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Google Matrix Analysis of DNA Sequences

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  • Vivek Kandiah
  • Dima L Shepelyansky

Abstract

For DNA sequences of various species we construct the Google matrix of Markov transitions between nearby words composed of several letters. The statistical distribution of matrix elements of this matrix is shown to be described by a power law with the exponent being close to those of outgoing links in such scale-free networks as the World Wide Web (WWW). At the same time the sum of ingoing matrix elements is characterized by the exponent being significantly larger than those typical for WWW networks. This results in a slow algebraic decay of the PageRank probability determined by the distribution of ingoing elements. The spectrum of is characterized by a large gap leading to a rapid relaxation process on the DNA sequence networks. We introduce the PageRank proximity correlator between different species which determines their statistical similarity from the view point of Markov chains. The properties of other eigenstates of the Google matrix are also discussed. Our results establish scale-free features of DNA sequence networks showing their similarities and distinctions with the WWW and linguistic networks.

Suggested Citation

  • Vivek Kandiah & Dima L Shepelyansky, 2013. "Google Matrix Analysis of DNA Sequences," PLOS ONE, Public Library of Science, vol. 8(5), pages 1-10, May.
    • Handle: RePEc:plo:pone00:0061519
    DOI: 10.1371/journal.pone.0061519
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    References listed on IDEAS

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    1. K. M. Frahm & D. L. Shepelyansky, 2010. "Ulam method for the Chirikov standard map," The European Physical Journal B: Condensed Matter and Complex Systems, Springer;EDP Sciences, vol. 76(1), pages 57-68, July.
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    Cited by:

    1. Young-Ho Eom & Pablo Aragón & David Laniado & Andreas Kaltenbrunner & Sebastiano Vigna & Dima L Shepelyansky, 2015. "Interactions of Cultures and Top People of Wikipedia from Ranking of 24 Language Editions," PLOS ONE, Public Library of Science, vol. 10(3), pages 1-27, March.
    2. Young-Ho Eom & Dima L Shepelyansky, 2013. "Highlighting Entanglement of Cultures via Ranking of Multilingual Wikipedia Articles," PLOS ONE, Public Library of Science, vol. 8(10), pages 1-10, October.

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