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Combinatorics and Algorithms for Quasi-Chain Graphs
Algorithmica. 2023. Vol. 85. No. 3. P. 642–664.
The class of quasi-chain graphs is an extension of the well-studied class of chain
graphs. This latter class enjoys many nice and important properties, such as bounded
clique-width, implicit representation, well-quasi-ordering by induced subgraphs, etc.
The class of quasi-chain graphs is substantially more complex. In particular, this class
is not well-quasi-ordered by induced subgraphs, and the clique-width is not bounded
in it. In the present paper, we show that the universe of quasi-chain graphs is at least as
complex as the universe of permutations by establishing a bijection between the class
of all permutations and a subclass of quasi-chain graphs.This implies, in particular, that
the induced subgraph isomorphism problem is NP-complete for quasi-chain graphs.
On the other hand, we propose a decomposition theorem for quasi-chain graphs that
implies an implicit representation for graphs in this class and efficient solutions for
some algorithmic problems that are generally intractable.
Buryak A., Clader E., Tessler R., Journal of Differential Geometry 2024 Vol. 128 No. 1 P. 1–75
We conclude the construction of $r$-spin theory in genus zero for Riemann surfaces with boundary. In particular, we define open $r$-spin intersection numbers, and we prove that their generating function is closely related to the wave function of the $r$th Gelfand--Dickey integrable hierarchy. This provides an analogue of Witten's $r$-spin conjecture in the open setting ...
Added: June 23, 2026
Buryak A., Shadrin S., Epijournal de Geometrie Algebrique 2024 Vol. 8
We present a family of conjectural relations in the tautological cohomology of the moduli spaces of stable algebraic curves of genus g with n marked points. A large part of these relations has a surprisingly simple form: the tautological classes involved in the relations are given by stable graphs that are trees and that are decorated only by powers ...
Added: June 23, 2026
Buryak A., Rossi P., Letters in Mathematical Physics 2024 Vol. 114 Article 97
We give explicit formulas for the number of meromorphic differentials on $CP^1$ with two zeros and any number of residueless poles and for the number of meromorphic differentials on $CP^1$ with one zero, two poles with unconstrained residue and any number of residueless poles, in terms of the orders of their zeros and poles. These ...
Added: June 23, 2026
Buryak A., Rossi P., Zvonkine D., Geometry and Topology 2024 Vol. 28 P. 2793–2824
We prove that the cohomology classes of the moduli spaces of residueless meromorphic differentials, ie the closures, in the moduli space of stable curves, of the loci of smooth curves whose marked points are the zeros and poles of prescribed orders of a meromorphic differential with vanishing residues, form a partial cohomological field theory (CohFT) of ...
Added: June 23, 2026
Buryak A., Труды Математического института им. В.А. Стеклова РАН 2024 Т. 325 С. 26–66
The main goal of the paper is to show that the DR hierarchies, introduced by the author in an earlier paper, allow one to establish, in the most clear way, a relation between the topology of the Deligne–Mumford compactification of the moduli space of smooth algebraic curves of genus g with n marked points and integrable systems ...
Added: June 23, 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
Atlasov B., Selskiy A., Russian Journal of Information Technology in Sports 2025 Vol. 2 No. 1 P. 13–21
The article examines the current state of the global virtual and augmented reality (VR/AR) technology market in sports, noting its growth, although slower than previously expected. Special attention is paid to the Russian market, where the development of VR technologies in sports lags behind world leaders such as the United States, EU countries and China, ...
Added: June 23, 2026
IEEE, 2026.
The 9th International Scientific Conference on Information, Control, and Communication Technologies (ICCT-2025) had been held October 7-11, 2025 in Gomel, Belarus. The main technical areas and applications covered by the proceedings are optoelectronics, acousto-optic, microwave technology, antenna systems, measuring technology, metamaterials, nanostructures, nanofilms, photonic crystals, biology and medicine, biophotonics, bioengineering, neural networks in communication technologies; ...
Added: June 23, 2026
Buzaev F., Mullakhmetov R., Bogachev R. et al., Association for Computational Linguistics, 2026.
Playlist generation based on textual queries using large language models (LLMs) is becoming an important interaction paradigm for music streaming platforms. User queries span a wide spectrum from highly personalized intent to essentially catalog-style requests. Existing systems typically rely on non-personalized retrieval/ranking or apply a fixed level of preference conditioning to every query, which can ...
Added: June 22, 2026
Herbert A., Cherednichenko O., Lybrand T. et al., International Journal of Molecular Sciences 2025 Vol. 26 No. 6 Article 2422
The double-stranded RNA editing enzyme ADAR1 connects two forms of genetic programming, one based on codons and the other on flipons. ADAR1 recodes codons in pre-mRNA by deaminating adenosine to form inosine, which is translated as guanosine. ADAR1 also plays essential roles in the immune defense against viruses and cancers by recognizing left-handed Z-DNA and ...
Added: June 22, 2026
Калужский печатный двор, 2026.
Conference Proceedings INTERNATIONAL CONFERENCE
“Mathematical Ideas of Academician
P.L. Chebyshev, Their Applications in Natural
Sciences and Artificial Intelligence Technologies”
dedicated to the 205th anniversary of his birth ...
Added: June 20, 2026
Джанбекова А. Р., Shvedov A. S., Математическое моделирование 2026 Т. 38 № 3 С. 159–176
Boundary value problems for the Black–Scholes partial differential equation, which describes the value of a financial instrument, may contain a free boundary condition if the financial instrument allows for early exercise. This article considers free boundary value problems for the Black–Scholes equation and the convection diffusion equation. For the convection diffusion equation, a finite difference ...
Added: June 20, 2026
Stognieva O., Чеснокова Н. Е., Отечественная и зарубежная педагогика 2026 Т. 1 № 3 (115) С. 123–131
Integration of generative artificial intelligence tools into educational practice highlights the need for pedagogically grounded approaches to their use in the creation of educational video content, which is increasingly applied in language and professionally oriented instruction.
The purpose of this article is to conduct a comparative analysis of educational video content created using generative AI tools ...
Added: June 20, 2026
Buryak A., Tessler R., Troshkin M., Journal of Geometry and Physics 2026 Vol. 223 Article 105783
We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to . We prove that the resulting sequence of partition functions, depending on , is a tau-sequence of ...
Added: June 19, 2026
Buryak A., Rossi P., Communications in Mathematical Physics 2025 Vol. 406 Article 205
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is , where is the metric ...
Added: June 19, 2026
Cherednichenko O., Herbert A., Poptsova M., Computational and Structural Biotechnology Journal 2025 Vol. 27 P. 992–1000
Large language models (LLMs) in genomics have successfully predicted various functional genomic elements. While their performance is typically evaluated using genomic benchmark datasets, it remains unclear which LLM is best suited for specific downstream tasks, particularly for generating whole-genome annotations. Current LLMs in genomics fall into three main categories: transformer-based models, long convolution-based models, and state-space models ...
Added: June 19, 2026
Poptsova M., Briefings in Bioinformatics 2025 Vol. 26 No. 2 P. 1–11
Kolmogorov–Arnold networks (KANs) emerged as a promising alternative for multilayer perceptrons (MLPs) in dense fully connected networks. Multiple attempts have been made to integrate KANs into various deep learning architectures in the domains of computer vision and natural language processing. Integrating KANs into deep learning models for genomic tasks has not been explored. Here, we ...
Added: June 19, 2026
Анненков А. Н., Nesterov R., Моделирование и анализ информационных систем 2026 Т. 33 № 2 С. 176–205
Declarative process models are widely used in process mining to describe flexible process behavior through sets of constraints. However, models discovered automatically from event logs may contain inconsistent constraints, which can make them difficult to interpret and unusable for execution, conformance checking, or further analysis. Existing methods for consistency analysis either rely on automata-based constructions ...
Added: June 18, 2026
Cham: Springer Publishing Company, 2026.
The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026.
The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...
Added: June 18, 2026
Nadutkina A., Tikhomirov A., Timushev D., Siberian Advances in Mathematics 2024 Vol. 34 No. 2 P. 146–153
We study the spectra of random weighted bipartite graphs. We establish that, under specific assumptions on the edge probabilities, the symmetrized empirical spectral distribution function of the graph’s adjacency matrix converges to the symmetrized Marchenko-Pastur distribution function. ...
Added: January 26, 2026
El-Mesady A., Farahat T., El-Shanawany R. et al., Algorithms 2023 Vol. 16 No. 7 Article 320
Nowadays, graph theory is one of the most exciting fields of mathematics due to the tremendous developments in modern technology, where it is used in many important applications. The orthogonal double cover (𝑂𝐷𝐶) is a branch of graph theory and is considered as a special class of graph decomposition. In this paper, we decompose the complete bipartite ...
Added: July 30, 2023
Grinblat A., Lopatkin V., Journal of Algebra and its Applications 2020 Vol. 20 No. 5 Article 2150083
The aim of this paper is to show that any finite undirected bipartite graph can be considered as a polynomial p∈N[x], and any directed finite bipartite graph can be considered as a polynomial p∈N[x,y], and vise verse. We also show that the multiplication in semirings N[x], N[x,y] correspondences to a operations of the corresponding graphs which looks like a ``perturbed'' ...
Added: September 27, 2021
Alecu B., Atminas A., Loozin V. V. et al., , in: International Workshop on Combinatorial Algorithms, 32nd International Workshop, IWOCA 2021, Ottawa, ON, Canada, July 5–7, 2021Vol. 12757.: Springer, 2021. P. 49–62.
The class of quasi-chain graphs is an extension of the well-studied class of chain graphs. The latter class enjoys many nice and important properties, such as bounded clique-width, implicit representation, well-quasi-ordering by induced subgraphs, etc. The class of quasi-chain graphs is substantially more complex. In particular, this class is
not well-quasi-ordered by induced subgraphs, and the ...
Added: July 1, 2021