Laboratoire de Physique Théorique
Toulouse - UMR 5152

Kandiah Vivek : Google matrix analysis of DNA sequences

For DNA sequences of various species we construct the Google matrix G of Markov transitions between nearby words composed of several letters. The statistical distribution of matrix elements of this matrix is shown to be described by a power law with the exponent being close to those of outgoing links in such scale-free networks as the World Wide Web (WWW). At the same time the sum of ingoing matrix elements is characterized by the exponent being significantly larger than those typical for WWW networks. This results in a slow algebraic decay of the PageRank probability determined by the distribution of ingoing elements. The spectrum of $G$ is characterized by a large gap leading to a rapid relaxation process on the DNA sequence networks. We introduce the PageRank proximity correlator between different species which determines their statistical similarity from the view point of Markov chains.

Alvarez Juan Pablo : Bose glass transition and spin-wave localization for 2D bosons in a random potential

A spin-wave (SW) approach of the zero temperature superfluid - insulator transition for two dimensional hard-core bosons in a random potential mu=+/- W is developed. While at the classical level there is no intervening phase between the Bose-condensed superfluid (SF) and the gapped disordered insulator, the introduction of quantum fluctuations lead to a much richer physics. Upon increasing the disorder strength W, the Bose-condensed fraction disappears first, before the SF. Then a gapless Bose-glass (BG) phase emerges over a finite region, until the insulator appears. Furthermore, in the strongly disordered SF regime, a mobility edge in the SW excitation spectrum is found at a finite frequency Omega_c, decreasing with W, and presumably vanishing in the BG phase.