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/