Symbolic high-order Markov chains: Entropy and compressibility
Abstract
Using the bilinear Markov chain approach, we study statistical properties of natural random symbolic sequences with complex correlation properties. In the limit of weak correlations, we present analytically the entropy of sequence by means of correlation functions of the second and third orders. We illustrate the applicability of the developed theory to some sequences naturally arising in biology and chaotic dynamics. We evaluate numerically the entropy of DNA nucleotide sequences and sequences obtained by dichotomization of a logistic map. Using the connection between the compressibility of random sequence and the algorithmic entropy, we compare the levels of entropies, obtained by means of a combination of analytical and numerical methods, with the algorithmic entropy calculated by the standard files archivers. We show that our method gives a much lower level of entropy as compared to the best archivers. Numerical simulations show also that an account of third-order correlation functions significantly decreases the entropy calculated in the framework of the additive Markov chain approach.
- Publication:
-
Physical Review E
- Pub Date:
- October 2018
- DOI:
- 10.1103/PhysRevE.98.042144
- Bibcode:
- 2018PhRvE..98d2144M