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

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          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.

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          Author and article information

          Journal
          19 January 2015
          Article
          10.1103/PhysRevE.90.052106
          1502.07363
          876b88d9-645d-4d1a-9754-03bb5eacf41d

          http://arxiv.org/licenses/nonexclusive-distrib/1.0/

          History
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          Phys. Rev. E 90, 052106 (2014)
          9 pages, 4 figures. arXiv admin note: substantial text overlap with arXiv:1411.2761, arXiv:1412.3692
          cond-mat.stat-mech cond-mat.dis-nn cs.IT math.IT physics.data-an

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