Hans J. Herrmann Computational Physics, IfB, ETH Zürich, Switzerland

1. Theories for Extreme Events Hans J. Herrmann Computational Physics, IfB, ETH Zürich, Switzerland New Views on Extreme Events Workshop of the Risk Center at SwissRe Adliswil, October 24-25, 2012

2. ETH Risk Center HazNETH Natural Hazards (Faber) ZISC Information Security (Basin) RiskLab Finance & Insurance (Embrechts) LSA Technology (Kröger) CSS Center forSecurity Studies (Wenger) Entrepre-neurialRisks (Sornette) Systemic Risks (Schweitzer) Decision Making (Murphy) ETH Risk Center Innovation Policy (Gersbach) Sociology (Helbing) Integrative RiskMgmt. (Bommier) Conflict Research(Cederman) Math. Finance(Embrechts) Traffic Systems(Axhausen) Comp. Physics(Herrmann) Forest Engineering (Heinimann)

3. ETH Risk Center

4. 24th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011 The three types of flooding flooding landscapes braided rivers breaking dam

5. 24th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011 The braided river The river carries sediments which deposit on the bottom of the bed until they reach the level of the water and create a natural dam clogging the branch. So this branch dies and a new branch is created somewhere else. Basic principle is a conservation law (here the mass of water) and the formation of local bottlenecks.Other examples: traffic, fatigue, electrical networks. + randomness

6. Traffic density fundamental diagram flux

7. Classical Probability Theory Gaussian distribution Poisson distribution Black-Scholes Model

8. Flooding landscapes When the water level of a lake rises in a random landscape it spills over into the neighboring basin and the sizes of these invasions follow a power law distribution. Basic principle is the existence of a local threshold at which discharging occurs.Other examples are earthquakes, brain activity. + randomness

9. Earthquakes

10. Frequency Distribution of Earthquakes Gutenberg-Richter law

11. Conclusion Paul Pierre Levy

12. Earthquake Model Spring-Block Model

13. Self-Organized Criticality (SOC) Per Bak

14. Sandpile Model Applet http://www.cmth.bnl.gov/~maslov/Sandpile.htm

15. Size distribution of avalanches

16. Avalanches on the Surface of a Sandpile

17. Self-Organized Criticality (SOC) The lazy burocrats

18. The Stockmarket

19. SOC Model for the Stockmarket Dupoyet et al 2011 Comparison with NASDAQ

20. Model for the distribution of price fluctuations Stauffer + Sornette, 1999

21. Examples for SOC • Earthquakes • Stockmarket • Evolution • Cerebral activity • Solar flares • Floodings • Landslides • ......

22. Breaking a dam Each time a dam is in danger to break it is repaired and made stronger. When finally the dam does one day break all the land is flooded at once. Basic principle is that the catastrophe is avoided by local repairs until it can not be withhold anymore.Other examples are volcanos + randomness

23. Volcano eruption

24. Branch pipes

25. The Black Swan Nassim Nicholas Taleb

26. The Black Swan Didier Sornette Dragon King

27. Explosive Percolation Product Rule (PR) • Consider a fully connected graph • Select randomly two bonds and occupy the one which creates the smaller cluster Dimitris Achlioptas classical percolation product rule D. Achlioptas, R. M. D’Souza, and J. Spencer, Science 323, 1453 (2009)

28. Largest Cluster Model • Select randomly a bond • if not related with the largest cluster occupy it • else, occupy it with probability Nuno Araújo Nuno Araújo and HJH, Phys. Rev. Lett. 105, 035701 (2010)

29. Largest Cluster Model order parameter: P∞ = fraction of sites in largest cluster

30. Phase transition of 1st order Sudden jump with our previous warning Its consequences touch the entire system. It is the worst case scenario.

31. Complex Systems antropoz metron Protagoraz

32. Internet

33. Scale-free networks Internet actors WWW: HEP neuroscience Model: Barabasi-Albert  = 3 scientific collaborations

34. Terrorist network September 11

35. Random AttackMaliciousAttack

36. European Power Grid The changes in the EU power grid (red lines are replaced by green ones) and the fraction of nodes in the largest connected cluster s(q) after removing a fraction of nodes q for the EU powergrid and its improved network

37. Collapse of the power grid in Italy and Switzerland, 2003 Coupled Networks

38. Collapse of two coupled networks Largest connected cluster Number of iterations Fraction of attacked nodes  Phase transition of 1st order

39. Reducing the risk by decoupling the networks through autonomous nodes Largest connected cluster Autonomous nodes attenuate the casacade! Fraction of attacked nodes

40. Proposal to improve robustness The blackout in Italy and Switzerland, 2003 4 autonomous nodes Original networks 39 communication servers (stars) + 310 power stations (circles) Random failure of 14 communication servers

41. Outlook • There exist unmeasurable risks. • Mending is dangerous, because the risk becomes more brittle. • Usually one can substantially reduce the risk in a network through rather minor changes. • Autonomous nodes make coupled networks more robust.