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Построение и анализ моделей русского языка в связи с исследованиями криптографических алгоритмов
Чебышевский сборник. 2022. Т. 23. № 2. С. 151–160.
The article provides a statistical analysis of the properties of lexical and n-gram models of the Russian language based on the news text corpus. A specialized corpus of political news articles of recent years has been created, reflecting a narrow area of language use. The token and n-gram dictionaries are compiled, the coverage values are found, as well as the values of entropy. Lemmatization of the original text corpus and extrapolation of the dictionary volumes are performed.
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026
This work presents a hierarchy of strictly local fault-tolerant routing algorithms for 3D mesh networks-on-chip, culminating in an algorithm that combines a live-neighbor selection rule with a bounded single-hop rollback mechanism. The proposed algorithms operate exclusively on immediate neighbor information, maintain O(1) per hop complexity, and require no global topology knowledge, additional virtual channels, or ...
Added: July 23, 2026
Pislyakov V., Вестник Томского государственного университета. Филология 2026 № 101 С. 175–192
This article examines the use of proverbs in academic texts—specifically, articles published in Russian research journals. For the experiment, ten proverbs were selected as the intersection of two fundamentally different paremiological surveys aimed at compiling lists of popular or common Russian proverbs. One of these surveys was conducted by the classic of paremiology, G.L. Permyakov, ...
Added: July 22, 2026
Korogod D., Shapeev A., Novikov I., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 No. 2 Article 024104
We present two models with explicit long-range electrostatics in the form of Coulomb interactions. Both models include point charges depending on their local atomic environments, and the second model also conserves a total charge of an atomic system. We combine the proposed long-range models with the local moment tensor potential (MTP) and demonstrate that they ...
Added: July 22, 2026
Sozykin K., Rybin N., Chertkov A. et al., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 113 No. 22 Article 224111
The global optimization of atomic clusters represents a fundamental challenge in computational chemistry and materials science due to the exponential growth of local minima with system size (i.e., the curse of dimensionality). We introduce a framework that overcomes this limitation by exploiting the low-rank structure of potential energy surfaces through tensor train (TT) decomposition. Our ...
Added: July 22, 2026
Singapore: Springer, 2024.
Included in the following conference series:
INdAM: INdAM Meeting: Kolmogorov Operators and their Applications Workshop
Conference proceedings info: INdAM 2022
Kolmogorov equations are a fundamental bridge between the theory of partial differential equations and that of stochastic differential equations that arise in several research fields.
This volume collects a selection of the talks given at the Cortona meeting by ...
Added: July 17, 2026
Veretennikov A., Pascucci A., Rondelli A., Stochastic Processes and their Applications 2026 Vol. 199 Article 104978
We present existence results for weak solutions to a broad class of degenerate McKean-Vlasov equations with rough coefficients, expanding upon and refining the techniques recently introduced by the third author. Under certain structural conditions, we also establish results concerning both weak and strong well-posedness. ...
Added: July 17, 2026
Veretennikov A., Ляппиева А. А., Теория вероятностей и ее применения 2026 Т. 71 № 2 С. 295–304
Установлен новый результат о сильной единственности для многомерного СДУ с невырожденной диффузией и частично нерегулярным сносом. Его можно рассматривать как комбинированный вариант на темы Ямада и Ватанабэ (1971), Звонкина (1974) и первого автора настоящей статьи (1980). ...
Added: July 17, 2026
Veretennikov A., Нуриева А. И., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 Т. 525 С. 24–30
Предложено новое достаточное условие в задаче о центральной предельной теореме в схеме серий для неоднородных цепей Маркова, с возможностью того, что минимум эргодического коэффициента Маркова–Добрушина может быть ближе к нулю, чем в основном условии Добрушина. ...
Added: July 17, 2026
О частных производных модифицированных полиномов Бернштейна–Станку для функций нескольких переменных
Veretennikov A., Мазутский Н. М., Математический сборник 2025 Т. 216 № 7 С. 3–27
Целью работы является доказательство аппроксимации смешанных производных второго порядка для функции нескольких переменных в норме L1 такими же производными модифицированных полиномов Бернштейна–Станку при минимальной возможной регулярности. ...
Added: July 17, 2026
Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2025 Т. 70 № 2 С. 211–227
В работе предложены новые версии слабого закона больших чисел (ЗБЧ) для слабо зависимых слагаемых (вообще говоря, разнораспределенных) как при наличии математического ожидания каждого из них, так и без такового. Одним из основных условий в первом из трех рассматриваемых случаев, в котором развиваются идеи из статьи Ю. Ш. Чау 1971 г., является равномерная интегрируемость слагаемых по Чезаро в духе работ по ЗБЧ для ...
Added: July 17, 2026
Veretennikov A., Stochastics and Dynamics 2024
A new weak existence result for degenerate multi-dimensional stochastic McKean–Vlasov equation is established under relaxed regularity conditions. ...
Added: July 17, 2026
Ахмярова А. Т., Veretennikov A., Теория вероятностей и ее применения 2024 Т. 69 № 3 С. 427–438
Предложен новый вариант усиленного закона больших чисел для попарно независимых случайных величин. Основная цель — ослабить требование существования математического ожидания каждого из слагаемых. Предположение о попарной независимости также ослаблено. ...
Added: July 17, 2026
Veretennikov A., Moscow Mathematical Journal 2024 Vol. 24 No. 1 P. 107–124
Second order recurrence are established for a d-dimensional diffusion with an additive Wiener process, with switching, and with one recurrent and one transient regime and constant switching intensities, under suitable conditions. As a corollary, the rate of convergence towards the invariant regime of order t^{−2} is claimed. The approach is based on embedded Markov chains ...
Added: July 16, 2026
Veretennikov A., Mathematics 2023 Vol. 11 No. 21 Article 4514
Positive recurrence for a single-server queueing system is established under generalized service intensity conditions, without the assumption of the existence of a service density distribution function, but with a certain integral type lower bound as a sufficient condition. Positive recurrence implies the existence of the invariant distribution and a guaranteed slow convergence to it in ...
Added: July 16, 2026
Veretennikov A., Markov Processes and Related Fields 2023 Vol. 23 No. 2 P. 259–294
The ergodic Bellman's (HJB) equation is proved for a one-dimensional controlled diffusion with switching with variable diffusion and drift coefficients both depending on control; the intensities of transitions of the discrete component are constant. Its existence and uniqueness is established. Also, the convergence of the reward iteration improvement algorithm is established to the cost constant ...
Added: July 16, 2026
Михайлов И. А., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 1 Article 8
Whole-slide histology images (WSIs) can exceed 100 k × 100 k pixels, making direct pixel-level segmentation infeasible and requiring patch-level classification as a practical alternative for downstream WSI segmentation. However, most approaches either treat patches independently, ignoring spatial and biological context, or rely on deep graph models prone to oversmoothing and loss of local tissue ...
Added: July 16, 2026
On recurrence, convergence and mixing rate for generalised Wright - Fisher's diffusion with mutation
Veretennikov A., Sineokiy R., Markov Processes and Related Fields 2023 Vol. 23 No. 2 P. 241–258
Generalised one-dimensional Fisher -- Wright diffusion process with mutations is consiedered. This is a well-known model in populational genetics. The goal of the paper is an exponential recurrence of the process, which also implies exponential rate of convergence towards the invariant measure. ...
Added: July 16, 2026
Veretennikov A., Mathematics 2023 Vol. 11 No. 14 Article 3096
Polynomial recurrence bounds for a class of stochastic differential equations with a rotational symmetric gradient type drift and an additive Wiener process are established, as well as certain a priori moment inequalities for solutions. The key feature of this paper is that the approach does not use Lyapunov functions because it is not clear how ...
Added: July 16, 2026
Kuninets A., Malygina E., Leevik A. G. et al., Journal of Computer Virology and Hacking Techniques 2026 No. 22 Article 62
In this work, we investigate the application of Barnes–Wall lattices in post-quantum cryptographic schemes. We survey and analyze several constructions of Barnes–Wall lattices, including subgroup chains, the generalized k-ing construction, and connections with Reed-Muller codes, highlighting their equivalence over both Z[i] and Z. Building on these structural insights, we introduce a new algorithm for efficient ...
Added: July 16, 2026
Bolbachan V., / Series math "arxiv.org". 2024.
Chow polylogarithms are some special functions arising in explicit description of the Beilinson regulator map. The most interesting functional equation for this function reflects its vanishing on the boundary in the Bloch's cycle complex. We show that this functional equation formally follows from more simple ones, namely skew-symmetry, functoriality and multiplicativity.
To prove this, we study ...
Added: July 16, 2026
А. Г. Малашина, Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2023 Т. 514 № 2 С. 138–149
В целях обеспечения защищенного информационного обмена в каналах связи необходимо предварительное исследование корректности работы соответствующих систем защиты информации. Несмотря на то что используемые в таких системах математические алгоритмы корректны и теоретически обеспечивают правильные статистические свойства выходного потока по сравнению с входным, на этапе реализации (программирования) данных алгоритмов защиты или на этапах сборки конечного оборудования (использования ...
Added: November 1, 2023
Malashina A., Baltic Journal of Modern Computing 2021 Vol. 9 No. 3 P. 363–376
We research n-gram dictionaries and estimate its coverage and entropy based on theweb corpus of English. We consider a method for estimating the coverage of empirically gen-erated dictionaries and an approach to address the disadvantage of low coverage. Based on theideas of Kolmogorov’s combinatorial approach, we estimate the n-gram entropy of the Englishlanguage and use ...
Added: September 13, 2021
Anastasia Malashina, , in: Entropy 2021: The Scientific Tool of the 21st Century. Conference Proceedings Book.: Porto: MDPI Open Access Publishing, 2021. P. 106–106.
When solving a number of information security problems, one of the problems is to estimate the number of possible meaningful texts of fixed length. To estimate this value, various approaches can be used, in each of which the key parameter is the information entropy. To estimate the number of short plaintexts, the entropy of n-grams ...
Added: May 5, 2021
Малашина А. Г., В кн.: Электронные средства и системы управления: материалы докладов XVI Международной научнопрактической конференции (18–20 ноября 2020 г.): в 2 ч.Ч. 2.: Томск: В-спектр, 2020. С. 85–88.
Added: April 23, 2021