New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Hans J. HerrmannComputational Physics, IfB, ETH
Zürich, Switzerland
Theories for Theories for Extreme EventsExtreme Events
New Views on Extreme EventsWorkshop of the Risk Center at SwissRe Adliswil, October 24-25, 2012
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
ETH Risk Center
ETHRisk Center
RiskLabFinance & Insurance
(Embrechts)
RiskLabFinance & Insurance
(Embrechts)
HazNETHNatural Hazards
(Faber)
HazNETHNatural Hazards
(Faber)
LSATechnology
(Kröger)
LSATechnology
(Kröger)
CSSCenter for
Security Studies(Wenger)
CSSCenter for
Security Studies(Wenger)
ZISCInformation Security
(Basin)
ZISCInformation Security
(Basin)
Systemic Risks
(Schweitzer)
Entrepre-neurial Risks
(Sornette)Innovation Policy (Gersbach
)
Integrative Risk Mgmt.
(Bommier)
Sociology(Helbing)
Conflict Research(Cederma
n)Math.
Finance(Embrecht
s)Traffic
Systems(Axhausen
)Comp. Physics
(Herrmann)
Forest Engineerin
g(Heinimann
)
Decision Making(Murphy)
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
ETH Risk Center
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 201224th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011
The three types of floodingThe three types of flooding
braided riversbraided riversflooding landscapesflooding landscapes
breaking breaking damdam
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 201224th Annual CSP Workshop, UGA, Athens, GA, February 21-25, 2011
The braided riverThe braided river
The river carries sediments which The river carries sediments which deposit on the bottom of the bed until deposit on the bottom of the bed until they reach the level of the water and they reach the level of the water and
create a natural dam clogging the create a natural dam clogging the branch. So this branch dies and a new branch. So this branch dies and a new
branch is created somewhere else. branch is created somewhere else.
Basic principle is a conservation law (here the mass of Basic principle is a conservation law (here the mass of water) and the formation of local bottlenecks.water) and the formation of local bottlenecks.
Other examples: traffic, fatigue, electrical networks.Other examples: traffic, fatigue, electrical networks.
+ randomness+ randomness
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
TrafficTraffic
fundamental fundamental diagramdiagram
densitydensity
fluxflux
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Classical Probability Theory
Poisson distribution Gaussian distribution
Black-Scholes Model
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Flooding landscapesFlooding landscapes
When the water level of a lake When the water level of a lake rises in a random landscape it rises in a random landscape it
spills over into the spills over into the neighboring basin and the neighboring basin and the
sizes of these invasions follow sizes of these invasions follow a power law distribution. a power law distribution.
Basic principle is the existence of a local threshold at which Basic principle is the existence of a local threshold at which discharging occurs.discharging occurs.
Other examples are earthquakes, brain activity. Other examples are earthquakes, brain activity.
+ randomness+ randomness
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
EarthquakesEarthquakes
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Frequency Distribution of Earthquakes
Gutenberg-Richter law
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Conclusion
Paul Pierre Levy
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Earthquake ModelEarthquake Model
Spring-Block Model
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Per BakPer Bak
Self-Organized Criticality (SOC)
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Sandpile Model
Applet
http://www.cmth.bnl.gov/~maslov/Sandpile.htm
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Size distribution of avalanches
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Avalanches on the Surface of a Sandpile
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
The lazy burocrats
Self-Organized Criticality (SOC)
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
The Stockmarket
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
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Model for the distribution of price fluctuations
Stauffer + Sornette, 1999
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
• ......
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Breaking a damBreaking a dam
Each time a dam is in danger to Each time a dam is in danger to break it is repaired and made break it is repaired and made
stronger. When finally the dam stronger. When finally the dam does one day break all the land does one day break all the land
is flooded at once.is flooded at once.
Basic principle is that the catastrophe is avoided by local Basic principle is that the catastrophe is avoided by local repairs until it can not be withhold anymore.repairs until it can not be withhold anymore.
Other examples are volcanos Other examples are volcanos
+ randomness+ randomness
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Volcano eruptionVolcano eruption
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Branch pipesBranch pipes
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
The Black SwanThe Black Swan
Nassim Nicholas Taleb
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
The Black SwanThe Black Swan
Dragon KingDragon King
Didier Sornette
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 percolationclassical percolation product ruleproduct rule Dimitris AchlioptasDimitris Achlioptas
Explosive Percolation
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Largest Cluster ModelLargest Cluster Model
• Select randomly a bond• if not related with the
largest cluster occupy it• else, occupy it with
probability
2
exps
ssq
Nuno Araújo and HJH, Phys. Rev. Lett. 105, 035701 (2010)
Nuno AraújoNuno Araújo
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Largest Cluster ModelLargest Cluster Model
order parameter: Porder parameter: P∞∞ = fraction of sites in largest cluster = fraction of sites in largest cluster
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
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Complex Systems
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
InternetInternet
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Scale-free networksScale-free networks
scientific collaborations
WWW:
2.4out 2.1in
Internet actors
HEP neuroscience
2.4 2.3
2.1
( )P k k
Model: Barabasi-Albert Model: Barabasi-Albert = 3 = 3
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Terrorist networkTerrorist network
September 11September 11
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Random AttackRandom Attack
MaliciousAttackMaliciousAttack
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
European Power GridEuropean Power GridThe 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
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
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Largest
connected cluster
Largest
connected cluster
Number of iterations
Number of iterations
Fraction of attacked nodesFraction of attacked nodes
Collapse of two coupled networks
Phase transition of 1st order
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
Fraction of attacked nodesFraction of attacked nodes
Reducing the risk by decoupling the networks through autonomous nodes
Largest
connected cluster
Largest
connected cluster
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, 2003Original networks 4 autonomous nodes
New Views on Extreme Events, Workshop at SwissRe, Adliswil, October 24-25, 2012
OutlookOutlook• 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.
