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 & Politics. The organization has 12873 authors who have published 23376 publications receiving 256396 citations.

3D Molecular Representations Based on the Wave Transform for Convolutional Neural Networks.

Abstract: Convolutional neural networks (CNN) have been successfully used to handle three-dimensional data and are a natural match for data with spatial structure such as 3D molecular structures. However, a direct 3D representation of a molecule with atoms localized at voxels is too sparse, which leads to poor performance of the CNNs. In this work, we present a novel approach where atoms are extended to fill other nearby voxels with a transformation based on the wave transform. Experimenting on 4.5 million molecules from the Zinc database, we show that our proposed representation leads to better performance of CNN-based autoencoders than either the voxel-based representation or the previously used Gaussian blur of atoms and then successfully apply the new representation to classification tasks such as MACCS fingerprint prediction.

Derived equivalences of gentle algebras via Fukaya categories

Abstract: Following the approach of Haiden–Katzarkov–Kontsevich (Publ Math Inst Hautes Etudes Sci 126:247–318, 2017), to any homologically smooth $$\mathbb {Z}$$-graded gentle algebra A we associate a triple $$(\Sigma _A, \Lambda _A; \eta _A)$$, where $$\Sigma _A$$ is an oriented smooth surface with non-empty boundary, $$\Lambda _A$$ is a set of stops on $$\partial \Sigma _A$$ and $$\eta _A$$ is a line field on $$\Sigma _A$$, such that the derived category of perfect dg-modules of A is equivalent to the partially wrapped Fukaya category of $$(\Sigma _A, \Lambda _A ;\eta _A)$$. Modifying arguments of Johnson and Kawazumi, we classify the orbit decomposition of the action of the (symplectic) mapping class group of $$\Sigma _A$$ on the homotopy classes of line fields. As a result we obtain a sufficient criterion for homologically smooth graded gentle algebras to be derived equivalent. Our criterion uses numerical invariants generalizing those given by Avella–Alaminos–Geiss in Avella et al. (J Pure Appl Algebra 212(1):228–243, 2008), as well as some other numerical invariants. As an application, we find many new cases when the AAG-invariants determine the derived Morita class. As another application, we establish some derived equivalences between the stacky nodal curves considered in Lekili and Polishchuk (J Topology 11:615–444, 2018)

Quasimap counts and bethe eigenfunctions

Abstract: We associate an explicit equivalent descendent insertion to any relative insertion in quantum K-theory of Nakajima varieties. This also serves as an explicit formula for off-shell Bethe eigenfunctions for general quantum loop algebras associated to quivers and gives the general integral solution to the corresponding quantum Knizhnik-Zamolodchikov and dynamical q-difference equations.

Invariance of Lyapunov exponents and Lyapunov dimension for regular and irregular linearizations

Abstract: Nowadays the Lyapunov exponents and Lyapunov dimension have become so widespread and common that they are often used without references to the rigorous definitions or pioneering works. It may lead to a confusion since there are at least two well-known definitions, which are used in computations: the upper bounds of the exponential growth rate of the norms of linearized system solutions (Lyapunov characteristic exponents, LCEs) and the upper bounds of the exponential growth rate of the singular values of the fundamental matrix of linearized system (Lyapunov exponents, LEs). In this work, the relation between Lyapunov exponents and Lyapunov characteristic exponents is discussed. The invariance of Lyapunov exponents for regular and irregular linearizations under the change of coordinates is demonstrated.

Appropriation and Subversion: Precommunist Literacy, Communist Party Saturation, and Postcommunist Democratic Outcomes

Abstract: Twenty-five years after the collapse of communism in Europe, few scholars disagree that the past continues to shape the democratic trajectories of postcommunist states. Precommunist education has featured prominently in this literature’s bundle of “good” legacies because it ostensibly helped foster resistance to communism. The authors propose a different causal mechanism—appropriation and subversion—that challenges the linearity of the above assumptions by analyzing the effects of precommunist literacy on patterns of Communist Party recruitment in Russia’s regions. Rather than regarding precommunist education as a source of latent resistance to communism, the authors highlight the Leninist regime’s successful appropriation of the more literate strata of the precommunist orders, in the process subverting the past democratic edge of the hitherto comparatively more developed areas. The linear regression analysis of author-assembled statistics from the first Russian imperial census of 1897 supports prior research: precommunist literacy has a strong positive association with postcommunist democratic outcomes. Nevertheless, in pursuing causal mediation analysis, the authors find, in addition, that the above effect is mediated by Communist Party saturation in Russia’s regions. Party functionaries were likely to be drawn from areas that had been comparatively more literate in tsarist times, and party saturation in turn had a dampening effect on the otherwise positive effects of precommunist education on postcommunist democracy.