PhD thesis public defense. Supervisors: Maxi San Miguel & Víctor M. Eguíluz
This thesis is an instance of the abstract journey that many physicists have begun. It is a journey that brings the traveller from a pure modelling framework that is sometimes flavoured 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.
We will begin by abstract modeling unrelated to particular data, 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. 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 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.