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This article introduces into the whole section on Social Sciences, edited by A. Nowak for this Encyclopedia, concentrating on the applications of mathematics and physics. Here under mathematics we include also all computer simulations if they are not taken from physics, while physics applications include simulations of models which basically existed already in physics before they were applied to social simulations. Thus obviously there is no sharp border between applications from physics and from mathematics in the sense of our definition. Also social science is not defined precisely. We will include some economics as well as some linguistics, but not social insects or fish swarms, nor human epidemics or demography. Also, we mention not only this section by also the section on agent-based modelling edited by F. Castiglione as containing articles of social interest.
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The birth and decline of disciplines are critical to science and society. However, no quantitative model to date allows us to validate competing theories of whether the emergence of scientific disciplines drives or follows the formation of social communities of scholars. Here we propose an agent-based model based on a emph{social dynamics of science,} in which the evolution of disciplines is guided mainly by the social interactions among scientists. We find that such a social theory can account for a number of stylized facts about the relationships between disciplines, authors, and publications. These results provide strong quantitative support for the key role of social interactions in shaping the dynamics of science. A science of science must gauge the role of exogenous events, such as scientific discoveries and technological advances, against this purely social baseline.
Statistical physics has proven to be a very fruitful framework to describe phenomena outside the realm of traditional physics. The last years have witnessed the attempt by physicists to study collective phenomena emerging from the interactions of individuals as elementary units in social structures. Here we review the state of the art by focusing on a wide list of topics ranging from opinion, cultural and language dynamics to crowd behavior, hierarchy formation, human dynamics, social spreading. We highlight the connections between these problems and other, more traditional, topics of statistical physics. We also emphasize the comparison of model results with empirical data from social systems.
This chapter introduces statistical methods used in the analysis of social networks and in the rapidly evolving parallel-field of network science. Although several instances of social network analysis in health services research have appeared recently, the majority involve only the most basic methods and thus scratch the surface of what might be accomplished. Cutting-edge methods using relevant examples and illustrations in health services research are provided.
In this paper, we provide a statistical analysis of high-resolution contact pattern data within primary and secondary schools as collected by the SocioPatterns collaboration. Students are graphically represented as nodes in a temporally evolving network, in which links represent proximity or interaction between students. This article focuses on link- and node-level statistics, such as the on- and off-durations of links as well as the activity potential of nodes and links. Parametric models are fitted to the on- and off-durations of links, inter-event times and node activity potentials and, based on these, we propose a number of theoretical models that are able to reproduce the collected data within varying levels of accuracy. By doing so, we aim to identify the minimal network-level properties that are needed to closely match the real-world data, with the aim of combining this contact pattern model with epidemic models in future work.
Most physics theories are deterministic, with the notable exception of quantum mechanics which, however, comes plagued by the so-called measurement problem. This state of affairs might well be due to the inability of standard mathematics to speak of indeterminism, its inability to present us a worldview in which new information is created as time passes. In such a case, scientific determinism would only be an illusion due to the timeless mathematical language scientists use. To investigate this possibility it is necessary to develop an alternative mathematical language that is both powerful enough to allow scientists to compute predictions and compatible with indeterminism and the passage of time. We argue that intuitionistic mathematics provides such a language and we illustrate it in simple terms.
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