2016/01/09 by Vladimir Al. Osipov · 1 citation
Biochemistry, Genetics and Molecular Biology · Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #Algorithm #Complex Systems and Time Series Analysis #Computer science #Context (archaeology) #De Bruijn sequence #Discrete mathematics #Dynamical systems theory #Extension (predicate logic) #Mathematical Dynamics and Fractals #Mathematics #Metric space #Pure mathematics #Symbolic data analysis #Symbolic dynamics #Theoretical computer science #Ultrametric space #advanced mathematical theories #math-ph #math.CO #math.MP #msc:05C10 #msc:37F20 #msc:92D20 #nlin.CD #q-bio.QM
paper · pdf · doi:10.1007/s10955-016-1537-5
arxiv created 2016/01/09 · openalex publication_date 2016/05/14 · arxiv updated 2016/06/22 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/05
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 \it 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 p