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Mención Internacional en el título de doctor SUMMARY, REMARKS AND FUTURE WORK. Culture is one of the classical examples that is normally used to define a complex system. The inherent complexity of humans interacting directly provides enough diversity of phenomena, but if we also consider sociological problems that live in wider timescales, then it becomes boundless. The subject of the interaction is no more the person alone, but the different social constructs that coexist within a society, as, for example, different kind of social norms and expressions. The growing complexity of social systems is also confusing because it has not been traditionally understood in this way, which is logical because we have studied society from the different perspectives that have appeared historically. Humanities have studied the different holistic products that appear from complexity, like literature, philosophy or the different types of artistic studies. As we stated in the introduction, a different perspective appeared when the scientific method started comparative studies of society, bringing new tools, mainly modelling of general effects and statistics. Herbert Spencer popularized the analogy of considering the society as a human being, this is, as a cooperative organization of the different organs and tissues in order to provide a collective structure. And this is the main spirit of complexity sciences, which started to have more importance in the end of the XX century, giving rise to a new wave on how to understand quantitatively social systems. At this moment, we recall the title of this thesis: Behavior and context. The problem in the description of the context is a methodological one. Context is the conjunction of relevant circumstances correlated with the social description of an individual. Traditionally, the social description of a variable has been related with socioeconomic indicators, where the presence of the social structure is only understood with scalar variables. In this work, we show the importance of the network structure in the resemblance of this social profile, and how geometry may act as a proxy of this social variables containing, potentially, more information than just scalar variables. The behavior is correlated with the geometry of this social profile. The importance of the network version of the social profile can be checked by its correlation with the cultural variables of the ego. This is important because it reveals an idiosyncratic manner of making social relationships, and, therefore, the role of social institutions. But the network version is not only a proxy for cultural variables, it is a true identifier of people. A proof of this is the connection between personal profiles and probability of connection, showing that the similarity in the close structural network may be a proxy for social homophily, connected, therefore, to personal and cultural values. Therefore, we have identified a unit component (in terms of measure) of the individual, social and cultural influence on individuals, providing a personal signature around which social homophily appears, even in a complex context where culture and social values play a key role. At the end of the day, this thesis could be summarized by saying that the geometric structure of the close social environment is a signature of the individual and of its social and cultural values. Similarity in this signature is related to social homophily. The other main message that can be extracted from this thesis is related to the importance of ethnic groups in social modelling. Social modelling can not be replicated easily with a markovian model with binary interactions. This is due to the inherent complexity that was pointed out at the beginning of the chapter. Social phenomena exist in several timescales, and because of this they have a lot of implicit information. An ethnic group may exist because of this implicit information, due to, for example, a pre-existing social symbolism; but, in order to arise spontaneously from the social outcome of a binary process (in the way game theory works), some optimization is needed. This is, the existence of a marker does not provide, necessarily, a social separation depending on that variable, if this variable does not provide some kind of improvement in the fitness. This advantage may exist due to an asymmetrical social configuration, for example, in the case of a hierarchy. Previous works have shown the spontaneous appearance of this kind of structures [102], remarking again the importance of the different timescales in this kind of phenomena. An asymmetric social configuration allows the function to be optimized with ethnic markers, and the arena where cultures may compete, reinforcing the roles of their individuals, and building therefore, the different social profiles. With respect to the experimental part, the results that we obtain suggest that ethnic markers experiment should be replicated in contexts with different social configurations, studying, again, as the title suggests, the dependence on the context. It would be interesting the replication of simple ethnic separation altogether with a hierarchy or some reputation system. Once more, following the spirit of all the thesis, connects the importance of the ethnic, personal identifications with the social organization, that regulates its importance in the social equilibrium. In view of these conclusions, future works in this field should go deeper into the importance of the geometric social profile of the ego networks as an individual identifier. In this case, more data needs to be collected, in order to research other sociological variables like different aspects of culture, religion, political views or socioeconomic measures. Note that in the case of the present work, we have focused on the nationality, as the dataset provided us with a diverse sample of nationalities and the control group. In order to study other sociological variables, like wealth, race, gender or a particular social norm, new data is needed that fits those necessities. Moreover, we have focused on networks centered in the ego, where we have a perspective on the close social structure. It would be also interesting to study how much information is needed in order to study different kinds of networks. This is interesting from a practical point of view, as it could help to use different datasets to provide further proofs of the existence of the social signature, but also to check more properties of this measure. It would be interesting, for example, to study if family networks provide us enough information to talk about the different social values and/or material conditions of different families. If the information about the signatures still can be extracted, new datasets could be reused to make a stronger point about the cultural signature, saving the time of collecting new ego networks. Another possible path to follow in the future could be the study of signed networks together with the cultural profile. In our works, we have studied the importance of the social signature in order to determine the cultural profile, and its importance in the outcome of a relationship. It would be interesting to show the connection between these two elements, providing a relationship between cultural or socioeconomic variables and the friends or enemies an individual may have. The final suggestion for future work is related to the measure of properties of this social signature.We have stressed in the introduction (and in several chapters of the thesis) that the cultural values are a holistic product, which may be assumed and created by collectivities. In this work we have focused on a model that is based in the relationship between individual and its environment (in a mean-field like approach), but this is not needed. Considering again the example of the family, perhaps the family could be understood as a whole, and study the problem of its close social environment from a perspective of networks. Given that the problem of culture exists in several scales, it would be interesting to check if new relationships arise from this point of view. At the end of the day, all of these suggestions are basically related to checking the potential of the measure. This poses also an ethical question: if the potential of the social signature is shown in more contexts, and it correlates with personal information, it is important that these studies (public or private) are carried with the utmost concert about their possible implications and misuses. Programa de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid Presidente: Jesús Gómez Gardeñes.- Secretario: Alberto Antonioni.- Vocal: Andreia Sofía Monteiro Teixeira

Mención Internacional en el título de doctor This thesis set out to contribute to the realm of social physics, with a particular focus on human social networks. Our approach, however, is somewhat di erent from what is typical in disciplines such as complex systems or statistical physics. Rather than simplifying the features of the constituents of our system (people), and stressing their rules of interaction, we focus on better understanding those very same constituents, modelling them as social atoms. Our rationale is that a better understanding of such an atom may shed light on how (and why) it interacts with other atoms to form social collectives. Given its robustness and the evolutionary roots of its premises, we use the Social Brain Hypothesis as our departure point. This theory states that the evolutionary drive behind the development of large brains in humans was the need to process social information and that the limited capacity of our brains imposes a limit to the number of relationships we can manage— the so-called “Dunbar’s number”, roughly 150. Moreover, evidence keeps revealing that these relationships are further organised in a series of hierarchically inclusive layers with decreasing emotional intensity, whose sizes exhibit a more or less constant scaling. Notwithstanding the empirical evidence, neither the presence of scaling in the organisation of personal networks nor its connection with limited cognitive skills had been explained so far. In Chapter 2 we present a mathematical model that solves this puzzle. The assumptions of the model are quite simple, and well founded on empirical evidence. Firstly, the number of relationships we maintain tends to be stable on average. Secondly, these relationships are costly, and our resources are limited. With these two premises, our results show that the hierarchical organisation emerges naturally from the principle of maximum entropy. Not only that, but we also predict a hitherto unnoticed regime of organisation whose existence we prove using several datasets from communities of immigrants. The former model considers that relationships can only belong to a discrete set of categories (layers). In Chapter 3 we extend it so that relationships are classified in a continuum. This modification allows us to test the model with data from very di erent sources such as online communications, face-to-face contacts, and phone calls. Our results show that the two regimes of organisation found in the previous model persist in this variant, and reveal the underlying existence of a (universal) scaling parameter which does not depend on any particular number of layers. To incorporate these ideas into socio-centric models, we build on the so-called Structural Balance Theory. This theory, underpinned by psychological motivations, posits that the structure of social networks of positive and negative relationships are highly interdependent. However, the theory has received little empirical validation, and negative social relationships are poorly understood—both from an ego-centric and a socio-centric perspective. For that reason, we turn to developing an experimental software in order to gather data within a school. In Chapters 4 and 5 we present results from these experiments. In Chapter 4 we analyse the socio-centric networks using machine learning techniques and find that the structure of positive and negative networks is indeed very much connected. Besides, we study the two types of networks separately, showing that they exhibit quite distinct features and that gender e ects in negative social networks are weak and asymmetrical for boys and girls. In Chapter 5, on the other hand, we focus on the structure of negative personal networks. Remarkably, using data from two di erent experimental settings, we show that the structure of personal networks of negative relationships mirrors that of the positive ones and exhibits a similar scaling—albeit their size is significantly smaller. Chapter 6 summarises our results and presents future (and current) lines of investigation. Among them, we outline a model of a social fluid that uses the insights gained with this thesis to build a model of social collectives as ensembles of personal networks. This model is compatible, at the micro-level, with the observations of the social brain hypothesis, and, at the macro-level, with the premises of the structural balance theory. This thesis would not have been possible without the support of Fundación BBVA through its 2016 call project ”Los números de Dunbar y la estructura de las sociedades digitales: modelización y simulación (DUNDIG)”, and we are very thankful for it. Support for early stages of this work through projects IBSEN (European Commission, H2020 FET Open RIA 662725) and VARIANCE (Ministerio de Economía y Competitividad/FEDER, project no. FIS2015-64349-P) is also acknowledged Programa Oficial de Doctorado en Ingeniería Matemática por la Universidad Carlos III de Madrid Presidente: Javier Martín Buldú.- Secretario: José Luis Molina González.- Vocal: Roberta Sinatra

The question of analyzing the predictability of human behavior has been widely studied in literature, to unveil how individuals move, how they can be mobilized and, more philosophically, to understand to what extent our decisions are random or whether we are free to choose. As a consequence of humans relate to each other, we also tend to live in groups at different hierarchies in a social way so it is interesting to analyze how individual features and choices affect the global structure of a society. In this work, we explore the limits of human predictability in terms of shopping behavior, observing that, even when we are constrained to a limited set of possible places where we can make a purchase, predicting where the next purchase will happen is not accurately possible to do by only observing the past. The next question is to study how individual decisions affect emergent phenomena such as the economy or information diffusion across a country. We analyze the contents, temporal and mobility patterns extracted from users’ social media publications to build a profile of the geographical regions that allow to predict the unemployment rate. Finally, we also use a mobile phone call dataset to test whether the dynamics at the urban level, how people create and destroy links within a city, affect the inter-urban diffusion of diseases, virus or rumors. Our results suggest that inter-regional structure is robust and does not vary significantly on time so diffusion processes can be well modeled in terms of static properties of the inter-urban network., Programa Oficial de Doctorado en Ingeniería Matemática, Presidente: Javier Borge Holthoefer.- Secretario: Rubén Cuevas Rumín.- Vocal: Josep Perelló Palou

Mención Internacional en el título de doctor, Cooperation and coordination is a desirable behavior that is fundamental for the harmonious development of society. People need to rely on cooperation with other individuals in many aspects of everyday life, such as teamwork and economic exchange in anonymous markets. However, cooperation may easily fall prey to exploitation by selfish individuals who only care about short-term gain. For cooperation to evolve, specific conditions and mechanisms are required, such as kinship, direct and indirect reciprocity through repeated interactions, or external interventions such as punishment. In this dissertation we investigate the effect of the network structure of the population on the evolution of cooperation and coordination. We consider several kinds of static and dynamical network topologies, such as Barabási–Albert, social network models and spatial networks. We perform numerical simulations and laboratory experiments using the Prisoner’s Dilemma and coordination games in order to contrast human behavior with theoretical results. We show by numerical simulations that even a moderate amount of random noise on the Barabási–Albert scale-free network links causes a significant loss of cooperation, to the point that cooperation almost vanishes altogether in the Prisoner’s Dilemma when the noise rate is high enough. Moreover, when we consider fixed social-like networks we find that current models of social networks may allow cooperation to emerge and to be robust at least as much as in scale-free networks. In the framework of spatial networks, we investigate whether cooperation can evolve and be stable when agents move randomly or performing L´evy flights in a continuous space. We also consider discrete space adopting purposeful mobility and binary birth-death process to discover emergent cooperative patterns. The fundamental result is that cooperation may be enhanced when this migration is opportunistic or even when agents follow very simple heuristics. In the experimental laboratory, we investigate the issue of social coordination between individuals located on networks of contacts. In contrast to simulations, we find that human players dynamics do not converge to the efficient outcome more often in a social-like network than in a random network. In another experiment, we study the behavior of people who play a pure coordination game in a spatial environment in which they can move around and when changing convention is costly. We find that each convention forms homogeneous clusters and is adopted by approximately half of the individuals. When we provide them with global information, i.e. the number of subjects currently adopting one of the conventions, global consensus is reached in most, but not all, cases. Our results allow us to extract the heuristics used by the participants and to build a numerical simulation model that agrees very well with the experiments. Our findings have important implications for policymakers intending to promote specific, desired behaviors in a mobile population. Furthermore, we carry out an experiment with human subjects playing the Prisoner’s Dilemma game in a diluted grid where people are able to move around. In contrast to previous results on purposeful rewiring in relational networks, we find no noticeable effect of mobility in space on the level of cooperation. Clusters of cooperators form momentarily but in a few rounds they dissolve as cooperators at the boundaries stop tolerating being cheated upon. Our results highlight the difficulties that mobile agents have to establish a cooperative environment in a spatial setting without a device such as reputation or the possibility of retaliation. i.e. punishment. Finally, we test experimentally the evolution of cooperation in social networks taking into account a setting where we allow people to make or break links at their will. In this work we give particular attention to whether information on an individual’s actions is freely available to potential partners or not. Studying the role of information is relevant as information on other people’s actions is often not available for free: a recruiting firm may need to call a job candidate’s references, a bank may need to find out about the credit history of a new client, etc.We find that people cooperate almost fully when information on their actions is freely available to their potential partners. Cooperation is less likely, however, if people have to pay about half of what they gain from cooperating with a cooperator. Cooperation declines even further if people have to pay a cost that is almost equivalent to the gain from cooperating with a cooperator. Thus, costly information on potential neighbors’ actions can undermine the incentive to cooperate in dynamical networks., Programa Oficial de Doctorado en Ingeniería Matemática, Presidente: José Antonio Cuesta Ruiz.- Secretario: Maxi San Miguel.- Vocal: Daniele Vilone

This thesis has been a joint project between Universidad Carlos III de Madrid and Telefónica Research (Spain). Specifically, the research has been conducted at the GISC (Grupo Interdisciplinar de Sistemas Complejos), group of Universidad Carlos III and at the analytics and data mining and user modelling research teams of Telefónica Research. The main interest of this research has been in understanding and characterizing large networks of human interactions as continuously changing objects, which members appear and disappear over time and which interactions are characterized by temporal correlations and inhomogeneities. This constitutes a very challenging and novel topic. In fact, although many real social networks are temporal or dynamical networks, which elements and properties continuously change over time, traditional approaches to social network analysis are essentially static: ties (and tie weights) are given by the aggregated activity observed in a given time period, nodes and ties are considered persistent over time, temporal inhomogeneities and correlations between interaction events are neglected, etc. Within this frame, therefore, the time dimension of human behavior has typically been projected out. Although much effort has been devoted in the last years to characterize the temporal patterns of human interaction, a general understanding of how dynamically model real social networks is still missing. In this thesis we contribute to advancing the state of the art in this area by investigating the instantaneous, instead than the aggregated, contact network and by analyzing the role of temporal activity patterns of human interaction in the description and modeling of real social networks. Specifically, we investigated the role that topological and, in particular, temporal patterns of human interaction play in three main topics of social network analysis and data mining: the characterization of time (or attention) allocation in social networks, the prediction of link decay and/or persistence and the analysis and modeling of information spreading phenomena. To this end, we have analyzed large anonymized data sets of phone call communication traces (Call Detail Records or CDR) over long periods of time. Access to these observations was granted by Telefónica Research. The availability of empirical data about such massive networks allowed us to analyze and measure global features of human behavior and interaction and to characterize phenomena and tendencies that might be invisible at small scale. At the same time, the fine-grained resolution of the datasets we had access to and the fact that they cover a large sample of the population, ensure the significance and universality of our findings. The findings that emerge from our research indicate that the observed inhomogeneities and correlations of human temporal patterns of interactions significantly affect the current view of social networks, shifting from a very steady to a highly complex entity. Temporal patterns of communication are essential not only for a better characterization of the inherent properties of human behavior, but also, and more importantly, for the understanding and modeling of all those phenomena which are triggered by the way in which people communicate and behave. Examples are diffusion of epidemics, information spreading, opinion and influence phenomena and group formation. Our results indicate the necessity to incorporate temporal patterns of communication in the analysis of social networks: since structure and dynamics are tightly coupled, the analysis and modeling of human behavior has to factor in both. The work of this thesis combines data mining, the analysis of large datasets, theoretical modeling, simulations and experiments on empirical data. In addition, this also has a wide range of applications in many business sectors. In particular, at Telefónica Research, part of our techniques and findings have been successfully applied to areas such as social networks analysis, modeling human influence, customer segmentation and targeting in viral marketing campaigns. We believe this work has made a contribution to understanding and modeling real social networks and and we are confident that it will encourages further research in this field., Entender la dinámica de comunicación entre personas en una red social es uno de los problemas clave de la ciencia contemporánea y juega un papel fundamental en situaciones tales como detección temprana de epidemias, pero también en procesos como la difusión de información comercial, marketing viral, propagación de noticias, opiniones o rumores. De hecho, todos esos procesos están estrictamente relacionados con la forma en que las personas están conectadas e interactúan y con los mecanismos que regulan la dinámica de esas interacciones. Tradicionalmente, el estudio de las redes sociales y de la dinámica de comunicación entre personas se ha basado principalmente en el análisis de cuestionarios y estudios dirigidos a pequeños grupos de individuos, limitando la generalización a gran escala de los resultados y por tanto una comprensión completa del comportamiento humano y de muchos procesos reales basados en ello. En los últimos años, la existencia de grandes bases de datos electrónicos sobre interacción entre personas, como e-mail, llamadas de teléfono o mensajes en redes sociales online como Facebook o Twitter, ha facilitado el estudio sobre el comportamiento humano y cambiado radicalmente la forma de entender y modelizar las redes sociales, tanto que se habla ya de un nuevo tipo de ciencia emergente: la ciencia de las redes sociales o ciencia social computacional. De hecho, el estudio del comportamiento humano basado en bases de datos electrónicos a gran escala y durante períodos largos de tiempo ofrece una oportunidad de estudiar y modelar los fenómenos sociales que no tiene precedentes en ciencias sociales, económicas o de sistemas complejos. La mayoría de estudios de redes sociales en las últimas décadas se han enfocado en caracterizar la estructura topológica de la red (con quién se relaciona cada individuo) y entender las propiedades de esa estructura durante un período de observación dado. Se ha observado, por ejemplo, que en las redes sociales la distancia topológica desde cualquier nodo de la red a otro es mucho más pequeña que el tamaño (número total de nodos) de la red (efecto de ”pequeño mundo”) o que en estas redes hay un número inusual de grandes conectores (hubs), que poseen la mayor parte de las conexiones sociales. Sin embargo, en estos estudios normalmente no se incluyen las propiedades temporales de la actividad humana y se asume que las redes sociales son objetos estáticos cuyas propiedades se obtienen agregando en el tiempo la actividad de los individuos: tanto los nodos de la red cuanto las conexiones sociales se consideran permanentemente activas y el peso o importancia de cada relación sólo depende del volumen total de interacción entre las dos personas involucradas. Además, se asume que los eventos no están relacionados entre sí y que la interacción entre dos personas ocurre de forma homogénea en el tiempo, o sea que puede ocurrir de forma aleatoria en cualquier instante. Sin embargo, estudios recientes de la actividad humana han demostrado que los patrones temporales de esta actividad son altamente heterogéneos. De hecho, las conexiones sociales se forman y se destruyen en el tiempo y la actividad humana, por ejemplo el número de email mandados por un mismo usuario al día o la interacción entre dos personas, se produce a ráfagas, es decir períodos muy intensos de conversaciones se alternan con largos períodos de inactividad. Además, se ha observado que la comunicación humana sucede en conversaciones en grupo, es decir, aunque se produce a ráfagas, ´estas ocurren a la vez entre los miembros de un grupo social. Esa heterogeneidad de los patrones temporales de la actividad humana afecta la forma de comprender y modelar las redes de interacción humana, las propiedades topológicas de las mismas, así como la dinámica de muchos procesos reales. Sin embargo, a pesar de su importancia, todavía se sabe muy poco de cómo incorporar las propiedades temporales en la descripción y modelización de las redes sociales. Nuestro principal objetivo ha sido avanzar en este problema y con dos propósitos principales. Por un lado, entender y cuantificar no solo las propiedades estructurales, sino también los patrones temporales de comunicación entre personas y comprender como afectan a la actual descripción de las redes sociales. Frente a la visión estática de una red social (cómo están conectados los individuos dentro de una red), nuestro estudio ha buscado entender también cuándo y cómo se producen esas relaciones sociales en el tiempo. Por otro lado, nos hemos interesado en entender cómo esos ritmos de interacción afectan procesos dinámicos globales con un particular interés en fenómenos de la difusión de informaciones en redes sociales. Como consecuencia, nuestro propósito más general ha sido proporcionar una mejor caracterización de las redes sociales como entidades dinámicas en lugar de estáticas, incluyendo no sólo las propiedades topológicas de la red sino también los patrones temporales. Este proyecto de tesis ha sido una colaboración entre la Universidad Carlos III de Madrid y Telefónica I+D, a través de la beca Becas de Formación de Doctores Telefónica I+D y Universidad Carlos III de Madrid y sucesivas colaboraciones. En particular, Telefónica I+D nos ha proporcionado el acceso a bases de datos totalmente anonimizadas de llamadas telefónicas (Call Detail Record o CDR), cuyo análisis nos ha permitido de investigar las propiedades estructurales y dinámicas de masivas redes sociales durante largos períodos de tiempo (aproximadamente 9.000 millones de llamadas entre 20 millones de usuarios durante períodos de 11-19 meses) construidas a partir de esos datos. Este gran volumen de datos y su extensión en tiempo garantiza la representatividad y universalidad de nuestros resultados. Nuestra metodología se ha basado entonces en el estudio de grandes redes sociales de llamadas telefónicas, en simulaciones sobre esas redes y la posterior análisis y modelización. Para alcanzar nuestros objetivos, en primer lugar hemos analizado y caracterizado las propiedades temporales de estas redes. De acuerdo con otros estudios, hemos observado que, dentro de la misma red egocéntrica de una persona, no todas las conexiones sociales tienen la misma importancia y que tanto los individuos como los enlaces entre ellos son altamente volátiles. Se ha observado además que la comunicación entre individuos no sucede de manera homogénea en el tiempo, sino que se produce a ráfagas y están organizadas en grupos de conversaciones. En segundo lugar hemos analizado el papel que todos estos aspectos temporales de la comunicación humana juegan en: (i) los procesos de organización y distribución de tiempo y atención de una persona dentro de su red de contactos, (ii) la caracterización de una relación social a partir de la observación de actividad entre dos personas y del rol que esa actividad tiene en la predicción de la persistencia o decaimiento de la misma relación en el futuro y (iii) procesos de difusión de información en redes sociales. Uno de los motivos por los cuales las redes sociales no han sido estudiadas de forma dinámica es el hecho de que los procesos de creación y destrucción de los enlaces sociales están enmascarados por la actividad a ráfagas de las interacciones humanas. La dificultad en el separar esos dos procesos, junta a la convicción de que la escala de tiempo que regula la creación y destrucción de los enlaces sociales es mucho mas lenta que la de interacción, han favorecido hasta ahora una descripción agregada y estática de las redes sociales, frente al estudio de la red instantánea. Sin embargo, nosotros hemos propuesto un método que nos permite separar las dos escalas de tiempo de esos dos procesos y analizar, con mucha precisión, la red instantánea de cada usuario. Este análisis nos ha permitido investigar cómo cantidades esenciales en el análisis de redes sociales, como la conectividad social de un individuo, están afectados por la continua formación (destrucción) de nuevos (antiguos) enlaces. Contrariamente a la infinita (o muy grande) capacidad social predicha por algunos modelos estáticos, nosotros hemos observado que existe un límite a dicha capacidad y que, a pesar que las conexiones sociales se forman y destruyen en el tiempo, cada individuo mantiene un número limitado y constante de contactos a lo largo del tiempo. Mientras el número de contactos que cada usuario mantiene en el tiempo nos da informaciones sobre su capacidad social, el número de conexiones creadas o destruidas en una dada ventana temporal mide su actividad social. La identificación y el análisis de estas dos medidas, que normalmente se consideran como una única cantidad (la conectividad social), nos han llevado al descubrimiento y caracterización de distintos tipos de estrategias de comunicación. Mientras algunos individuos mantienen en el tiempo siempre el mismo conjunto de contactos (estrategia estable), otros prefieren explorar varias partes de la red (estrategia exploradora) y están caracterizados por un círculo social muy volátil y muy poco conectado entre sí. Además hemos visto que la estrategia de comunicación de un individuo también caracteriza la estrategia de sus contactos, siendo estas dinámicas asortativas en la red. Es decir, la red est´a formada por grupos de individuos muy conectados y persistentes separados por grupos muy vol´atiles y desconectados. Este comportamiento afecta no sólo las dinámicas de cómo la gente distribuye su tiempo y atención entre su círculo social sino también, y más importante, procesos globales como la transmisión de información. En concreto nuestro estudio demuestra que, contrariamente al sentido común, las estrategias estables son más eficientes que las exploradoras para conocer antes información. El estudio de las propiedades dinamicas de la comunicación humana también nos ha llevado a demostrar que la forma en la que dos individuos interactúan en el tiempo permite caracterizar mucho más que el número total de comunicaciones: nos da información sobre el tipo de relación social que existe entre ellos. Por ello, hemos introducido simples cantidades para medir la duración total o el nivel de heterogeneidad temporal en una relación social. Esas cantidades, no sólo permiten distinguir entre distintos tipos de enlaces sociales, cosa imposible considerando sólo el número de llamadas, sino también nos dan información sobre el estado de la red social en una ventana futura. De hecho, aplicando un modelo sencillo de clasificación, hemos demostrado que tanto como las propiedades topológicas de los enlaces sociales, sus patrones temporales nos permiten predecir si un enlace, observado en un dado período temporal, es más o menos probable que decaiga o persista en el tiempo. Este estudio tiene importantes aplicaciones no sólo en la caracterización de un enlace social, sino en la predicción y gestión de la actividad en redes sociales. Finalmente, hemos analizado el impacto que los patrones temporales de comunicación tienen en el proceso de propagación de información. Para abordar este tema hemos utilizado simulaciones de uno de los modelos estándar en la propagación de epidemias e infecciones, el modelo SIR (Susceptible-Infectado-Recuperado), sobre las secuencias reales de llamadas entre personas. De esta forma, hemos podido tener en cuenta todos los aspectos de la comunicación real y analizar desde un punto de vista no sólo cualitativo, sino también cuantitativo, los efectos que esos aspectos tienen en el número de gente a la que puede llegar la información y en la velocidad de dicho proceso. La principal conclusión del estudio es que el hecho que las interacciones humanas suceden en ráfagas ralentiza la difusión de información, ya que los grandes períodos de inactividad en la comunicación entre dos personas hacen menos probable el traspaso de una información de una a otra. Por otro lado, las conversaciones entre grupos de personas aceleran la difusión de información dentro de esos grupos. Esos dos efectos compiten y son los ingredientes fundamentales en el proceso de difusión en redes sociales y, en general, en todos los procesos donde el tiempo entre eventos de actividad humana es decisivo. Por último, hemos propuesto una simple forma para representar las redes sociales dentro del esquema tradicional estático, pero teniendo en cuenta también las propiedades temporales de la interacción humana a través de lo que hemos definido fuerza dinámica de un enlace, contrariamente a la fuerza estática dada por el volumen de comunicación entre dos personas. Nuestro estudio permite por primera vez una descripción básica de las redes sociales en donde la fuerza de los enlaces incluye algunos aspectos de la dinámica de las interacciones y abre la puerta a su utilización para modelizar, entender y analizar redes sociales dinámicas. El proyecto constituye una combinación de simulación, modelización teórica, experimentación en redes sociales empíricas y aplicación al entorno empresarial. En este aspecto, por ejemplo, Telefónica I+D ha mostrado amplio inter´es por los resultados de nuestra investigación y, de hecho, parte de los resultados y del trabajo realizado se han aplicado con éxito al análisis de redes sociales y a campañas de marketing viral.