Correlations in binary sequences and a generalized Zipf analysis

A. Czirók, Rosario N. Mantegna, Shlomo Havlin, H. Eugene Stanley

Research output: Contribution to journalArticle

61 Citations (Scopus)

Abstract

We investigate correlated binary sequences using an n-tuple Zipf analysis, where we define "words" as strings of length n, and calculate the normalized frequency of occurrence ω(R) of "words" as a function of the word rank R. We analyze sequences with short-range Markovian correlations, as well as those with long-range correlations generated by three different methods: inverse Fourier transformation, Lévy walks, and the expansion-modification system. We study the relation between the exponent α characterizing long-range correlations and the exponent ζ characterizing power-law behavior in the Zipf plot. We also introduce a function P(ω), the frequency density, which is related to the inverse Zipf function R(ω), and find a simple relationship between ζ and ψ, where ω(R)∼R-ζ and P(ω)∼ω-ψ. Further, for Markovian sequences, we derive an approximate form for P(ω). Finally, we study the effect of a coarse-graining "renormalization" on sequences with Markovian and with long-range correlations.

Original languageEnglish
Pages (from-to)446-452
Number of pages7
JournalPhysical Review E - Statistical, Nonlinear, and Soft Matter Physics
Volume52
Issue number1
DOIs
Publication statusPublished - 1995

Fingerprint

Long-range Correlations
Binary Sequences
Exponent
n-tuple
Coarse-graining
Inverse Method
Fourier Transformation
exponents
Walk
Renormalization
Fourier transformation
Power Law
Strings
Calculate
strings
plots
occurrences
Range of data
expansion

ASJC Scopus subject areas

  • Mathematical Physics
  • Physics and Astronomy(all)
  • Condensed Matter Physics
  • Statistical and Nonlinear Physics

Cite this

Correlations in binary sequences and a generalized Zipf analysis. / Czirók, A.; Mantegna, Rosario N.; Havlin, Shlomo; Stanley, H. Eugene.

In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics, Vol. 52, No. 1, 1995, p. 446-452.

Research output: Contribution to journalArticle

Czirók, A. ; Mantegna, Rosario N. ; Havlin, Shlomo ; Stanley, H. Eugene. / Correlations in binary sequences and a generalized Zipf analysis. In: Physical Review E - Statistical, Nonlinear, and Soft Matter Physics. 1995 ; Vol. 52, No. 1. pp. 446-452.
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