1.
SHLOMO HAVLIN
Bar-Ilan University
Explain or Predict
1. Explaining and understanding a physical phenomena
usually leads to predictions:
Examples: the Higgs Boson, photo electric ….
2. Theory without predictions of new phenomena and
the 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(iii) Early prediction of El-Nino events (Unpublished)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 AND Predict

2.
Based on theoretical paper of Cohen, Havlin and ben-Avraham, PRL 91, 247901 (2003)

3.
Single and coupled networks: Robustness
ER
Remove randomly (or targeted) a
fraction 1 − p nodes
P∞ Size of the largest
connected component (cluster)
pc Breakdown threshold
Giant component and breakdown
thresholds are predicted 1
Single ER
for these models
P∞ = p[1 − exp(− k P∞ )] Coupled
P∞
Single networks:
Continuous abrupt
Continuous transition
Cascades,
Sudden
Coupled networks: breakdown
New paradigm-Abrupt transition 0
0 pc p pc 1
Cascading Failures

4.
Network of Networks (tree)
n=5
For ER, ki = k full coupling ,
ALL loopless topologies (chain, star, tree):
P∞ = p[1 − exp(− k P∞ )] n
P∞
n=1 known ER- 2nd order
n=1
n=5
pc = 1/ k
n=2
Vulnerability increases significantly with n Buldyrev et al Nature (2010)
Gao et al PRL (2011)