Abstract: Rare but potentially catastrophic real-world phenomena such as stock market crashes, are often referred to as rare or extreme ‘events’ on the assumption that they have a well-defined change (eg price-change) in some macroscopically measurable quantity (eg stock price) occurring at a particular point in space (eg Dow Jones) and time (eg at 10am), over a specific time-interval (eg 1 hour). If this idealization is indeed the case, then histograms can be obtained using historical data and, assuming the system is stationary, approximate point probabilities deduced to quantify the likelihood of future occurrence--albeit subject to the usual inaccuracies associated with performing sparse number statistics. However, as emphasized by Sornette, extreme'behaviors' such as the mysterious 2010 flash crash in stock prices shown in Fig. 1 in principle invoke an entirely different layer of difficulty, because (1) they do not have a well-defined duration, and hence may be missed when evaluating histograms of changes for a particular fixed, pre-defined time increment (eg 1 minute, 1 hour or 1 day); and (2) even if their duration and maximum size are well defined, they can take on an effectively infinite number of possible temporal profiles during that period, ie has its own characteristic time-dependence during. Hence for a given maximum drop size and duration, there are a priori myriad possible temporal forms of versus. This chapter takes a step toward examining whether these temporal profiles (ie vs. during) exhibit particular classes of behavior–and shows, for the case of a nontrivial toy model of a complex system, that there is indeed a taxonomy of such rare and extreme behaviors.
[edit database entry]
Bongard's work focuses on understanding the general nature of cognition, regardless of whether it is found in humans, animals or robots. This unique approach focuses on the role that morphology and evolution plays in cognition. Addressing these questions has taken him into the fields of biology, psychology, engineering and computer science.
Danforth is an applied mathematician interested in modeling a variety of physical, biological, and social phenomenon. He has applied principles of chaos theory to improve weather forecasts as a member of the Mathematics and Climate Research Network, and developed a real-time remote sensor of global happiness using messages from Twitter: the Hedonometer. Danforth co-runs the Computational Story Lab with Peter Dodds, and helps run UVM's reading group on complexity.
Laurent studies the interaction of structure and dynamics. His research involves network theory, statistical physics and nonlinear dynamics along with their applications in epidemiology, ecology, biology, and sociology. Recent projects include comparing complex networks of different nature, the coevolution of human behavior and infectious diseases, understanding the role of forest shape in determining stability of tropical forests, as well as the impact of echo chambers in political discussions.
Hines' work broadly focuses on finding ways to make electric energy more reliable, more affordable, with less environmental impact. Particular topics of interest include understanding the mechanisms by which small problems in the power grid become large blackouts, identifying and mitigating the stresses caused by large amounts of electric vehicle charging, and quantifying the impact of high penetrations of wind/solar on electricity systems.
Bagrow's interests include: Complex Networks (community detection, social modeling and human dynamics, statistical phenomena, graph similarity and isomorphism), Statistical Physics (non-equilibrium methods, phase transitions, percolation, interacting particle systems, spin glasses), and Optimization(glassy techniques such as simulated/quantum annealing, (non-gradient) minimization of noisy objective functions).