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.

Order and stochasticity in the folding of individual Drosophila genomes.

Mammalian and Drosophila genomes are partitioned into topologically associating domains (TADs). Although this partitioning has been reported to be functionally relevant, it is unclear whether TADs represent true physical units located at the same genomic positions in each cell nucleus or emerge as an average of numerous alternative chromatin folding patterns in a cell population. Here, we use a single-nucleus Hi-C technique to construct high-resolution Hi-C maps in individual Drosophila genomes.

Brownian flights over a circle.

The stationary radial distribution, P(ρ), of a random walk with the diffusion coefficient D, which winds at the tangential velocity V around an impenetrable disk of radius R for R≫D/V converges to the distribution involving the Airy function. Typical trajectories are localized in the circular strip [R,R+δR^{1/3}], where δ is a constant which depends on the parameters D and V and is independent of R.

Self-isolation or borders closing: What prevents the spread of the epidemic better?

Pandemic propagation of COVID-19 motivated us to discuss the impact of the human network clustering on epidemic spreading. Today, there are two clustering mechanisms which prevent of uncontrolled disease propagation in a connected network: an "internal" clustering, which mimics self-isolation (SI) in local naturally arranged communities, and an "external" clustering, which looks like a sharp frontiers closing (FC) between cities and countries, and which does not care about the natural connections of network agents. SI networks are "evolutionarily grown" under the condition of maximization of small cliques in the entire network, while FC networks are instantly created.

Non-backtracking walks reveal compartments in sparse chromatin interaction networks.

Chromatin communities stabilized by protein machinery play essential role in gene regulation and refine global polymeric folding of the chromatin fiber. However, treatment of these communities in the framework of the classical network theory (stochastic block model, SBM) does not take into account intrinsic linear connectivity of the chromatin loci. Here we propose the polymer block model, paving the way for community detection in polymer networks.

Spectral peculiarity and criticality of a human connectome.

We have performed the comparative spectral analysis of structural connectomes for various organisms using open-access data. Our results indicate new peculiar features of connectomes of higher organisms. We found that the spectral density of adjacency matrices of human connectome has maximal deviation from the one of randomized network, compared to other organisms.

Many-body contacts in fractal polymer chains and fractional Brownian trajectories.

We calculate the probabilities that a trajectory of a fractional Brownian motion with arbitrary fractal dimension d_{f} visits the same spot n≥3 times, at given moments t_{1},...

Anomalous one-dimensional fluctuations of a simple two-dimensional random walk in a large-deviation regime.

The following question is the subject of our work: could a two-dimensional (2D) random path pushed by some constraints to an improbable "large-deviation regime" possess extreme statistics with one-dimensional (1D) Kardar-Parisi-Zhang (KPZ) fluctuations? The answer is positive, though nonuniversal, since the fluctuations depend on the underlying geometry. We consider in detail two examples of 2D systems for which imposed external constraints force the underlying stationary stochastic process to stay in an atypical regime with anomalous statistics. The first example deals with the fluctuations of a stretched 2D random walk above a semicircle or a triangle.

Heterogeneous continuous-time random walks.

We introduce a heterogeneous continuous-time random walk (HCTRW) model as a versatile analytical formalism for studying and modeling diffusion processes in heterogeneous structures, such as porous or disordered media, multiscale or crowded environments, weighted graphs or networks. We derive the exact form of the propagator and investigate the effects of spatiotemporal heterogeneities onto the diffusive dynamics via the spectral properties of the generalized transition matrix. In particular, we show how the distribution of first-passage times changes due to local and global heterogeneities of the medium.

How anisotropy beats fractality in two-dimensional on-lattice diffusion-limited-aggregation growth.

We study the fractal structure of diffusion-limited aggregation (DLA) clusters on a square lattice by extensive numerical simulations (with clusters having up to 10^{8} particles). We observe that DLA clusters undergo strongly anisotropic growth, with the maximal growth rate along the axes. The naive scaling limit of a DLA cluster by its diameter is thus deterministic and one-dimensional.

Finite plateau in spectral gap of polychromatic constrained random networks.

We consider critical behavior in the ensemble of polychromatic Erdős-Rényi networks and regular random graphs, where network vertices are painted in different colors. The links can be randomly removed and added to the network subject to the condition of the vertex degree conservation. In these constrained graphs we run the Metropolis procedure, which favors the connected unicolor triads of nodes.

First passage times for multiple particles with reversible target-binding kinetics.

We investigate the first passage problem for multiple particles that diffuse towards a target, partially adsorb there, and then desorb after a finite exponentially distributed residence time. We search for the first time when m particles undergoing such reversible target-binding kinetics are found simultaneously on the target that may trigger an irreversible chemical reaction or a biophysical event. Even if the particles are independent, the finite residence time on the target yields an intricate temporal coupling between particles.

Unraveling intermittent features in single-particle trajectories by a local convex hull method.

We propose a model-free method to detect change points between distinct phases in a single random trajectory of an intermittent stochastic process. The local convex hull (LCH) is constructed for each trajectory point, while its geometric properties (e.g.