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.

On the Complexity of Approximating Wasserstein Barycenter

Abstract: We study the complexity of approximating Wassertein barycenter of $m$ discrete measures, or histograms of size $n$ by contrasting two alternative approaches, both using entropic regularization. The first approach is based on the Iterative Bregman Projections (IBP) algorithm for which our novel analysis gives a complexity bound proportional to $\frac{mn^2}{\varepsilon^2}$ to approximate the original non-regularized barycenter. Using an alternative accelerated-gradient-descent-based approach, we obtain a complexity proportional to $\frac{mn^{2.5}}{\varepsilon} $. As a byproduct, we show that the regularization parameter in both approaches has to be proportional to $\varepsilon$, which causes instability of both algorithms when the desired accuracy is high. To overcome this issue, we propose a novel proximal-IBP algorithm, which can be seen as a proximal gradient method, which uses IBP on each iteration to make a proximal step. We also consider the question of scalability of these algorithms using approaches from distributed optimization and show that the first algorithm can be implemented in a centralized distributed setting (master/slave), while the second one is amenable to a more general decentralized distributed setting with an arbitrary network topology.

Quantum Painlevé-Calogero correspondence

Abstract: The Painleve-Calogero correspondence is extended to auxiliary linear problems associated with Painleve equations. The linear problems are represented in a new form which has a suggestive interpretation as a “quantized” version of the Painleve-Calogero correspondence. Namely, the linear problem responsible for the time evolution is brought into the form of non-stationary Schrodinger equation in imaginary time, ∂tψ=(12∂x2+V(x,t))ψ, whose Hamiltonian is a natural quantization of the classical Calogero-like Hamiltonian H=12p2+V(x,t) for the corresponding Painleve equation. In present paper, we present explicit constructions for the first five equations from the Painleve list.

Time Perspective Profiles of Cultures

Abstract: This chapter summarises some results of the International Time Perspective Research Project, which is a collaborative cross-cultural study of time perspective carried out in 24 countries. The highlights of structural equivalence assessment study are presented, showing the cross-cultural invariance of 36 items of the Zimbardo Time Perspective Inventory (ZTPI) scale. The associations between country-level ZTPI scores and other culture-level indicators, including the Human Development Index and Hofstede cultural dimensions, are presented and discussed. Using hierarchical cluster analysis, five distinct profiles of time perspective were found (future-oriented, present-oriented, balanced, moderately fatalistic, and negative), and significant differences in the prevalence of these profiles across cultures were found. Implications and perspectives for future research are discussed.

Superplastic deformation behaviour and microstructure evolution of near-α Ti-Al-Mn alloy

Abstract: Superplastic deformation behaviour of conventional sheets of a near-α titanium alloy (Ti-2.5Al-1.8Mn) was studied by a step-by-step decrease of the strain rate and constant strain rate tests in a temperature range of 790–915 °C. The research found that superplastic deformation is possible in a temperature range of 815–890 °С and a constant strain rate range of 2 × 10 −4 to 1 × 10 −3 s −1 with elongation above 300% and m -index above 0.4. Also, the research identified the optimum superplastic temperature range of 815–850 °C and constant strain rate of 4 × 10 −4 s −1 which provide a maximum elongation of 600–650%. Strain hardening is accelerated by dynamic grain growth at high temperatures of 865 and 890 °С. High dislocation activity is observed at superplastic flow in α-phase. Constitutive modelling of superplastic deformation behaviour is performed, and possible deformation mechanisms are discussed. It is suggested that grain boundary sliding between the α-grains is accommodated by a dislocation slip/creep mechanism.