SHLOMO HAVLIN Bar-Ilan University Explain or Predict1. 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Abrupt breakdown of a system of systems represented as “network of networks” (iii) Early prediction of El-Nino events (Unpublished) Explain AND Predict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 thresholdGiant component and breakdownthresholds are predicted 1 Single ERfor these models P∞ = p[1 − exp(− k P∞ )] Coupled P∞Single networks: Continuous abruptContinuous transition Cascades, SuddenCoupled networks: breakdownNew paradigm-Abrupt transition 0 0 pc p pc 1Cascading Failures
Network of Networks (tree) n=5For 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)
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