Hernández, Damián G. (2015) Fenómenos colectivos en estructuras complejas / Collective phenomena in complex structures. Tesis Doctoral en Física, Universidad Nacional de Cuyo, Instituto Balseiro.
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Resumen en español
En este trabajo estudiamos la relación entre el comportamiento colectivo de un sistema y los elementos individuales que lo componen, desde dos perspectivas. Desde un enfoque del modelado, analizamos como la dinámica de los agentes y su patrón de interacciones afecta el estado global del sistema. Por otro lado, desde un punto de vista del análisis de datos, nos embarcamos en la tarea de encontrar las interacciones entre los elementos, dado determinado estado del sistema. La primera parte se lleva a cabo considerando varias aristas particulares del asunto. Primero, estudiamos la diversidad en el estado asintótico de una población que participa de un juego evolutivo de dos estrategias como función del tamaño del grupo de interacción. Para tal caso, se observa la presencia de un fenómeno critico. En segundo lugar, se analizan la supervivencia y extinción de estrategias en un juego cíclico, donde introducimos la cooperación entre agentes débiles dentro de tripletes, obteniendo que tal cooperación solo beneficia la estrategia que la emplea cuando esta supera cierto umbral. Finalmente, estudiamos el problema de distribución de recursos en una población desde una original perspectiva evolutiva. En este contexto, nos preguntamos como un factor de incertidumbre, asociado a la cantidad de recursos de los oponentes, modifica las estrategias asintóticas adoptadas por los agentes. La segunda parte |esto es, como detectar dependencias entre los elementos de un sistema, dado cierto estado global| se encara desde el marco de la teoría de la información, y se aplica al caso particular de interacciones entre palabras en lenguaje escrito. A través de técnicas de máxima entropía, proponemos un análisis de tríos de variables para revelar la estructura de dependencias. Con este método, no solo somos capaces de encontrar interacciones puras de a tres, sino que también podemos detectar interacciones de a dos que se explican por medio de una tercera variable.
Resumen en inglés
In this work we study the relation between the collective behavior of a system and its individual component elements, from two perspectives. From a modeling approach, we analyze how the dynamics of the agents and their pattern of interaction affects the global state of a system. On the other side, from a point of view of data analysis, we embark in the task of nding the interactions between the elements, given a certain state of the system. The rst part is carried out considering several particular angles. Firstly, we study the diversity in the asymptotic state of a population involved in a two-strategy evolutionary game as a function of the size of the group of interaction, observing the presence of a critical phenomenon. Secondly, the survival and extinction of strategies are analyzed in a cyclic game, where we introduce the cooperation between weak agents within triplets, obtaining that cooperation only benet the strategy that employs it when it exceeds certain threshold. Finally, we study the problem of resource allocation in a population from a novel evolutionary perspective. In this context, we ask how an uncertainty factor, regarding the amount of resources of the opponents, modify the asymptotic strategies adopted by the agents. The second part |that is, how to detect dependencies between elements of a system, given certain global state| is faced from the framework of information theory, and it is applied to the particular case of interactions between words in written language. Through maximum entropy techniques, we propose an analysis of triplet of variables to unveil the structure of dependencies. By this methodology, we are not only able to nd pure triple interactions, but we also can detect pairwise dependencies that are explained through a third variable.
| Tipo de objeto: | Tesis (Tesis Doctoral en Física) |
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| Palabras Clave: | Game theory; Teoría de juego; Entropy; Entropía; [Collective behavior; Comportamiento colectivo; Dependencies; Dependencias; Evolutionary game theory; Teoría de los juegos evolutivos] |
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| Materias: | Física > Sistemas complejos |
| Divisiones: | Gcia. de área de Investigación y aplicaciones no nucleares > Gcia. de Física > Sistemas complejos y altas energías > Física estadística interdisciplinaria |
| Código ID: | 1001 |
| Depositado Por: | Tamara Cárcamo |
| Depositado En: | 13 Jun 2022 10:44 |
| Última Modificación: | 13 Jun 2022 10:44 |
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