Definition of the Subject
Herein we introduce the section of this Encyclopedia devoted to Social Sciences, edited by A. Nowak, which concentrates on the application ofmathematics and physics to this field. Under “mathematics” we include also all computer simulations if they are not taken from physics; whilephysics applications include model simulations derived from physics that were applied to social simulations. Thus, obviously there is no sharp borderbetween applications from physics and from mathematics in the sense of our definition. Also social science is not defined precisely. Included areeconomics and linguistics, but not social insects or fish swarms, nor human epidemics or demography. It should further be noted that the section of theEncyclopedia on agent-based modeling edited by F. Castiglione also contains articles of social interest.
Introduction
If mathematical/physical methods are applied to social sciences, a major problem is the mutual lack of literature knowledge. Take...
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- Cellular automata:
-
Discrete variables on a discrete lattice change in discrete time steps.
- Ising model:
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Neighboring variables prefer to be the same but exceptions are possible. The probability for such exceptions is an exponential function of “temperature”.
- Percolation:
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Each site is randomly either occupied or empty, leading to random clusters. At the percolation threshold for the first time an infinite cluster is formed.
- Universality:
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Certain properties are the same for a whole set of models or of real objects.
Bibliography
Primary literature
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Mantegna RN (2005) Presentation of the English translation of Ettore Majorana's paper: The value of statistical laws in physics and social sciences. Quant Finance 5:133
Weidlich W (2000) Sociodynamics; A Systematic Approach to Mathematical Modelling in the Social Sciences. Harwood Academic Publishers, Amsterdam; reprint: Dover, New York
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Stauffer D (2007) Opinion Dynamics with Hopfield Neural Networks. arXiv:0712.4364
Levy M, Levy H, Solomon S (2000) Microscopic Simulation of Financial Markets. Academic Press, New York; Samanidou E, Zschichang R, Stauffer D, Lux T (2007) Rep Progr Phys 70:404; Lux T (2007) Stochastic behavioral asset pricing models and the stylized facts. In: Hens T, Schenk‐Hoppé K (eds) Handbook on Financial Economics. (draft)
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Books and Reviews
Stauffer D, de Oliveira SM, de Oliveira PMC, Sá Martins JS (2006) Biology, Sociology, Geology by Computational Physicists. Elsevier, Amsterdam
Billari FC, Fent T, Prskawetz A, Scheffran J (2006) Agent-based computational modelling. Physica, Heidelberg
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Stauffer, D., Solomon, S. (2009). Physics and Mathematics Applications in Social Science. In: Meyers, R. (eds) Encyclopedia of Complexity and Systems Science. Springer, New York, NY. https://doi.org/10.1007/978-0-387-30440-3_408
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