Orientador: Daniela Renata Cantane / Resumo: Este trabalho utiliza um modelo epidemiológico para analisar o comportamento de crises bancárias que possuem origem em um determinado país e são propagadas para outros países atingindo proporções mundiais. O modelo matemático epidemiológico Suscetíveis, Infectados e Recuperados (SIR) empregado permite simular a dinâmica da crise separando os países em três estados: suscetíveis, infectados e recuperados, em cada instante de tempo, além de prever a extensão da crise. Os parâmetros do modelo são obtidos da literatura para cada país envolvido e a crise segue uma dinâmica diferente dependendo do país de origem. Uma breve descrição da importância dos bancos em nível macroeconônico e suas funções básicas são apresentadas. Também são apresentadas algumas definições desta crise, denominada crise sistêmica, bem como os canais de transmissão de como um banco com problemas financeiros, denominado infectado, transmite esta condição para outro. Considerada a possibilidade de uma crise sistêmica, o Banco Central deve intervir nos bancos com problemas. Esta tarefa pode ser modelada como um problema de controle ótimo inserindo uma variável de controle no modelo SIR, que representa a intervenção do Banco Central, e uma função objetivo, em que o custo dessa intervenção deve ser minimizado. O objetivo deste trabalho é investigar um modelo de otimização aplicado ao risco bancário e propor o método heurístico \textit{Variable Neighbourhood Search} (VNS) para resolução do problema de controle ótimo... (Resumo completo, clicar acesso eletrônico abaixo) / Abstract: This work uses an epidemiological model to analyze the behavior of bank crises that originate in a given country and are propagated to other countries reaching worldwide proportions. The epidemiological mathematical model Susceptible, Infected and Recovered (SIR) used allows to simulate the dynamics of the crisis separating the countries in three states: susceptible, infected and recovered, in each instant of time, in addition to predicting the extent of the crisis. The model parameters are obtained from the literature for each country involved and the crisis follows a different dynamic depending on the country of origin. A brief description of the importance of banks at the macroeconomic level and their basic functions is presented. Some definitions of this crisis, called systemic crisis, are also presented, as well as the transmission channels of how a bank with financial problems, called infected, transmits this condition to another. Considering the possibility of a systemic crisis, the Central Bank must intervene in troubled banks. This task can be xiv modeled as an optimal control problem by inserting a control variable in the SIR model, which represents Central Bank intervention, and an objective function involving the cost of this intervention and must be minimized. The objective of this work is to investigate an optimization model applied to banking risk and propose the Variable Neighborhood Search (VNS) heuristic method to solve the proposed optimal control problem. ... (Complete abstract click electronic access below) / Mestre

Dans cette thèse nous avons étudié la diffusion de l'information dans les grands graphes de terrain, en se focalisant sur les patterns structurels de la propagation. Sur le plan empirique, il s'est avéré difficile de capturer la structure des cascades de diffusion en termes de mesures simples. Sur le plan théorique, l'approche classique consiste à étudier des modèles stochastiques de contagion. Néanmoins, l'analyse formelle de ces modèles reste limité, car les graphes de terrain ont généralement une topologie complexe et le processus de diffusion se produit dans une fenêtre de temps limitée. Par conséquent, une meilleure compréhension des données empiriques, des modèles théoriques et du lien entre les deux est également cruciale pour la caractérisation de la diffusion dans les grands graphes de terrain. Après un état de l'art sur les graphes de terrain et la diffusion dans ce contexte au premier chapitre, nous décrivons notre jeu de données et discutons sa pertinence au chapitre 2. Ensuite, dans le chapitre 3, nous évaluons la pertinence du modèle SIR simple et de deux extensions qui prennent en compte des hétérogénéités de notre jeu de données. Dans le chapitre 4, nous explorons la prise en compte du temps dans l'évolution du réseau sous-jacent et dans le modèle de diffusion. Dans le chapitre 5, nous évaluons l'impacte de la structure du graphe sous-jacent sur la structure des cascades de diffusion générées avec les modèles étudiés dans les chapitres précédents. Nous terminons la thèse par un bilan des résultats et des perspectives ouvertes par les travaux menés dans cette thèse. / Understanding information diffusion on complex networks is a key issue from a theoretical and applied perspective. Epidemiology-inspired SIR models have been proposed to model information diffusion. Recent papers have analyzed this question from a data-driven perspective. We complement these findings investigating if epidemic models calibrate with a systematic procedure are capable of reproducing key spreading cascade properties. We first identify a large-scale, rich dataset from which we can reconstruct the diffusion trail and the underlying network. Secondly, we examine the simple SIR model as a baseline model and conclude that it was unable to generate structurally realistic spreading cascades. We found the same result examining model extensions to which take into account heterogeneities observed in the data. In contrast, other models which take into account time patterns available in the data generate qualitatively more similar cascades. Although one key property was not reproduced in any model, this result highlights the importance of taking time patterns into account. We have also analyzed the impact of the underlying network structure on the models examined. In our data the observed cascades were constrained in time, so we could not rely on the theoretical results relating the asymptotic behavior of the epidemic and network topological features. Performing simulations we assessed the impact of these common topological properties in time-bounded epidemic and identified that the distribution of neighbors of seed nodes had the most impact among the investigated properties in our context. We conclude discussing identifying perspectives opened by this work.

This monograph is an analytical study of the character of Sir John Falstaff in The First and Second Parts of Henry The Fourth, and The Merry Wives of Windor, by William Shakespeare, its purpose being to assist in an accurate portrayal of the character upon the stage. It is, then, an acting thesis in three parts: a study of the historical element of the character, analysis of the masterpieces as created by Shakespeare, and an intensive research of the character as portrayed by the best actors from Shakespeare's original production in the Globe Theatre to the present day.

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In mathematical epidemiology, disease transmission is commonly assumed to behave in accordance with the law of mass action; however, other disease incidence terms also exist in the literature. A homogeneous Susceptible-Infectious-Removed (SIR) model with a generalized incidence term is presented along with analytic and numerical results concerning effects of the generalization on the global disease dynamics. The spatial heterogeneity of the metapopulation with nonrandom directed movement between populations is incorporated into a heterogeneous SIR model with nonlinear incidence. The analysis of the combined effects of the spatial heterogeneity and nonlinear incidence on the disease dynamics of our model is presented along with supporting simulations. New global stability results are established for the heterogeneous model utilizing a graph-theoretic approach and Lyapunov functions. Numerical simulations confirm nonlinear incidence gives raise to rich dynamics such as synchronization and phase-lock oscillations.

This thesis examines the Lady of the Lake as an active chivalric player in the thirteenth century Lancelot-Grail Cycle (also known as the Prose Lancelot) and in Thomas Malory's fifteenth-century Le Morte Darthur. To study the many codes of chivalry, particularly in regard to women, I use two popular chivalric handbooks from the Middle Ages: Ramon Lull's Book of Knighthood and Chivalry, Geoffroi de Charny'sKnight's Own Book of Chivalry. Traditionally, the roles of women in medieval chivalry are passive, and female characters are depicted as objects to win or to inspire knights to greatness. The Lady of the Lake, I argue, uses her supernatural origins and nature to break with female chivalric conventions and become an instructress of chivalry to King Arthur's knights. As a purely human character, her power would be limited. As a guardian fairy and/or enchantress, the Lady is allowed to exercise more autonomy

Thèse numérisée par la Direction des bibliothèques de l'Université de Montréal.

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