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Theoretical and experimental upper and lower bounds on the efficiency of convolutional codes in a binary symmetric channel
Problems of Information Transmission. 2022. Vol. 58. No. 2. P. 122–136.
We propose a new approach to the analytical estimation of the error burst probability, the probability of erroneous decoding, and the probability of error per bit for convolutional codes with Viterbi decoding in a binary symmetric channel (BSC). Upper and lower estimates of the probability of error per bit and of the erroneous decoding probability are based on active distances and the distance spectrum of active distances for a convolutional code. The estimates are derived for rate 1/2 convolutional codes, but they can also be generalized to any convolutional code with rate 1/n. Calculation of the estimates described here has linear time complexity in the error burst minimal length if code distance properties are known. The computational complexity does not depend on the crossover probability of a BSC. Simulation results show that the considered estimates are rather tight, especially for small crossover probabilities.
Publication based on the results of:
Фирсанова В. И., ACM, 2026.
The inclusion of autistic people can be augmented by a mobile app that provides information without a human mediator making information perception more liberating for people in the spectrum. This paper is an overview of a doctoral work dedicated to the development of a web-based mobile tool for supporting the inclusion of people on the ...
Added: August 4, 2026
Фирсанова В. И., Хлусова Я. К., CEUR Workshop Proceedings, 2025.
Knowledge graphs are widely used in Retrieval Augmented Generation (RAG) and Explainable AI (XAI), since they can illustrate semantic relationships generated by Large Language Models (LLMs). Recent studies focus on generating knowledge graphs from unstructured data to improve RAG performance; however, they do not explain the underlying graph structure. The analysis of synthetic graphs behind ...
Added: August 4, 2026
Spiridonov V. P., Belousov N. M., Sarkissian G. A., Analysis and Mathematical Physics 2026 Vol. 16 Article 96
Hyperbolic hypergeometric integrals are defined as Barnes-type integrals of products of hyperbolic gamma functions. Their reduction to ordinary hypergeometric functions is well known. We study in detail their degeneration to complex hypergeometric functions. Namely, using uniform bounds on the integrands, we prove that the univariate hyperbolic beta integral and the conical function degenerate to two-dimensional ...
Added: August 4, 2026
Gayfullin S., Kikteva V., Results in Mathematics 2026 Vol. 81 No. 5 Article 146
In this paper we obtain a criterion of flexibility for an affine complexity-zero horospherical variety. This result generalizes previously known results on flexibility of normal horospherical varieties, horospherical varieties with an action of a semisimple group, and non-normal toric varieties. ...
Added: August 3, 2026
Lunts V., Функциональный анализ и его приложения 2026 Т. 60 № 3 С. 127–129
Доказано, что канонические полуортогональные разложения производной категории диаграммной схемы индуцируют аналогичные разложения подкатегории совершенных комплексов. ...
Added: August 3, 2026
Belomestny D., Gasnikov A., Gladin E. et al., Russian Mathematical Surveys 2026 Vol. 81 No. 4(490) P. 3–90
Reinforcement learning (RL) is increasingly grounded in tools from probability, optimization, and operator theory. This survey organizes the mathematical structures that underpin the design and analysis of modern algorithms in RL. We begin from Markov decision processes (MDPs) and the Bellman operators, emphasizing contraction mappings, monotonicity, and fixed-point theory that yield convergence guarantees and rates ...
Added: August 3, 2026
Chepovskiy A., Мастерская Печати Идей, 2026.
The textbook presents methods and algoгithms for automatic analysis
of соrроrа of texts in natural languages. It is intended fоr sfudenБ of
methods of processing texts in паtчrаl languages and creating training
arays of texts.
Fоr students, graduate students and researchers studying methods
of computational linguistics and word processing. ...
Added: August 1, 2026
A. Radomskii, Mathematical notes 2026 Vol. 119 No. 6 P. 1136–1147
We obtain an upper bound for the sum $\sum_{n\leq N} (a_{n}/\varphi (a_{n}))^{s}$, where $\varphi$ is Euler's totient function, $s\in\mathbb{N}$, and $a_{1},\ldots, a_{N}$ are positive integers (not necessarily distinct) with some restrictions. As applications, for any $t>0$, we obtain an upper bound for the number of $n\in [1,N]$ such that $a_{n}/ \varphi (a_{n})> t$. ...
Added: July 31, 2026
Абызов А. Н., Буутай П. Н., Математика и теоретические компьютерные науки 2026 Т. 4 № 2 С. 4–75
This paper is expository and methodological in nature and is devoted to the development of E.I. Zolotarev’s ideas embedded in his approach to the proof of the quadratic reciprocity law (1872). We consider extensions of Zolotarev’s approach to abstract number rings presented in the work of A. Brunyate and P.L. Clark (2015), and to finite ...
Added: July 30, 2026
Ponomarenko A., / Series Computer Science "arxiv.org". 2025.
This paper addresses the challenge of merging hierarchical navigable small world (HNSW) graphs, a critical operation for distributed systems, incremental indexing, and database compaction. We propose three algorithms for this task: Naive Graph Merge (NGM), Intra Graph Traversal Merge (IGTM), and Cross Graph Traversal Merge (CGTM). These algorithms differ in their approach to vertex selection ...
Added: July 30, 2026
Уилкокс П., Romanov A., М.: ДМК Пресс, 2025.
Книга, которую вы держите в руках, продолжает серию «Книжная полка истового
инженера», которая издается при поддержке компании YADRO.
Данная книга представляет собой учебник по теоретическим основам продвинутой
функциональной верификации и содержит лучшие практики, используемые в настоящее
время. В ней подробно описана унифицированная методология верификации
(UVM) и раскрыты такие темы, как функциональный виртуальный прототип, функциональное
покрытие, утверждения, формальная верификация, тестбенчи, косимуляция,
эмуляция, аппаратное ...
Added: July 30, 2026
Mikhaylets E. V., Razorenova A. М., Chernyshev V. L. et al., Scientific Reports 2026 Vol. 16 Article 23560
Meditation offers a naturalistic paradigm for studying introspection, yet the neural dynamics of advanced tantric practices remain largely unexplored. Buddhist Highest Yoga Tantra (BHYT) comprises a sequence of eight dissolution stages culminating in the “clear light” state. We recorded EEG during eyes-closed BHYT meditation performed in monasteries and hermitages (51 sessions from 36 male practitioners; ...
Added: July 29, 2026
Попеленский Ф. Ю., Математический сборник 2026 Т. 217 № 2 С. 108–153
In a recent paper Buchstaber and the author introduced a new structure on the cohomology of Hopf algebras in terms of the Buchstaber spectral sequence (Bss). We fully calculate this structure on the cohomology (known for a long time) of the important Hopf subalgebra A(1) of the classical Steenrod algebra A2.
As part of a demonstration ...
Added: July 28, 2026
Metlov K., Andrei B. Bogatyrëv, Annalen der Physik 2026 Vol. 538 No. 6 Article e70234
Thanks to the recent progress in bulk full three-dimensional nanoscale magnetization distribution imaging, there is a growing
interest to three-dimensional (3D) magnetization textures, promising new high information density spintronic applications.
Compared to 1D domain walls or 2D magnetic vortices/skyrmions, they are a much harder challenge to represent, analyze and
reason about. Here we build analytical representation for such ...
Added: July 28, 2026
Думкин Н. А., Alexandrov D., Прозорский М. А., Труды Института системного программирования РАН 2026 Т. 38 № 1 С. 255–274
A theoretically sound approach to adaptive client-side video fragment restoration is proposed using
machine learning and scene analysis methods. The method includes a formal problem statement, a finite-state
machine model for decision making, a restoration cost function, and a new stage in video preparation: scene
dynamics assessment followed by recording a feature in an HLS playlist. This feature ...
Added: July 27, 2026
Menovshchikov A., Ukhlov A., Rendiconti del Circolo Matematico di Palermo 2026 Vol. 75 Article 91
We consider the nonlinear Neumann eigenvalue problem in outward cuspidal domains with a weighted measure. Using composition operators on Sobolev spaces, we establish embeddings of Sobolev spaces into weighted Lebesgue spaces. These embeddings give the solvability of the Neumann spectral problem in this setting and provide estimates for the corresponding weighted Neumann eigenvalues. ...
Added: July 27, 2026
Menovshchikov A., Journal of Mathematical Sciences 2026 Vol. 298 P. 608–618
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
Логвиненко Т. И., Стрельцова А. В., Otstavnov N. et al., Вопросы образования 2025 № 2 С. 101–141
The aim of this article is to review empirical studies, meta-analyses and systematicreviews on educational interventions for developing and improving reading compre-hension in adolescents, including both typically developing readers and those ex-periencing reading difficulties. We distinguish seven intervention types aimed at im-proving reading comprehension, each targeting different components as the basisfor intervention: decoding and reading ...
Added: December 11, 2025
Ilina A., Planche L., Shchur V., Lobachevskii Journal of Mathematics 2025 No. 46 P. 3537–3544
Many modern human populations contain archaic Neanderthal segments through the archaic introgression event, which occurred 45,000–55,000 years ago. There are a few computational methods that could infer such tracts. The results of their inference is used in the downstream analysis to better understand the impact of the archaic component on the genetic diversity of modern ...
Added: November 29, 2025
Alina M. Veresova, Andrei A. Ovchinnikov, , in: 2024 IEEE 3rd International Conference on Problems of Informatics, Electronics and Radio Engineering (PIERE).: IEEE, 2024. P. 1130–1134.
The article discusses the data transmission using convolutional codes over channels where the noise process can be described by a Markov chain with two states: a simple binary Markov channel and the Gilbert channel. Using the classical Viterbi algorithm with the Hamming metric for these channels does not guarantee low error probabilities. Additionally, the use ...
Added: May 14, 2025
Veresova A., Ovchinnikov A., Научно-технический вестник информационных технологий, механики и оптики 2025 Т. 25 № 1 С. 160–168
The problem of error correction in communication channel may be solved by finding the most probable error vector
in the channel. The equivalent in some cases problem may be formulated as finding the vector of least weight. To
perform this, the distance function is needed matched to communication channel. Hamming and Euclid metrics are
traditionally used in classical ...
Added: May 14, 2025
Lazarevich I., Prokin I., Гуткин Б. С. et al., PLoS Computational Biology 2023 Vol. 19 No. 1 P. 1–18
Modern well-performing approaches to neural decoding are based on machine learning
models such as decision tree ensembles and deep neural networks. The wide range of algorithms
that can be utilized to learn from neural spike trains, which are essentially time-series
data, results in the need for diverse and challenging benchmarks for neural decoding, similar
to the ones in the ...
Added: March 18, 2024
Aksiotis V., Ossadtchi A., В кн.: Сборник тезисов XXIV съезда физиологического общества им. И. П. Павлова, 11–15 сентября 2023 года.: СПб.: ООО "Издательство ВВМ", 2023. С. 307–307.
Несмотря на последние достижения (Fajardo et al., 2020; Okorokova et al., 2015), создание систем, сочетающих распознавание по электромиографической активности естественных намерений к движению отдельными пальцами или сложными жестами остается проблемой (Pasluosta et al., 2022). Актуальной является задача создания систем обучения пациентов управлению протезом на ранних этапах ампутации. Исследование включает разработку системы бесконтактного сбора синхронной кинематики ...
Added: December 1, 2023
Никольская Т. Е., Павлина С. Ю., Вестник Волгоградского государственного университета. Серия 2: Языкознание 2019 Т. 18 № 1 С. 132–145
The article investigates inter-cultural artistic communication which occurs through multimodal texts in general and feature films in particular. Artistic communication faces a challenge when its source and target belong to different ethnic and/or generational cohorts. The similarity or difference of communication codes depends on the level of adequacy of the sender’s and the recipient’s discursive ...
Added: September 19, 2023