О формулах суммирования и интерполяции

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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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О формулах суммирования и интерполяции

Чебышевский сборник. 2001. Т. 1. № 1. С. 52–71.

Ustinov A.

This paper is devoted to applications of discrete analogs of Bernoulli polynomials — polynomials introduced by Korobov. In particular, summation and interpolation formulas are proved for functions defined on a discrete set of points.

Language: Russian

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Generalized chord diagrams and weight systems

Kazaryan M., Krasilnikov E., Lando S. et al., Russian Mathematical Surveys 2025 Vol. 80 No. 6(486) P. 73–136

The paper is devoted to a description of the recent progress in understanding the extension of Lie algebra weight systems to permutations. Lie algebra weight systems are functions on chord diagrams arising naturally in Vassiliev's theory of finite-type knot invariants. These functions satisfy certain linear restrictions known as Vassiliev's 4-term relations. Chord diagrams can be interpreted as fixed-point-free involutions in ...

Added: December 4, 2025

Результаты Устинова

Ustinov A., В кн.: Теоретико-числовые методы в приближенном анализе.: МЦНМО, 2004.

Added: October 16, 2025