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Mutual Information Functions Versus Correlation Functions in Binary Sequences

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Part of the book series: NATO ASI Series ((NSSB,volume 208))

Abstract

Mutual information is a well known concept used in information theory [1]. Recently, it has been suggested that it can be used in the study of chaotic dynamical systems [2] and for the characterization of spatial complex patterns [3]. Although it has been shown that mutual information is a better quantity than correlation function in the determination of the time delay for the delayed signal in reconstructing the phase space of the chaotic trajectory [4], there is no attempt to systematically compare it with the more frequently used correlation functions. Binary sequences provide an excellent example for this comparative study. Some results are included here, for more details see Ref [5].

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References

  1. C.E.Shannon, “The mathematical theory of communication”, Bell Syst. Techn. Journal, 27, 379–423 (1948).

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  2. Rob Shaw, “The dripping faucet as a model chaotic system”, (Aerial Press) (1984); and unpublished ideas.

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  3. Gregory J. Chaitin, “Toward a mathematical definition of life’ ”, The Maximum Entropy Formalism, ed. Levine and Tribus, ( MIT Press 1979 ).

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  4. A.M. Fraser, H.L. Swinney, “Independent coordinates for strange attractors from mutual information ”, Physical Review A, 33, 1134–1140 (1986).

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  5. Wentian Li, “Mutual information versus correlation functions”, (CCSR Tech Report, CCSR, Univ. of Illinois, 1989 ).

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  6. Wentian Li, Problems in Complex Systems (Ph.D thesis, Columbia University, 1989); “Context-free languages can give 1/f spectra”, (CCSR Tech Report No.10, CCSR Univ. of Illinois, 1988 ).

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  7. ed. Stephen Wolfram, Theory and Application of Cellular Automata, (World Scientific, 1986 ).

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  8. Chris Langton, Norman Packard, Wentian Li, “Bifurcation-like phenomena in cellular automata rule space”, (paper in preparation, 1989 ).

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  9. Wentian Li, “Correlation analysis of JFK’s inaugural speech”, (work in progress).

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© 1989 Plenum Press, New York

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Li, W. (1989). Mutual Information Functions Versus Correlation Functions in Binary Sequences. In: Abraham, N.B., Albano, A.M., Passamante, A., Rapp, P.E. (eds) Measures of Complexity and Chaos. NATO ASI Series, vol 208. Springer, Boston, MA. https://doi.org/10.1007/978-1-4757-0623-9_35

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  • DOI: https://doi.org/10.1007/978-1-4757-0623-9_35

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4757-0625-3

  • Online ISBN: 978-1-4757-0623-9

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