Compression and Diffusion: A Joint Approach to Detect Complexity

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Article discussing a joint approach to detect complexity by combining the Compression Algorithm Sensitive To Regularity (CASToRe) and Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA) procedures.

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28 p.

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Allegrini, Paolo; Benci, V. (Vieri); Grigolini, Paolo; Hamilton, P.; Ignaccolo, Massimiliano; Menconi, Giulia et al. February 2003.

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Article discussing a joint approach to detect complexity by combining the Compression Algorithm Sensitive To Regularity (CASToRe) and Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA) procedures.

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28 p.

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This is the preprint version of the article. Reprinted with permission from Elsevier Science Ltd., all rights reserved. The final definitive version is available here: http://dx.doi.org/10.1016/S0960-0779(02)00136-4

Abstract: The adoption of the Kolmogorov-Sinai (KS) entropy is becoming a popular research tool among physicists, especially when applied to a dynamical system fitting the conditions of validity of the Pesin theorem. The study of time series that are a manifestation of system dynamics whose rules are either unknown or too complex for a mathematical treatment, is still a challenge since the KS entropy is not computable, in general, in that case. Here the authors present a plan of action based on the joint action of two procedures, both related to the KS entropy, but compatible with computer implementation through fast and efficient programs. The former procedure, called Compression Algorithm Sensitive To Regularity (CASToRe), establishes the amount of order by the numerical evaluation of algorithmic compressibility. The latter, called Complex Analysis of Sequences via Scaling AND Randomness Assessment (CASSANDRA), establishes the complexity degree through the numerical evaluation of the strength of an anomalous effect. This is the departure, of the diffusion process generated by the observed fluctuations, from ordinary Brownian motion. The CASSANDRA algorithm shares with CASToRe a connection with the Kolmogorov complexity. This makes both algorithms especially suitable to study the transition from dynamics to thermodynamics, and the case of non-stationary time series as well. The benefit of the joint action of these two methods is proven by the analysis of artificial sequences with the same main properties as the real time series to which the joint use of these two methods will be applied in future research work.

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  • Chaos, Solitons and Fractals, 2003, New York: Elsevier Science Ltd., pp. 517-535

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  • Publication Title: Chaos, Solitons and Fractals
  • Volume: 15
  • Issue: 3
  • Page Start: 517
  • Page End: 535
  • Peer Reviewed: Yes

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The Scholarly Works Collection is home to materials from the University of North Texas community's research, creative, and scholarly activities and serves as UNT's Open Access Repository. It brings together articles, papers, artwork, music, research data, reports, presentations, and other scholarly and creative products representing the expertise in our university community.** Access to some items in this collection may be restricted.**

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  • February 2003

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  • Feb. 1, 2013, 9:58 a.m.

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  • April 1, 2015, 3:54 p.m.

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Allegrini, Paolo; Benci, V. (Vieri); Grigolini, Paolo; Hamilton, P.; Ignaccolo, Massimiliano; Menconi, Giulia et al. Compression and Diffusion: A Joint Approach to Detect Complexity, article, February 2003; [New York, New York]. (digital.library.unt.edu/ark:/67531/metadc139462/: accessed February 26, 2017), University of North Texas Libraries, Digital Library, digital.library.unt.edu; crediting UNT College of Arts and Sciences.