For a positive integer $r$ and graphs $F$, $G$, and $H$, the graph Ramsey arrow notation $F \longrightarrow (G)^H_r$ means that for every $r$-colouring of the subgraphs of $F$ isomorphic to $H$, there exists a subgraph $G'$ of $F$ isomorphic to $G$ such that all the subgraphs of $G'$ isomorphic to $H$ are coloured the same. Graph Ramsey theory is the study of the graph Ramsey arrow and related arrow notations for other kinds of ``graphs" (\emph{e.g.}, ordered graphs, or hypergraphs). This thesis surveys finite graph Ramsey theory, that is, when all structures are finite. One aspect surveyed here is determining for which $G$, $H$, and $r$, there exists an $F$ such that $F \longrightarrow (G)^H_r$. The existence of such an $F$ is guaranteed when $H$ is complete, whether ``subgraph" means weak or induced, and existence results are also surveyed when $H$ is non-complete. When such an $F$ exists, other aspects are surveyed, such as determining the order of the smallest such $F$, finding such an $F$ in some restricted family of graphs, and describing the set of minimal such $F$'s.

Les travaux de cette thèse concernent la modélisation et l'optimisation de chaînes d’approvisionnement en biomasses pour de futures bio-raffineries. En effet, des chaînes d'approvisionnement efficaces sont essentielles pour fournir aux installations de conversion, de façon régulière, des quantités suffisantes de biomasse de qualité à des prix raisonnables. Le problème est tout d'abord décrit puis modélisé.Un modèle de réseau et un modèle de données sont ensuite développés pour permettre de décrire la structure de la chaîne d'approvisionnement et ses données, sans affecter le modèle mathématique sous-jacent. Ce dernier (MILP) combine pour la première fois divers aspects, soit originaux, soit gérés séparément dans la littérature. A partir des demandes de la raffinerie, une résolution exacte précise les activités logistiques dans le réseau et les équipements nécessaires, afin de minimiser le coût total composé des coûts de récoltes, de transport et de stockage. Des études de cas sont décrites pour illustrer ce modèle de planification tactique multi-biomasse et multi-période. Un modèle plus compact est aussi élaboré pour traiter des instances de très grandes tailles. Il est illustré par une étude de cas réelle pour une bio-raffinerie prévue près de Compiègne. Pour finir, les développements effectués pour la mise en place d’un prototype logiciel d’aide à la décision sont présentés et des recommandations d’un futur logiciel commercial sont proposées / The research works of this thesis address the problem of modeling and optimizing biomass supply chains for biorefineries. Indeed, efficient supply chains are essential to provide conversion facilities with sufficient quantities of quality biomass at reasonable prices. The problem is described and modeled.A network model and a data model are developed to allow to describe the structure of the supply chain and its data, without affecting the underlying mathematical model. The latter is a mixed-integer linear programming that combines for the first time various aspects, either original or tackled separately in the literature. For given refinery needs, its exact resolution by CPLEX specifies the logistic activities in the network (amounts harvested, baled, transported, stored etc.) and the necessary equipment, in order to minimize a total cost including harvesting costs, transport costs and storage costs. Case studies are described to illustrate this multi-biomass and multi-period tactical planning model.A more compact model is also elaborated to cope with large-scale instances. It is illustrated using a real case study for a bio-refinery planned near Compiègne, France.Finally, the developments conducted for the implementation of a prototype of decision-support application are presented and recommendations for coming to a commercial software are proposed

Le formalisme des états graphes consiste à modéliser des états quantiques par des graphes. Ce formalisme permet l'utilisation des notions et des outils de théorie des graphes (e.g. flot, domination, méthodes probabilistes) dans le domaine du traitement de l'information quantique. Ces dernières années, cette modélisation combinatoire a permis plusieurs avancées décisives, notamment (i) dans la compréhension des propriétés de l'intrication quantique (ii) dans l'étude des modèles de calcul particulièrement prometteurs en terme d'implémentation physique, et (iii) dans l'analyse et la construction de protocoles de cryptographie quantique. L'objectif de cette thèse est d'étudier les propriétés graphiques émergeant des problématiques d'informatique quantique, notamment pour la simulation quantique. En particulier, l'étude des propriétés de causalité et de localité des états graphes, en étendant par exemple la notion existante de flot de causalité à une notion intégrant des contraintes de localité, permettrait d'ouvrir de nouvelles perspectives pour la simulation de systèmes quantiques à l'aide d'états graphes. Des connections formelles avec les automates cellulaires quantiques bruités pourront également émerger de cette étude. / Graph States formalism consist in using graphs to model quantum states. This formalism allows us to use notion and tools of graph theory (e.g. flow, domination, probabilistic methods) in quantum information processing. Last years, this combinatorial modelisation had lead to many decisiv breakthroughs, in particular (i) in the comprehension of the quantum entranglement properties (ii) in very promising in term of physical implementation quantum calculus model, and (iii) in the analysis and construction of quantum cryptography protocols. The goal of this thesis is to study the graphic properties emerging of those quantum information processing problematics, especially for quantum simulation. In particular, the properties of causality and locality in graph states, by extanding for exemple the existing notion of causality flows to a notion integring the locality constraints, would allow new perspectives for the quantum system simulation using graphs states. Formal connections with noisy quantum cellular automata would emerge from this study.

Neste estudo são apresentados os resultados do trabalho sobre simulações de redes de conexões complexas. Foram simuladas redes regulares, intermediárias e aleatórias com o número de nós e de conexões variando entre 103 e 5x103 e entre 2x104 e 105, respectivamente, e com probabilidade variando de 0 a 1 com passo de 0.1, com o enfoque na Teoria Espectral. Utilizando a linguagem C e o software Matlab, as redes são representadas pela sua matriz adjacência, com o objetivo de observar-se o comportamento de seus autovalores através de histogramas. A finalidade é a caracterização de redes complexas. Observa-se que a distribuição dos autovalores segue a lei semicircular de Wigner. / This study presents the results of the work about simulations of networks of complex connections. They were simulate regular networks, middlemen and aleatory with the number of nodes and of connections varying between 103 and 5x104 and between 2x104 and 105, respectively, and with probability varying from 0 to 1 with step of 0.1, with the focus in the Spectral Theory. Using the language C and the software Matlab, the networks are represented by its adjacency matrix, with the objective of observing the behavior of its eigenvalues through histograms. The purpose is the characterization of complex networks. Its observed that the eigenvalues distribution follows the Wigners semicircular law.

We investigate into the limitations of the sum-product algorithm for binary low density parity check (LDPC) codes having isolated short cycles. Independence assumption among messages passed, assumed reasonable in all configurations of graphs, fails the most in graphical structures with short cycles. This research work is a step forward towards understanding the effect of short cycles on error floors of the sum-product algorithm. We propose a modified sum-product algorithm by considering the statistical dependency of the messages passed in a cycle of length 4. We also formulate a modified algorithm in the log domain which eliminates the numerical instability and precision issues associated with the probability domain. Simulation results show a signal to noise ratio (SNR) improvement for the modified sum-product algorithm compared to the original algorithm. This suggests that dependency among messages improves the decisions and successfully mitigates the effects of length-4 cycles in the Tanner graph. The improvement is significant at high SNR region, suggesting a possible cause to the error floor effects on such graphs. Using density evolution techniques, we analysed the modified decoding algorithm. The threshold computed for the modified algorithm is higher than the threshold computed for the sum-product algorithm, validating the observed simulation results. We also prove that the conditional entropy of a codeword given the estimate obtained using the modified algorithm is lower compared to using the original sum-product algorithm.

La thèse étudie plusieurs problématiques centrales et actuelles de la finance moderne : la rationalité limitée des agents et leurs biais comportementaux vis-à-vis des valeurs nominales,le problème de la juste évaluation du prix des actions, la refonte du paysage de l'industrie post-négociation en Europe suite à l'introduction du projet de l'Euro système Target-2 Securities, ainsi que les modèles de défaut et les méthodes d’estimation des cycles de défaut pour un secteur donné. Les techniques employées sont variées: enquêtes sur données individuelles, économétrie, théorie des jeux, théorie des graphes, simulations de Monte-Carlo,chaînes de Markov cachées. Concernant l’illusion monétaire, les résultats confirment la robustesse des résultats d’études précédentes tout en dévoilant de nouvelles perspectives de recherche, par exemple tenter d’expliquer la disparité des réponses selon les caractéristiques individuelles des répondants,en particulier leur formation universitaire. L’étude du modèle de la Fed montre que la relation de long terme entre taux nominal des obligations d’Etat et rendement des actions n’est ni robuste, ni utile à la prédiction sur des horizons temporels réduits. L’étude sur Target 2 Securities a été confirmée par les faits. Enfin, le modèle d’estimation des défauts à partir de chaînes de Markov cachées fait preuve de bonnes performances dans un contexte européen, malgré la relative rareté des données pour sa calibration. / The thesis studies various themes that are central to modern finance : economic agents rationality and behavioural biases with respect to nominal values, the problem of asset fundamental valuation, the changing landscape of the European post-trade industry catalysed by the Eurosystem project Target 2 Securities, and models of defaults and methods to estimate defaults cycles for a given sector. Techniques employed vary: studies on individual data,econometrics, game theory, graph theory, Monte-Carlo simulations and hidden Markov chains. Concerning monetary illusion, results confirm those of previous study while emphasizing new areas for investigation concerning the interplay of individual characteristics, such as university education, and money illusion. The study of the Fed model shows that the long term relationship assumed between nominal government bond yield and dividend yield is neither robust, nor useful for reduced time horizons. The default model based on hidden Markov chains estimation gives satisfactory results in a European context, and this besides the relative scarcity of data used for its calibration.

Made available in DSpace on 2016-06-02T19:06:12Z (GMT). No. of bitstreams: 1 5931.pdf: 2655791 bytes, checksum: 6eafe016c175143a8d55692b4681adfe (MD5) Previous issue date: 2014-05-05 / Financiadora de Estudos e Projetos / Classification is a very important step in pattern recognition, as it aims to categorize objects from a set of inherent features, through its labeling. This process can be supervised, when there is a sample set of labeled training classes, semi-supervised, when the number of labeled samples is limited or nearly inexistent, or unsupervised, where there are no labeled samples. This project proposes to explore minimum information paths in graphs for classification problems, through the definition of a supervised, non-parametric, graph-based classification method, by means of a contextual approach. This method proposes to construct a graph from a set of training samples, where the samples are represented by vertices and the edges are links between samples that belongs to a neighborhood system. From the graph construction, the method calculates the local observed Fisher information, a measurement based on the Potts model, for all vertices, identifying the amount of information that each sample has. Generally, different class vertices when connected by an edge, have a high information level. After that, it is necessary to weight the edges by means of a function that penalizes connecting vertices with high information. During this process, it is possible to identify and select high information vertices, which will be chosen to be prototype vertices, namely, the nodes that define the classes boundaries. After the definition, the method proposes that each prototype sample conquer the remaining samples by offering the shortest path in terms of information, so that when a sample is conquered it receives the label of the winning prototype, occurring the classification. To evaluate the proposed method, statistical methods to estimate the error rates, such as Hold-out, K-fold and Leave-One- Out Cross-Validation will be considered. The obtained results indicate that the method can be a viable alternative to the existing classification techniques. / A classificação é uma etapa muito importante em reconhecimento de padrões, pois ela tem o objetivo de categorizar objetos a partir de um conjunto de características inerentes a ele, atribuindo-lhe um rótulo. Esse processo de classificação pode ser supervisionado, quando existe um conjunto de amostras de treinamento rotuladas que representam satisfatoriamente as classes, semi-supervisionado, quando o conjunto de amostras é limitado ou quase inexistente, ou não-supervisionado, quando não existem amostras rotuladas. Este trabalho propõe explorar caminhos de mínima informação em grafos para problemas de classificação, por meio da criação de um método de classificação supervisionado, não paramétrico, baseado em grafos, seguindo uma abordagem contextual. Esse método propõe a construção de um grafo a partir do conjunto de amostras de treinamento, onde as amostras serão representadas pelos vértices e as arestas serão as ligações entre amostras pertencentes a uma relação de adjacência. A partir da construção do grafo o método faz o calculo da informação de Fisher Local Observada, uma medida baseada no modelo de Potts, para todos os vértices, identificando o grau de informação que cada um possui. Geralmente vértices de classes distintas quando conectados por uma aresta possuem alta informação (bordas). Feito o calculo da informação, é necessário ponderar as arestas por meio de uma função que penaliza a ligação de vértices com alta informação. Enquanto as arestas são ponderadas é possível identificar e selecionar vértices altamente informativos os quais serão escolhidos para serem vértices protótipos, ou seja, os vértices que definem a região de borda. Depois de ponderadas as arestas e definidos os protótipos, o método propõe que cada protótipo conquiste as amostras oferecendo o menor caminho até ele, de modo que quando uma amostra é conquistada ela receba o rótulo do protótipo que a conquistou, ocorrendo a classificação. Para avaliar o método serão utilizados métodos estatísticos para estimar as taxas de acertos, como K-fold, Hold-out e Leave-one-out Cross- Validation. Os resultados obtidos indicam que o método pode ser um uma alternativa viável as técnicas de classificação existentes.

Este estudo apresenta resultados experimentais sobre a escalabilidade da formação de estruturas de coalizão para grafos reais que passam de 5 mil vértices. Um algoritmo heurístico simples denominado Algoritmo de Propagação para Formação de Estrutura de Coalizão (APFEC) com garantias experimentais é apresentado e sondado, com base em uma versão de propagação balanceada de rótulos para detecção de comunidades em grafos muito grandes. Os limites da proposta são avaliados, comparando-o com o estado-da-arte em relação aos algoritmos exatos (ODP-IP - A junção do algoritmo IP, baseado em representação de partições de inteiros, e ODP, programação dinâmica ótima) e heurístico (CFSS - Formação de coligação para grafos esparsos). Os experimentos são executados com um conjunto de 14 grafos do mundo real, e os resultados mostram que esta abordagem consegue calcular estruturas de coalizão de maneira rápida, mesmo na presença das limitações discutidas. Finalmente, os resultados preliminares são analisados considerando a influência da habilidade e a inter-relação entre os agentes na avaliação das coalizões. / This study presents experimental results on the scalability of the coalition’s structures formation for real graphs that go from 5 thousand vertices. A simple heuristic algorithm called Propagation Algorithm for Coalition Structure Formation (APFEC in Portuguese) with experimental guarantees is presented and probed, based on a balanced label propagation version for detection of communities in very large graphs. The limits of the proposal are evaluated, comparing it with the state-of-the-art in relation to the exact algorithms (ODP-IP - The IP algorithm, based on representation of integer partitions, and ODP, optimal dynamic programming) and heuristic (CFSS - Coalition Formation for Sparse Synergies). The experiments are performed with a set of 14 real-world graphs, and the results show that this approach can calculate coalition structures quickly, even in the presence of the limitations discussed. Finally, the preliminary results are analyzed considering the influence of the ability and the interrelation between the agents in the evaluation of the coalitions.

Made available in DSpace on 2015-03-03T15:15:30Z (GMT). No. of bitstreams: 1 GerdivaneFD_DISSERT.pdf: 2461999 bytes, checksum: afd653d46e87e83d8b0144e8086a3d19 (MD5) Previous issue date: 2014-02-21 / Coordena??o de Aperfei?oamento de Pessoal de N?vel Superior / In this work a study of social networks based on analysis of family names is presented. A basic approach to the mathematical formalism of graphs is developed and then main theoretical models for complex networks are presented aiming to support the analysis of surnames networks models. These, in turn, are worked so as to be drawn leading quantities, such as aggregation coefficient, minimum average path length and connectivity distribution. Based on these quantities, it can be stated that surnames networks are an example of complex network, showing important features such as preferential attachment and small-world character / Neste trabalho ? apresentado um estudo das redes sociais baseado na an?lise dos nomes de fam?lias. Faz-se uma abordagem b?sica do formalismo matem?tico dos grafos e em seguida apresenta-se os principais modelos te?ricos para as Redes Complexas com o objetivo de fundamentar a an?lise das redes dos sobrenomes. Estas, por sua vez, s?o trabalhadas de modo a serem extra?das as principais grandezas, tais como coe ciente de agrega??o, menor caminho m?dio e distribui??o de conectividades. Com base nestas grandezas, pode-se a rmar que as redes de sobrenomes s?o um exemplo de rede complexa, exibindo caracter?sticas importantes como liga??o preferencial e o car?ter de mundo pequeno.

Neste estudo são apresentados os resultados do trabalho sobre simulações de redes de conexões complexas. Foram simuladas redes regulares, intermediárias e aleatórias com o número de nós e de conexões variando entre 103 e 5x103 e entre 2x104 e 105, respectivamente, e com probabilidade variando de 0 a 1 com passo de 0.1, com o enfoque na Teoria Espectral. Utilizando a linguagem C e o software Matlab, as redes são representadas pela sua matriz adjacência, com o objetivo de observar-se o comportamento de seus autovalores através de histogramas. A finalidade é a caracterização de redes complexas. Observa-se que a distribuição dos autovalores segue a lei semicircular de Wigner. / This study presents the results of the work about simulations of networks of complex connections. They were simulate regular networks, middlemen and aleatory with the number of nodes and of connections varying between 103 and 5x104 and between 2x104 and 105, respectively, and with probability varying from 0 to 1 with step of 0.1, with the focus in the Spectral Theory. Using the language C and the software Matlab, the networks are represented by its adjacency matrix, with the objective of observing the behavior of its eigenvalues through histograms. The purpose is the characterization of complex networks. Its observed that the eigenvalues distribution follows the Wigners semicircular law.