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

2. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 ETH Risk Center ETH Risk Center RiskLab Finance & Insurance (Embrechts) RiskLab Finance & Insurance (Embrechts) HazNETH Natural Hazards (Faber) HazNETH Natural Hazards (Faber) LSA Technology (Kröger) LSA Technology (Kröger) CSS Center for Security Studies (Wenger) CSS Center for Security Studies (Wenger) ZISC Information Security (Basin) ZISC Information Security (Basin) Systemic Risks (Schweitzer) Entrepre- neurial Risks (Sornette) Innovation Policy (Gersbach ) Integrative Risk Mgmt. (Bommier) Sociology (Helbing) Conflict Research (Cederman) Math. Finance (Embrechts) Traffic Systems (Axhausen) Comp. Physics (Herrmann ) Forest Engineering (Heinimann) Decision Making (Murphy)

3. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 ETH Risk Center

4. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 24th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011 The three types of flooding braided rivers flooding landscapes breaking dam

5. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 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. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Traffic fundamental diagram density flux

7. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Classical Probability Theory Poisson distribution Gaussian distribution Black-Scholes Model

8. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 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. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Earthquakes

10. Frequency Distribution of Earthquakes Gutenberg-Richter law

11. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Conclusion Paul Pierre Levy

12. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Earthquake Model Spring-Block Model

13. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Per Bak Self-Organized Criticality (SOC)

14. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Sandpile Model Applet http://www.cmth.bnl.gov/~maslov/Sandpile.htm

15. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Size distribution of avalanches

16. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Avalanches on the Surface of a Sandpile

17. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 The lazy burocrats Self-Organized Criticality (SOC)

18. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 The Stockmarket

19. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 SOC Model for the Stockmarket Comparison with NASDAQ Dupoyet et al 2011

20. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Model for the distribution of price fluctuations Stauffer + Sornette, 1999

21. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Examples for SOC Earthquakes Stockmarket Evolution Cerebral activity Solar flares Floodings Landslides......

22. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 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. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Volcano eruption

24. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Branch pipes

25. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 The Black Swan Nassim Nicholas Taleb

26. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 The Black Swan Dragon King Didier Sornette

27. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Product Rule (PR) D. Achlioptas, R. M. D’Souza, and J. Spencer, Science 323, 1453 (2009) Consider a fully connected graph Select randomly two bonds and occupy the one which creates the smaller cluster classical percolation product rule Dimitris Achlioptas Explosive Percolation

28. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Largest Cluster Model Select randomly a bond if not related with the largest cluster occupy it else, occupy it with probability Nuno Araújo and HJH, Phys. Rev. Lett. 105, 035701 (2010) Nuno Araújo

29. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Largest Cluster Model order parameter: P ∞ = fraction of sites in largest cluster

30. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Sudden jump with our previous warning Its consequences touch the entire system. It is the worst case scenario. Phase transition of 1st order

31. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Complex Systems  

32. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012Internet

33. Scale-free networks scientific collaborations WWW: Internetactors HEPneuroscience Model: Barabasi-Albert  = 3

34. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Terrorist network September 11

35. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Random Attack MaliciousAttack

36. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 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. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Collapse of the power grid in Italy and Switzerland, 2003 Coupled Networks

38. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Largest connected cluster Largest connected cluster Number of iterations Fraction of attacked nodes Collapse of two coupled networks  Phase transition of 1st order

39. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 Fraction of attacked nodes Reducing the risk by decoupling the networks through autonomous nodes Largest connected cluster Largest connected cluster

40. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 39 communication servers (stars) + 310 power stations (circles) Random failure of 14 communication servers Proposal to improve robustness The blackout in Italy and Switzerland, 2003 Original networks 4 autonomous nodes

41. New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012 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.