Highly Optimized Tolerance: Robustness and Power Laws in Complex Systems

We introduce highly optimized tolerance (HOT), a mechanism that connects evolving structure and power laws in interconnected systems. HOT systems arise, e.g., in biology and engineering, where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, specialized, structured configurations, and (4) power laws. We introduce HOT states in the context of percolation, and contrast properties of the high density HOT states with random configurations near the critical point. While both cases exhibit power laws, only HOT states display properties (1-3) associated with design and evolution.Comment: 4 pages, 2 figure

Power Laws, Highly Optimized Tolerance, and Generalized Source Coding

We introduce a family of robust design problems for complex systems in uncertain environments which are based on tradeoffs between resource allocations and losses. Optimized solutions yield the “robust, yet fragile” features of highly optimized tolerance and exhibit power law tails in the distributions of events for all but the special case of Shannon coding for data compression. In addition to data compression, we construct specific solutions for world wide web traffic and forest fires, and obtain excellent agreement with measured data

Highly Optimized Tolerance: Robustness and Design in Complex Systems

Highly optimized tolerance (HOT) is a mechanism that relates evolving structure to power laws in interconnected systems. HOT systems arise where design and evolution create complex systems sharing common features, including (1) high efficiency, performance, and robustness to designed-for uncertainties, (2) hypersensitivity to design flaws and unanticipated perturbations, (3) nongeneric, specialized, structured configurations, and (4) power laws. We study the impact of incorporating increasing levels of design and find that even small amounts of design lead to HOT states in percolation

Design degrees of freedom and mechanisms for complexity

We develop a discrete spectrum of percolation forest fire models characterized by increasing design degrees of freedom (DDOF’s). The DDOF’s are tuned to optimize the yield of trees after a single spark. In the limit of a single DDOF, the model is tuned to the critical density. Additional DDOF’s allow for increasingly refined spatial patterns, associated with the cellular structures seen in highly optimized tolerance (HOT). The spectrum of models provides a clear illustration of the contrast between criticality and HOT, as well as a concrete quantitative example of how a sequence of robustness tradeoffs naturally arises when increasingly complex systems are developed through additional layers of design. Such tradeoffs are familiar in engineering and biology and are a central aspect of the complex systems that can be characterized as HOT

Applications of remote sensing in resource management in Nebraska

There are no author-identified significant results in this report

Tracer Dispersion in a Self-Organized Critical System

We have studied experimentally transport properties in a slowly driven granular system which recently was shown to display self-organized criticality [Frette {\em et al., Nature} {\bf 379}, 49 (1996)]. Tracer particles were added to a pile and their transit times measured. The distribution of transit times is a constant with a crossover to a decaying power law. The average transport velocity decreases with system size. This is due to an increase in the active zone depth with system size. The relaxation processes generate coherently moving regions of grains mixed with convection. This picture is supported by considering transport in a $1D$ cellular automaton modeling the experiment.Comment: 4 pages, RevTex, 1 Encapsulated PostScript and 4 PostScript available upon request, Submitted to Phys. Rev. Let

Stick-Slip Motion and Phase Transition in a Block-Spring System

We study numerically stick slip motions in a model of blocks and springs being pulled slowly. The sliding friction is assumed to change dynamically with a state variable. The transition from steady sliding to stick-slip is subcritical in a single block and spring system. However, we find that the transition is continuous in a long chain of blocks and springs. The size distribution of stick-slip motions exhibits a power law at the critical point.Comment: 8 figure