Vladimir OsipovUltrametric arrangement of symbolic sequencesAbstract
Symbolic sequence is a fundamental object, which plays important role in
mathematical modelling in various areas of modern
science and technology. In the talk we introduce a notion of $p$close sequences and
utilize it to construct an ultrametric distance on the set of symbolic sequences of
a given length. We show, that the sequences are organized into hierarchically nested
clusters with irregular brunching parameter. We study statistics of clusters using
equivalence of the problem to the one of counting
degenerates in the length spectrum of de Bruijn graphs (a standard mathematical tool
for visualization of sequences) and employ methods of random matrix theory for
calculation of the obtained multidimensional integrals. In the talk a special
attention will be payed to such applied problems as (i) classification of periodic
orbits in quantum
chaotic systems for calculation of spectral correlations and (ii) choice of
parameters in the DNA sequence assembling algorithms.
