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 2 • Complexity • Historical background • Power laws • Networks
Cybernetics 3 • Norbert Wiener (1894-1964) • Science of communication and control • Circularity • Process and change • Further development into general systems theory
General systems theory 4 • Ludwig von Bertalanffy (1901-1972)
Catastrophe theory 5 • René Thom (1923-2002) • Catastrophes as discontinuities in morphogenetic landscapes
Chaos theory 6 • E. N. Lorenz • Chaotic dynamics generated by deterministic processes Butterfly effect Strange attractor
Non-equilibrium physics 7 • Dissipative structures are organized arrangement in non- equilibrium systems that are dissipating energy and thereby generate entropy Ilya Priogogine Convection patterns
Self-organized criticality 8 log f f Input Output s - α log s s Complex System • 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 Per Bak
Self-organized criticality 9 Per Bak’s sand pile Power-law distributed avalanches in a rice pile
Strogatz: Exploring complex networks ( Nature 2001 ) 10 • Problems to overcome: 1. structural complexity 2. network evolution 3. connection diversity 4. dynamic complexity 5. node diversity Steven H. Strogatz 6. meta-complication
Between order and randomness 11 Watts and Strogatz’s Beta Model Short path length & high clustering Duncan Watts
The small-world experiment 12 “Six degrees of separation” Sharon, MA Stanley Milgram Omaha, NE
Two degree distributions 13 log p(k) log p(k) p(k) p(k) log k log k k k Normal distribution Power law
Scale-free networks 14 • Barabási and Albert’s 1999 model of the Internet: • Constantly growing network • Preferential attachments: – p ( k ) = k / Σ i k i
Cumulative war-size plot, 1820-1997 15 log P(S>s) (cumulative frequency) 1.0 log P(S>s) = 1.27 – 0.41 log s 2 R = 0.985 N = 97 0.1 WWI Data Source: Correlates WWII of War 0.01 2 3 4 5 6 7 8 log s Project (COW) 10 10 10 10 10 10 10 (severity)
Tooling 16 • RePast http://repast.sourceforge.net/ • JUNG http://jung.sourceforge.net/ • R SNA package http://erzuli.ss.uci.edu/R.stuff/ • Pajek http://vlado.fmf.uni-lj.si/pub/networks/pajek/
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