Usando a generalização de Grauwin et al. [Ref. 3] do modelo de segregação de Schelling foi possível estudar, em um modelo simplificado, as consequências da guerra fiscal travada entre os estados de uma federação e os resultados da chamada guerra da taxa que os bancos adotaram depois de implantada a portabilidade de crédito bancário. No modelo de Grauwin a cidade é dividida em Q quarteirões e todos os quarteirões possuem a mesma função utilidade dependente da densidade u(m,?), que mede a satisfação dos agentes que ali residem. Inserimos um parâmetro de desordem m_b em um dos blocos para torná-lo mais atrativo que os demais. Ter um dos blocos diferente é a essência do modelo de guerra entre os quarteirões. Foi analisada uma aplicação deste modelo fazendo um paralelo com o cenário de uma guerra fiscal entre os estados de uma nação. Para tal, interpretamos os agentes econômicos como sendo as de indústrias (ou pessoas) que tomam decisões em busca de aumentar sua própria satisfação e os quarteirões como os estados de uma federação. A guerra fiscal é um instrumento usado por alguns estados brasileiros que reduzem impostos, cedem terrenos, fornecem infra-estrutura, etc para atrair investimentos na sua região. Esta guerra no primeiro momento pode ser benéfica para a sociedade, pois contribui para a descentralização da economia e reduz as diferenças de PIB e social entre os estados. Porém, em âmbito nacional, o embate econômico entre os estados geralmente resulta em perda de arrecadação para a nação. Um Estado totalmente desocupado, caso queira roubar empresas de Estados já consolidados, precisa dar muito mais incentivos para atrair investimento por conta da sua baixa população e consequentemente baixa utilidade. Neste trabalho tentamos quantificar os gastos que os Estados têm com este tipo de ação. Outra releitura dos resultados pode ser aplicada ao modelo de portabilidade de crédito, onde interpretamos os agentes econômicos de Grauwin como tomadores de empréstimo e os quarteirões como bancos de crédito ao varejo. A taxa de juros cobrada de cada banco dependerá do tamanho da carteira que este possui. Ter um banco com uma taxa de juros diferenciada o torna mais atrativo que os demais e este começa a roubar clientes dos outros bancos, contudo, o mercado reage e também reduz suas taxas, criando uma guerra da taxa no mercado financeiro. Estudando o cenário egoísta (onde o governo não desestimule a troca entre bancos) e supondo que a quantidade de tomadores no mercado seja suficientemente pequena, a dinâmica conduzirá a uma situação onde teremos apenas alguns bancos coexistindo e outros falindo. No limite egoísta o banco que se dispôs a dar incentivo terá a carteira maior que os demais bancos com taxas menores e isto vai ser invertendo à medida que o governo impõe comportamento mais altruísta da sociedade. Estudamos analiticamente os efeitos das variações da densidade e dos parâmetros (m) e altruísmo (a) no cenário global bem como os resultados esperados com a inserção de uma desordem (m_b) em um dos blocos. E por fim foram feitas simulações em computador para verificar se comportamento das dinâmicas em todos os cenários eram compatíveis com as soluções obtidas. / Using Grauwins generalization [Ref. 3] of Schelling\'s segregation model we study, in a simplified model, some consequences of the \"fiscal war\" waged between the states of a federation, and of the rate tax generated by the recent Brazilian Central Bank regulation of bank credit portability. In Grauwins model the city is divided into blocks and all blocks have the same utility function, which measures the satisfaction of agents living there and depends on the density of agents. We introduced a disorder parameter in one of the blocks to make it more attractive than the others, in order to mimick the essential igredient of competition between states or banks. We first analyze an application of this model in the scenario of a fiscal war between the states of a nation. We interpret blocks as the states of a federation and economic agents as the industries (or people) who make decisions seeking to increase their own satisfaction. The fiscal war is an instrument used by some Brazilian states consisting in reducing taxes, subsidize land, provide infrastructure, etc in order to attract investment. This war at first can be beneficial for society as it contributes to the decentralization of the economy and reduces the differences of GDP and social discrepancies between states. Nationwide, however, the economic struggle between states usually results in loss of revenue at the global level. A vacated state, in order to attract agents already established elsewhere, need to give more incentives to attract investment because of its low population and consequently low utility. In this work we try to quantify the costs that states have with this kind of action. Another analysis of the results can be applied to a bank credit portability model, where we interpret economic agents as customers and blocks as retail credit banks. The interest rate levied on each bank will depend on the size of the portfolio of that bank. Having a bank with a differentiated interest rate makes it more attractive than others, and it begins to \"steal\" customers from other banks.However, those react and also reduce their rates, creating a \"war tax\" in the financial market. Studying the selfish scenario (where the government doesnt discourage a client from taking his/her debt to another bank), and assuming that the number of customers in the market is sufficiently small, the dynamics leads to a situation where we have just a few coexisting banks, the others having gone bankrupt. In the selfish limit the bank that was willing to give encouragement will have the largest portfolio while offering lower interest rates than the others, but this will be reversed as the government imposes a more altruistic behavior to the clients. We study analytically the effects, at the global level, of variations in the density, in the altruism parameter and in the parameter determining the utility function at saturation, as well as the effects of introducing disorder in one or more blocks. Finally, computer simulations were performed to check that the dynamic behavior in all scenarios was consistent with those obtained solutions.

Machine learning enables machines to learn automatically from data. In literature, graph-based methods have received increasing attention due to their ability to learn from both local and global information. In these methods, each data instance is represented by a vertex and is linked to other vertices according to a predefined affinity rule. However, they usually have unfeasible time cost for large problems. To overcome this problem, techniques can employ a heuristic to find suboptimal solutions in a feasible time. Early heuristic optimization methods exploit nature-inspired collective processes, such as ants looking for food sources and swarms of bees. Nowadays, advances in the field of complex systems provide powerful tools to assess and to understand dynamical systems. Complex networks, which are graphs with nontrivial topology, are among these theoretical tools capable of describing the interplay of topology, structure, and dynamics of complex systems. Therefore, machine learning methods based on complex networks and collective dynamics have been proposed. They encompass three steps. First, a complex network is constructed from the input data. Then, the simulation of a distributed collective system in the network generates rich information. Finally, the collected information is used to solve the learning problem. The coordination of the individuals in the system permit to achieve dynamics that is far more complex than the behavior of single individuals. In this research, I have explored collective dynamics in machine learning tasks, both in unsupervised and semi-supervised scenarios. Specifically, I have proposed a new collective system of competing particles that shifts the traditional vertex-centric dynamics to a more informative edge-centric one. Moreover, it is the first particle competition system applied in machine learning task that has deterministic behavior. Results show several advantages of the edge-centric model, including the ability to acquire more information about overlapping areas, a better exploration behavior, and a faster convergence time. Also, I have proposed a new network formation technique that is not based on similarity and has low computational cost. Since addition and removal of samples in the network is cheap, it can be used in real-time application. Finally, I have conducted analytical investigations of a flocking-like system that was needed to guarantee the expected behavior in community detection tasks. In conclusion, the result of the research contributes to many areas of machine learning and complex systems. / Aprendizado de máquina permite que computadores aprendam automaticamente dos dados. Na literatura, métodos baseados em grafos recebem crescente atenção por serem capazes de aprender através de informações locais e globais. Nestes métodos, cada item de dado é um vértice e as conexões são dadas uma regra de afinidade. Todavia, tais técnicas possuem custo de tempo impraticável para grandes grafos. O uso de heurísticas supera este problema, encontrando soluções subótimas em tempo factível. No início, alguns métodos de otimização inspiraram suas heurísticas em processos naturais coletivos, como formigas procurando por comida e enxames de abelhas. Atualmente, os avanços na área de sistemas complexos provêm ferramentas para medir e entender estes sistemas. Redes complexas, as quais são grafos com topologia não trivial, são uma das ferramentas. Elas são capazes de descrever as relações entre topologia, estrutura e dinâmica de sistemas complexos. Deste modo, novos métodos de aprendizado baseados em redes complexas e dinâmica coletiva vêm surgindo. Eles atuam em três passos. Primeiro, uma rede complexa é construída da entrada. Então, simula-se um sistema coletivo distribuído na rede para obter informações. Enfim, a informação coletada é utilizada para resolver o problema. A interação entre indivíduos no sistema permite alcançar uma dinâmica muito mais complexa do que o comportamento individual. Nesta pesquisa, estudei o uso de dinâmica coletiva em problemas de aprendizado de máquina, tanto em casos não supervisionados como semissupervisionados. Especificamente, propus um novo sistema de competição de partículas cuja competição ocorre em arestas ao invés de vértices, aumentando a informação do sistema. Ainda, o sistema proposto é o primeiro modelo de competição de partículas aplicado em aprendizado de máquina com comportamento determinístico. Resultados comprovam várias vantagens do modelo em arestas, includindo detecção de áreas sobrepostas, melhor exploração do espaço e convergência mais rápida. Além disso, apresento uma nova técnica de formação de redes que não é baseada na similaridade dos dados e possui baixa complexidade computational. Uma vez que o custo de inserção e remoção de exemplos na rede é barato, o método pode ser aplicado em aplicações de tempo real. Finalmente, conduzi um estudo analítico em um sistema de alinhamento de partículas. O estudo foi necessário para garantir o comportamento esperado na aplicação do sistema em problemas de detecção de comunidades. Em suma, os resultados da pesquisa contribuíram para várias áreas de aprendizado de máquina e sistemas complexos.

Higher education in post-independence Kenya from 1963 to 2009 has been characterized by rapid expansion - both in terms of student enrolment and in a sharp increase in the number of both private and public universities. While national and institutional mechanisms, such as the establishment of a revolving fund, the Higher Education Loans Board and the introduction of the Privately Sponsored Students Programme, have been initiated to address the sharp demand for higher education against a backdrop of diminishing financial support, violent student unrest - which seriously undermined these efforts - has persisted. A sustained period of student unrest has characterized Kenya‟s higher education. This has manifested itself in the form of violent protests, riots, boycotts and strikes. Statistics indicate that the intensity/frequency and violence of the strikes has steadily increased over the years. For example, between 1969 and 2000 sixty-nine cases of student strikes were recorded at all the public universities. Of these cases, twenty-two (31.88%) occurred within a time span of 20 years (1969-1989) while forty-seven cases (68.12%) occurred in a short period of just one decade (1990-2000).At Moi University twenty-four cases of strikes, which affected its colleges and campuses, were recorded between 1985 and 2009. In terms of radical policy adaptation at both national and institutional levels, one would expect a downward trend in unrest. Instead, however, the frequency and intensity of violence associated with strikes has increased at an alarming rate with several deaths being reported. As such, this study has investigated the factors that have contributed to, and informed, a sustained period of student unrest with a specific focus on Moi University in order to identify policy lessons. Global, national and institutional aspects were examined. A case study strategy was applied - with Moi University as its focus. Data was collected through an in-depth review of the relevant literature, document analysis and interviews. Past and present senior management staff members at Moi University, including Deans of Faculties, Deans of Students, Heads of Departments, and Heads of Sections as well as former student leaders were interviewed. The study concludes in its findings that the university is operating within a highly dynamic and unstable social-political environment, leading to the emergence of inadequate policy adaptations. The resultant shortcomings in the operations of the university attract the wrath of an informed student population in the form of unrest. The students action is not however simply reactionary, as they too, as change agents have their own agenda that evolves over time as they seize opportunities created by the policy shortcomings to pursue it. The study summarized the salient factors responsible for the violent unrest in five broad thematic areas. These include: (i) Unrest associated with flawed international and national policies and social pressure; (ii) Unrest associated with critical national issues and identification with progressive change agents; (iii) Unrest associated with student politics;(iv) Unrest associated with social identity and threats of their welfare from organized groups; and (v) Unrest associated with the prevalence of institutional catalyzing factors. A typical strike develops through four main phases: (i) The development/ brewing phase; (ii) The heightened tension phase; (iii) The full blown strike phase; and (iv) The dissipation/uneasy calm phase. Organizational disequilibrium describes the general state of instability characterizing the university, while organizational paranoia is associated with instances of devastating strikes during a heightened tension phase. A strike matrix of Spontaneous vs Orchestrated and Flash vs Protracted typify the strikes. Unrest has led to the disruption of academic programmes; the destruction of property and deaths; a loss of critical study time; and damage to students‟ careers caused by suspensions and expulsions. The need for a well-considered policy that involves exhaustive consultation with all the stake-holders emerges as critical for the future stability of universities. / Thesis (PhD)--University of Pretoria, 2013. / am2013 / Education Management and Policy Studies / unrestricted

La phorèse est un mécanisme physico-chimique par lequel certains colloïdes microscopiques dérivent à travers les gradients d'un champ de concentration de soluté dans un fluide. Ce mécanisme est exploité par des particules autophorétiques, ou colloïdes actifs chimiquement, pour auto-propulser. Ces particules influencent les mouvements de leurs voisines par le biais d'interactions chimiques et hydrodynamiques et sont donc étudiées pour leur comportement collectif. La modélisation de ces interactions a fait l'objet de recherches approfondies au cours des dernières années, à la fois d'un point de vue physique pour comprendre les mécanismes précis des interactions, et d'un point de vue expérimental pour expliquer les observations de la formation de structures cohérentes à grande échelle. Cependant, une modélisation exacte de ces suspensions actives est difficile en raison des interactions à grand nombre de particules. Jusqu'à présent, la plupart des modèles proposés reposent sur la superposition d'approximations de champ lointain pour les signatures chimiques et hydrodynamiques de chaque particule, qui ne sont valides que de manière asymptotique dans la limite de suspensions très diluées. Un cadre analytique systématique et unifié basé sur la méthode classique de réflexion (MoR) est développé ici pour les problèmes de Laplace et de Stokes afin d'obtenir les interactions entre particules phorétiques et les vitesses résultantes avec un ordre de précision arbitraire en terme du rapport du rayon et de la distance typique entre deux particules voisines.Un système comprenant uniquement des particules autophorétiques homogènes et isotropes chimiquement et géométriquement est ensuite considéré en détail. On sait que de telles particules isotropes ne peuvent se propulser seules; cependant, en présence d'autres particules identiques, la symétrie du champ de concentration est brisée et les particules forment spontanément des agrégats ou clusters denses. De manière remarquable, ceux-ci peuvent s'auto-propulser si leur arrangement est présente une asymétrie. Ce résultat identifie donc une nouvelle voie pour briser la symétrie du champ de concentration et ainsi générer un mouvement, qui ne repose pas sur une conception anisotrope des particules individuelles, mais sur les interactions collectives de particules actives identiques et homogènes. Un argument pour l'origine de ce comportement auto-propulsif des clusters, basé sur la MoR, est proposé. De plus, en utilisant des simulations numériques complètes combinées à un modèle théorique réduit, nous caractérisons les propriétés statistiques de l'autopropulsion. / Diffusiophoresis is a physico-chemical mechanism by which certain microscopic colloids drift through gradients of a solute concentration field in a fluid. This mechanism is exploited by autophoretic particles, which are chemically active synthetic colloids, to achieve self-propulsion. These particles influence each others' motion through chemical and hydrodynamic interactions and are hence known to exhibit collective behaviour. Modeling these interactions is a subject of intense research over the past decades, both from a physical perspective to understand the precise mechanisms of the interactions, as well as from an experimental point of view to explain the observations of formation of coherent large-scale structures. However, an exact modeling of is difficult due to multi-body interactions and surface effects. Most efforts so far rely on the superposition of far-field approximations for each particle's signature, which are only valid asymptotically in the dilute suspension limit. A systematic and unified analytical framework based on the classical Method of Reflections (MoR) is developed here for both Laplace and Stokes' problems to obtain the multi-body interactions and the resulting velocities of phoretic particles, up to any order of accuracy in the radius-to-distance ratio of the particles.A system comprising only of chemically- and geometrically-isotropic autophoretic particles is then considered in detail. It is known that such isotropic particles cannot self-propel in isolation; however, in the presence of other identical particles, the symmetry of the concentration field is broken and the particles spontaneously form close packed clusters. Remarkably, these clusters are observed to self-propel based on their geometric arrangement. This result thus identifies a new route to symmetry-breaking for the concentration field and to self-propulsion, that is not based on an anisotropic design, but on the collective interactions of identical and homogeneous active particles. An argument for origin of this self-propulsive behaviour of clusters is made based on MoR. Furthermore, using full numerical simulations and theoretical model for clustering, we characterize the statistical properties of self-propulsion of the system.

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This doctoral study consists of two parts. In the first part, the quantum statistical effects on the formation process of the heavy ion fusion reactions have been investigated by using the c-number quantum Langevin equation approach. It has been shown that the quantum effects enhance the over-passing probability at low temperatures. In the second part, we have developed a simulation technique for the quantum noises which can be approximated by two-term exponential colored noise.

Bien que la dynamique des réseaux périodiques non-linéaires ait été investiguée dans les domainestemporel et fréquentiel, il existe un réel besoin d’identifier des relations pratiques avec lephénomène de la localisation d’énergie en termes d’interactions modales et topologies de bifurcation.L’objectif principal de cette thèse consiste à exploiter le phénomène de la localisation pourmodéliser la dynamique collective d’un réseau périodique de résonateurs non-linéaires faiblementcouplés.Un modèle analytico-numérique a été développé pour étudier la dynamique collective d’unréseau périodique d’oscillateurs non-linéaires couplés sous excitations simultanées primaire et paramétrique,où les interactions modales, les topologies de bifurcations et les bassins d’attraction ontété analysés. Des réseaux de pendules et de nano-poutres couplés électrostatiquement ont étéinvestigués sous excitation extérieure et paramétrique, respectivement. Il a été démontré qu’enaugmentant le nombre d’oscillateurs, le nombre de solutions multimodales et la distribution desbassins d’attraction des branches résonantes augmentent. Ce modèle a été étendu pour investiguerla dynamique collective des réseaux 2D de pendules couplés et de billes sphériques en compressionsous excitation à la base, où la dynamique collective est plus riche avec des amplitudes de vibrationplus importantes et des bandes passantes plus larges. Une deuxième investigation de cettethèse consiste à identifier les solitons associés à la dynamique collective d’un réseau périodique etd’étudier sa stabilité. / Although the dynamics of periodic nonlinear lattices was thoroughly investigated in the frequencyand time-space domains, there is a real need to perform profound analysis of the collectivedynamics of such systems in order to identify practical relations with the nonlinear energy localizationphenomenon in terms of modal interactions and bifurcation topologies. The principal goal ofthis thesis consists in exploring the localization phenomenon for modeling the collective dynamicsof periodic arrays of weakly coupled nonlinear resonators.An analytico-numerical model has been developed in order to study the collective dynamics ofa periodic coupled nonlinear oscillators array under simultaneous primary and parametric excitations,where the bifurcation topologies, the modal interactions and the basins of attraction havebeen analyzed. Arrays of coupled pendulums and electrostatically coupled nanobeams under externaland parametric excitations respectively were considered. It is shown that by increasing thenumber of coupled oscillators, the number of multimodal solutions and the distribution of the basinsof attraction of the resonant solutions increase. The model was extended to investigate the collectivedynamics of periodic nonlinear 2D arrays of coupled pendulums and spherical particles underbase excitation, leading to additional features, mainly larger bandwidth and important vibrationalamplitudes. A second investigation of this thesis consists in identifying the solitons associated tothe collective nonlinear dynamics of the considered arrays of periodic structures and the study oftheir stability.

Ride-pooling (or ride-sharing) services combine trips of multiple customers along similar routes into a single vehicle. The collective dynamics of the fleet of ride-pooling vehicles fundamentally underlies the efficiency of these services. In simplified models, the common features of these dynamics give rise to scaling laws of the efficiency that are valid across a wide range of street networks and demand settings. However, it is unclear how constraints of the vehicle fleet impact such scaling laws. Here, we map the collective dynamics of capacity-constrained ride-pooling fleets to services with unlimited passenger capacity and identify an effective fleet size of available vehicles as the relevant scaling parameter characterizing the dynamics. Exploiting this mapping, we generalize the scaling laws of ride-pooling efficiency to capacity-constrained fleets. We approximate the scaling function with a queueing theoretical analysis of the dynamics in a minimal model system, thereby enabling mean-field predictions of required fleet sizes in more complex settings. These results may help to transfer insights from existing ride-pooling services to new settings or service locations.

L’analyse dynamique des structures de grandes dimensions incluant de nombreux paramètres incertains et des non-linéarités localisées ou réparties peut être numériquement prohibitive. Afin de surmonter ce problème, des modèles d’approximation peuvent être développés pour reproduire avec précision et à faible coût de calcul la réponse de la structure.L’objectif de la première partie de ce mémoire est de développer des modèles numériques robustes vis-à-vis des modifications structurales (non-linéarités localisées, perturbations ou incertitudes paramétriques) et « légers » au sens de la réduction de la taille. Ces modèles sont construits, selon les approches de condensation directe et par synthèse modale, en enrichissant des bases de réduction tronquées, modale et de Craig-Bampton respectivement, avec des résidus statiques prenant compte des modifications structurales. Pour propager les incertitudes, l’accent est mis particulièrement sur la méthode du chaos polynomial généralisé. Sa combinaison avec les modèles réduits ainsi obtenus permet de créer des métamodèles mono et bi-niveaux, respectivement. Les deux métamodèles proposés sont comparés à d’autres métamodèles basés sur les méthodes du chaos polynomial généralisé et du Latin Hypercube appliquées sur des modèles complets et réduits. Les métamodèles proposés permettent d’approximer les comportements structuraux avec un coût de calcul raisonnable et sans perte significative de précision.La deuxième partie de ce mémoire est consacrée à l’analyse dynamique des structures périodiques non-linéaires en présence des imperfections : perturbations des paramètres structuraux ou incertitudes paramétriques. Deux études : déterministe ou stochastique, respectivement, sont donc menées. Pour ces deux configurations, un modèle analytique discret générique est proposé. Il consiste à appliquer la méthode des échelles multiples et la méthode de perturbation pour résoudre l’équation de mouvement et de projecter la solution obtenue sur des modes d’ondes stationnaires. Le modèle proposé conduit à un ensemble d’équations algébriques complexes couplées, fonctions du nombre et des positions des imperfections dans la structure. La propagation des incertitudes à travers le modèle ainsi construit est finalement assurée par les méthodes du Latin Hypercube et du chaos polynomial généralisé. La robustesse de la dynamique collective vis-à-vis des imperfections est étudiée à travers l’analyse statistique de la dispersion des réponses fréquentielles et des bassins d’attraction dans le domaine de multistabilité. L’étude numérique montre que la présence des imperfections dans une structure périodique renforce sa non-linéarité, élargit son domaine de multistabilité et génère une multiplicité de branches multimodale. / Dynamic analysis of large scale structures including several uncertain parameters and localized or distributed nonlinearities may be computationally unaffordable. In order to overcome this issue, approximation models can be developed to reproduce accurately the structural response at a low computational cost.The purpose of the first part of this thesis is to develop numerical models which must be robust against structural modifications (localized nonlinearities, parametric uncertainties or perturbations) and reduce the size of the initial problem. These models are created, according to the direct condensation and the component mode synthesis, by enriching truncated reduction modal bases and Craig-Bampton transformations, respectively, with static residual vectors accounting for the structural modifications. To propagate uncertainties through these first-level and second-level reduced order models, respectively, we focus particularly on the generalized polynomial chaos method. This methods combination allows creating first-level and second-level metamodels, respectively. The two proposed metamodels are compared to other metamodels based on the polynomial chaos method and Latin Hypercube method applied on reduced and full models. The proposed metamodels allow approximating the structural behavior at a low computational cost without a significant loss of accuracy.The second part of this thesis is devoted to the dynamic analysis of nonlinear periodic structures in presence of imperfections: parametric perturbations or uncertainties. Deterministic or stochastic analyses, respectively, are therefore carried out. For both configurations, a generic discrete analytical model is proposed. It consists in applying the multiple scales method and the perturbation theory to solve the equation of motion and then on projecting the resulting solution on standing wave modes. The proposed model leads to a set of coupled complex algebraic equations, depending on the number and positions of imperfections in the structure. Uncertainty propagation through the proposed model is finally done using the Latin Hypercube method and the generalized polynomial chaos expansion. The robustness the collective dynamics against imperfections is studied through statistical analysis of the frequency responses and the basins of attraction dispersions in the multistability domain. Numerical results show that the presence of imperfections in a periodic structure strengthens its nonlinearity, expands its multistability domain and generates a multiplicity of multimodal branches.