L’optimisation de l’opération des réseaux mobiles a toujours été d'un très grand intérêt pour les opérateurs, surtout avec une augmentation rapide du trafic mobile, des attentes qualité de service encore plus élevées des utilisateurs, et l’émergence de nouveaux services requérant des contraintes spécifiques et différentes. Le concept de gestion autonome des réseaux (SON) a été introduit par la 3rd Generation Partnership Project comme étant une solution prometteuse pour simplifier l’opération et la gestion des réseaux complexes. Aujourd’hui, plusieurs fonctions SON sont déjà déployées dans les réseaux. Cependant, les actions conduites par les fonctions SON dans le réseau dépendent de la configuration de l’algorithme même de ces fonctions, et aussi du contexte du réseau et de l’environnement ou cette fonction est déployée. D’autre part, un réseau radio mobile auto-organisant serait idéalement un réseau où toutes les fonctions autonomes (SON) fonctionnent de manière coordonnée et cohérente pour répondre à des objectifs de haut niveau de l’opérateur. L’entité autonome serait donc le réseau capable de s’autogérer pour répondre à une stratégie globale de l’opérateur, exprimée en termes d’objectifs de haut niveau de l’opérateur. A cette fin, nous proposons dans cette thèse une approche qu'on appel « Cognitive Policy Based SON Management » (C-PBSM). Le C-PBSM est capable d’apprendre des configurations optimales des fonctions SON selon les exigences de l’opérateur. Il a également la capacité d’améliorer sa décision au cours du temps en apprenant de son expérience passée, et de s’adapter avec les changements de l’environnement. Nous étudions plusieurs approches pour mettre en place la boucle cognitive en se basant sur l’apprentissage par renforcement (RL). Nous analysons la convergence et la scalabilité de ces approches et proposons des solutions adaptées. Nous prenons en compte la non stationnarité des réseaux, notamment la variation de trafic. Nous proposons également des solutions pour mettre en œuvre un apprentissage collaboratif et un transfert des connaissances. Une architecture SDN (software defined networks) est proposée pour le déploiement des agents d’apprentissage dans le réseau. / The pressure on operators to improve the network management efficiency is constantly growing for many reasons: the user traffic that is increasing very fast, higher end users expectations, emerging services with very specific requirements. Self-Organizing Networks (SON) concept was introduced by the 3rd Generation Partnership Project as a promising solution to simplify the operation and management of complex networks. Many SON modules are already being deployed in today’s networks. Such networks are known as SON enabled networks, and they have proved to be useful in reducing the complexity of network management. However, SON enabled networks are still far from realizing a network that is autonomous and self-managed as a whole. In fact, the behavior of the SON functions depends on the parameters of their algorithm, as well as on the network environment where it is deployed. Besides, SON objectives and actions might be conflicting with each other, leading to incompatible parameter tuning in the network. Each SON function hence still needs to be itself manually configured, depending on the network environment and the objectives of the operator. In this thesis, we propose an approach for an integrated SON management system through a Cognitive Policy Based SON Management (C-PBSM) approach, based on Reinforcement Learning (RL). The C-PBSM translates autonomously high level operator objectives, formulated as target Key Performance Indicators (KPIs), into configurations of the SON functions. Furthermore, through its cognitive capabilities, the C-PBSM is able to build its knowledge by interacting with the real network. It is also capable of adapting with the environment changes. We investigate different RL approaches, we analyze the convergence time and the scalability and propose adapted solutions. We tackle the problem of non-stationarity in the network, notably the traffic variations, as well as the different contexts present in a network. We propose as well an approach for transfer learning and collaborative learning. Practical aspects of deploying RL agents in real networks are also investigated under Software Defined Network (SDN) architecture.

Les membranes d'alumine nano-poreuses suscitent depuis quelques années un grand intérêt dans la synthèse de nano-objets. Ces membranes présentent des pores très verticaux naturellement organisés en un réseau hexagonal (structure en nid d'abeilles). Le diamètre des pores peut varier entre 20 et 200nm espacés de 60 à 540nm et l'épaisseur de la membrane peut varier de 100nm à plusieurs centaines de µm. Durant ces travaux de thèse, deux approches ont été envisagées pour synthétiser des nano-structures. La première consiste à utiliser ces membranes comme nano-réservoirs. La couche barrière formée au fond de la membrane dont l'épaisseur est environ égale au diamètre des pores est diminuée à 10nm par voie chimique. Puis des dépôts de divers matériaux (Au, Co, Si) ont été réalisés dans des membranes avec des pores de 180nm et 40nm préalablement dégazées. Ces objets 3D ont été fabriqués sous ultra-vide (10-10 mbar), concfinés à l'intérieur des nano-réservoirs, transparents aux électrons. Les études en TEM permettent d'avoir accès à la morphologie des nanoparticules, qui se révèlent être cristallines, selon plusieurs directions cristallographiques. En vue plane, perpendiculairement à l'interface, pour ceux déposés au fond du nano-réservoir et en vue transverse pour ceux déposés sur les parois. Il a par ailleurs été possible de réaliser des études de recuits in-situ en température (RT à 1000° C) dansle TEM pour des particules d'or. La seconde approche repose sur l'utilisation des membranes ouvertes comme masque pour l'évaporation. Cette technique permet de dupliquer le motif de la membrane sur le substrat préalablement nettoyé pour former un réseau de nanoparticules correspondant au matériau déposé. Nous avons réalisé de manière reproductible, sous ultravide,des réseaux de plots d'or à l'aide de membranes dont le diamètre des pores est de 180 nm / The nanoporous alumina membrane rise in recent years a great interest in the synthesis of nanoobjects. These membranes have pores naturally very vertical organized in a hexagonal lattice(honeycomb structure). The pore diameter may vary between 20 and 200nm spaced 60 to 540nmand the thickness of the membrane can vary from 100nm several hundred microns. During this thesis work, two approaches have been explored to synthesize nano-structures. The first is touse these membranes as nano-tanks. The barrier layer formed at the bottom of the membrane whose thickness is about equal to the diameter of pores is reduced to 10nm by chemical etching. Then deposits from materials (Au, Co, Si) were performed in membranes with pores of 180nmand 40nm previously degassed. These 3D objects have been produced under ultra-high vacuum(10-10 mbar), confined within nano-tanks, transparent to electrons. TEM studies allow accessto the morphology of nanoparticles, which are proving to be crystallin, according to several crystallographic directions. In plane view perpendicular to the interface for those deposited atthe bottom of the nano-tank and cross-sectional view for those deposited on the walls. It has also been possible to perform studies of in-situ annealing (RT to 1000° C) in TEM of Au particles. The second approach relies on the use of membranes opened as an evaporation mask. This technique allows to duplicate the pattern of the membrane to the substrate previously cleaned, to form a network of nanoparticles corresponding to the material deposited. We have achieved reproducible, gold dot arrays, under UHV conditions using membranes with a pore size of 180 nm.

Mémoire numérisé par la Division de la gestion de documents et des archives de l'Université de Montréal.

Dans leur célèbre article de 1987, les physiciens Per Bak, Chao Tang et Kurt Wiesenfeld ont montré que certains systèmes complexes, composés d'un nombre important d'éléments en interaction dynamique, évoluent vers un état critique, sans intervention extérieure. Ce phénomène, appelé criticalité auto-organisée, peut être observé empiriquement ou simulé par ordinateur pour de nombreux modèles. Cependant leur analyse mathématique est très ardue. Même des modèles dont la définition est apparemment simple, comme les modèles décrivant la dynamique d'un tas de sable, ne sont pas bien compris mathématiquement. Le but de cette thèse est la construction d'un modèle de criticalité auto-organisée, qui est aussi simple que possible, et qui est accessible à une étude mathématique rigoureuse. Pour cela, nous modifions le modèle d'Ising Curie-Weiss généralisé en introduisant un contrôle automatique du paramètre de température. Pour une classe de distributions symétriques satisfaisant une certaine condition d'intégrabilité, nous montrons que la somme Sn des variables aléatoires du modèle a le comportement typique du modèle d'Ising Curie-Weiss généralisé critique: les fluctuations sont d'ordre n^(3/4) et la loi limite est C exp(- lambda*x^4) dx, où C et lambda sont des constantes strictement positives. Notre étude nous a menés à généraliser ce modèle dans plusieurs directions : cas de la dimension supérieure, fonctions d'interactions plus générales, extension à des auto-interactions menant à des fluctuations d'ordre n^(5/6). Nous étudions aussi des modèles dynamiques dont la distribution invariante est la loi de notre modèle d'Ising Curie-Weiss de criticalité auto-organisée. / In their famous 1987 article, Per Bak, Chao Tang and Kurt Wiesenfeld showed that certain complex systems, composed of a large number of dynamically interacting elements, are naturally attracted by critical points, without any external intervention. This phenomenon, called self-organized criticality, can be observed empirically or simulated on a computer in various models. However the mathematical analysis of these models turns out to be extremely difficult. Even models whose definition seems simple, such as the models describing the dynamics of a sandpile, are not well understood mathematically. The goal of this thesis is to design a model exhibiting self-organized criticality, which is as simple as possible, and which is amenable to a rigorous mathematical analysis. To this end, we modify the generalized Ising Curie-Weiss model by implementing an automatic control of the inverse temperature. For a class of symmetric distributions whose density satisfies some integrability conditions, we prove that the sum Sn of the random variables behaves as in the typical critical generalized Ising Curie-Weiss model: the fluctuations are of order n^(3/4) and the limiting law is C exp(- lambda*x^4) dx where C and lambda are suitable positive constants. Our study led us to generalize this model in several directions: the multidimensional case, more general interacting functions, extension to self-interactions leading to fluctuations with order n^(5/6). We also study dynamic models whose invariant distribution is the law of our Curie-Weiss model of self-organized criticality.

As teorias científicas surgiram da necessidade do homem entender o funcionamento das coisas. Novos métodos e técnicas são então criados com o objetivo não só de melhor compreender, mas também de desenvolver essas próprias teorias. Nesta dissertação, vamos estudar várias dessas técnicas (aqui chamadas de algoritmos) com o objetivo de obter estados fundamentais em sistemas de spin e de revelar suas possíveis propriedades de auto-organização crítica. No segundo capítulo desta dissertação, apresentamos os algoritmos de otimização: simulated annealing, algoritmo genético, otimização extrema (EO) e evolutivo de Bak-Sneppen (BS). No terceiro capítulo apresentamos o conceito de criticalidade auto-organizada (SOC), usando como exemplo o modelo da pilha de areia. Para uma melhor compreensão da importância da criticalidade auto-organizada, apresentamos vários outros exemplos de onde o fenômeno é observado. No quarto capítulo apresentamos o modelo de relógio quiral de p-estados que será nosso sistema de testes. No caso unidimensional, determinamos a matriz de transferência e utilizamos o teorema de Perron-Frobenius para provar a inexistência de transição de fase a temperaturas finitas a temperaturas finitas. Esboçamos os diagramas de fases dos estados fundamentais que obtivemos de maneira analítica e numérica para os casos de p = 2, 3, 4, 5 e 6, no caso numérico fazendo uso do algoritmo de Bak-Sneppen com sorteio (BSS). Apresentamos ainda um breve estudo do número de mínimos locais para o modelo de relógio quiral de p-estados, para os casos de p = 3 e 4. Por último, no quinto capítulo, propomos uma dinâmica Bak-Sneppen com ruído (BSR) como uma nova técnica de otimização para tratar sistemas discretos. O ruído é introduzido diretamente no espaço de configuração de spins. Conseqüentemente, o fitness (adaptabilidade) passa a assumir valores contínuos, num pequeno intervalo em torno do seu valor original (discreto). Os resultados dessa dinâmica indicam a presença de criticalidade auto-organizada, evidenciada pelo decaimento em leis de potências das correlações espacial e temporal. Também estudamos o método EO e obtivemos uma confirmação numérica de que sua dinâmica exibe um comportamento não crítico com alcance espacial infinito e decaimento exponencial das avalanches. Finalmente, para o modelo de relógio quiral, comparamos a eficiência das três dinâmicas (EO, BSS e BSR) no que tange às suas habilidades de encontrar o estado fundamental do sistema. / In order to understand how things work, man has formulated scientific theories. New methods and techniques have been created not only to increase our understanding on the subject but also to develop and even expand those theories. In this thesis, we study several techniques (here called algorithms) designed with the objective to get the ground states of some spin systems and eventually to reveal possible properties of critical self-organization. In the second chapter, we introduce four fundamental optimization algorithms: simulated annealing, genetics algorithms, extremal optimization (EO) and Bak-Sneppen (BS). In the third chapter we present the concept of self-organized criticality (SOC), using as an example the sandpile model. To understand the importance of the self-organized criticality, we show many other situations where the phenomenon can be observed. In the fourth chapter, we introduce the p-states chiral clock model. This will be our test or toy system. For the one-dimensional case, we first determined the corresponding transfer-matrix and then proved the nonexistence of phase transitions by using the Perron-Frobenius theorem. We calculate the ground state phase diagrams both analytically and numerically in the cases of p = 2, 3, 4, 5 and 6. We also present a brief study of the number of local minima for the cases p = 3 and 4 of the chiral clock model. Finally, in the fifth chapter, we propose a Bak-Sneppen dynamics with noise (BSN) as a new technique of optimization to treat discrete systems. The noise is directly introduced into the spin configuration space. Consequently, the fitness now take values in a continuum but small interval around its original value (discrete). The results of this dynamics indicate the presence of self-organized criticality, which becomes evident with the power law scaling of the spacial and temporal correlations. We also study the EO algorithm and found a numerical con_rmation that it does not show a critical behavior since it has an in_nite space range and an exponential decay of the avalanches. At the end, we compare the e_ciency of the three dynamics (EO, BSD and BSN) for the chiral clock model, concerning their abilities to _nd the system\'s ground state.

As teorias científicas surgiram da necessidade do homem entender o funcionamento das coisas. Novos métodos e técnicas são então criados com o objetivo não só de melhor compreender, mas também de desenvolver essas próprias teorias. Nesta dissertação, vamos estudar várias dessas técnicas (aqui chamadas de algoritmos) com o objetivo de obter estados fundamentais em sistemas de spin e de revelar suas possíveis propriedades de auto-organização crítica. No segundo capítulo desta dissertação, apresentamos os algoritmos de otimização: simulated annealing, algoritmo genético, otimização extrema (EO) e evolutivo de Bak-Sneppen (BS). No terceiro capítulo apresentamos o conceito de criticalidade auto-organizada (SOC), usando como exemplo o modelo da pilha de areia. Para uma melhor compreensão da importância da criticalidade auto-organizada, apresentamos vários outros exemplos de onde o fenômeno é observado. No quarto capítulo apresentamos o modelo de relógio quiral de p-estados que será nosso sistema de testes. No caso unidimensional, determinamos a matriz de transferência e utilizamos o teorema de Perron-Frobenius para provar a inexistência de transição de fase a temperaturas finitas a temperaturas finitas. Esboçamos os diagramas de fases dos estados fundamentais que obtivemos de maneira analítica e numérica para os casos de p = 2, 3, 4, 5 e 6, no caso numérico fazendo uso do algoritmo de Bak-Sneppen com sorteio (BSS). Apresentamos ainda um breve estudo do número de mínimos locais para o modelo de relógio quiral de p-estados, para os casos de p = 3 e 4. Por último, no quinto capítulo, propomos uma dinâmica Bak-Sneppen com ruído (BSR) como uma nova técnica de otimização para tratar sistemas discretos. O ruído é introduzido diretamente no espaço de configuração de spins. Conseqüentemente, o fitness (adaptabilidade) passa a assumir valores contínuos, num pequeno intervalo em torno do seu valor original (discreto). Os resultados dessa dinâmica indicam a presença de criticalidade auto-organizada, evidenciada pelo decaimento em leis de potências das correlações espacial e temporal. Também estudamos o método EO e obtivemos uma confirmação numérica de que sua dinâmica exibe um comportamento não crítico com alcance espacial infinito e decaimento exponencial das avalanches. Finalmente, para o modelo de relógio quiral, comparamos a eficiência das três dinâmicas (EO, BSS e BSR) no que tange às suas habilidades de encontrar o estado fundamental do sistema. / In order to understand how things work, man has formulated scientific theories. New methods and techniques have been created not only to increase our understanding on the subject but also to develop and even expand those theories. In this thesis, we study several techniques (here called algorithms) designed with the objective to get the ground states of some spin systems and eventually to reveal possible properties of critical self-organization. In the second chapter, we introduce four fundamental optimization algorithms: simulated annealing, genetics algorithms, extremal optimization (EO) and Bak-Sneppen (BS). In the third chapter we present the concept of self-organized criticality (SOC), using as an example the sandpile model. To understand the importance of the self-organized criticality, we show many other situations where the phenomenon can be observed. In the fourth chapter, we introduce the p-states chiral clock model. This will be our test or toy system. For the one-dimensional case, we first determined the corresponding transfer-matrix and then proved the nonexistence of phase transitions by using the Perron-Frobenius theorem. We calculate the ground state phase diagrams both analytically and numerically in the cases of p = 2, 3, 4, 5 and 6. We also present a brief study of the number of local minima for the cases p = 3 and 4 of the chiral clock model. Finally, in the fifth chapter, we propose a Bak-Sneppen dynamics with noise (BSN) as a new technique of optimization to treat discrete systems. The noise is directly introduced into the spin configuration space. Consequently, the fitness now take values in a continuum but small interval around its original value (discrete). The results of this dynamics indicate the presence of self-organized criticality, which becomes evident with the power law scaling of the spacial and temporal correlations. We also study the EO algorithm and found a numerical con_rmation that it does not show a critical behavior since it has an in_nite space range and an exponential decay of the avalanches. At the end, we compare the e_ciency of the three dynamics (EO, BSD and BSN) for the chiral clock model, concerning their abilities to _nd the system\'s ground state.

[pt] Esta tese busca utilizar os novos conceitos físicos relacionados à física do estado sólido e à mecânica estatística - teoria do caos e geometria fractal - na análise do comportamento de sistemas dinâmicos não-lineares. Mais pormenorizadamente, trata-se de estudar o comportamento de um modelo numérico elasto-plástico com função de escoamento de Mohr-Coulomb, usualmente empregado em simulações de materiais geológicos - cimentados ou não -, quando submetido a carregamentos externos, situação esta geralmente encontrada em problemas afeitos à mecânica dos solos e das rochas (p/ex., estabilidade de taludes e escavações subterrâneas). Mostra-se que tal modelo geomecânico de muitos corpos (many-body) interagentes é conduzido espontaneamente, ao longo de sua evolução temporal, à chamada criticalidade auto-organizada (self- organized criticality - SOC), estado caracterizado por apresentar evolução na fronteira entre ordem e caos, sensibilidade extrema a qualquer pequena perturbação, e desenvolvimento de interações espaço-temporais de longo alcance. Como a evolução de qualquer sistema dinâmico pode ser vista como um fluxo ininterrupto de informações entre suas partes constituintes, avaliou-se, para tal sistema, a entropia de Tsallis, formulação original proposta pelo físico brasileiro Constantino Tsallis, do Centro Brasileiro de Pesquisas Físicas (CBPF), tendo se mostrado adequada à sua descrição. Em especial, determinou-se para tal sistema, pela primeira vez, o valor do índice entrópico, que parametriza a aludida forma entrópica alternativa. Ademais, como é característico de sistemas fora do equilíbrio regidos por uma dinâmica de limiar, mostra-se que tal sistema geomecânico, durante o seu desenvolvimento, teve a sua simetria translacional inicial quebrada, sendo substituída pela simetria por escala, auto-semelhante (i.é., fractal). Em decorrência, o modelo exibe a chamada invariância discreta de escala (discrete scale invariance - DSI), fruto do processo mesmo de ruptura progressiva do material heterogêneo. Especificamente, as simulações numéricas sugeriram que o processo de ruptura progressiva do material elasto-plástico se dá por uma transferência multiplicativa de tensões, em diferentes escalas de observação hierarquicamente dispostas, acarretando o aparecimento de sinais bastante peculiares, caracterizados por desvios oscilatórios sistemáticos do padrão em lei de potência, o que possibilita a previsão de sua ruína, quando ainda em fase preparatória. Assim, esta pesquisa mostrou a eficiência de tal método de previsão, aplicado, pela primeira vez, não somente aos resultados das simulações numéricas do referido modelo geomecânico, como aos ensaios de laboratório em rochas sedimentares, realizados no Centro de Pesquisas da Petrobrás (CENPES). Por fim, é interessante assinalar que o material elasto-plástico investigado neste trabalho teve seu comportamento compartilhado por um modelo matemático bastante simples, fundamentado na função binomial multifractal, reconhecida por descrever processos multiplicativos em diferentes escalas. / [en] This thesis aims at applying new concepts from solid state physics and statistical mechanics - chaos theory and fractal geometry - to the study of nonlinear dynamic systems. More precisely, it deals with a two-dimensional continuum elastoplastic Mohr-Coulomb model, commonly used to simulate pressure-sensitive materials (e.g., soils, rocks and concrete) subjected to stress-strain fields, normally found in general soil or rock mechanics problems (e.g., slope stability and underground excavations). It is shown that such many-body system is spontaneously driven to a state at the edge of chaos, called self- organized criticality (SOC), capable of developing long- range interactions in space and long-range memory in time. A new entropic form proposed by C. Tsallis is presented and shown that it is the suitable theoretical framework to deal with these problems. Furthermore, the index q of the Tsallis entropy, which measures the degree of non- additivity of the system, is calculated, for the first time, for an elastoplastic model. In addition, as is usual in non-equilibrium systems with threshold dynamics, the model changes its symmetry, from translational to fractal (that is, self-similar), leading to what is called discrete scale invariance. It is shown that this special type of scale invariance, characterized by systematic oscillatory deviations from the fundamental power-law behavior, can be used to predict the failure of heterogeneous materials, while the process is still being build-up, i.e., from precursory signals, typical of progressive failure processes. Specifically, this framework was applied, for the first time, not only to the elastoplastic geomechanical model, but to laboratory tests in sedimentary rocks as well. Finally, it is interesting to realize that the above- mentioned behaviors are also displayed by the binomial multifractal function, known to adequately describe multiplicative cascading processes.

In order to cope with system complexity and dynamic environments, modern industries are investing in a variety of sensor networks and data acquisition systems to increase information visibility. Multi-sensor systems bring the proliferation of high-dimensional functional Big Data that capture rich information on the evolving dynamics of natural and engineered processes. With spatially and temporally dense data readily available, there is an urgent need to develop advanced methodologies and associated tools that will enable and assist (i) the handling of the big data communicated by the contemporary complex systems, (ii) the extraction and identification of pertinent knowledge about the environmental and operational dynamics driving these systems, and (iii) the exploitation of the acquired knowledge for more enhanced design, analysis, monitoring, diagnostics and control. My methodological and theoretical research as well as a considerable portion of my applied and collaborative work in this dissertation aims at addressing high-dimensional functional big data communicated by the systems. An innovative contribution of my work is the establishment of a series of systematic methodologies to investigate the complex system informatics including multi-dimensional modeling, feature extraction and selection, model-based monitoring and root cause diagnostics. This study presents systematic methodologies to investigate spatiotemporal informatics of complex systems from multi-dimensional modeling and feature extraction to model-driven monitoring, fault identification and root cause diagnostics. In particular, we developed a multiscale adaptive basis function model to represent and characterize the high-dimensional nonlinear functional profiles, thereby reducing the large amount of data to a parsimonious set of variables (i.e., model parameters) while preserving the information. Furthermore, the complex interdependence structure among variables is identified by a novel self-organizing network algorithm, in which the homogeneous variables are clustered into sub-network communities. Then we minimize the redundancy of variables in each cluster and integrate the new set of clustered variables with predictive models to identify a sparse set of sensitive variables for process monitoring and fault diagnostics. We evaluated and validated our methodologies using real-world case studies that extract parameters from representation models of vectorcardiogram (VCG) signals for the diagnosis of myocardial infarctions. The proposed systematic methodologies are generally applicable for modeling, monitoring and diagnosis in many disciplines that involve a large number of highly-redundant variables extracted from the big data. The self-organizing approach was also innovatively developed to derive the steady geometric structure of a network from the recurrence-based adjacency matrix. As such, novel network-theoretic measures can be achieved based on actual node-to-node distances in the self-organized network topology.

This thesis is concerned with the analysis of economic network formation. There are three novel sections to this thesis (Chapters 5, 6 and 8). In the first, the non-cooperative communication network formation model of Bala and Goyal (2000) (BG) is re-assessed under conditions of no inertia. It is found that the Strict Nash circle (or wheel) structure is still the equilibrium outcome for n = 3 under no inertia. However, a counter-example for n = 4 shows that with no inertia infinite cycles are possible, and hence the system does not converge. In fact, cycles are found to quickly dominate outcomes for n > 4 and further numerical simulations of conditions approximating no inertia (probability of updating > 0.8 to 1) indicate that cycles account for a dramatic slowing of convergence times. These results, together with the experimental evidence of Falk and Kosfeld (2003) (FK) motivate the second contribution of this thesis. A novel artificial agent model is constructed that allows for a vast strategy space (including the Best Response) and permits agents to learn from each other as was indicated by the FK results. After calibration, this model replicates many of the FK experimental results and finds that an externality exploiting ratio of benefits and costs (rather than the difference) combined with a simple altruism score is a good proxy for the human objective function. Furthermore, the inequity aversion results of FK are found to arise as an emergent property of the system. The third novel section of this thesis turns to the nature of network formation in a trust-based context. A modified Iterated Prisoners' Dilemma (IPD) model is developed which enables agents to play an additional and costly network forming action. Initially, canonical analytical results are obtained despite this modification under uniform (non-local) interactions. However, as agent network decisions are 'turned on' persistent cooperation is observed. Furthermore, in contrast to the vast majority of non-local, or static network models in the literature, it is found that a-periodic, complex dynamics result for the system in the long-run. Subsequent analysis of this regime indicates that the network dynamics have fingerprints of self-organized criticality (SOC). Whilst evidence for SOC is found in many physical systems, such dynamics have been seldom, if ever, reported in the strategic interaction literature.

Self-organization is a hot topic as it has the potential to create surface patterns on the nanoscale avoiding cost-intensive top-down approaches. Although chemists have promising results in this area, ion irradiation can create self-organized surface patterns in a more controlled manner. Different regimes of pattern formation under ion irradiation were described so far by 2D models. Here, two new regimes have been studied experimentally, which require modeling in 3D: subsurface point defect kinetics as well as ion impact-induced melt pool formation. This thesis deals with self-organized pattern formation on Ge and Si surfaces under normal incidence irradiation with heavy monatomic and polyatomic ions of energies up to several tens of keV. Irradiation has been performed using liquid metal ion sources in a focused ion beam facility with mass-separation as well as by conventional broad beam ion implantation. Irradiated samples have been analyzed mainly by scanning electron microscopy. Related to the specific irradiation conditions, investigation and discussion of pattern formation has been divided into two parts: (i) formation of Ge morphologies due to point defect kinetics and (ii) formation of Ge and Si morphologies due to melt pool dynamics. Point defect kinetics dominates pattern formation on Ge under irradiation with monatomic ions at room temperature. Irradiation of Ge with Bi and Ge ions at fluences up to 10^17 cm^(-2) has been performed. Comprehensive studies show for the first time that morphologies change from flat surfaces over hole to nanoporous, sponge-like patterns with increasing ion energy. This study is consistent with former irradiations of Ge with a few ion energies. Based on my studies, a consistent, qualitative 3D model of morphology evolution has been developed, which attributes the ion energy dependency of the surface morphology to the depth dependency of point defect creation and relaxation. This model has been proven by atomistic computer experiments, which reproduce the patterns found in real irradiation experiments. At extremely high energy densities deposited by very heavy ions another mechanism dominates pattern formation. The formation of Ge and Si dot patterns by very heavy, monatomic and polyatomic Bi ion irradiation has been studied in detail for the first time. So far, this formation of pronounced dot pattern cannot be explained by any model. Comprehensive, experimental studies have shown that pattern formation on Ge is related to extremely high energy densities deposited by each polyatomic ion locally. The simultaneous impact of several atoms leads to local energy densities sufficient to cause local melting. Heating of Ge substrates under ion irradiation increases the achievable energy density in the collision cascade substantially. This prediction has been confirmed experimentally: it has been found that the threshold for nanomelting can be lowered by substrate heating, which allows pattern formation also under heavy, monatomic ion irradiation. Extensive studies of monatomic Bi irradiation of heated Ge have shown that morphologies change from sponge-like over highly regular dot patterns to smooth surfaces with increasing substrate temperature. The change from sponge-like to dot pattern is correlated to the melting of the ion collision cascade volume, with energy densities sufficient for melt pool formation at the surface. The model of pattern formation on Ge due to extremely high deposited energy densities is not specific to a single element. Therefore, Si has been studied too. Dot patterns have been found for polyatomic Bi ion irradiation of hot Si, which creates sufficiently high energy densities to allow ion impact-induced melt pool formation. This proves that pattern formation by melt pool formation is a novel, general pattern formation mechanism. Using molecular dynamics simulations of project partners, the correlation between dot patterning and ion impact-induced melt pool formation has been proven. The driving force for dot pattern formation due to high deposited energy densities has been identified and approximated in a first continuum description.