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News
June 2, 2026
Discovering Science through Russian Language: HSE Prep Year Students Present at International Conference in Kazan
On May 23, 2026, the V International Scientific and Practical Conference ‘Discovering the World of Science’ took place in Kazan at the Preparatory Faculty for International Students of Kazan Federal University. Four students of the HSE International Preparatory Year took part in the event: two delivered their presentations in person, while two participated online. Their work was supervised by Acting Director of the International Prep Year Irina Isaeva and lecturer Ekaterina Kozhemyakova.
May 25, 2026
HSE Scientists Train Neural Network to 'Hear' Faults in Electric Motors
Researchers at the AI and Digital Science Institute of the HSE Faculty of Computer Science have developed a new method—the Signature-Guided Data Augmentation (SGDA) framework—that achieves 99% accuracy in motor fault detection and 86% accuracy in fault classification. The application of this approach can reduce industrial equipment repair costs, minimise downtime, and improve production safety. The study results have been published in Engineering Applications of Artificial Intelligence.
May 25, 2026
'The Humanities Serve as a Conscience'
Maria Mizernaia studies Soviet literature and the history of book publishing. In this interview for the HSE Young Scientists project, she discusses plans to publish a novel about besieged Leningrad, AI-provoked reflections on what it means to be human, and how novels can help satisfy our dopamine hunger.

 

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Дискретная математика

M. : -, 2010.
Nabebin A. A.
Priority areas: IT and mathematics
Language: Russian
Full text
Keywords: графдискретная математикамодулярная арифметикакомбинаторикаконечный автоматкриптографияалгебра логикилогика предикатов
Дискретная математика
Similar publications
ML-based Fast Simulation of FARICH Responses
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Natural hazard database from Internet publications: text mining with a large language model
Derkacheva A., Sakirkina M., Kraev G. et al., /. 2026.
Comprehensive data on natural hazards and their consequences are crucial for effective for risk assessment, adaptation planning, and emergency response. However, many countries face challenges with fragmented, inconsistent, and inaccessible data, particularly regarding local-scale events. To address this data gap in Russia, we developed an end-to-end processing pipeline that scrapes news from various online sources, ...
Added: April 28, 2026
Algorithmic overlaps as thermodynamic variables: from local to cluster Monte Carlo dynamics in critical phenomena
Pilé I., Deng Y., Shchur L., / Series arXiv "math". 2026. No. 2604.10254.
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Svendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for two models in different universality classes: the Ising model and the Potts model with three components. The overlap of two ...
Added: April 20, 2026
Using predefined vector systems to speed up neural network multimillion class classification
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Системы обеспечения информационной безопасности с помощью криптографических механизмов
Стародубов К. В., Елистратов А. А., Громов Ю. Ю. et al., М.: Издательский дом Академии Жуковского, 2025.
Пособие представляет собой всестороннее руководство по теоретическим основам и практическому применению криптографических методов для защиты информации. В издании подробно рассматриваются современные алгоритмы шифрования, методы аутентификации, электронные подписи, а также принципы построения и функционирования криптографических протоколов. Особое внимание уделено вопросам оценки стойкости криптографических систем, нормативно-правовой базе и актуальным угрозам информационной безопасности. Пособие проиллюстрировано рассмотрением практических примеров. Большое внимание уделено вопросам методологического характера. Учебное пособие представляет ...
Added: February 27, 2026
Iterative Ricci-Foster Curvature Flow with GMM-Based Edge Pruning: A Novel Approach to Community Detection
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Implementing Transport Coding in OMNeT++ for Message Delay Reduction
Petrovanov I., Sergeev A., / Series Computer Science "arxiv.org". 2025. No. 2512.18332.
Transport coding reduces message delay in packet-switched networks by introducing controlled redundancy at the transport layer:  original packets are encoded into  coded packets, and the message is reconstructed after the first  successful deliveries, effectively shifting latency from the maximum packet delay to the -th order statistic. We present a concise, reproducible discrete-event implementation of transport coding in OMNeT++, including ...
Added: December 24, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Determining the boundary of dynamical chaos in the generalized Chirikov map via machine learning
Chernyshov D., Satanin A., Shchur L., / Series arXiv "math". 2025.
We investigate the boundary separating regular and chaotic dynamics in the generalized Chirikov map, an extension of the standard map with phase-shifted secondary kicks. Lyapunov maps were computed across the parameter space (K,K(α, τ)) and used to train a convolutional neural network (ResNet18) for binary classification of dynamical regimes. The model reproduces the known critical ...
Added: November 21, 2025
Эффективный алгоритм торговли на фондовом рынке: ретроспективный анализ, основанный на данных по S&P-500.
Rubchinskiy A., Chubarova D., / Series WP7 "Математические методы анализа решений в экономике, бизнесе и политике". 2025. No. WP7/2025/01.
The article examines one of the most famous examples of socio-economic systems, characterized by significant uncertainty – the S&P-500 stock market, where shares of 500 largest US companies are traded. No assumptions are made about the probabilistic characteristics of the stock market. A flexible algorithm for daily trading has been developed, based on both known fixed data ...
Added: November 9, 2025
Geometry of unimodular systems
Artamkin I., / Series arXiv "math". 2023.
A collection of vectors in a real vector space is called a unimodular system if any of its maximal linearly independent subsets generates the same free abelian group. This notion is closely connected with totally unimodular matrices: rows or columns of a totally unimodular matrix form a unimodular system and the matrix of coefficients of ...
Added: November 1, 2025
Diffusion on language model embeddings for protein sequence generation
Meshchaninov V., Strashnov, P., Shevtsov A. et al., / Cornell University. Серия CoRR, arXiv:2403.03726 "Computing Research Repository,". 2025.
Protein design requires a deep understanding of the inherent complexities of the protein universe. While many efforts lean towards conditional generation or focus on specific families of proteins, the foundational task of unconditional generation remains underexplored and undervalued. Here, we explore this pivotal domain, introducing DiMA, a model that leverages continuous diffusion on embeddings derived ...
Added: October 5, 2025
Smoothie: Smoothing Diffusion on Token Embeddings for Text Generation
Shabalin A., Meshchaninov V., Vetrov D., / Series cs.CL, arXiv:2505.18853 "Computation and Language". 2025.
Diffusion models have achieved state-of-the-art performance in generating images, audio, and video, but their adaptation to text remains challenging due to its discrete nature. Prior approaches either apply Gaussian diffusion in continuous latent spaces, which inherits semantic structure but struggles with token decoding, or operate in categorical simplex space, which respect discreteness but disregard semantic ...
Added: October 5, 2025
A Feature Engineering Framework for Computer Vision Based on Topological Data Analysis
Абрамов А. С., Chernyshev V. L., Mikhaylets E. et al., / Series Social Science Research Network "Social Science Research Network". 2025.
Computer vision is one of the most relevant modern research areas with broad practical applications. However, traditional solutions based on deep learning have signicant limitations and can be misleading. Topological data analysis, on the other hand, is a modern approach to solving similar problems using mathematically deterministic methods of algebraic topology that reduce the risk ...
Added: September 23, 2025
On the construction of frieze patterns from partitions of convex polygons by nonintersecting diagonals
Kochetkov Y., / Series arXiv.org e-print archive "arXiv.math". 2025. No. 07600.
We demonstrate in an elementary way how to construct a frieze pattern of width m-3 from a partition of a convex m-gon by not intersecting diagonals. ...
Added: September 17, 2025
Генезис и семантический кризис новизны
Khestanov R., Suvalko A., Социологическое обозрение 2025 Т. 24 № 2 С. 164–189
The article examines the genesis of the concept of novelty and argues that modern difficulties in defining and identifying the new are a symptom of a semantic crisis, which is based on the loss of strategic normativity of novelty in modern culture. Three historical-semantic models of novelty are identified and analyzed: cyclical (characteristic of prehistoric ...
Added: June 29, 2025
Об одном комбинаторном приложении теории ультрафильтров: новая конструкция графов без треугольников и с произвольно большим хроматическим числом
Polyakov N. L., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 522 № 1 С. 40–49
The paper describes a new method for constructing graphs without triangles and with an arbitrarily large chromatic number. The properties of various types of ultrafilter extensions of functions and predicates are used to justify the method. ...
Added: June 3, 2025
Алгоритм построения матриц, уменьшающих расстояние кода
Воднев А. А., Информационно-управляющие системы 2025 № 1 С. 23–28
Введение: уменьшение кодового расстояния представляет собой важный инструмент для решения некоторых задач в теории информации и криптографии. Например, в криптографических кодовых системах, таких как система Мак-Элиса, снижение кодового расстояния напрямую влияет на уменьшение длины открытого ключа, что является критически важным фактором для повышения эффективности и применимости кодовых криптосистем. Цель: разработать алгоритм построения матриц, способный эффективно уменьшать расстояние кода. Результаты: предложен ...
Added: April 4, 2025
Моделирование транспортно-логистических систем и исследование их структурной устойчивости.
Кочкаров А. А., Яцкин Д. В., Кочкаров Р. А., Управленческие науки 2020 Т. 10 № 1 С. 102–111
An important parameter of the transport and logistics task is the structural stability of the system to external influences. In modern literature, the concept of structural stability is defined in its own way for each individual task, as a result of which there are difficulties in applying the developed methods to new problems. The transport ...
Added: March 7, 2025
Проектирование транспортно-логистических систем, устойчивых к структурным разрушениям
Кочкаров А. А., Яцкин Д. В., Кочкаров Р. А., Теоретическая и прикладная экономика 2020 № 1 С. 1–9
This article is dedicated to designing of the transport and logistics systems with built-in resistance to structural failures. The sustainability indicators reflect the impact of the failure of one or several hubs (communication channels) upon working capacity of the already functioning system. In the process of designing the system, the sustainability indicators also provide opportunities ...
Added: March 7, 2025
Оценка структурной устойчивости транспортно-логистических систем при решении оптимизационных задач.
Кочкаров А. А., Яцкин Д. В., Кочкаров Р. А., Нелинейный мир 2019 Т. 17 № 5 С. 14–23
Постановка проблемы. Понятие структурной устойчивости определяется применительно для каждой индивидуальной задачи, в результате чего появляются сложности применения разработанных методов в новых задачах. Структурное воздействие на транспортно-логистическую систему представлено элементарными событиями над графом, в том числе их суперпозицией. В работе используется понятие структурного разрушения графа, что подразумевает разбиение графа на несвязные компоненты. Цель. Рассмотреть фундаментальный подход к ...
Added: March 7, 2025
Топология, геометрия, комбинаторика и математическая физика
М.: Математический институт им. В. А. Стеклова РАН, 2024.
This volume is dedicated to the 80th birthday of Victor Matveevich Buchstaber, Corresponding Member of the Russian Academy of Sciences. The volume includes articles on topology, geometry, combinatorics, and mathematical physics, the areas in which V. M. Buchstaber is a recognized world leader and the head of an active scientific school. Most of the articles are written ...
Added: January 15, 2025
О последовательных факторах нижнего центрального ряда прямоугольных групп Кокстера
Veryovkin Y., Рахматуллаев Т. А., Математические заметки 2024 Т. 116 № 1 С. 10–33
We study the lower central series of a right-angled Coxeter group RCK and the corresponding associated graded Lie algebra L(RCK) and describe the basis of the fourth graded component of L(RCK) for any K. ...
Added: January 15, 2025
Алгебра, теория чисел, дискретная математика и многомасштабное моделирование: современные проблемы, приложения и проблемы истории. Материалы XXII Международной конференции, посвящённой 120-летию со дня рождения академика Андрея Николаевича Колмогорова и 60-летию со дня открытия школы-интерната № 18 при Московском университете
[б.и.], 2023.
The collection contains materials presented at the XXII International Conference "Algebra, Number Theory, Discrete Geometry and Multiscale Modeling: modern problems, applications and problems of history", dedicated to the 120th anniversary of the birth of Academician Andrei Nikolaevich Kolmogorov and the 60th anniversary of the opening of boarding school No. 18 at Moscow University. The conference ...
Added: April 24, 2024
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