National Research University – Higher School of Economics

About: National Research University – Higher School of Economics is a education organization based out in Moscow, Russia. It is known for research contribution in the topics: Population & Computer science. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

Yangians and cohomology rings of Laumon spaces

Abstract: Laumon moduli spaces are certain smooth closures of the moduli spaces of maps from the projective line to the flag variety of GL n. We construct the action of the Yangian of sln in the cohomology of Laumon spaces by certain natural correspon- dences. We construct the action of the affine Yangian (two-parametric deformation of the universal enveloping algebra of the universal central extension of sln(s ±1 , t)) in the cohomology of the affine version of Laumon spaces. We compute the matrix coefficients of the generators of the affine Yangian in the fixed point basis of coho- mology. This basis is an affine analog of the Gelfand-Tsetlin basis. The affine analog of the Gelfand-Tsetlin algebra surjects onto the equivariant cohomology rings of the affine Laumon spaces. The cohomology ring of the moduli space Mn,d of torsion free sheaves on the plane, of rank n and second Chern class d, trivialized at infinity, is

Resetting processes with noninstantaneous return.

Abstract: We consider a random two-phase process which we call a reset-return one. The particle starts its motion at the origin. The first, displacement, phase corresponds to a stochastic motion of a particle and is finished at a resetting event. The second, return, phase corresponds to the particle's motion toward the origin from the position it attained at the end of the displacement phase. This motion toward the origin takes place according to a given equation of motion. The whole process is a renewal one. We provide general expressions for the stationary probability density function of the particle's position and for the mean hitting time in one dimension. We perform explicit analysis for the Brownian motion during the displacement phase and three different types of the return motion: return at a constant speed, return at a constant acceleration with zero initial speed, and return under the action of a harmonic force. We assume that the waiting times for resetting events follow an exponential distribution or that resetting takes place after a fixed waiting period. For the first two types of return motion and the exponential resetting, the stationary probability density function of the particle's position is invariant under return speed (acceleration), while no such invariance is found for deterministic resetting, and for exponential resetting with return under the action of the harmonic force. We discuss necessary conditions for such invariance of the stationary PDF of the positions with respect to the properties of the return process, and we demonstrate some additional examples when this invariance does or does not take place.

Effective Connectivity within the Default Mode Network: Dynamic Causal Modeling of Resting-State fMRI Data.

Abstract: The Default Mode Network (DMN) is a brain system that mediates internal modes of cognitive activity, showing higher neural activation when one is at rest. Nowadays, there is a lot of interest in assessing functional interactions between its key regions, but in the majority of studies only association of BOLD (Blood-oxygen-level dependent) activation patterns is measured, so it is impossible to identify causal influences. There are some studies of causal interactions (i.e. effective connectivity), however often with inconsistent results. The aim of the current work is to find a stable pattern of connectivity between four DMN key regions: the medial prefrontal cortex mPFC, the posterior cingulate cortex PCC, left and right intraparietal cortex LIPC and RIPC. For this purpose fMRI (functional magnetic resonance imaging) data from 30 healthy subjects (1000 time points from each one) was acquired and spectral dynamic causal modeling (DCM) on a resting-state fMRI data was performed. The endogenous brain fluctuations were explicitly modeled by Discrete Cosine Set at the low frequency band of 0.0078–0.1 Hz. The best model at the group level is the one where connections from both bilateral IPC to mPFC and PCC are significant and symmetrical in strength (p<0.05). Connections between mPFC and PCC are bidirectional, significant in the group and weaker than connections originating from bilateral IPC. In general, all connections from LIPC/RIPC to other DMN regions are much stronger. One can assume that these regions have a driving role within the DMN. Our results replicate some data from earlier works on effective connectivity within the DMN as well as provide new insights on internal DMN relationships and brain’s functioning at resting state.

Variational Autoencoder with Arbitrary Conditioning

Abstract: We propose a single neural probabilistic model based on variational autoencoder that can be conditioned on an arbitrary subset of observed features and then sample the remaining features in "one shot". The features may be both real-valued and categorical. Training of the model is performed by stochastic variational Bayes. The experimental evaluation on synthetic data, as well as feature imputation and image inpainting problems, shows the effectiveness of the proposed approach and diversity of the generated samples.