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News
August 25, 2026
Scientists Develop Algorithm for More Reliable Processors in Data Centres
Researchers from HSE MIEM and Samara University have developed the LRF-3D algorithm to automatically bypass idle nodes in three-dimensional networks-on-chip. Thanks to its hierarchical architecture, the algorithm outperforms existing solutions in both speed and path accuracy, improving processor reliability for use in data centres, supercomputers, and AI computing. The source code and test results are publicly available.
August 24, 2026
Researchers Develop Method for Direct Generation of Regulatory DNA
Researchers at HSE University have developed a model for generating promoters and enhancers—DNA sequences that regulate gene activity. The model works directly with DNA nucleotides, without first transforming them into a continuous numerical representation. This solution could be useful for applications in synthetic biology and gene therapy. The study results were presented at the ICLR 2026 Workshop ‘Generative AI in Genomics (Gen^2): Barriers and Frontiers.’
August 21, 2026
Social Integration: At the Crossroads of Knowledge and Values
The International Laboratory for Social Integration Research (ILSIR) at HSE University studies the challenges faced by vulnerable groups and explores ways to help them participate fully in everyday life. To develop effective solutions, the laboratory’s researchers combine cutting-edge methods with practical fieldwork. In this interview with the HSE News Service, Laboratory Head Elena Iarskaia-Smirnova discusses the laboratory’s work.

 

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Соболевская регулярность для бесконечномерного уравнения Монжа-Ампера

Доклады Академии наук. 2012. Т. 44. № 2. С. 131–136.
Kolesnikov A., Богачев В. И.
Language: Russian
Full text
Keywords: Monge-Kantorovich problemWiener spaceGaussian measureMonge-Ampere equationSobolev spacesзадача Монжа-Канторовичагауссовские мерыуравнение Монжа-Амперапространство Винерапространства Соболева
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We study the set of (p, q)-eigenvalues of the p-Laplace operator with no-flux boundary conditions. We show that this set is closed and that its smallest positive element (the first nontrivial eigenvalue) admits a variational characterization. Moreover, we establish lower bounds for this eigenvalue in cuspidal domains. ...
Added: July 27, 2026
The Sobolev space W_2^{1/2}: Simultaneous improvement of functions by a homeomorphism of the circle
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued  function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a  change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that  the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.  We obtain new results on simultaneous improvement of functions by a single  change of variable in relation ...
Added: May 14, 2026
Пространства Соболева $W_{p}^{1}(\mathbb{R}^{n})$ на $d$-толстых замкнутых подмножествах $\mathbb{R}^{n}$
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Пусть $S \subset \mathbb{R}^{n}$ -- замкнутое непустое множество такое, что для некоторых $d \in [0,n]$ и $\varepsilon > 0$ $d$-вместимость по Хаусдорфу $\mathcal{H}^{d}_{\infty}(S \cap Q(x,r)) \geq \varepsilon r^{d}$ для всех кубов $Q(x,r)$ с центрами в $x \in S$ и длинами ребер $2r \in (0,2]$. Для каждого $p>\max{1,n−d}$ мы даем внутреннюю характеризацию пространства следов $W_{p}^{1}(\mathbb{R}^{n})|_{S}$ на множестве ...
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Restrictions of Sobolev $W^{1}_{p}(\mathbb{R}^{2})$-spaces to planar rectifiable curves
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Пусть $(X,d,\mu)$ – метрическое пространство с равномерно локально удваивающей мерой $\mu$. При $p \in (1,\infty)$ предположим, что $(X,d,\mu)$ допускает слабое локальное $(1,p)$-неравенство Пуанкаре.  Мы даем харакетризацию следов пространства Соболева первого порядка $W_{p}^{1}(X)$  на подмножествах $S$ пространства $X$, которые могут быть представлены как конечное объединение $\cup_{i=1}^{N}S_{i}$, $N \in \mathbb{N}$, регулярных по Альфорсу--Давиду множеств $S_{i} \subset X$, $i ...
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Added: December 25, 2025
The Sobolev space W_2^{1/2} : Simultaneous improvement of functions by a homeomorphism of the circle
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Injectivity in second-gradient nonlinear elasticity
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We study injectivity for models of Nonlinear Elasticity that involve the second gradient. We assume that $\Omega \subset \mathbb{R}^n$ is a domain, $f \in W^{2,q}(\Omega, \mathbb{R}^n)$ satisfies $|J_f^{-a}| \in L^1$ and that $f$ equals a given homeomorphism on $\partial\Omega$. Under suitable conditions on $q$ and $a$ we show that $f$ must be a homeomorphism. As a main new tool we find an ...
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Regularity of Distributions of Sobolev Mappings in Abstract Settings
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Added: November 20, 2024
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Menovshchikov A., Ukhlov A., Journal of Mathematical Sciences 2023 Vol. 276 No. 1 P. 117–136
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Added: November 20, 2024
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Menovshchikov A., Ukhlov A., Journal of Mathematical Analysis and Applications 2024 Vol. 531 No. 1 Article 127826
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We provide estimates for the constant in the weighted Sobolev–Poincaré inequality for a special class of planar domains and weights. We obtain lower bounds for the first nonzero eigenvalue $\mu_\rho$ of the Neumann Laplacian with density $\rho$. These estimates depend on the density function and geometry of the domain. We show that $\mu_\rho$ can be ...
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In this paper we further develop the theory of f-divergences for log-concave functions and their related inequalities. We establish Pinsker inequalities and new affine invariant entropy inequalities. We obtain new inequalities on functional affine surface area and lower and upper bounds for the Kullback-Leibler divergence in terms of functional affine surface area. The functional inequalities ...
Added: June 23, 2023
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