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Коды с малой плотностью проверок, основанные на полях Галуа
Информационные процессы. 2012. Т. 12. № 1. С. 68–83.
Methods for constructing a mapping of the elements of a multiplicative group of a Galois field onto a symmetric group of permutation matrices are proposed. A technique minimizing the order of the symmetric group is suggested. The results are used for constructing an ensemble of low-density parity-check codes. The obtained code constructions are tested on an iterative belief propagation (sum-product) decoding algorithm on transmission of a code word through a binary channel with an additive Gaussian white noise.
Language:
Russian
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Seul: PMLR, 2026.
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 2026
Gnetov F., Konakov V., Успехи математических наук 2026 Т. 81 № 3 (489) С. 161–162
Пусть M обозначает симметрическое пространство некомпактного типа ранга 1. Опираясь на фундаментальную работу [1], в [2] было показано, что плотность соответствующим образом нормированной суммы независимых Hn-значных случайных величин, определенная через сложение Мёбиуса в модели шара Пуанкаре, сходится к фундаментальному решению соответствующего уравнения теплопроводности. Пределом являлся нормальный закон на Hn, соответствующий ядру теплопроводности, определяемому оператором Лапласа–Бельтрами. ...
Added: June 2, 2026
Silakov D., Системный администратор 2026 № 3 С. 28–33
В статье про платформы для разработки открытого ПО в Китае мы рассказали про GitCode – молодой проект, позиционируемый как площадка для разработчиков со всего мира. Сейчас на GitCode размещаются проекты, созданные в КНР, но некоторые из них уже известны и на международной арене. Помочь открытым проектам в становлении, развитии и расширению аудитории призван фонд OpenAtom ...
Added: June 2, 2026
Slivnitsin P., Mylnikov L., Engineering Applications of Artificial Intelligence 2026 Vol. 179 Article 115185
The paper describes a applied artificial intelligence task of recognition-by-components method of real objects based on the recognition of a limited set of primitives or components. The recognition-by-components makes it possible to determine the components, that compose an object, and increase the number of recognizable objects without degrading the recognition quality. Training is performed on ...
Added: May 29, 2026
Gorbounov Vassily, Kazakov A., Data Analytics and Topology 2025 Vol. 1 No. 1 P. 33–45
A classic problem in data analysis is studying the systems of subsets defined by either a similarity or a dissimilarity function on X which is either observed directly or derived from a data set.
For an electrical network there are two functions on the set of the nodes defined by the resistance matrix and the response ...
Added: May 28, 2026
Mokienko O., Zisman M. A., Bobrov P. et al., American Journal of Physical Medicine and Rehabilitation 2026 Vol. 105 No. 6 P. 555–563
Brain-computer interfaces (BCIs) represent a promising technology for restoring lower limb motor functions and gait after stroke. The application of BCIs in this field is supported by a limited number of studies. The objective of the review was to systematically and critically evaluate the current evidence on the use of BCIs for lower limb function ...
Added: May 28, 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
Dorovskiy A., / Series arXiv "math". 2026.
In this paper the structural stability of generic families of vector fields of the PC-HC class on the two-dimensional sphere is proved. A classification of these families up to moderate equivalence in neighborhoods of their large bifurcation supports is presented, based on such invariants as the configuration and the characteristic set. The realization lemma is proved. ...
Added: May 14, 2026
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 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
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 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
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 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
Osipov D., / Series arXiv "math". 2022. No. 1.
This paper devotes to comparison of different cod- ing schemes (various constructions of Polar and LDPC codes, Product codes and BCH codes) for the case when information is transmitted over AWGN channel with quantization with lowest possible complexity and resolution: 1-bit. We examine performance (in terms of Frame-error-rate — FER) for schemes mentioned above and ...
Added: December 27, 2022
Угловский А., Алексеев И., Щукин В. et al., В кн.: ИТиС 2022: Сборник трудов 46-й междисциплинарной школы-конференции ИППИ РАН "Информационные технологии и системы 2022".: Институт проблем передачи информации им. А.А. Харкевича РАН, 2022. С. 1–11.
Одной из ключевых проблем МПП-кодов является оценка низкого уровня ошибок, возникающего при относительно высоком уровне отношения сигнал – шум (SNR). Данное явление обусловлено в основном замедленным декодированием таких особенных структур как Трэппинг Сет (Trapping Set, TS), которые даже при высоком SNR могут привести к ошибке декодера. Исследование и оценка сверхнизкого уровня ошибок являются важными и ...
Added: October 26, 2022
Мельников И., Kreshchuk A., Kureev A., В кн.: ИТиС 2022: Сборник трудов 46-й междисциплинарной школы-конференции ИППИ РАН "Информационные технологии и системы 2022".: Институт проблем передачи информации им. А.А. Харкевича РАН, 2022. С. 1–8.
При использовании стандартного алгоритма декодирования кодов с малой плотностью проверок (МПП, англ.: Low-Density Parity-Check, LDPC) можно значительно уменьшить сложность декодирования за счёт хранения предвычисленной суммы всех сообщений в узлах переменных. Декодер Information Bottleneck (IB) значительно снизил пространственную сложность декодирования за счёт снижения разрядности всех сообщений. Для этого прямая сумма заменяется на локально оптимальную дискретную бинарную ...
Added: October 26, 2022