We review pro and contra of the hypothesis that generic polymer properties of topological
constraints are behind many aspects of chromatin folding in eukaryotic cells. For that …

The classical Fourier transform is one of the most widely used mathematical tools in
engineering. However, few engineers know that extensions of harmonic analysis to …

The fractal globule state is a popular model for describing chromatin packing in eukaryotic
nuclei. Here we provide a scaling theory and dissipative particle dynamics computer …

Topological constraints can affect both equilibrium and dynamic properties of polymer
systems and can play a role in the organization of chromosomes. Despite many theoretical …

A single polymer macromolecule is considered with disorder types such as branches, knots,
and heterogeneous sequences of chemical units. In all cases, simple theoretical …

A new method is presented here for temporal modelling and visualization of the spatial
complexity changes of landscape boundaries. The method is based on topological braid …

The study of knots and links from a probabilistic viewpoint provides insight into the behavior
of “typical” knots, and opens avenues for new constructions of knots and other topological …

The main statistical characteristics of locally free groups: the growth, the drift and the entropy
are considered and relations between them are established. Our results assert that:(i) the …

We prove an isoperimetric inequality for wreath products of Markov chains with variable
fibers. We use isoperimetric inequalities for wreath products to estimate the return probability …

We study random knotting by considering knot and link diagrams as decorated,(rooted)
topological maps on spheres and pulling them uniformly from among sets of a given number …