1. Explaining and understanding a physical phenomena usually leads to predictions: Examples: the Higgs Boson, photo electric ….

2. Theory without predictions of new phenomena andthe possibility of testing the predictions is usually not regarded as a valid theory!

3. I will present three examples from my current field: (i) Early predicting of epidemic spreading (ii) Abrupt breakdown of a system of systems represented as “network of networks”

(iii) Early prediction of El-Nino events (Unpublished)

Explain or Predict

Explain AND Predict

SHLOMO HAVLIN Bar-Ilan University

Based on theoretical paper of Cohen, Havlin and ben-Avraham, PRL 91, 247901 (2003)

Single and coupled networks: Robustness

P∞

1

0 1

Continuous abrupt

cp

Remove randomly (or targeted) afraction nodes1 p−

P∞ Size of the largest connected component (cluster)

p

Giant component and breakdownthresholds are predicted for these models

Single networks:Continuous transition

0 cp

ER

Coupled networks:New paradigm-Abrupt transitionCascading Failures

Single ERCoupled

Cascades,Suddenbreakdown

Breakdown threshold cp

[1 exp( )]P p k P∞ ∞= − −

Network of Networks (tree)

Buldyrev et al Nature (2010)Gao et al PRL (2011)

n=5

For ER, full coupling ,ALL loopless topologies (chain, star, tree):

Vulnerability increases significantly with n

n=1 known ER- 2nd order

1/cp k=

[1 exp( )]nP p k P∞ ∞= − − P∞

ik k=

n=1

n=2

n=5