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News
September 4, 2026
‘Hedgehog Versus ‘Relatives: Researchers Measure How the Brain Responds to Unexpected Words During Natural Speech
Russian neurophysiologists, including researchers from HSE University, have demonstrated the feasibility of using event-related fields (ERFs) to study brain activity during natural speech perception. The researchers showed that this approach can be applied not only to individual words but also to continuous speech. Their findings indicate that words whose meanings differ significantly from the preceding context require longer processing times. The study also reveals that the brain processes function words in two stages: first, it identifies their grammatical role and then uses this information to predict the next word. The study has been published in Frontiers in Human Neuroscience.
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.’

 

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Непрерывная выборка приближенных решений Монжа в задаче Канторовича с параметром

Функциональный анализ и его приложения. 2024. Т. 58. № 2. С. 137–156.
Popova S.
Research target: Mathematics
Language: Russian
DOI
Keywords: оптимальная транспортировказадача Канторовичазадача Монжанепрерывность по параметру
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Saito theory associates to an isolated singularity rich structure that plays an important role in mirror symmetry. In this note we construct Saito theory for A and D type Landau-Ginzburg orbifolds. Namely, for the pairs (f,G), where f defines an isolated singularity of A and D type and G is a group of symmetries of ...
Added: September 1, 2026
Non-axiomatizability of modal predicate logics of Dedekind-complete linear orders with constant domains
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We prove Pi-1-1-hardness, and thus lack of recursive axiomatizability, of constant-domain modal predicate logics defined by a class of Dedekind complete linear Kripke frames containing a frame with an infinitely increasing chain of worlds. The result holds even for the language with one unary predicate letter, one propositional letter, and two individual variables. ...
Added: September 1, 2026
Semi-Interlaced Polytopes
Селянин Ф. И., Moscow Mathematical Journal 2026 Vol. 26 No. 2 P. 167–187
Minkowski mixed volume of n subpolytopes D1,…,Dn of a polytope P⊂Rn clearly does not exceed the normalized volume n!Vol(P). Equality holds if and only if the subpolytopes are interlaced, i.e., each proper face F⊊P intersects at least dim(F)+1 of the polytopes Di. Efficiently computing mixed volumes for more general collections of subpolytopes is crucial for estimating the complexity of numerically solving polynomial systems. Motivated by relaxing the bound dim(F)+1 to dim(F), we ...
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A new spin on polynomial relations among kappa classes
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We prove a recent conjecture of the fourth named author with P. Norbury that states a system of universal polynomial relations among the kappa classes on the moduli spaces of algebraic curves. The proof involves localization and materialization analysis of the spin Gromov–Witten theory of the projective line and is dictated by Z 2 -equivariant ...
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Any Topological Recursion on a Rational Spectral Curveis KP Integrable
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We prove that for any initial data on a genus zero spectral curve the cor responding correlation differentials of topological recursion are KP integrable. As an application we prove KP integrability of partition functions associated via ELSV-type formulas to the r-th roots of the twisted powers of the log canonical bundles ...
Added: August 31, 2026
Сплетенный мир: кошка перевернулась. Доклад Римскому клубу
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Механизм происходящих в мире изменений носит эволюционный, а не экологический характер. Иначе говоря, Человечество столкнулось с кризисом развития, который имеет три независимые составляющие: кризис индустриального общества (фазовый кризис), кризис научного мышления (эпистемный кризис) и кризис формата существования разума (социосистемный кризис). Доклад посвящён аспектам этого триединого кризиса и возможным путям его преодоления, не сводящимся к первичному ...
Added: August 31, 2026
Multiplicity-free products of Schubert divisors
Devyatov R. A., Mathematical notes 2026 Vol. 119 No. 3 P. 782–786
Let G/B be a flag variety over ℂ, where G is a simple algebraic group with a simply laced Dynkin diagram, and B is a Borel subgroup. We say that the product of classes of Schubert divisors in the Chow ring is multiplicity free if it is possible to multiply it by a Schubert class ...
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Mukai models of Fano varieties
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We give a self-contained and simplified proof of Mukai’s classification of prime Fano threefolds of index 1 and genus g ≥ 6 with at most factorial terminal singularities, and of its extension to higher dimension. ...
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Mukai bundles on Fano threefolds
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We give a proof of Mukai’s theorem on the existence of certain exceptional vector bundles on prime Fano threefolds. To our knowledge this is the first complete proof in the literature. The result is essential for Mukai’s biregular classification of prime Fano threefolds, and for the existence of semiorthogonal decompositions in their derived categories. Our ...
Added: August 30, 2026
Full exceptional collections on the symplectic isotropic Grassmannians
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We prove that the Kuznetsov–Polishchuk exceptional collections on rational homogeneous spaces of the symplectic groups Sp(2n,C) are full and consist of vector bundles. To achieve this, we construct several classes of complexes, which we call generalized staircase complexes, symplectic staircase complexes and secondary staircase complexes — each of which may be of independent interest. ...
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Exceptional pairs on del Pezzo surfaces and spaces of compatible Feigin-Odesskii brackets
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We prove that for every relatively prime pair of integers (d,r) with r>0, there exists an exceptional pair (O,V) on any del Pezzo surface of degree 4, such that V is a bundle of rank r and degree d. As an application, we prove that every Feigin-Odesskii Poisson bracket on a projective space can be ...
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Analog of theta-lifting for a curve over dual numbers over a finite field
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We continue the study of automorphic functions associated with a curve C over the ring k[ε]/(ε²), where k is a finite field, begun in arXiv:2303.16259. Namely, we study an example of theta-lifting in this framework and show that it can be understood in terms of the orbit decomposition of the space of automorphic functions S(SL₂(F)\SL₂(A_C)) ...
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A radio-physical system, namely, a two-mode van der Pol generator, is considered. It is shown that this system demonstrates two types of chaos: with one and two zero Lyapunov exponents. The regions of the second type of chaos are surrounded by bifurcation lines of invariant tori doubling. Quasi-periodic structures of various shapes are embedded within ...
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Approximation of continuous functions on a compact set by solutions of elliptic equations. Quantitative results.
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Added: August 29, 2026
Оптимальная транспортировка векторных мер
Popova S., Известия РАН. Серия математическая 2026 Т. 90 № 2 С. 25–61
В данной работе изучаются задачи Монжа и Канторовича оптимальной транспортировки векторных мер. Доказывается существование оптимальных планов Канторовича. Сформулирована двойственность, и доказано равенство оптимальных значений в прямой и двойственной задаче для полунепрерывных снизу функций стоимости. Доказано равенство инфимумов в векторных задачах Монжа и Канторовича в случае выполнения условия теоремы Ляпунова, гарантирующей существование отображений Монжа для векторных ...
Added: October 28, 2025
О нелинейных задачах Канторовича для функций стоимости специального вида
Popova S., Алгебра и анализ 2024 Т. 36 № 4 С. 165–194
В данной работе изучаются задачи Канторовича оптимальной транспортировки мер для нелинейных функций стоимости, зависящих от условных мер транспортных планов. Рассматривается ряд нелинейных задач Канторовича для функций стоимости специального вида и доказываются результаты о существовании (или несуществовании) оптимальных решений. Также устанавливается связь между нелинейной задачей Канторовича с функцией стоимости некоторого специального вида и задачей Монжа с ...
Added: November 19, 2024
Расстояния Хаусдорфа между каплингами и оптимальная транспортировка с параметром
Bogachev V., Popova S., Математический сборник 2024 Т. 215 № 1 С. 33–58
Рассматривается оптимальная транспортировка мер на метрических и топологических пространствах в случае, когда функция стоимости и маргинальные распределения зависят от параметра со значениями в метрическом пространстве. Расстояние Хаусдорфа между множествами вероятностных мер с заданными проекциями оценивается через расстояния между самими проекциями. Эта оценка используется для доказательства непрерывности стоимости оптимальной транспортировки относительно параметра в случае непрерывной зависимости функции стоимости и маргинальных ...
Added: February 3, 2024
Auctions and mass transportation
Kolesnikov A., / Series arXiv "math". 2023.
In this survey paper we present classical and recent results relating the auction design  and the optimal transportation theory. ...
Added: December 13, 2023
Существование решений нелинейной задачи Канторовича оптимальной транспортировки
Bogachev V., Резбаев А. В., Математические заметки 2022 Т. 112 № 3 С. 360–370
В работе исследуется существование решений задачи Канторовича оптимальной транспортировки с нелинейным функционалом стоимости, порожденным функцией стоимости, которая зависит от плана транспортировки. Рассмотрен также случай функции стоимости, зависящей от условных мер плана транспортировки. Получены широкие достаточные условия существования оптимальных планов для радоновских маргинальных распределений на вполне регулярных пространствах и полунепрерывной снизу функции стоимости. ...
Added: November 14, 2022
Nonlinear Kantorovich Problems with a Parameter
Vladimir I. Bogachev, Ilya I. Malofeev, Известия Иркутского государственного университета. Серия: Математика 2022 Vol. 41 P. 96–106
New results on nonlinear Kantorovich problems depending on a parameter are presented. ...
Added: November 14, 2022
Задачи Канторовича с параметрами и ограничениями на плотности
Bogachev V., Сибирский математический журнал 2022 Т. 63 № 1 С. 42–57
Изложены новые реультаты о задаче Канторовича с ограничениями на плотности. ...
Added: November 14, 2022
Задача Канторовича оптимальной транспортировки мер: новые направления исследований
Bogachev V., Успехи математических наук 2022 Т. 77 № 5(467) С. 3–52
Изложены новые результаты о нелинейной задаче Канторовича оптимальной транспортировки мер ...
Added: November 14, 2022
The Kantorovich Problem with a Parameter and Density Constraints
V. I. Bogachev, Doledenok A. N., I. I. Malofeev, Mathematical notes 2021 Vol. 110 No. 5-6 P. 952–955
В задаче Канторовича с ограничениями на плотность получены новые результаты о зависимости решений от параметра. ...
Added: October 31, 2022
Existence of solutions to the nonlinear Kantorovich problem of optimal transportation
Bogachev V., Резбаев А. В., Математические заметки 2022 Т. 112 № 3 С. 360–370
We study the existence of solutions of Kantorovich problem  where cost function depends on transport plan.  We then consider the case of the cost function depending on  the conditional measures of transport plan.  A wide sufficient conditions for the existence of optimal plans  for Radon marginal distributions are obtained on completely regular spaces  and a lower semicontinuous cost function. ...
Added: June 24, 2022
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