Assessing Catastrophes-Dragon-Kings, Black, and Gray Swans-for Science-Policy

The threat of catastrophic incidents-from nonroutine events to extreme ones, such as Dragon-Kings (DK), Black Swans (BS), and Gray Swans-induces precautionary initiatives that, before the fact, may encounter public resistance or after the fact recriminations. This study develops three aspects of these events: (1) generating mechanisms, (2) the statistical distributions of near and far-term consequences, and (3) the aggregation of expert opinions about assumptions, mechanisms, and consequences that informs science-policy. This study shows how causal analysis should account for the: (1) nonlinear catastrophic behaviors that generate predictions, (2) common and power-law distributions of the consequences, (3) self-organizing criticality and self-similarity, and (4) feedbacks and couplings between mechanisms that produce snaps, crackles, and pops as precursor, warning signals. The distribution of the consequences associated with catastrophic incidents has longer and fatter right tails than those expected from failure analysis based on known nonroutine events. DK are extreme events that deviate from these fat tail distributions, have a much higher frequency than expected, and can be predicted unlike BS. This shows how to combine divergent expert individual beliefs over assumptions, causation, and results, and a paradox that affects agreements obtained by majority rule.

Generalized q analysis of log-periodicity: applications to critical ruptures

We introduce a generalization of the q analysis, which provides a nonparametric tool for the description and detection of log-periodic structures associated with discrete scale invariance. We use this generalized q analysis to construct a signature called the (H,q) derivative of discrete scale invariance, which we use to detect the log-periodicity in the cumulative energy release preceding the rupture of five pressure tanks made of composite carbon-matrix material. We investigate the significance level of the spectral Lomb periodogram of the optimal (H,q) derivative. We confirm and strengthen previous parametric results that the cumulative energy release exhibits log-periodicity before rupture. However, our tests to use this method as a scheme for the prediction of the critical value of the stress at rupture are not encouraging.

Predictability of catastrophic events: material rupture, earthquakes, turbulence, financial crashes, and human birth

We propose that catastrophic events are "outliers" with statistically different properties than the rest of the population and result from mechanisms involving amplifying critical cascades. We describe a unifying approach for modeling and predicting these catastrophic events or "ruptures," that is, sudden transitions from a quiescent state to a crisis. Such ruptures involve interactions between structures at many different scales. Applications and the potential for prediction are discussed in relation to the rupture of composite materials, great earthquakes, turbulence, and abrupt changes of weather regimes, financial crashes, and human parturition (birth). Future improvements will involve combining ideas and tools from statistical physics and artificial/computational intelligence, to identify and classify possible universal structures that occur at different scales, and to develop application-specific methodologies to use these structures for prediction of the "crises" known to arise in each application of interest. We live on a planet and in a society with intermittent dynamics rather than a state of equilibrium, and so there is a growing and urgent need to sensitize students and citizens to the importance and impacts of ruptures in their multiple forms.