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

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


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)


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


TrafficTraffic

fundamental fundamental diagramdiagram

densitydensity

fluxflux


Classical Probability Theory

Poisson distribution Gaussian distribution

Black-Scholes Model


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.



EarthquakesEarthquakes


Frequency Distribution of Earthquakes

Gutenberg-Richter law


Conclusion

Paul Pierre Levy


Earthquake ModelEarthquake Model

Spring-Block Model


Per BakPer Bak

Self-Organized Criticality (SOC)


Sandpile Model

Applet

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


Size distribution of avalanches


Avalanches on the Surface of a Sandpile


The lazy burocrats

Self-Organized Criticality (SOC)


The Stockmarket


SOC Model for the Stockmarket

Comparison with NASDAQ

Dupoyet et al 2011


Model for the distribution of price fluctuations

Stauffer + Sornette, 1999


Examples for SOC

• Earthquakes

• Stockmarket

• Evolution

• Cerebral activity

• Solar flares

• Floodings

• Landslides

• ......


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



Volcano eruptionVolcano eruption


Branch pipesBranch pipes


The Black SwanThe Black Swan

Nassim Nicholas Taleb


The Black SwanThe Black Swan

Dragon KingDragon King

Didier Sornette


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


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


Largest Cluster ModelLargest Cluster Model

order parameter: Porder parameter: P∞∞ = fraction of sites in largest cluster = fraction of sites in largest cluster


Sudden jump with our previous warning

Its consequences touch the entire system.

It is the worst case scenario.

Phase transition of 1st order


Complex Systems


InternetInternet


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


Terrorist networkTerrorist network

September 11September 11


Random AttackRandom Attack

MaliciousAttackMaliciousAttack


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


Collapse of the power grid in Italy and Switzerland, 2003

Coupled Networks


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


Fraction of attacked nodesFraction of attacked nodes

Reducing the risk by decoupling the networks through autonomous nodes

Largest

connected cluster

Largest

connected cluster


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


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.

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

Documents

extreme events workshop

extreme events new views

swissre adliswil

new branch

dam slide

randomness slide

eth risk center slide

th annual csp workshop