Eikonal Blog

2010.03.16

Avalanches

Filed under: mathematics — Tags: — sandokan65 @ 14:46

Source: “Unusual calms tell of coming storms”; Kimberly Patch; TRN (Technology Research News); 2001.08.22
URL: http://www.nd.edu/~networks/linked/ (EXPIRED, now the article is at: http://www.trnmag.com/Stories/2001/082201/Unusual_calms_tell_of_coming_storms_082201.html).

  • The authors consider the complex (“large”) systems where population of numerous elements (“agents”) competes for a limited resource.
    System Agents Resource
    computer networks data packets network bandwidth
    commuter traffic cars road space
    stock market stock traders monetary gain
  • The macroscopic behavior of the system is predictable to certain degree. Typically the macroscopic behavior is characterized by one or more phenomenological quantities (“order parameters”) such as traffic speed or market prices.
  • Presence of internal flow: Although many big changes seem to happen randomly and almost without cause, large systems contain an internal flow. Example: The market produces its own dynamics in the absence of significant news, which is most of the time.
  • Presence of various agent strategies stabilizes the system.
    • Predictability also has to do with how stable a system is.
    • For commuter traffic: usually everyone drives differently, at slightly different speeds and with slightly different strategies — this gives the traffic flow some kind of stability. If everyone is driving at the same speed, in the same way, with the same distance between, then this is unstable. This is because if something happens to one car, it is more likely to cause a chain reaction. If something appears on the road, it will cause a massive disruption.
  • Stability: In stable regime the success of an individual strategy is random – i.e. any strategy is as good as a random one; i.e. any random strategy is a good one.
    • Usually a system rolls along with only reasonably small changes like the daily changes in the stock market or the traffic speed in the usual nightly commute home from the office… During these periods, changes are almost random… If you want to predict whether the stock will go up or down or whether one lane or another on the highway will be best, than you might as well flip a coin.
    • This is because the internal forces in the system are finely balanced. Example: there’s a large force created by traders who want to buy, but an almost equal and opposite force created by traders who want to sell, he said. “These changes are essentially random and hence unpredictable,” he said.
  • A Crowd Effect: The level of predictability goes up just before a large change. Strategy selection amongst agents seems to converge. Without communicating, or even knowing the existence of each other, agents begin to lock into a particular behavior just before a large change. The change is a consequence of the global state of the system, and not something simply triggered by an isolated, random event.
  • Phase transition: When the forces become unbalanced, an avalanche-like effect happens whereby small glimpses of a pattern momentarily emerge and, by chance, become amplified. It is during this amplification period that the predictability of the system grows. The agents start taking up definite positions — the two opposing forces are now momentarily out of balance. Quickly the imbalance begins to show itself as a definite trend in change of order parameter.

More:

  • “Predictability of large future changes in a competitive evolving population”; D. Lamper, S. Howison, N. F. Johnson; arXiv: cond-mat/0105258; 2001.05.14 – http://arxiv.org/abs/cond-mat/0105258.
    • Abstract: The dynamical evolution of many economic, sociological, biological and physical systems tends to be dominated by a relatively small number of unexpected, large changes (`extreme events’). We study the large, internal changes produced in a generic multi-agent population competing for a limited resource, and find that the level of predictability actually increases prior to a large change. These large changes hence arise as a predictable consequence of information encoded in the system’s global state.
  • “Application of multi-agent games to the prediction of financial time-series”; N. F. Johnson, D. Lamper, P. Jefferies, M. L. Hart, S. Howison; Work presented at the NATO Workshop on Econophysics. Prague (Feb 2001). To appear in Physica A. Also in arXiv: cond-mat/0105303; 2001.05.15 – http://arxiv.org/abs/cond-mat/0105303.
    • Abstract: We report on a technique based on multi-agent games which has potential use in the prediction of future movements of financial time-series. A third-party game is trained on a black-box time-series, and is then run into the future to extract next-step and multi-step predictions. In addition to the possibility of identifying profit opportunities, the technique may prove useful in the development of improved risk management strategies.
  • “Anatomy of extreme events in a complex adaptive system”; Paul Jefferies, David Lamper, Neil F. Johnson; arXiv: cond-mat/0201540; 2002.02.04 – http://arxiv.org/abs/cond-mat/0201540.
    • Abstract: We provide an analytic, microscopic analysis of extreme events in an adaptive population comprising competing agents (e.g. species, cells, traders, data-packets). Such large changes tend to dictate the long-term dynamical behaviour of many real-world systems in both the natural and social sciences. Our results reveal a taxonomy of extreme events, and provide a microscopic understanding as to their build-up and likely duration.
  • “Crash Avoidance in a Complex System”; Michael L. Hart, David Lamper, Neil F. Johnson; arXiv: cond-mat/0206228; 2002.06.13 – http://arxiv.org/abs/cond-mat/0206228.
    • Abstract: Complex systems can exhibit unexpected large changes, e.g. a crash in a financial market. We examine the large endogenous changes arising within a non-trivial generalization of the Minority Game: the Grand Canonical Minority Game (GCMG). Using a Markov Chain description, we study the many possible paths the system may take. This `many-worlds’ view not only allows us to predict the start and end of a crash in this system, but also to investigate how such a crash may be avoided. We find that the system can be `immunized’ against large changes: by inducing small changes today, much larger changes in the future can be prevented.
  • “An Investigation of Crash Avoidance in a Complex System”; Michael L. Hart, David Lamper, Neil F. Johnson; arXiv: cond-mat/0207588; 2002.07.24 – http://arxiv.org/abs/cond-mat/0207588.
    • Abstract: Complex systems can exhibit unexpected large changes, e.g. a crash in a financial market. We examine the large endogenous changes arising within a non-trivial generalization of the Minority Game: the Grand Canonical Minority Game (GCMG). Using a Markov Chain description, we study the many possible paths the system may take. This ‘many-worlds’ view not only allows us to predict the start and end of a crash in this system, but also to investigate how such a crash may be avoided. We find that the system can be ‘immunized’ against large changes: by inducing small changes today, much larger changes in the future can be prevented.
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