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 Power laws Networks

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

General systems theory Ludwig von Bertalanffy (1901-1972)

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

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

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

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

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

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

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

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

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

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

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)

Tooling 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/