From mechanisms to data-inspired modeling of collective social phenomena

Abstract

Statistical physics is at the core of the study of complex systems. A complex system is one composed by simple entities which interact and through their interactions global emergent phenomena appear. These phenomena are impossible to derive given the study of the isolated units, as they arise from the interaction of those particles. Statistical physics creates specifically the link between microscopic mechanisms and global behavior. It has been successful in the traditional study of physics for example in describing phase transitions. But its success is not restricted to physics and it has been applied also in other fields such as biology, medicine, or computer science. Social phenomena are also being studied using this framework, as the book emph{Micromotives and Macrobehavior} by T. Schelling. This framework aims at explaining global regularities, such as the sudden appearance of fashions, or the adoption of one of two apparently equivalent technological innovations, or the sudden massive spread of a fad starting from the microscopic interactions of the entities in the system. In society the basic entities of the system are humans and as such they are very complex and their specific dynamics may be very difficult to describe. Nevertheless statistical physics teaches us that in many cases the specific details of the interaction are not important in order to qualitatively describe the behavior of the system. Symmetries, dimensionality and conservation laws are usually sufficient to know the behavior of the system. This concept is called universality and motivates the study of social phenomena using minimal models which isolate mechanisms (not individuals) and describe their consequences at the global level. The so called emph{Big Data} era has also clearly influenced the development of research here reproduced. In social phenomena this refers to the fast growing amount of data produced and stored, shaping the digital trace of virtually all individuals, organizations and other entities in (the developed) society. In this field computer scientist have the lead, as they are able to produce the tools that can properly handle this vast amount of data. Nevertheless the typical focus of those scientists is in extracting information from the data or creating informatics tools that can reproduce the data in an automated way (data-driven modeling, machine learning, Bayesian inference methods, pattern recognition).

As physicists what we have to offer is different, namely modeling from a theoretical perspective. The framework of Big Data offers the physicist the opportunity to test, compare and refine model results in order to devise the mechanisms in society responsible for a large class of social phenomena (diffusion of opinions or cultural traits, spreading of infectious diseases, traffic allocation problems among others). And why are models interesting or useful? On one side from a model one gains universal knowledge, that can be applied anywhere inside the frame of the model. On the other side a validated model lets the researcher investigate situations and apply measures which may be unfeasible in the real world, but can be reproduced with the use of computer simulations. Therefore they are useful for predicting unobserved situations or forecasting. This thesis is an instance of the abstract journey that many physicists have began. It is a journey that brings the traveler from a pure modeling framework that is sometimes flavored with a motivation coming from results of data analysis, toward bringing together information from the data and the theoretical mechanisms in a systematic way, both for having better informed models and for contrasting their results with real world data. Just modeling social systems from a Statistical physics perspective obliges the researcher to be between disciplines, but the addition of big data opens an extra dimension, which makes much more challenging the research. This thesis exemplifies just partly this journey and from a particular viewpoint, which is the one gained through the research and interactions with other scientists (mainly my advisors) I have developed in the last four years. So we will begin by abstract modeling unrelated to particular data (chapter~ref{ch1}), investigating the consequences of having states on the edges of a network. Typically social dynamics in the Statistical Physics framework had been studied by using individual based models, where agents are represented by nodes on a network and where the links between them represent their social relations.

Then the nodes usually are endowed with variables which encode their social option or state and evolve following certain microscopic rules that depend on their network environment. In this first work we change the focus in order to evaluate the consequences of several types of relation (states on the links of the social network) competing in a society under a majority rule. We find results that were not to be expected when using the node states-paradigm on the same network. In the next step we have as a starting point empirical results that show that human timing of interactions is highly heterogeneous. As usually this characteristic had not been taken into account, we develop a framework to add this characteristic in individual based models and show that implementing it may change the qualitative behavior of the studied models and not only changing the timescales. In the third step we go almost to the core of the data world, as we study hospital dynamics in the US, in particular hospital transfers and their characteristics referring to spreading processes. The last stop in the journey is the most complete of all, as it brings together data analysis of electoral data; bibliography research on social, political and physical sciences; model development both analytically and through simulations; naturally bringing real data into the model framework; and contrastation of the model results against real data. This effort is rewarded by a model that reproduces statistical regularities found in election data. The model is not just a model for elections, but an opinion dynamics model, giving us insights into the way opinions and hopefully cultural traits or even innovations diffuse in society. Furthermore it triggers further theoretical questions on the role of heterogeneities on diffusion processes. As a summary, this thesis follows from an effort of bringing together several disciplines, methodologies and points of view, and trying to accommodate the different inputs coming from them together in a unifying framework.