Path Counting on Tree-like Graphs with a Single Entropic Trap: Critical Behavior and Finite Size Effects.

It is known that maximal entropy random walks and partition functions that count long paths on graphs tend to become localized near nodes with a high degree. Here, we revisit the simplest toy model of such a localization: a regular tree of degree with one special node ("root") that has a degree different from all the others. We present an in-depth study of the path-counting problem precisely at the localization transition.

Analysis of English free association network reveals mechanisms of efficient solution of Remote Association Tests.

We study correlations between the structure and properties of a free association network of the English language, and solutions of psycholinguistic Remote Association Tests (RATs). We show that average hardness of individual RATs is largely determined by relative positions of test words (stimuli and response) on the free association network. We argue that the solution of RATs can be interpreted as a first passage search problem on a network whose vertices are words and links are associations between words.

Model of chromosomal loci dynamics in bacteria as fractional diffusion with intermittent transport.

The short-time dynamics of bacterial chromosomal loci is a mixture of subdiffusive and active motion, in the form of rapid relocations with near-ballistic dynamics. While previous work has shown that such rapid motions are ubiquitous, we still have little grasp on their physical nature, and no positive model is available that describes them. Here, we propose a minimal theoretical model for loci movements as a fractional Brownian motion subject to a constant but intermittent driving force, and compare simulations and analytical calculations to data from high-resolution dynamic tracking in E.

A statistical model of intra-chromosome contact maps.

A statistical model describing a fine structure of the intra-chromosome maps obtained by a genome-wide chromosome conformation capture method (Hi-C) is proposed. The model combines hierarchical chain folding with a quenched heteropolymer structure of primary chromatin sequences. It is conjectured that the observed Hi-C maps are statistical averages over many different ways of hierarchical genome folding.

How a viscoelastic solution of wormlike micelles transforms into a microemulsion upon absorption of hydrocarbon: new insight.

In this article, we investigate the effect of hydrocarbon addition on the rheological properties and structure of wormlike micellar solutions of potassium oleate. We show that a viscoelastic solution of entangled micellar chains is extremely responsive to hydrocarbons-the addition of only 0.5 wt % n-dodecane results in a drastic drop in viscosity by up to 5 orders of magnitude, which is due to the complete disruption of micelles and the formation of microemulsion droplets.

Phase transition in random planar diagrams and RNA-type matching.

We study the planar matching problem, defined by a symmetric random matrix with independent identically distributed entries, taking values zero and one. We show that the existence of a perfect planar matching structure is possible only above a certain critical density, p(c), of allowed contacts (i.e.

Number of common sites visited by N random walkers.

We compute analytically the mean number of common sites, W(N)(t), visited by N independent random walkers each of length t and all starting at the origin at t = 0 in d dimensions. We show that in the (N-d) plane, there are three distinct regimes for the asymptotic large-t growth of W(N)(t). These three regimes are separated by two critical lines d = 2 and d = d(c)(N) = 2N/(N-1) in the (N-d) plane.