Advanced

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

Osipov, Vladimir LU (2016) In Journal of Statistical Physics 164(1). p.142-165
Abstract

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... (More)

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.

(Less)
Please use this url to cite or link to this publication:
author
organization
publishing date
type
Contribution to journal
publication status
published
subject
keywords
De Bruijn sequences, DNA sequence assembly, Dynamical systems, Symbolic sequences, Ultrametrics, Wavelet
in
Journal of Statistical Physics
volume
164
issue
1
pages
24 pages
publisher
Springer
external identifiers
  • scopus:84968547766
  • wos:000377785800007
ISSN
0022-4715
DOI
10.1007/s10955-016-1537-5
language
English
LU publication?
yes
id
6d2818a1-a20f-41aa-895d-030a1e64c20e
date added to LUP
2016-07-04 10:40:55
date last changed
2017-01-01 08:29:47
@article{6d2818a1-a20f-41aa-895d-030a1e64c20e,
  abstract     = {<p>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.</p>},
  author       = {Osipov, Vladimir},
  issn         = {0022-4715},
  keyword      = {De Bruijn sequences,DNA sequence assembly,Dynamical systems,Symbolic sequences,Ultrametrics,Wavelet},
  language     = {eng},
  month        = {07},
  number       = {1},
  pages        = {142--165},
  publisher    = {Springer},
  series       = {Journal of Statistical Physics},
  title        = {Wavelet Analysis on Symbolic Sequences and Two-Fold de Bruijn Sequences},
  url          = {http://dx.doi.org/10.1007/s10955-016-1537-5},
  volume       = {164},
  year         = {2016},
}