Endosomes are dynamic vesicular structures which transport cargo molecules internalized into the cell via endocytosis. Endosomal trafficking of cargo involves a large number of individual endosomes that regularly interact with each other via fusion and fission and thus form a dynamic network wherein endocytosed cargo is sorted and transported to various other intracellular compartments. In this study we present a general theoretical framework that takes into account individual endosomes and several key microscopic interaction processes among them. By combining theory with quantitative experiments, we seek to address the fundamental question of how the behaviour of the endosomal network emerges from the interactions among many individual endosomes of different sizes and cargo contents. Our theory is based on distributions of endosomes of various sizes and cargo amount. We compare our theory to experimental time course distributions of LDL, a degradative cargo, in a population of early endosomes. Early endosomes display a broad distribution of cargo with a characteristic power law, which we show is a consequence of stochastic fusion events of cargo carrying early endosomes. A simple model can quantitatively describe time-dependent statistics of LDL distributions in individual early endosomes. From fits of the theory to experimental data we can determine key parameters of endosomal trafficking such as the endosome fusion rate and the fluxes of cargo into and out of the network. Our theory predicts several experimentally confirmed scaling behaviours, which arise as a result of endosome fusion. Our theory provides a link between the dynamics at individual endosome level and average properties of the endosomal network. We show from our theory that some features of the endosomal distributions, which arise from interactions among individual endosomes, are sensitive to alterations in chosen parameters. This provides a direct means to study perturbation experiments wherein the cargo distribution can vary in response to changes of the endocytic system. Our analysis provides a powerful tool for the study of genetic and chemical perturbations that may alter specific systems properties and for extracting various kinetic rates involved in endosomal trafficking from only still images at different points.

Interactions are what gives us the knowledge of the world around us. Interactions on all levels may fundamentally be seen as an exchange of information and a possible response of the same. Whether it is an electron in an electrical field or a handsome dude in a bar responding to a flirtation---interactions make things happen. In this sense we can see that objects without the capability of interacting with each other also are invisible to each other. Chains of pairwise interacting entities can serve as mediators of indirect interactions between objects. Nonetheless, in the limit of no interactions, we get into a philosophical debate whether we actually may consider anything to exist since it can not be detected in any way. Interactions between matter tend to be organized and show a hierarchical structure in which smaller sub-systems can be seen as parts of a bigger system, which in turn might be a smaller part of an even bigger system. This is reflected by the fact that we have sciences that successfully study specific interactions between objects or matter---physics, chemistry, biology, ecology, sociology,... What happens in a situation where all length scales are important? How does the structure of the underlying network of interactions affect the dynamical properties of a system? What network structures do we find and how are they created? This thesis is a physicist's view of collective dynamics, from superconductors to social systems and navigation in city street networks.

京都大学 / 新制・課程博士 / 博士(工学) / 甲第23929号 / 工博第5016号 / 新制||工||1783(附属図書館) / 京都大学大学院工学研究科化学工学専攻 / (主査)教授 山本 量一, 教授 宮原 稔, 教授 安達 泰治 / 学位規則第4条第1項該当 / Doctor of Philosophy (Engineering) / Kyoto University / DFAM

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Le changement du paradigme agricole met en évidence les initiatives des acteurs locaux en matière de développement durable. À partir de l’expérience pratiquée au sein du Groupement des agriculteurs biologiques et biodynamiques du département du Gers (GABB32) autour de la diffusion et du transfert des techniques de production agro-écologiques entre agriculteurs biologiques et conventionnels, cette thèse propose d’analyser le rôle de la dynamique collective dans la transition agro-écologique des exploitations agricoles. Pour étudier l’innovation et son processus, nous avons développé une méthodologie compréhensive qui combine entretiens, observations participatives et non-participatives et analyses documentaires. Ce qui a permis de suivre 30 exploitations agricoles appartenant au groupe couverts végétaux du GABB32. Au total, nous avons effectué 55 entretiens semi-directifs auprès des acteurs locaux : agriculteurs et professionnels agricoles, institutions, associations et citoyens. Les résultats ont porté sur la gestion de l’exploitation, les pratiques participatives d’échanges et de construction de connaissances au sein du groupe et intégrées à des dynamiques au sein du réseau territorial. Nous montrons qu’il existe plusieurs paramètres de nature individuelle et collective. Au niveau individuel, c’est la stratégie et les valeurs de l’agriculteur qui ont un effet sur l’intensité d’innovation. Au niveau collectif, c’est la dynamique qui contribue à avancer par un processus d’innovation. À partir de là, il est possible d’avoir une évolution positive du point de vue de la durabilité des exploitations agricoles. La création d’espaces en faveur des échanges de connaissances entre agriculteurs et les changements vers des pratiques plus durables, ouvrent des interactions en réseau entre différents acteurs et crée de nouvelles coopérations. Les résultats de l’action collective contribuent à la dynamique de développement de l’AB. / Changing agricultural paradigm reveals local actors initiatives with regard to sustainable development. Based on the organics farmers union GABB32 experience around organic and conventional farmers agro-ecological techniques transfer and dissemination, this thesis proposes to analyze the role of collective dynamics in agro-ecological farms transition. In order to study innovations and its processes, we have developed a comprehensive methodology that combines the use of data collection such as interviews, participative and non-participative observation, and documentary analysis, which allowed following 30 farms belonging from the organic farmers union GABB32 cover crops group. In total, we realized 55 semi-structured interviews conducted with the main local actors: farmers, agricultural professional bodies, institutions, associations, and citizens. Results were articulated with farm management, group knowledge exchange and participatory approach, and territorial network dynamics. We reveal several individual and collective parameters in transitions. At the individual level, farmer strategies and values have an impact on the intensity of innovation. At the collective level, dynamics contribute to the advancement of innovation processes. From there, it is possible for farms to obtain a sustainable positive evolution. Creating spaces for knowledge exchange between farmers and changing practices toward sustainability opens network interactions and multi-actors cooperation’s. Collective action results show that they encourage organic farming development.

Private cars are responsible for 15% of carbon emissions in the European Union. Ride hailing services like taxis could serve the door-to-door mobility demand of private car users with fewer overall vehicles. If the service combines multiple user trips, it might even reduce the distance driven compared to private cars which becomes ecologically sustainable. Such ride sharing services are particularly sustainable when many users share one vehicle. But connecting the trips of all users yields many small detours. These detours reduce if some users walk a short distance to a neighboring stop. When multiple stops are combined, vehicles drive to fewer stops. Such stop pooling promises to make ride sharing even more sustainable. Some ride sharing services already integrate short user walks into their system. But the effects of stop pooling on ride sharing systems are yet to be understood. Methods from theoretical physics like mean-field theory and agent-based modeling enable a systemic analysis of complex ride sharing systems. This thesis demonstrates that ride sharing may be more sustainable when users accept short walks. With stop pooling, users wait shorter for vehicles and drive shorter because of more direct vehicle routes. In consequence, the user travel time decreases on average despite additional walk time at constant fleet size. Put differently, stop pooling allows to reduce the fleet size at constant travel time. This also reduces the distance driven by all vehicles that is proportional to the fleet size when sufficient users share one vehicle. This result is robust in a data-driven model using taxi trip data from Manhattan (New York City, USA) with fluctuating demand over the day. At constant fleet size the travel time fluctuates with the demand and might deviate a lot from the expected average travel time. Such unreliable travel times might deter users from ride sharing. However, stop pooling reduces the travel time, the more the higher the travel time without walking. Consequently, stop pooling also reduces the fluctuations in the travel time. This effect is particularly large when adapting the maximum allowed walk distance to the current demand. In adaptive stop pooling users walk further at higher demand. Then, the travel time in ride sharing is more reliable when users accept short walks. All in all, this thesis contributes to the fundamental understanding of the collective dynamics of ride sharing and the effect of stop pooling at a systemic level while also explaining underlying mechanisms. The results suggest that ride sharing providers and users benefit from integrating adaptive stop pooling into the service. Based on the results, a framework can be established that roughly adjusts fleet size to demand to ensure that the ride sharing service operates sustainably. Even if this fleet size remains constant throughout the day, adaptive stop pooling keeps the travel time reliable.:1. Introduction 1 1.1. Private Cars are Unsustainable . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 1.2. Potentially More Sustainable Ride Sharing Faces Detours . . . . . . . . . . . . . 2 1.3. Less Detours in Ride Sharing with Walking to Pooled Stops . . . . . . . . . . . . 4 1.4. Physics Methods Help Understanding Ride Sharing . . . . . . . . . . . . . . . . . 5 1.5. Outline . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2. Fundamentals - A Physics Perspective on Ride Sharing 7 2.1. State of Research on Ride Sharing . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.1. Ride Sharing Systems are Complex . . . . . . . . . . . . . . . . . . . . . . 8 2.1.2. Measuring Efficiency and Sustainability of Ride Sharing Services . . . . . 8 2.1.3. Ride Sharing might be More Sustainable when Users Accept Short Walks 10 2.1.4. Data-Driven Analysis Yields more Detailed Results . . . . . . . . . . . . . 11 2.1.5. Open Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2. Theoretical Physics Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.1. What is a Complex System? . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.2. Mean-Field Theory Simplifies Complex Systems . . . . . . . . . . . . . . 13 2.2.3. Model Complex Systems Based on Agents, not on Equations . . . . . . . 14 2.2.4. Methods from Statistical Physics to Evaluate Multi-Agent Simulations . . 14 2.2.5. Model Street Networks Using Graph Theory . . . . . . . . . . . . . . . . 20 3. Model for Ride Sharing with Walking to Pooled Stops 25 3.1. Ride Sharing Combines Trips with Similar Directions . . . . . . . . . . . . . . . . 25 3.2. Stop Pooling with Dynamic Stop Locations Maintains Flexibility . . . . . . . . . 26 3.3. Simple Algorithm Assigns Users by Reducing Bus Detour . . . . . . . . . . . . . 28 3.3.1. Standard Ride Sharing Algorithm . . . . . . . . . . . . . . . . . . . . . . 28 3.3.2. Stop Pooling Algorithm at Similar Speed . . . . . . . . . . . . . . . . . . 29 3.4. Basic Setting in Continuous Space . . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.1. Uniform Request Distribution . . . . . . . . . . . . . . . . . . . . . . . . . 31 3.4.2. Heterogeneous Request Distribution . . . . . . . . . . . . . . . . . . . . . 32 3.5. Analysis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33 3.5.1. Relative Distance Driven Measures Ecological Sustainability . . . . . . . . 33 3.5.2. Measure Service Quality by Average User Travel Time . . . . . . . . . . . 34 3.5.3. Further Observables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 3.5.4. Bisection Method to Find Minimal Travel Time with Small Effort . . . . 36 3.6. Model Extensions Yield More Detailed Results . . . . . . . . . . . . . . . . . . . 37 3.6.1. Fine-Grained Street Network Enables Short Walk Distances . . . . . . . . 38 iii Contents 3.6.2. Data-Driven Demand is Heterogeneous . . . . . . . . . . . . . . . . . . . . 39 3.6.3. Explicit Stop Times Ensure Penalty For Each Stop . . . . . . . . . . . . . 41 3.6.4. Imbalanced Demand Requires Rebalancing of Buses . . . . . . . . . . . . 42 3.6.5. More Detailed Assignment Algorithm Uses Constraints . . . . . . . . . . 43 4. Quantifying Sustainability of Ride Sharing 45 4.1. Two Mechanisms Influence Ride Sharing Sustainability . . . . . . . . . . . . . . . 46 4.1.1. Pickup Detours Increase Distance Driven . . . . . . . . . . . . . . . . . . 46 4.1.2. Trip Overlap Reduces Distance Driven . . . . . . . . . . . . . . . . . . . . 47 4.2. Distance Driven Reduces with Bus Occupancy . . . . . . . . . . . . . . . . . . . 48 4.3. Ride Sharing is more Sustainable than Private Cars for Sufficient Load . . . . . . 50 4.4. Result is Robust for more Complex Models . . . . . . . . . . . . . . . . . . . . . 52 4.5. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54 5. Ride Sharing Sustainability with Stop Pooling 55 5.1. Ride Sharing Trades Sustainability for Travel Time . . . . . . . . . . . . . . . . . 57 5.2. Stop Pooling is more Sustainable at Same Travel Time . . . . . . . . . . . . . . . 58 5.2.1. Roughly Constant Distance Driven Despite Saved Stops . . . . . . . . . . 58 5.2.2. Stop Pooling Reduces Travel Time . . . . . . . . . . . . . . . . . . . . . . 59 5.2.3. Stop Pooling Breaks The Trade-off Between Sustainability And Travel Time 60 5.3. Higher Stop Pooling Effect for High Loads . . . . . . . . . . . . . . . . . . . . . . 61 5.3.1. Stop Pooling Limits Growth of Best Travel Time . . . . . . . . . . . . . . 62 5.3.2. Stop Pooling Breaks Trade-off for Sufficient Load . . . . . . . . . . . . . . 63 5.4. Robust Effect for Simple Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 5.5. Robust Effect with More Detailed Model . . . . . . . . . . . . . . . . . . . . . . . 66 5.5.1. Load Quantifies Stop Pooling Sustainability . . . . . . . . . . . . . . . . . 67 5.5.2. Already 1.2 Minutes Walk Time might Save 1 Minute Travel Time . . . . 68 5.5.3. Robust Result for Different Parameters . . . . . . . . . . . . . . . . . . . 69 5.6. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69 6. Ride Sharing Reliability with Stop Pooling 71 6.1. Unreliable Standard Ride Sharing with Fluctuating Demand . . . . . . . . . . . . 72 6.2. More Reliable Stop Pooling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73 6.3. Robust Effect of Stop Pooling with Limited User Delay . . . . . . . . . . . . . . 77 6.4. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 6.5. Outlook . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78 7. Discussion 81 7.1. Results and Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81 7.1.1. When is Ride Sharing More Sustainable than Private Cars? . . . . . . . . 81 7.1.2. How Does Stop Pooling Influence Sustainability of Ride Sharing? . . . . . 82 7.1.3. How Does Stop Pooling Influence Reliability of Ride Sharing? . . . . . . . 82 7.2. Limitations of the Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82 7.2.1. Simple Algorithms for Ride Sharing and Stop Pooling . . . . . . . . . . . 82 7.2.2. Integrate Adaptive Stop Pooling into Virtual Bus Stops . . . . . . . . . . 83 7.2.3. Distance Driven as Estimator for Ecological Sustainability . . . . . . . . . 83 7.2.4. Deviations from Load Prediction . . . . . . . . . . . . . . . . . . . . . . . 84 7.2.5. Mean-Field Factors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.2.6. Further Effects . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 7.3. Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 A. Appendix 87 A.1. Manhattan Street Network Resembles Grid . . . . . . . . . . . . . . . . . . . . . 87 A.2. Computation Details of Bisection Method . . . . . . . . . . . . . . . . . . . . . . 88 A.3. Average Pickup Distance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89 A.4. Robustness of Ride Sharing Sustainability . . . . . . . . . . . . . . . . . . . . . . 90 A.5. Stop Pooling Saves Stops . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90 A.6. Stop Pooling Effectively Reduces Load . . . . . . . . . . . . . . . . . . . . . . . . 92 A.7. Example Breaking of Trade-off in Simple Model . . . . . . . . . . . . . . . . . . . 93 A.8. Transition in Best Walk Limit . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94 A.9. Maximal Trade-off Shift Increases with Load . . . . . . . . . . . . . . . . . . . . 95 A.10.Rebalancing Buses is more Important with Constraint . . . . . . . . . . . . . . . 97 A.11.Breaking of Trade-off in Complex Model . . . . . . . . . . . . . . . . . . . . . . . 98 A.12.More Stop Pooling at Destinations and High Demand . . . . . . . . . . . . . . . 99 A.13.Roughly Constant Wait and Drive Time in Adaptive Stop Pooling . . . . . . . . 100 A.14.Influence of Capacity Constraint . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 A.15.Walk Time of Rejected Users . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101 Bibliography 101 Acknowledgment 116 Statement of Contributions 118

L'émergence de mouvements cohérents à grande échelle a été abondamment observée dans les populations animales (nuées d'oiseaux, bancs de poissons, essaims de bactéries...) et plus récemment au sein de systèmes artificiels. De tels ensembles d'individus auto-propulsés, susceptibles d'aligner leurs vitesses, présentent des propriétés physiques singulières. Cette thèse théorique étudie divers aspects de ces systèmes actifs polaires.Dans un premier temps, nous avons modélisé une population de colloïdes auto-propulsés. En étroite association avec les travaux expérimentaux, nous avons décrit la dynamique du niveau individuel à l'échelle macroscopique. Les résultats théoriques expliquent l'émergence et la structure de motifs cohérents : (i) transition vers le mouvement collectif, (ii) propagation de structures spatiales polarisées, (iii) amortissement des fluctuations de densité dans un liquide polaire, (iv) vortex hétérogène dans des géométries confinées.D'un point de vue plus fondamental, nous avons ensuite étudié les excitations non linéaires qui se propagent dans les systèmes actifs polaires. L'analyse des théories hydrodynamiques de la matière active, à l'aide d'outils issus des systèmes dynamiques, a permis de rationaliser les observations expérimentales et numériques reportées jusqu'ici.Enfin, nous avons proposé une approche complémentaire pour caractériser les populations actives. Associant étude numérique et résultats analytiques, nous avons étudié les propriétés géométriques des trajectoires individuelles, ainsi que leur enchevêtrement au sein de groupes tridimensionnels. Ces observables pourraient permettre de sonder efficacement la dynamique de populations animales. / The emergence of coherent motion at large scale has been widely observed in animal populations (bird flocks, fish schools, bacterial swarms...) and more recently in artificial systems. Such ensembles of self-propelled individuals, capable of aligning their velocities, are commonly referred to as polar active materials. They display unique physical properties, which we investigate in this theoretical thesis.We first describe a population of self-propelled colloids. In strong connection with the experiments, we model the dynamics from the individual level to the macroscopic scale. The theoretical results account for the emergence and the structure of coherent patterns: (i)~transition to collective motion, (ii)~propagation of polar spatial structures, (iii)~damping of density fluctuations in a polar liquid, (iv)~heterogeneous vortex in confined geometries.We then follow a more formal perspective, and study the non-linear excitations which propagate in polar active systems. We analyze the hydrodynamic theories of active matter using a dynamical-system framework. This approach makes it possible to rationalize the experimental and numerical observations reported so far.Finally, we propose a complementary approach to characterize active populations. Combining numerical and analytical results, we study the geometric properties of the individual trajectories and their entanglement within three-dimensional flocks. We suggest that these observables should provide powerful tools to describe animal flocks in the wild.

Endosomes are dynamic vesicular structures which transport cargo molecules internalized into the cell via endocytosis. Endosomal trafficking of cargo involves a large number of individual endosomes that regularly interact with each other via fusion and fission and thus form a dynamic network wherein endocytosed cargo is sorted and transported to various other intracellular compartments. In this study we present a general theoretical framework that takes into account individual endosomes and several key microscopic interaction processes among them. By combining theory with quantitative experiments, we seek to address the fundamental question of how the behaviour of the endosomal network emerges from the interactions among many individual endosomes of different sizes and cargo contents. Our theory is based on distributions of endosomes of various sizes and cargo amount. We compare our theory to experimental time course distributions of LDL, a degradative cargo, in a population of early endosomes. Early endosomes display a broad distribution of cargo with a characteristic power law, which we show is a consequence of stochastic fusion events of cargo carrying early endosomes. A simple model can quantitatively describe time-dependent statistics of LDL distributions in individual early endosomes. From fits of the theory to experimental data we can determine key parameters of endosomal trafficking such as the endosome fusion rate and the fluxes of cargo into and out of the network. Our theory predicts several experimentally confirmed scaling behaviours, which arise as a result of endosome fusion. Our theory provides a link between the dynamics at individual endosome level and average properties of the endosomal network. We show from our theory that some features of the endosomal distributions, which arise from interactions among individual endosomes, are sensitive to alterations in chosen parameters. This provides a direct means to study perturbation experiments wherein the cargo distribution can vary in response to changes of the endocytic system. Our analysis provides a powerful tool for the study of genetic and chemical perturbations that may alter specific systems properties and for extracting various kinetic rates involved in endosomal trafficking from only still images at different points.

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.

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.