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The Problem of a Symmetric Graph with a Maximum Number of Vertices and Minimum Diameter
Lobachevskii Journal of Mathematics. 2023. Vol. 44. No. 12. P. 5453–5459.
The paper gives a solution for the problem of the topology of the communication subsystem graph for high-performance multi-core computing systems. In this graph, each vertex is connected to four neighbors, and the number of vertices is the maximum for a given graph diameter. The solution to this problem is the family of circulants C(D(D+1)+1; 1, 2D+1) , D – diameter. This graph is invariant under transforming its arbitrary vertex into any other, and its vertices are located densely in the vicinity of the root vertex, which determines its compliance with the diameter optimality criterion. All statements formulated during the solution of the problem are proven.
Language:
English
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
Radomskii A., 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
Cham: Springer, 2026.
This open access set, LNAI 16688-16689, constitutes the proceedings of the 13th International Joint Conference, IJCAR 2026, held in Lisbon, Portugal, during July 26–29, 2026.
The 41 full research papers and 8 short papers included in these two volumes were carefully reviewed and selected from 112 submissions. The papers cover the following topical sections:
Part I: Theorem ...
Added: July 26, 2026
Edward R. Rzaev, Aleksandr Y. Romanov, Andrey M. Sukhov, IEEE Access 2026 Vol. 14 P. 2169–3536
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
Malikov M., Romanov A., IEEE Access 2025 Vol. 13 P. 148803–148815
Networks-on-chip (NoCs) widespread in computing system design are used in many applications. A critical NoC aspect is the interaction between computing cores and in particular the traffic patterns. The relevance of this work stems from the fact that traffic patterns in NoCs are poorly understood and have no general classification; and there are no universal ...
Added: September 16, 2025
Romanov A., Lerner A., Amerikanov A., The Journal of Supercomputing 2024 No. 80 P. 22462–22478
On-chip networks (NoCs) have become a popular choice for designing large multiprocessor architectures. Software-based emulation is often used to perform the design verifcation. However, if the considered design is sufciently large, softwarebased emulation becomes impractically slow. To avoid this limitation, multi-FPGA emulation was introduced, where multiple interconnected FPGAs collectively emulate a single circuit. The number ...
Added: June 30, 2024
Mikhail Yu. Romashikhin, , in: Proceedings 2024 International Russian Smart Industry Conference (SmartIndustryCon), 25-29 March 2024.: Sochi: IEEE, 2024. P. 104–108.
This article describes the implementation of regular topologies for networks-on-chip. The complexity of network development and its main parameters depend on the choice of topology. The rationale for the influence of topology on network bandwidth is given. Software that automates the generation of configuration files (bitstream) for the implementation of networks-on-chip with different topologies and ...
Added: May 13, 2024
Sukhov A., Romanov A., Selin M., Symmetry 2024 Vol. 16 No. 1 Article 127
In this work, the circulant topology as an alternative to 2D mesh in networks-on-chip is considered. A virtual coordinate system for numbering nodes in the circulant topology is proposed, and the principle of greedy promotion is formulated. The rules for constructing the shortest routes between the two nodes based on coordinates are formulated. A technique ...
Added: March 8, 2024
Sukhov A., Romanov A., Глушак Е. В., Ученые записки Казанского университета. Серия: Физико-математические науки 2023 Т. 165 № 3 С. 282–293
The article discusses routing methods in two-dimensional circulant graphs (each vertex is connected to four neighboring ones). The unique group of symmetries of the circulant graph makes it possible to use it as a topology for high performance computing devices, including networks-on-chip and cluster supercomputers. It is shown that the minimum number of transitions along ...
Added: January 5, 2024
Romanov A., Big Data and Cognitive Computing 2023 Vol. 7 No. 2 Article 80
This article presents software for the synthesis of circulant graphs and the dataset obtained. An algorithm and new methods, which increase the speed of finding optimal circulant topologies, are proposed. The results obtained confirm an increase in performance and a decrease in memory consumption compared to the previous implementation of the circulant topologies synthesis method. ...
Added: June 4, 2023
Aleksandr Y. Romanov, Nikolay M. Myachin, Evgenii V. Lezhnev et al., Micromachines 2023 Vol. 14 No. 1 Article 141
This article considers the usage of circulant topologies as a promising deadlock-free topology for networks-on-chip (NoCs). A new high-level model, Newxim, for the exploration of NoCs with any topology is presented. Two methods for solving the problem of cyclic dependencies in circulant topologies, which limit their applications for NoCs due to the increased possibility of ...
Added: January 31, 2023
El-Mesady A., Romanov A., Amerikanov A. et al., Algorithms 2023 Vol. 16 No. 1 Article 10
Recent developments in commutative algebra, linear algebra, and graph theory allow us to approach various issues in several fields. Circulant graphs now have a wider range of practical uses, including as the foundation for optical networks, discrete cellular neural networks, small-world networks, models of chemical reactions, supercomputing and multiprocessor systems. Herein, we are concerned with ...
Added: January 17, 2023
Monakhova E. A., Monakhov O. G., Romanov A., IEEE Transactions on Network Science and Engineering 2023 Vol. 10 No. 1 P. 413–425
The solution of the problem of organizing optimal communications in circulant networks of degree four is considered. For a family of optimal circulant networks with the minimum diameter and average distance for any number of nodes in a graph, we propose an optimal pair routing algorithm of constant complexity based on using the relative addressing ...
Added: November 18, 2022
Alijon F. Fatullaev, Edward R. Rzaev, Aleksandr Yu. Romanov, , in: 2022 International Russian Automation Conference (RusAutoCon).: IEEE, 2022. P. 419–423.
The article presents a study of clustering of Paley graphs with the arrangement of prime numbers in polar coordinates and a comparison of the resulting groups in terms of their static parameters; the application of fault-tolerant self-organizing routing method for new topologies is also considered. This article is a continuation of a series of articles ...
Added: October 2, 2022