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Об одном характеристическом функционале слов над конечным алфавитом
Информационные технологии. 2017. № 5. С. 333–341.
Ulyanov M., Сметанин Ю. Г.
The objects studied in the article are finite words over some finite alphabet. These words are symbolical codes of the investigated objects and processes that are analyzed further. A formalization of the entropy on words function is proposed that is based on the of the entropy of discrete distributions. Using the results of analysis of sets of words with fixed length over a given alphabet, a notion of entropy function majorant is proposed. The entropy on words function and the majorant form the basis for the forms of a characteristic functional proposed in the article, which give a quantitative estimation of the proximity of the tested finite word to a subword of the same length, randomly selected from a random infinite word over the same alphabet. The proposed forms of the functional may be used for solving different tasks of data analysis, including clustering and pattern recognition tasks.
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
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
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
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
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
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
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
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
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
Ivanova I., Scientometrics 2025 Vol. 130 No. 6 P. 3109–3126
This paper reviews research topics that I have had the fortune to explore with Loet Leydesdorff over the past decade. What initially seemed to be different areas of research have eventually been brought together into a unified framework for a theory of meaning in inter-social communication. The sociology of communication laid the foundations for a ...
Added: September 2, 2025
Аллеманд А. О., Чебышевский сборник 2024 Т. 25 № 4 С. 27–41
In this paper we consider mutual information for a pair of random variables and find a third variable (condition) that maximise conditional mutual information of three of them. ...
Added: April 29, 2025
Fayzulin M., Финансы и бизнес 2024 Т. 20 № 2 С. 27–52
В работе исследуется взаимосвязь между разнородным поведением частных инвесторов и динамикой цен наиболее обсуждаемых акций российский акций, включая также динамику российского фондового рынка. На основе текстового анализа были разработаны метрики сентимента, учитывающие мнения пользователей инвестиционных онлайн-платформ и поведение биржевых характеристик рыночных активов. Такой подход позволил обнаружить ряд взаимосвязей между гетерогенным сентиментом участников рынка и отрицательной ...
Added: August 27, 2024
Yu. A. Dubnov, A. Yu. Popkov, Polishchuk V. Y. et al., Automation and Remote Control 2023 Vol. 84 No. 1 P. 64–81
Randomized machine learning focuses on problems with considerable uncertainty in data and models. Machine learning algorithms are formulated in terms of a functional entropylinear programming problem. We adapt these algorithms to forecasting problems on an example of the evolution of thermokarst lakes area in permafrost zones. Thermokarst lakes generate methane, a greenhouse gas affecting climate ...
Added: February 5, 2024
Dubnov Y. A., Bulychev A., Информационные технологии и вычислительные системы 2023 № 1 С. 71–81
In this paper, we investigate a method of approximate entropy estimation, designed to speed up the classical method of maximum entropy estimation due to the use of regularization in the optimization problem. This method is compared with the method of maximum likelihood and Bayesian estimation, both experimentally and in terms of theoretical calculations for some ...
Added: June 16, 2023
Dubnov Y. A., Bulychev A., Информационные технологии и вычислительные системы 2022 № 4 С. 69–80
The work is devoted to the development of an entropy estimation method with “soft” randomization for restoring the parameters of probabilistic mathematical models from the available observations. Soft randomization refers to the technique of adding regularization to the information entropy functional to simplify the optimization problem and speed up learning process compared to the traditional ...
Added: June 16, 2023
Los A., Mironkin V., М.: Издательская группа URSS, 2023.
This book is a textbook combining two related disciplines — "Information Theory" and "Coding Theory", describing the main stages of information transformation: from its formation using a message source and primary transformation — coding procedures — to its transmission over a communication channel and final conversion by the addressee into the required format — decoding ...
Added: April 11, 2023
Vorontsova T., Булеев А. А., Ефимов А. В. et al., В кн.: Межвузовская научно-техническая конференция студентов, аспирантов и молодых специалистов им. Е.В. Арменского.: МИЭМ НИУ ВШЭ, 2018. Гл. 159 С. 220–222.
Added: March 12, 2021
Popkov Y., Popkov A., Dubnov Y. A. et al., Mathematics 2020 Vol. 8 No. 7: 1119 P. 1–20
We propose a new forecasting procedure that includes randomized hierarchical dynamic regression models with random parameters, measurement noises and random input. We developed the technology of entropy-randomized machine learning, which includes the estimation of characteristics of a dynamic regression model and its testing by generating ensembles of predicted trajectories through the sampling of the entropy-optimal ...
Added: October 31, 2020
Popkov Y., Попков А. Ю., Dubnov Y. A., М.: ЛЕНАНД, 2019.
Проблема извлечения и последующего накопления знаний в конечном счете сводится к знаниям о модели, которые формализуются путем оценивания ее характеристик. Последнее интерпретируется как обучение модели с использованием данных. Современное представление о машинном обучении предполагает, что его результатом являются «обученные» детерминированные модели, снабженные эмпирическими вероятностными оценками их достоверности.
В настоящей монографии развивается новое направление в машинном обучении — рандомизированное машинное обучение, которое направлено на ...
Added: February 12, 2019
Dubnov Y. A., Bulychev A., Труды Института системного анализа Российской академии наук 2017 № 2 С. 51–63
The work is devoted to the evaluation of the influence of fundamental science on macroeconomic indicators. The regression model of the specific gross domestic product elasticity is considered with the aim of revealing the dependence between the indicators of innovation and economic development. As a tool for restoring model parameters, a method of entropy-robust estimation ...
Added: December 27, 2017
Popkov Y., Dubnov Y. A., Popkov A. Y., Mathematics 2016 Vol. 4 No. 1 P. 1–16
We propose a new method of randomized forecasting (RF-method), which operates with models described by systems of linear ordinary differential equations with random parameters. The RF-method is based on entropy-robust estimation of the probability density functions (PDFs) of model parameters and measurement noises. The entropy-optimal estimator uses a limited amount of data. The method of ...
Added: February 28, 2017
Popkov Y., Dubnov Y. A., Automation and Remote Control 2016 Vol. 77 No. 5 P. 839–854
This paper suggests a new randomized forecasting method based on entropy-robust estimation for the probability density functions (PDFs) of random parameters in dynamic models described by the systems of linear ordinary differential equations. The structure of the PDFs of the parameters and measurement noises with the maximal entropy is studied. We generate the sequence of ...
Added: February 28, 2017