Quantized vortices in a complex wave field described by a defocusing nonlinear Schrödinger equation witha space-varying dispersion coefficient are studied theoretically and compared to vortices in the Gross-Pitaevskii model with external potential. A discrete variant of the equation is used to demonstrate numerically that vortex knots in three-dimensional arrays of oscillators coupled by specially tuned weak links can exist for as long times as many tens of typical vortex turnover periods. [PRE 100, 012205 (2019)].

Due to the development of the chromosome conformation capture (Hi-C) method, it has become possible to get insight into the chromatin organization by measuring the frequency of physical contacts between different parts of genome. The mechanism of active loop extrusion holds great promise for explaining the key features of the contact maps obtained from the Hi-C data. The loop extrusion model assumes that ATP-dependent process allows nanometer-size molecular machines to organize chromosomes by producing dynamically expanding chromatin loops. In this talk I will give a brief introduction into the loop extrusion model and demonstrate that analytical predictions extracted from this model in its simplest version, where chromatin fiber is treated as an ideal Gaussian chain, are in agreement with experimentally measured statistics of contacts in the interphase chromosomes.

The structure of the edge of a QHE edge is constrained, but not dictated, by the topology of the bulk. Particularly interesting is the class of hole-conjugate fractional QH states. For such states the edge hosts counter-propagating modes that are responsible for quantized electrical and thermal conductance. In the coherent quantum limit renormalized edge modes emerge, which may involve neutral modes with non-trivial exchange statistics. I will discuss the behavior of topology-influenced transport coefficient both in the coherent and the fully equilibrated regimes, topological classification of non-equilibrium shot noise, and the relation to recent experiments.