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Power laws, highly optimized tolerance, and generalized source coding

Doyle1, Carlson

  • 1Control and Dynamical Systems, California Institute of Technology, Pasadena, California 91125, USA.

Physical Review Letters
|September 16, 2000
PubMed
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This study presents robust design problems for complex systems facing uncertainty, revealing "robust yet fragile" properties and power law distributions in events. These findings apply to data compression, web traffic, and forest fires.

Area of Science:

  • Complex Systems Science
  • Systems Engineering
  • Statistical Physics

Background:

  • Real-world systems often operate under uncertainty, requiring robust designs.
  • Optimized systems can exhibit unexpected fragility and event distributions.

Purpose of the Study:

  • Introduce a framework for robust design problems in uncertain environments.
  • Analyze tradeoffs between resource allocation and system losses.
  • Investigate the emergent properties of optimized complex systems.

Main Methods:

  • Formulated robust design problems based on resource allocation-loss tradeoffs.
  • Developed optimized solutions for complex systems.
  • Applied the framework to data compression, web traffic, and forest fire models.

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Main Results:

  • Identified "robust, yet fragile" characteristics in optimized systems.
  • Observed power law tails in event distributions, except for Shannon coding.
  • Achieved excellent agreement between model predictions and empirical data for web traffic and forest fires.

Conclusions:

  • The proposed robust design framework captures essential system behaviors under uncertainty.
  • The findings have implications for understanding and managing complex systems like networks and ecological processes.