article · Physical Review E · 2014

Entropy of finite random binary sequences with weak long-range correlations

Cited by 8Open access

Abstract

We study the N-step binary stationary ergodic Markov chain and analyze its differential entropy. Supposing that the correlations are weak we express the conditional probability function of the chain through the pair correlation function and represent the entropy as a functional of the pair correlator. Since the model uses the two-point correlators instead of the block probability, it makes it possible to calculate the entropy of strings at much longer distances than using standard methods. A fluctuation contribution to the entropy due to finiteness of random chains is examined. This contribution can be of the same order as its regular part even at the relatively short lengths of subsequences. A self-similar structure of entropy with respect to the decimation transformations is revealed for some specific forms of the pair correlation function. Application of the theory to the DNA sequence of the R3 chromosome of Drosophila melanogaster is presented.

Cite this paper

APA 7

Melnik, S., & Usatenko, O. V. (2014). Entropy of finite random binary sequences with weak long-range correlations. Physical Review E, 90(5), 052106. https://doi.org/10.1103/physreve.90.052106

MLA 9

Melnik, S.S., and O. V. Usatenko. “Entropy of finite random binary sequences with weak long-range correlations.” Physical Review E, vol. 90, no. 5, 2014, p. 052106, https://doi.org/10.1103/physreve.90.052106.

Chicago

Melnik, S.S., and O. V. Usatenko. 2014. “Entropy of finite random binary sequences with weak long-range correlations.” Physical Review E 90 (5): 052106. https://doi.org/10.1103/physreve.90.052106.

Harvard

Melnik, S. and Usatenko, O.V. (2014) ‘Entropy of finite random binary sequences with weak long-range correlations’, Physical Review E, 90(5), p. 052106. Available at: https://doi.org/10.1103/physreve.90.052106.

BibTeX

@article{melnik2014entropy,
  title = {{Entropy of finite random binary sequences with weak long-range correlations}},
  author = {Melnik, S.S. and Usatenko, O. V.},
  journal = {Physical Review E},
  volume = {90},
  number = {5},
  pages = {052106},
  year = {2014},
  doi = {10.1103/physreve.90.052106}
}

Made from the index record. Check names, capitalisation and page numbers against the paper. Need another style? AI for Research has over 10,000.