Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights

Seungsik Min, Ki Hong Shin, Woonhak Baek, Kyungsik Kim, Cheol Hwan You, Dong In Lee, Seong Soo Yum, Wonheung Kim, Ki Ho Chang

Research output: Contribution to journalArticle

Abstract

In this paper, the utility and the correlation technique of the detrended cross-correlation analysis and the combined detrended cross-correlation analysis methods are treated for the stochastic properties of the random walk and the Lévy flight via nucleotide sequence data. Data are extracted definitely from twelve genomic DNA sequences (HUMHBB 1-6, Amazonmolly, Bushbaby, Cow, Dolphin, Elephant, and Tarsier) of the GenBank databank. We mainly simulate and analyze scaling exponents for three methods in 1D and 2D random walks and Lévy flights. To compare each other between one gene and the other gene in the twelve genomic DNA sequences, the value of the detrended cross-correlation coefficient ρDCCA in {HUMHBB3} and {Dolphin} genes is shown the largest value 0.214 in the 1D Lévy flight with μ=1.5 compared to other sets. The detrended cross-correlation coefficient ρDCCA in {HUMHBB4} and {HUMHBB6} genes is shown the smallest value -0.231 in the 1D Lévy flight with μ=1.5. We particularly find that the combined detrended cross-correlation coefficient ρCDCCA in the two cases of {HUMHBB3}+{Bushbaby} and {HUMHBB6}+{Dolphin} has the largest value 0.331 in the 1D random walk compared to other sets, while that in {HUMHBB3}+{Tarsier} and {HUMHBB4}+{Elephant} has the smallest value -0.295 in the 1D Lévy flight with μ=1.5.

Original languageEnglish
Article number122872
JournalPhysica A: Statistical Mechanics and its Applications
Volume539
DOIs
Publication statusPublished - 2020 Feb 1

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Correlation Analysis
Cross-correlation
random walk
Dynamical Behavior
cross correlation
Random walk
dolphins
genes
flight
correlation coefficients
Correlation coefficient
Gene
DNA Sequence
Genomics
deoxyribonucleic acid
nucleotides
Scaling Exponent
exponents
scaling

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Condensed Matter Physics

Cite this

Min, Seungsik ; Shin, Ki Hong ; Baek, Woonhak ; Kim, Kyungsik ; You, Cheol Hwan ; Lee, Dong In ; Yum, Seong Soo ; Kim, Wonheung ; Chang, Ki Ho. / Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights. In: Physica A: Statistical Mechanics and its Applications. 2020 ; Vol. 539.
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Dynamical behavior of combined detrended cross-correlation analysis methods in random walks and Lévy flights. / Min, Seungsik; Shin, Ki Hong; Baek, Woonhak; Kim, Kyungsik; You, Cheol Hwan; Lee, Dong In; Yum, Seong Soo; Kim, Wonheung; Chang, Ki Ho.

In: Physica A: Statistical Mechanics and its Applications, Vol. 539, 122872, 01.02.2020.

Research output: Contribution to journalArticle

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