Lars-Erik Cederman and Luc Girardin
description
Transcript of Lars-Erik Cederman and Luc Girardin
Lars-Erik Cederman and Luc GirardinCenter for Comparative and International Studies (CIS)
Swiss Federal Institute of Technology Zurich (ETH)http://www.icr.ethz.ch/teaching/compmodels
Advanced Computational Modelingof Social Systems
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Today‘s agenda
• Complexity• Historical background• Power laws• Networks
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Cybernetics
• Norbert Wiener(1894-1964)
• Science of communication and control
• Circularity• Process and change• Further
development into general systems theory
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General systems theory
• Ludwig von Bertalanffy(1901-1972)
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Catastrophe theory
• René Thom (1923-2002)
• Catastrophes as discontinuities in morphogenetic landscapes
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Chaos theory
• E. N. Lorenz• Chaotic dynamics
generated by deterministic processes
Butterfly effect
Strange attractor
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Non-equilibrium physics
• Dissipative structures are organized arrangement in non-equilibrium systems that are dissipating energy and thereby generate entropy
Convection patterns
Ilya Priogogine
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• 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
Self-organized criticality
Input Output
Complex System
log f
log s
f
s
s-
Per Bak
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Self-organized criticality
Per Bak’s sand pile Power-law distributedavalanches in a rice pile
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Strogatz: Exploring complex networks (Nature 2001)
• Problems to overcome:1. structural complexity2. network evolution3. connection diversity4. dynamic complexity5. node diversity6. meta-complication Steven H. Strogatz
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Between order and randomness
Watts and Strogatz’s Beta Model
Short path length & high clusteringDuncan Watts
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The small-world experiment
Stanley Milgram
Sharon, MA
Omaha, NE
“Six degrees of separation”
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Two degree distributions
p(k) p(k)
k kNormal distribution Power law
log p(k)
log k
log p(k)
log k
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Scale-free networks
• Barabási and Albert’s 1999 model of the Internet:
• Constantly growing network
• Preferential attachments:– p(k) = k / i ki
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Cumulative war-size plot, 1820-1997
Data Source:Correlatesof WarProject (COW)
1.0
0.1
0.01
log P(S>s) = 1.27 – 0.41 log s
2 3 4 5 6 7 810 10 10 10 10 10 10
WWI
WWII
2R = 0.985 N = 97
log P(S>s) (cumulative frequency)
log s (severity)
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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/