Dans ce travail, notre contribution est double. Nous développons un cadre d’apprentissage stochastique distribué pour la recherche des équilibres de Nash dans le cas de fonctions de paiement dépendantes d’un état. La plupart des travaux existants supposent qu’une expression analytique de la récompense est disponible au niveau des noeuds. Nous considérons ici une hypothèse réaliste où les noeuds ont seulement une réalisation quantifiée de la récompense à chaque instant et développons un modèle stochastique d’apprentissage à temps discret utilisant une perturbation en sinus. Nous examinons la convergence de notre algorithme en temps discret pour une trajectoire limite définie par une équation différentielle ordinaire (ODE). Ensuite, nous effectuons une analyse de la stabilité et appliquons le schéma proposé dans un problème de commande de puissance générique dans les réseaux sans fil. Nous avons également élaboré un cadre de partage de ressources distribuées pour les réseaux –cloud– en nuage. Nous étudions la stabilité de l’évolution de l’équilibre de Nash en fonction du nombre d’utilisateurs. Dans ce scénario, nous considérons également le comportement des utilisateurs sociaux. Enfin nous avons également examiné un problème de satisfaction de la demande où chaque utilisateur a une demande propre à lui qui doit être satisfaite / As systems are becoming larger, it is becoming difficult to optimize them in a centralized manner due to insufficient backhaul connectivity and dynamical systems behavior. In this thesis, we tackle the above problem by developing a distributed strategic learning framework for seeking Nash equilibria under state dependent payoff functions. We develop a discrete time stochastic learning using sinus perturbation with the realistic assumption, that each node only has a numerical realization of the payoff at each time. We examine the convergence of our discrete time algorithm to a limiting trajectory defined by an ordinary differential equation (ODE). Finally, we conduct a stability analysis and apply the proposed scheme in a generic wireless networks. We also provide the application of these algorithms to real world resource utilization problems in wireless. Our proposed algorithm is applied to the following distributed optimization problems in wireless domain. Power control, beamforming and Bayesian density tracking in the interference channel. We also consider resource sharing problems in large scale networks (e.g. cloud networks) with a generalized fair payoff function. We formulate the problem as a strategic decision-making problem (i.e. a game). We examine the resource sharing game with finite and infinite number of players. Exploiting the aggregate structure of the payoff functions, we show that, the Nash equilibrium is not an evolutionarily stable strategy in the finite regime. Then, we introduce a myopic mean-field response where each player implements a mean-field-taking strategy. We show that such a mean-field-taking strategy is evolutionarily stable in both finite and infinite regime. We provide closed form expression of the optimal pricing that gives an efficient resource sharing policy. As the number of active players grows without bound, we show that the equilibrium strategy converges to a mean-field equilibrium and the optimal prices for resources converge to the optimal price of the mean-field game. Then, we address the demand satisfaction problem for which a necessary and sufficiency condition for satisfactory solutions is provided

Nous entendons confronter pratique des mathématiques et réflexions sur les mathématiques dans l'œuvre de Weyl. Nous étudierons : (a) ses monographies en analyse complexe, en relativité générale et en mécanique quantique, (b) les articles en lien avec ces ouvrages, (c) certains de ses cours, (d) sa correspondance avec divers scientifiques, principalement A. Einstein, E. Cartan, J. von Neumann. Nous voulons savoir si les théories mathématiques qu'il investit conditionnent ses positions sur les fondements des mathématiques. Inversement, nous montrerons que les philosophies auxquelles il se réfère – essentiellement le criticisme kantien, l'idéalisme fichtéen et la phénoménologie de Husserl – conditionnent ses recherches. Tout d'abord, nous reviendrons sur Die Idee der Riemannschen Fläche (première éd. 1913). Nous montrerons qu'il opte alors pour un formalisme mitigé. Il se revendique de deux traditions incarnées par Klein et par Hilbert. Ensuite, nous étudierons les éditions successives de Raum, Zeit, Materie (1918-1923). Nous aborderons le projet d'une géométrie purement infinitésimale qui permet à Weyl de proposer une théorie unifiée des champs, cette dernière étant réfutée par Einstein, Pauli, Reichenbach, Hilbert and Eddington. Nous décrirons aussi la construction et la résolution de son « problème de l'espace » (1921-1923). Nous indiquerons comment la référence aux philosophies de Fichte et de Husserl permet d'éclairer ces deux projets. Enfin, nous commenterons l'article de Weyl sur les groupes de Lie (1925-1926) ainsi que son ouvrage Gruppentheorie und Quantenmechanik (1928, 1931). Son article sur les groupes de Lie manifeste la voie moyenne entre formalisme et intuitionnisme qu'il adopte en 1924. Son ouvrage en mécanique quantique incarne quant à lui un « tournant empirique » dans son épistémologie qu'il conviendra de comparer \`a l'« empirisme logique ». / Our purpose consists in comparing Weyl's mathematical practice with his philosophical reflections on mathematics. We will study (a) his monographs on complex analysis, general relativity and quantum mechanics, (b) the articles which are linked to these books, (c) some of his lecture courses, (d) his correspondence with different scientists, mainly A. Einstein, E. Cartan, J. von Neumann. We will show that his mathematical research has a strong influence on the different stands he successively takes regarding the foundations of mathematics. Conversely, we will show that the philosophical systems he refers to (mainly kantian criticism, fichtean idealism and husserlian phenomenology) have a real impact on his investigations in mathematics. We will first analyse Die Idee der Riemannschen Fläche (first edition 1913). In this book, Weyl seems to take up a formalist point of view, but this is partly true. In fact, he is influenced by two traditions respectively embodied by Hilbert and Klein. Then, we will study the successive editions of Raum, Zeit, Materie (1918-1923). We will describe Weyl's project of a “purely infinitesimal geometry”. Thanks to this geometrical framework, he builds a unified fields theory, which will be disproved by Einstein, Pauli, Reichenbach, Hilbert and Eddington. During this short period, Weyl also constructs and solves the so-called space problem (1921-1923). Weyl's references to Fichte and Husserl have a significant impact on these two projects. Finally, we will comment Weyl's main article on Lie groups (1925-1926) and his monograph on quantum mechanics, i.e. Gruppentheorie und Quantenmechanik (1rst ed. 1928, 2nd ed. 1931). Weyl's article on Lie groups is in accordance with his compromise between intuitionism and formalism (1924). On the other hand, Weyl's book on quantum mechanics encapsulates an “empirical turn” in his epistemology, which will be compared with the so-called empirical logicism.

Orientador: Prof. Dr. Marco Antonio Bueno Filho / Dissertação (mestrado) - Universidade Federal do ABC, Programa De Pós-Graduação em Ensino, História, Filosofia das Ciências e Matemática, 2017. / Este estudo teve como objetivo identificar os conteúdos conceituais e os processos cognitivos gerais mobilizados durante a resolução de tarefas que envolvem a interface entre os campos de conceitos da Cinética Química e da Estrutura e Reatividade por estudantes de graduação sob a luz da Teoria dos Campos Conceituais. Em face disso, buscou-se responder: i. A interação entre estudantes e entre estudantes e professor, enquanto estratégia de ensino para a discussão de transformações enzimáticas, pode mobilizar e entrelaçar conceitualmente o Campo Conceitual Estrutural (CCE) ao do Campo da Cinética Química (CCC)? ii. Em caso afirmativo, quais invariantes operatórios são importantes na interface entre o Campo Conceitual Estrutural (CCE) e o Campo Conceitual da Cinética Química (CCC)? iii. Considerando que as resoluções de tarefas em Bioquímica podem envolver estes campos, qual é a dinâmica ou a contribuição destes campos nos esquemas de ação dos estudantes? Para responder essas questões, um minicurso extracurricular com foi oferecido com tarefas experimentais investigativas onde os estudantes participantes deveriam relacionar conhecimentos conceituais do Campo Estrutural ao Campo da Cinética Química. As explicações sobre estas tarefas foram registradas em vídeo. Estes registros foram analisados com o auxílio do software Transana® com vistas a categorização de acordo com Mullins (2008) e por Justi e Gilbert (1999a; 1999b). Os dados também foram submetidos à análise de correlação entre os conceitos e entre conceitos e as operações do pensamento utilizando-se o coeficiente de Jaccard/Tanimoto (TAN et al., 2006). Os resultados mostraram que os estudantes possuem dificuldade para estabelecer relações conceituais pertinentes e que estas relações quando existentes são caracterizadas pelo estabelecimento de relações de dependência, pela elaboração de hipóteses e pela percepção da simultaneidade de conceitos relativos aos Campos Conceituais da Cinética Química e da Estrutura e Reatividade como principais operações de pensamento. É importante salientar a constatação de esquemas individuais e coletivos, assim como se ressalta, também, a importância da mediação constante do professor no momento do aprendizado e no manejo dos conceitos durante a resolução de tarefas em sala de aula. / This study is devoted to identify the conceptual contents and general cognitive processes mobilized during the resolution of tasks that involve the interface between the fields of concepts of Chemical Kinetics and Structure and Reactivity by undergraduate students under the light of Conceptual Field Theory. In this context, it was sought to answer: i. Can the interplay among students and between students and teachers, as a teaching strategy for discussing enzymatic transformations, conceptually mobilize and interweave the Structural Conceptual Field (CCE) to that of the Field of Chemical Kinetics (CCC)?. ii. If so, which operative invariants are important at the interface between the Structural Conceptual Field (CCE) and the Conceptual Field of Chemical Kinetics (CCC)? iii. Considering that task resolutions in Biochemistry may involve these fields, what are the dynamics or contributions of these fields in the student action schemes? In order to explore these questions, an extracurricular mini-course containing experimental research tasks was offered in which the participating students should relate conceptual knowledge of the Structural Field to the Field of Chemical Kinetics. Explanations of these tasks were recorded on video. These records were analyzed with the help of Transana® software for categorization according to Mullins (2008) and by Justi and Gilbert (1999a; 1999b). The data were also submitted to the correlation analysis throughout concepts and also between concepts and thought operations using the Jaccard / Tanimoto coefficient (TAN et al., 2006). The results showed that students have difficulty in establishing pertinent conceptual relations and that the establishment of dependency relations characterizes these relations when they exist, by the elaboration of hypotheses and by the perception of the simultaneity of concepts related to Conceptual Fields of Chemical Kinetics and Structure and Reactivity as main operations of thought. It is important to emphasize the observation of individual and collective schemes, as well as emphasizing the importance of constant teacher arbitration in the moment of learning and in the concepts¿ handling during the resolution of tasks in the classroom.