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Lars-Erik Cederman and Luc Girardin

Advanced Computational Modeling of Social Systems. Lars-Erik Cederman and Luc Girardin Center for Comparative and International Studies (CIS) Swiss Federal Institute of Technology Zurich (ETH) http://www.icr.ethz.ch/teaching/compmodels. Today‘s agenda. Complexity Historical background

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Lars-Erik Cederman and Luc Girardin

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  1. Advanced Computational Modelingof Social Systems Lars-Erik Cederman and Luc Girardin Center for Comparative and International Studies (CIS) Swiss Federal Institute of Technology Zurich (ETH) http://www.icr.ethz.ch/teaching/compmodels

  2. Today‘s agenda • Complexity • Historical background • Power laws • Networks

  3. Cybernetics • Norbert Wiener(1894-1964) • Science of communication and control • Circularity • Process and change • Further development into general systems theory

  4. General systems theory • Ludwig von Bertalanffy(1901-1972)

  5. Catastrophe theory • René Thom (1923-2002) • Catastrophes as discontinuities in morphogenetic landscapes

  6. Chaos theory • E. N. Lorenz • Chaotic dynamics generated by deterministic processes Butterfly effect Strange attractor

  7. Non-equilibrium physics • Dissipative structures are organized arrangement in non-equilibrium systems that are dissipating energy and thereby generate entropy Ilya Priogogine Convection patterns

  8. Self-organized criticality log f • Slowly driven systems that fluctuate around state of marginal stability while generating non-linear output according to a power law. • Examples: sandpiles, semi-conductors, earthquakes, extinction of species, forest fires, epidemics, traffic jams, city populations, stock market fluctuations, firm size f Input Output s-a log s s Complex System Per Bak

  9. Self-organized criticality Power-law distributed avalanches in a rice pile Per Bak’s sand pile

  10. Strogatz: Exploring complex networks (Nature 2001) • Problems to overcome: • structural complexity • network evolution • connection diversity • dynamic complexity • node diversity • meta-complication Steven H. Strogatz

  11. Between order and randomness Watts and Strogatz’s Beta Model Short path length & high clustering Duncan Watts

  12. The small-world experiment “Six degrees of separation” Sharon, MA Stanley Milgram Omaha, NE

  13. log p(k) log k Two degree distributions log p(k) p(k) p(k) log k k k Normal distribution Power law

  14. Scale-free networks • Barabási and Albert’s 1999 model of the Internet: • Constantly growing network • Preferential attachments: • p(k) = k / iki

  15. Cumulative war-size plot, 1820-1997 Data Source: Correlates of War Project (COW)

  16. Tooling • RePasthttp://repast.sourceforge.net/ • JUNGhttp://jung.sourceforge.net/ • R SNA packagehttp://erzuli.ss.uci.edu/R.stuff/ • Pajekhttp://vlado.fmf.uni-lj.si/pub/networks/pajek/

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