The self-similarity properties and multifractal analysis of DNA sequences
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Autores: G. Durán Meza, José Luis López García
, J. L. Del Rio Correa
- Localización: Applied Mathematics and Nonlinear Sciences, ISSN-e 2444-8656, Vol. 4, Nº. 1, 2019, págs. 261-272
- Idioma: inglés
- DOI: 10.2478/amns.2019.1.00023
- Enlaces
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Resumen
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.
