Applied Mathematics and Nonlinear Sciences (Jun 2019)

The self-similarity properties and multifractal analysis of DNA sequences

  • Durán-Meza G.,
  • López-García J.,
  • del Río-Correa J.L.

DOI
https://doi.org/10.2478/AMNS.2019.1.00023
Journal volume & issue
Vol. 4, no. 1
pp. 267 – 278

Abstract

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In this work is presented a pedagogical point of view of multifractal analysis deoxyribonucleic acid (DNA) sequences is presented. The DNA sequences are formed by 4 nucleotides (adenine, cytosine, guanine, and tymine). Following Jeffrey’s paper we associated a simple contractive function to each nucleotide, and constructed the Hutchinson’s operator W, which was used to build covers of different sizes of the unitary square Q, thus Wk(Q) is a cover of Q, conformed by 4k squares Qk of size 2−k, as each Qk corresponds to a unique subsequence of nucleotides with length k : b1b2...bk. Besides, it is obtained the optimal cover Ck to the fractal F generated for each DNA sequence was obtained. We made a multifractal decomposition of Ck in terms of the sets Jα conformed by the Qk’s with the same value of the Holder exponent α, and determined f (α), the Hausdorff dimension of Jα, using the curdling theorem.

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