Dynamic Entropies, Long-range Correlations and Fluctuations
in Complex Linear Structures
Werner Ebeling, Alexander Neiman, Thorsten Pvschel
in Coherent Approach to Fluctuations (Proc. Hayashibara Forum 95) ,
ed. M. Suzuki (World Scientific, 1995?)
Abstract
We investigate symbolic sequences and in particular information carriers as e.g.
books and DNA--strings. First the higher order Shannon entropies are calculated,
a characteristic root law is detected. Then the algorithmic entropy is estimated
by using Lempel--Ziv compression algorithms. In the third section the correlation
function for distant letters, the low frequency Fourier spectrum and the
characteristic scaling exponents are calculated. We show that all these measures
are able to detect long--range correlations. However, as demonstrated by shuffling
experiments, different measures operate on different length scales. The longest
correlations found in our analysis comprise a few hundreds or thousands of letters
and may be understood as long--wave fluctuations of the composition.
