Background: Entropy can be used to detect the complexity of Sequences. various concepts of
entropy appeared, such as metric entropy, Kolmogorov-Sinai entropy, Renyi entropy and topological
entropy. Topological entropy is a difficult definition used to decipher the structure of DNA sequences, due
to finite dimensional problems.
Method: Different from the generalized topological entropy, a vector topological entropy is presented,
which is based on the idea of multi-scale analysis of DNA sequences. Subsequently the complexity of
promoter regions between Chromosome X and Y is detected by the use of a quantity topological entropy.
Results: It is shown that the quantity topological entropy of promoters is less than the coding regions in all
the Chromosomes. The mean of topological entropy of promoters is 3 standard deviations higher than the
mean of coding regions in Chromosomes. The results show that the quantity topological entropy of coding
regions is significantly higher than that of promoters.
Conclusion: The topological entropy is a useful tool for detecting the structure of DNA sequences, and
the result of the comparisons shows the promoter regions as being more regular, which implies that the
promoters are more functionally important.