1. 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)

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 ( )

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 f
Input
Output
s-a
log s
Complex System s
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
In the late 1980s, physicists discovered a large family of complex systems that generate power-law regularities. Per Bak, coined the term self-organized criticality:
Paradigmatic example: sandpile. If trickle sand slowly on a sandpile ==> pile will grow, but not in an even fashion. From time to time, there will be avalanches of various sizes.
More abstractly put, there is a linear input building up tensions held back by thresholds. When disturbances happen, they follow a power law. (hyperbolic curve)
Sandpile differs from Newtonian physics (e.g. billiard balls)
scale invariance: avalanches of all sizes possible; no typical size (fractals)
history matters: path dependence, butterfly effect, but unlike chaos because output is not just random
threshold effects and positive feedback (friction holding back the sand, or like pushing a piano over a rugged floor, sometimes is slides)
Simple analogy: applying SOC to our puzzle
Linear input: technological change building up tension
Thresholds: decisions to go to war
Positive feedback: avalanches through interdependent decisions
==> ABM standard approach in non-equil. theory
Per Bak

9. Self-organized criticality
Per Bak’s sand pile
Power-law distributed
avalanches in a rice 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. Two degree distributions
log p(k)
log p(k)
log 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 / i ki

15. Cumulative war-size plot, 1820-1997
Since Richardson’s pioneering efforts to collect quantitative data about conflict processes in the 1940s, we know that war sizes are power-law distributed. Using logarithmic axes, the diagram plots cumulative war frequencies as a function of war size. A straight line in a log-log plot suggests the presence of a power law.
Data Source:
Correlates
of War
Project (COW)

16. Tooling RePast http://repast.sourceforge.net/
JUNG
R SNA package
Pajek