2 research outputs found
L\'{e}vy scaling: the Diffusion Entropy Analysis applied to DNA sequences
We address the problem of the statistical analysis of a time series generated
by complex dynamics with a new method: the Diffusion Entropy Analysis (DEA)
(Fractals, {\bf 9}, 193 (2001)). This method is based on the evaluation of the
Shannon entropy of the diffusion process generated by the time series imagined
as a physical source of fluctuations, rather than on the measurement of the
variance of this diffusion process, as done with the traditional methods. We
compare the DEA to the traditional methods of scaling detection and we prove
that the DEA is the only method that always yields the correct scaling value,
if the scaling condition applies. Furthermore, DEA detects the real scaling of
a time series without requiring any form of de-trending. We show that the joint
use of DEA and variance method allows to assess whether a time series is
characterized by L\'{e}vy or Gauss statistics. We apply the DEA to the study of
DNA sequences, and we prove that their large-time scales are characterized by
L\'{e}vy statistics, regardless of whether they are coding or non-coding
sequences. We show that the DEA is a reliable technique and, at the same time,
we use it to confirm the validity of the dynamic approach to the DNA sequences,
proposed in earlier work.Comment: 24 pages, 9 figure