• Corpus ID: 3021835

# Statistical measures of complexity for strongly interacting systems

@article{Sol1999StatisticalMO,
title={Statistical measures of complexity for strongly interacting systems},
author={Ricard V. Sol{\'e} and Bartolo Luque},
journal={Research Papers in Economics},
year={1999}
}
• Published 1 August 1999
• Mathematics
• Research Papers in Economics
In recent studies, new measures of complexity for nonlinear systems have been proposed based on probabilistic grounds, as the LMC measure (Phys. Lett. A 209 (1995) 321). All these measures share an intuitive consideration: complexity seems to emerge in nature close to instability points, as for example the phase transition points characteristic of critical phenomena. Here we discuss these measures and their reliability for detecting complexity close to critical points in complex systems…

## Figures from this paper

Measuring Mutual Information in Random Boolean Networks
• Computer Science
Complex Syst.
• 2000
This paper invests in the behavior of random booleannetworks (RBNs) as they undergo their order–disorder phase transition, and is able to reproduce analytically the amount of mutual informationcontained in the system as measured from numerical simulations.
Information theory and learning: a physical approach
It is proved that predictive information provides the unique measure for the complexity of dynamics underlying the time series and there are classes of models characterized by {\em power-law growth of the predictive information} that are qualitatively more complex than any of the systems that have been investigated before.
Predictability, Complexity, and Learning
• Computer Science
Neural Computation
• 2001
It is argued that the divergent part of Ipred(T) provides the unique measure for the complexity of dynamics underlying a time series.
Predictability , Complexity , and Learning
It is argued that the divergent part of Ipred(T), the mutual information between the past and the future of a time series, provides the unique measure for the complexity of dynamics underlying aTime series.
Logical Reduction of Biological Networks to Their Most Determinative Components
• Computer Science
Bulletin of mathematical biology
• 2016
This article considers a recently introduced method for reducing a Boolean network to its most determinative nodes that yield the highest information gain and obtains a stronger result than in previous works, showing that a large information gain from a set of input nodes generates increased sensitivity to perturbations of those inputs.
Causal architecture, complexity and self-organization in time series and cellular automata
• Computer Science
• 2001
This work develops computational mechanics for four increasingly sophisticated types of process—memoryless transducers, time series, transducers with memory, and cellular automata, and proves the optimality and uniqueness of the e-machine's representation of the causal architecture, and gives reliable algorithms for pattern discovery.
An Information Theory Framework for the Analysis of Scene Complexity
• Computer Science
Comput. Graph. Forum
• 1999
A new framework for the analysis of scene visibility and radiosity complexity is presented and experiments illustrate that the best mesh of a given scene among a number of alternatives corresponds to the one with the highest discrete mutual information.
SymGeons: A Prototype Model of Visual Complexity with Implications For Visual Control Tasks
• Computer Science
Cognition, Technology & Work
• 2001
The derivation and ongoing development of the ‘SymGeon’ model and how it compares to human perception of visual complexity are outlined and the application of the model to understanding complex human-in-the-loop problems associated with visual remote control operations, e.g. control of remotely operated vehicles, is discussed.
Measurement of network complexity and capability in command and control system
• Computer Science, Business
• 2014
Two case studies of an anti-aircraft defence C2 network and partial tank division network are carried out to illustrate the computation processes of the proposed network complexity and capability.

## References

SHOWING 1-10 OF 39 REFERENCES
Chaos
or "What a lie", or "How could I have said so"? or demanded at once that she should be sent for. Yet, he never on one single occasion, before others, spoke to Mrs. Cox on the subject. The only
Complexity Metaphors, Models, and Reality
• Psychology
• 1994
* Fundamental Concepts * Examples of Complex Adaptive Systems * Nonadaptive Systems, Scaling, Self-Similarity, and Measures of Complexity * General Discussion * Afterwords
Phys
• Let. A 223 (1996) 348; D. P. Feldman and J. P. Crutchfield, Phys. Lett. A, 238
• 1998
Matt Davison and P
• T. Landsberg Phys. Rev E 59(2)
• 1999
ORIGINS OF ORDER
Int. J. Theor. Phys
• Int. J. Theor. Phys
• 1986
Phys. Lett. A
• Phys. Lett. A
• 1995
Phys. Lett. A
• Phys. Lett. A
• 1995
J. Phys. A: Math. Gen
• J. Phys. A: Math. Gen
• 1988