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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    (iii) Early prediction of El-Nino events (Unpublished)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
Based on theoretical paper of Cohen, Havlin and ben-Avraham, PRL 91, 247901 (2003)
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
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)
Havlin
Havlin
Havlin

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Havlin

  • 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.
  • 4. 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
  • 5. 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)