Predictability: a way to characterize complexity

By Guido Boffetta, M. Cencini, M. Falcioni, Angelo Vulpiani. 2001

323 citations recorded by the source corpus.

Abstract Different aspects of the predictability problem in dynamical systems are reviewed. The deep relation among Lyapunov exponents, Kolmogorov–Sinai entropy, Shannon entropy and algorithmic complexity is discussed. In particular, we emphasize how a characterization of the unpredictability of a system gives a measure of its complexity. Adopting this point of view, we review some developments in the characterization of the predictability of systems showing different kinds of complexity: from low-dimensional systems to high-dimensional ones with spatio-temporal chaos and to fully developed turbulence. A special attention is devoted to finite-time and finite-resolution effects on predictability, which can be accounted with suitable generalization of the standard indicators. The problems involved in systems with intrinsic randomness is discussed, with emphasis on the important problems of distinguishing chaos from noise and of modeling the system. The characterization of irregular behavior in systems with discrete phase space is also considered.

Subfields: Economics and Econometrics, Global and Planetary Change, Statistical and Nonlinear Physics

View Paper: https://www.semanticscholar.org/paper/27020ebf464e41bbc2ecf932f48ac41c77f82306

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In Economics and Econometrics

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Citations in the corpus

Prediction (2010, unknown): “24 20 v1 [ ph ys ic s. ge o- This chapter first presents a rather personal view of some diff rent aspects of predictability, going in crescendo from simple linear systems to high-dimensional nonlinear systems with stochastic forcing, which exhibit emergent properties such as phase transitions and…”
Engineering design complexity: an investigation of methods and measures (2008, background): “As a result, various measures of complexity, including entropy (Braha and Maimon 1998a, b), randomness (Grassberger 1991), and predictability ( Boffetta et al. 2002 ), have emerged aimed at valuation of inherent complexities of different objects.”
An information-theoretic primer on complexity, self-organization, and emergence (2009, background): “Essentially, the algorithmic complexity implies a deterministic description of an object (it defines the information content of an individual sequence), while the statistical complexity implies a statistical description (it refers to an ensemble of sequences generated by a certain source) [25, 26].”
Fluctuation-dissipation: Response theory in statistical physics (2008, background): “evolving according the linearized dynamics (inmathematical terms, δx(τ) is a tangent vector of the system) [46], and a lower bound for L(2) is given by 2λ.”