Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences

Research output: Contribution to journalArticle


The concept of symbolic sequences play important role in study of complex systems. In the work we are interested in ultrametric structure of the set of cyclic sequences naturally arising in theory of dynamical systems. Aimed at construction of analytic and numerical methods for investigation of clusters we introduce operator language on the space of symbolic sequences and propose an approach based on wavelet analysis for study of the cluster hierarchy. The analytic power of the approach is demonstrated by derivation of a formula for counting of two-fold de Bruijn sequences, the extension of the notion of de Bruijn sequences. Possible advantages of the developed description is also discussed in context of applied problem of construction of efficient DNA sequence assembly algorithms.


  • Vladimir Osipov
Research areas and keywords

Subject classification (UKÄ) – MANDATORY

  • Physical Chemistry


  • De Bruijn sequences, DNA sequence assembly, Dynamical systems, Symbolic sequences, Ultrametrics, Wavelet
Original languageEnglish
Pages (from-to)142-165
Number of pages24
JournalJournal of Statistical Physics
Issue number1
Publication statusPublished - 2016 Jul 1
Publication categoryResearch