescente da energia, o setor industrial desenvolve equipamentos que atendem a minimização dos seus custos operacionais. A implantação destas exigências geram uma demanda por projetos e implementações de sistemas de controle de alto desempenho. A teoria de controle ótimo é uma alternativa para solucionar este problema, porque considera no seu projeto as especificações normativas de projeto do sistema, como também as relativas aos seus custos operacionais. Motivado por estas perspectivas, apresenta-se o estudo de métodos e o desenvolvimento de algoritmos para solução aproximada da Equação Hamilton-Jacobi-Bellman, do tipo Equação Discreta de Riccati, livre e dependente de modelo do sistema dinâmico. As soluções propostas são desenvolvidas no contexto de programação dinâmica adaptativa (ADP) que baseiam-se nos métodos para o projeto on-line de Controladores Ótimos, do tipo Regulador Linear Quadrático Discreto. A abordagem proposta é avaliada em modelos de sistemas dinâmicos multivariáveis, tendo em vista a implementação on-line de leis de controle ótimo.

Cette thèse s'inscrit dans le domaine de l'analyse harmonique et plus exactement, des estimations à poids. Un intérêt particulier est porté aux estimations Lp à poids des transformées de Riesz sur des variétés Riemanniennes complètes ainsi qu'à l'optimalité des résultats en terme de la puissance de la caractéristique des poids. On obtient un premier résultat (en terme de la linéarité et de la non dépendance de la dimension) sur des espaces pas nécessairement de type homogène, lorsque p = 2 et la courbure de Bakry-Emery est positive. On utilise pour cela une approche analytique en exhibant une fonction de Bellman concrète. Puis, en utilisant des techniques stochastiques et une domination éparse, on démontre que les transformées de Riesz sont bornées sur Lp, pour p ∈ (1, +∞) et on déduit également le résultat précèdent. Enfin, on utilise un changement élégant dans la preuve précèdente pour affaiblir l'hypothèse sur la courbure et la supposer minorée. / The topics addressed in this thesis lie in the field of harmonic analysis and more pre- cisely, weighted inequalities. Our main interests are the weighted Lp-bounds of the Riesz transforms on complete Riemannian manifolds and the sharpness of the bounds in terms of the power of the characteristic of the weights. We first obtain a linear and dimensionless result on non necessarily homogeneous spaces, when p = 2 and the Bakry-Emery curvature is non-negative. We use here an analytical approach by exhibiting a concrete Bellman function. Next, using stochastic techniques and sparse domination, we prove that the Riesz transforms are Lp-bounded for p ∈ (1, +∞) and obtain the previous result for free. Finally, we use an elegant change in the precedent proof to weaken the condition on the curvature and assume it is bounded from below.

Conselho Nacional de Desenvolvimento Científico e Tecnológico / Nowadays, the Brazilian electric systems need the development of new researches and tools, in order to obtain a logic solution to maintain and improve the reliability and the quality of the power delivered to customers. Therefore, the study of the appropriate connection of distributed generation sources is an essential topic to be analyzed, since this process may provide positive impacts along the feeders. An appropriate DG site is an important aspect mentioned in the PRODIST (Proceedings of Electric Energy Distribution on Electrical National System), inside section 3. For now, the PRODIST is just an orientating tool established by the ANEEL - National Regulatory Agency of Electric Energy. It is important to observe that after the approval of PRODIST, this tool will be the standard for several processes considering planning and operation of distribution systems in Brazil. During the development of this work the main types of distributed energy sources were presented in order to observe their characteristics and their applications on distributions networks. Besides, the main effects of the DG operation inside three distribution system models were analyzed through the software DigSilent®, considering power losses and voltage levels. Moreover, this study intends to perform a multi-objective analysis defining some quantitative and qualitative parameters evaluated by specific softwares, according to the types of parameters. It is important to emphasize that the appropriate choice of these parameters is essential to support the final results, since a wrong choice or a lacking of an import parameter may provide undesirable outputs. These parameters were applied on the Bellman-Zadeh algorithm and the membership fuzzy functions, in order to find the appropriate DG site inside a distribution system model. These two methods are described separately. However, the methods are applied on a practical example together. Therefore it is possible to analyze the main characteristics of each method, emphasizing its applications on the multi-objective analysis. The developed methodology intends to provide positive effects in distribution networks and also work towards the planning of distribution systems. It is important to observe that the methodology presented in this study may be applied to distribution system feeders to find in which feeder will be the most appropriate DG location, and to any node inside a determined feeder providing a specific place for the appropriate DG site. / Avaliando o momento atual do setor elétrico brasileiro, percebe-se a crescente necessidade de se encontrar novos caminhos para o avanço dos setores de distribuição de energia elétrica. Desta forma a inserção de fontes de geração distribuída (GD) apresenta-se como uma alternativa estratégica para o desenvolvimento do sistema energético brasileiro. A adequada localização das fontes de GD é um importante aspecto citado nos Procedimentos de Distribuição de Energia Elétrica no Sistema Elétrico Nacional (PRODIST) Módulo 3, sendo este um instrumento orientativo criado pela Agência Nacional de Energia Elétrica (ANEEL). Durante o desenvolvimento deste trabalho foram pesquisados os principais tipos de fontes de geração distribuída com o objetivo de avaliar as características e aplicações das mesmas. Além disso, foram observadas as principais conseqüências da conexão de fontes de GD em três protótipos de sistemas de distribuição, considerando perdas de potência e níveis de tensão, simulados através do software DigSilent®. Com base em uma análise multicriterial foram definidos parâmetros quantitativos e qualitativos, avaliados previamente através de softwares específicos para cada tipo de parâmetro. Deve-se observar a importância da correta escolha destes parâmetros, pois a ausência de um único parâmetro, que possua uma elevada importância para o sistema em questão, pode comprometer a validade dos resultados obtidos. Estes parâmetros foram aplicados em uma metodologia utilizando o algoritmo de Bellman-Zadeh e os conjuntos fuzzy, com o objetivo de encontrar a localização mais adequada de uma fonte de geração distribuída em um sistema de distribuição. Estes dois métodos serão descritos separadamente e avaliados de forma conjunta, visando estabelecer suas principais características a suas diferentes aplicações em análises multicriteriais. A metodologia desenvolvida neste estudo visa o correto desenvolvimento dos sistemas de distribuição de média tensão, contribuindo para futuros planejamentos deste sistema. Outro importante fato a ser observado é que a metodologia proposta neste estudo pode ser aplicada tanto na análise de um sistema de distribuição com intuito de determinar qual é o alimentador mais adequado a se instalar a fonte de GD, quanto na análise de determinados alimentadores buscando especificamente qual é o local dentro de cada alimentador onde deve ser instalada a fonte de GD.