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Hypergraph Edge Representations with the Use of Homological Paths
Journal of Applied and Industrial Mathematics (перевод журналов "Сибирский журнал индустриальной математики" и "Дискретный анализ и исследование операций"). 2023. Vol. 17. No. 3. P. 678–686.
M. N. Vyalyi, Karpov V. E.
We consider the problem of realization of hypergraphs on a graph provided each hyperedge is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to Cycle Double Cover conjecture. We prove that checking the existence of realization is computationally hard. The hardness is proved in various settings: for realizations on all graphs, on simple graphs, and on graphs from several restricted classes.
Publication based on the results of:
Springer, 2026.
Two volumes of the SPECOM 2026 proceedings contain a collection of submitted papers presented at SPECOM 2026, which were thoroughly reviewed by members of the Program Committee and additional reviewers consisting of almost 80 experts in the conference topic areas. In total, 65 regular full papers out of 99 submissions made via the EasyChair electronic ...
Added: September 20, 2026
Medvedev V., Annals of Global Analysis and Geometry 2026 Vol. 70 No. 2 P. 8–23
This paper studies three-dimensional compact static manifolds with boundary and positive scalar curvature. We prove that, under a suitable bound on the Ricci curvature, the orientable quotient of the Nariai static manifold with boundary is the only such manifold with connected boundary, provided that the zero-level set of the potential is connected and does not intersect ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 323–334
In this paper, an improved approach for automatic wildlife detection in natural environments based on the integration of a neural network architecture with a two-stream attention mechanism and a novel preclassification step based on infrared data has been presented. The proposed method addresses one of the key challenges in environmental monitoring: the need for scalable ...
Added: September 19, 2026
Aleksei Samarin, Nazarenko A., Kotenko E. et al., Proceedings of the ACM on Management of Data, USA 2026 Vol. 4 No. 1 P. 1–28
Modern knowledge and large volumes of data are increasingly encoded within neural networks, making the task of simplifying their structures and reducing the number of parameters especially relevant, both to improve efficiency and to facilitate deployment in resource-constrained environments. This paper presents a novel approach to neural network compression that addresses redundancy at both the ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2025 Vol. 35 No. 2 P. 148–158
This paper describes our research on creating classifiers for microbial images (micrococci microscopy images) obtained from pictures of unfixed microscopic scenes. In our work, we propose an AutoML approach based on the automatic generation and analysis of the feature space for constructing the most optimal descriptors of microorganism images for subsequent classification. This makes it ...
Added: September 19, 2026
Aleksei Samarin, Alexander Savelev, Aleksei Toropov et al., Pattern Recognition and Image Analysis 2026 Vol. 36 No. 2 P. 302–312
The lack of annotated microscopic datasets remains a major obstacle to training robust deep learning models for microbial classification. In this paper, a novel data augmentation pipeline that uses visual–linguistic large-scale models to generate synthetic microscopic images of six different bacterial and nonbacterial classes has been proposed. Synthetic samples have gradually been added to the ...
Added: September 19, 2026
Springer, Cham, 2026.
computer vision ...
Added: September 19, 2026
Springer, Cham, 2026.
Added: September 19, 2026
FRUCT Oy, 2024.
Added: September 19, 2026
FRUCT Oy, 2024.
Added: September 19, 2026
FRUCT Oy, 2025.
Added: September 19, 2026
FRUCT Oy, 2026.
Added: September 19, 2026
Onoprienko A., Доклады Российской академии наук. Математика, информатика, процессы управления (ранее - Доклады Академии Наук. Математика) 2025 № 527 С. 206–216
We study the algorithmic complexity of the cooperative card game Hanabi. The feature of Hanabi is that players see each other’s cards but not their own, and exchange information through hints. Even in the model with one player who has full information about the deck, Hanabi remains NP-hard. We found the minimal parameters ofthe game ...
Added: November 23, 2025
S. M. Dudakov, Karlov B. N., S. L. Kuznetsov et al., Algebra and Logic 2021 Vol. 60 No. 5 P. 308–326
The Lambek calculus with the unit can be defined as the atomic theory (algebraic logic) of the class of residuated monoids. This calculus, being a theory of a broader class of algebras than Heyting ones, is weaker than intuitionistic logic. Namely, it lacks structural rules: permutation, contraction, and weakening. We consider two extensions of the ...
Added: November 12, 2023
Vyalyi M., Карпов В. Е., Дискретный анализ и исследование операций 2023 Т. 30 № 3(157) С. 81–95
We consider a problem of realization of hypergraphs on graphs provided each hyperedge is realized by a subgraph in which exactly two vertices have odd degree. This problem is related to Cycle Double Cover conjecture. We prove that checking the existence of realization is computationally hard. The hardness is proved in various settings: for realizations ...
Added: October 31, 2023
Solomadin G., Arnold Mathematical Journal 2022 P. 1–46
In this paper, for any Milnor hypersurface, we find the largest dimension of effective
algebraic torus actions on it. The proof of the corresponding theorem is based on
the computation of the automorphism group for any Milnor hypersurface. We find
all generalized Buchstaber–Ray and Ray hypersurfaces that are toric varieties. We
compute the Betti numbers of these hypersurfaces and ...
Added: April 25, 2022
Shabanov D. A., Discrete Applied Mathematics 2020 Vol. 282 P. 168–183
The paper deals with estimating the r-colorability threshold for a random k-uniform hypergraph in the binomial model H(n,k,p). We consider the sparse case, when the expected number of edges is a linear function of n and prove a new lower bound for the sharp threshold of the property that H(n,k,p) is r-colorable. ...
Added: June 6, 2020
Akhmejanova M., Shabanov D. A., Discrete Applied Mathematics 2020 Vol. 276 P. 2–12
The paper deals with an extremal problem concerning equitable colorings of uniform hypergraphs. Recall that a vertex coloring of a hypergraph is called proper if there are no monochromatic edges under this coloring. A hypergraph is said to be equitably r-colorable if there is a proper coloring with r colors such that the sizes of ...
Added: October 31, 2019
Shabanov D. A., Akhmejanova M., Discrete Mathematics 2020 Vol. 343 No. 4 P. 1–11
The paper deals with an extremal problem concerning colorings of hypergraphs with bounded edge degrees. Consider the family of b-simple hypergraphs, in which any two edges do not share more than b common vertices. We prove a new lower bound for the maximum edge degree in a n-uniform b-simple non-r-colorable hypergraph. We also establish some ...
Added: October 31, 2019
Kravtsov D., Krokhmal N., Shabanov D. A., Russian Mathematical Surveys 2018 Vol. 73 No. 4 P. 731–733
The paper deals with the problem of finding the probability threshold for the
existence of a panchromatic colouring for a random hypergraph in the binomial
model. ...
Added: November 15, 2018
Avdoshin S. M., Набебин А. А., М.: ДМК Пресс, 2019.
The book contains the necessary information from the algorithm theory, graph theory, combinatorics. It is considered partially recursive functions, Turing machines, some versions of the algorithms (associative calculus, the system of substitutions, grammars, Post's productions, Marcov's normal algorithms, operator algorithms). The main types of graphs are described (multigraphs, pseudographs, Eulerian graphs, Hamiltonian graphs, trees, bipartite ...
Added: August 24, 2018
Shabanov D. A., Doklady Mathematics 2017 Vol. 96 No. 1 P. 321–325
The problem on the limit distribution of the chromatic number of a random uniform hypergraph in the sparse case is studied. It is shown that, for most parameters values, the limit distribution of the chromatic number is concentrated at precisely one point, which can be found explicitly. ...
Added: March 6, 2018
Shabanov D. A., Kupavskii A., Combinatorics Probability and Computing 2018 Vol. 27 No. 2 P. 245–273
This paper deals with a combinatorial problem concerning colourings of uniform hypergraphs
with large girth. We prove a new lower bound for the maximum edge degree for an n-uniform non-r-colourable simple hypergraph. As an application of our probabilistic technique we establish a lower bound for the classical
van der Waerden number W(n, r), the minimum natural N ...
Added: February 22, 2018
Shabanov D. A., Akolzin I., Discrete Mathematics 2016 Vol. 339 No. 12 P. 3020–3031
The paper deals with the classical extremal problem concerning colorings of hypergraphs. The problem is to find the value m(n,r), equal to the minimum number of edges in a n-uniform hypergraph with chromatic number greater than r. We obtain new upper and lower bounds for m(n,r) in the case when the parameter r is very ...
Added: September 4, 2016