46 research outputs found
Dragon-kings: mechanisms, statistical methods and empirical evidence
This introductory article presents the special Discussion and Debate volume
"From black swans to dragon-kings, is there life beyond power laws?" published
in Eur. Phys. J. Special Topics in May 2012. We summarize and put in
perspective the contributions into three main themes: (i) mechanisms for
dragon-kings, (ii) detection of dragon-kings and statistical tests and (iii)
empirical evidence in a large variety of natural and social systems. Overall,
we are pleased to witness significant advances both in the introduction and
clarification of underlying mechanisms and in the development of novel
efficient tests that demonstrate clear evidence for the presence of
dragon-kings in many systems. However, this positive view should be balanced by
the fact that this remains a very delicate and difficult field, if only due to
the scarcity of data as well as the extraordinary important implications with
respect to hazard assessment, risk control and predictability.Comment: 20 page
Extreme events and predictability of catastrophic failure in composite materials and in the Earth
Despite all attempts to isolate and predict extreme earthquakes, these nearly always occur without obvious warning in real time: fully deterministic earthquake prediction is very much a âblack swanâ. On the other hand engineering-scale samples of rocks and other composite materials often show clear precursors to dynamic failure under controlled conditions in the laboratory, and successful evacuations have occurred before several volcanic eruptions. This may be because extreme earthquakes are not statistically special, being an emergent property of the process of dynamic rupture. Nevertheless, probabilistic forecasting of event rate above a given size, based on the tendency of earthquakes to cluster in space and time, can have significant skill compared to say random failure, even in real-time mode. We address several questions in this debate, using examples from the Earth (earthquakes, volcanoes) and the laboratory, including the following. How can we identify âcharacteristicâ events, i.e. beyond the power law, in model selection (do dragon-kings exist)? How do we discriminate quantitatively between stationary and non-stationary hazard models (is a dragon likely to come soon)? Does the system size (the size of the dragonâs domain) matter? Are there localising signals of imminent catastrophic failure we may not be able to access (is the dragon effectively invisible on approach)? We focus on the effect of sampling effects and statistical uncertainty in the identification of extreme events and their predictability, and highlight the strong influence of scaling in space and time as an outstanding issue to be addressed by quantitative studies, experimentation and models