<abstract xmlns="http://www.w3.org/1999/xhtml">

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 <italic>W</italic>, which was used to build covers of different sizes of the unitary square <italic>Q</italic>, thus <italic>Wk</italic>(<italic>Q</italic>) is a cover of <italic>Q</italic>, conformed by 4<italic>k</italic> squares <italic>Qk</italic> of size 2<italic>−k</italic>, as each <italic>Qk</italic> corresponds to a unique subsequence of nucleotides with length <italic>k</italic> : <italic>b</italic>1<italic>b</italic>2<italic>...bk</italic>. Besides, it is obtained the optimal cover <italic>Ck</italic> to the fractal <italic>F</italic> generated for each DNA sequence was obtained. We made a multifractal decomposition of <italic>Ck</italic> in terms of the sets <italic>Jα</italic> conformed by the <italic>Qk</italic>’s with the same value of the Holder exponent <italic>α</italic>, and determined <italic>f</italic> (<italic>α</italic>), the Hausdorff dimension of <italic>Jα</italic>, using the curdling theorem.</abstract>

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.

The self-similarity properties and multifractal analysis of DNA sequences

Applied Mathematics and Nonlinear Sciences

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"The self-similarity properties and multifractal analysis of DNA sequences"}

In this work is presented a pedagogical point of view of multifractal analysis deoxyribonucleic acid (DNA) sequences is presented. The DNA sequences are formed...

The self-similarity properties and multifractal analysis of DNA sequences

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: Jun 29, 2019

Page range: 267 - 278

Received: Dec 15, 2018

Accepted: Apr 07, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00023

Keywords
Multifractals DNA sequences self-affine Hutchinson operator Holder exponents

© 2019 G. Durán-Meza et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

The self-similarity properties and multifractal analysis of DNA sequences

Article Category: Papers dedicated to the memory of Valetnin Afraymovich (1945-2018)

Published Online: Jun 29, 2019

Page range: 267 - 278

Received: Dec 15, 2018

Accepted: Apr 07, 2019

DOI: https://doi.org/10.2478/AMNS.2019.1.00023

KeywordsMultifractals DNA sequences self-affine Hutchinson operator Holder exponents

© 2019 G. Durán-Meza et al., published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Keywords
Multifractals DNA sequences self-affine Hutchinson operator Holder exponents