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Homological mirror symmetry for the symmetric squares of punctured spheres
Advances in Mathematics. 2023. Vol. 418. Article 108942.
Lekili Y., Polishchuk A.
For an appropriate choice of a -grading structure, we prove that the wrapped Fukaya category of the symmetric square of a -punctured sphere, i.e. the Weinstein manifold given as the complement of generic lines in is quasi-equivalent to the derived category of coherent sheaves on a singular surface constructed as the boundary of a toric Landau-Ginzburg model . We do this by first constructing a quasi-equivalence between certain categorical resolutions of both sides and then localizing. We also provide a general homological mirror symmetry conjecture concerning all the higher symmetric powers of punctured spheres. The corresponding toric LG-models are constructed from the combinatorics of curves on the punctured sphere and are related to small toric resolutions of the singularity .
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 ...
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Degtyarev A., Bakhurin S., Yudin N., DSPA 2026 P. 1–6
This paper investigates one possible solution to the problem of self-interference cancellation (SIC) arising in the design of in-band full-duplex (IBFD) communication systems. Self-interference cancellation is performed in the digital domain using multilayer nonlinear models adapted via gradient-based optimization. The presence of local minima and saddle points during the adaptation of multilayer models limits the ...
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Ilyashenko Y., Shilin I., Stanislav Minkov, Russian Journal of Mathematical Physics 2026 Vol. 33 No. 1 P. 89–106
In this paper, new numerical invariants of structurally unstable vector fields in the plane
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occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological
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Gusev I., Maksaev A., Promyslov V., Journal of Mathematical Sciences 2025 Vol. 299 No. 6
The regular graph of the space of n × m matrices over a field F is defined as the undirected graph whose vertices are matrices of rank min(n, m), and distinct matrices A and B are connected by an edge if and only if rk(A + B) < min(n, m). In this paper, for |F| ...
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Tyukin I., Tyukina T., van Helden D. P. et al., Information Sciences 2024 Vol. 678 Article 120856
AI errors pose a significant challenge, hindering real-world applications. This work introduces a novel approach to cope with AI errors using weakly supervised error correctors that guarantee a specific level of error reduction. Our correctors have low computational cost and can be used to decide whether to abstain from making an unsafe classification. We provide ...
Added: May 23, 2026
Zaikin A., Sviridov I., Sosedka A. et al., Technologies 2026 Vol. 14 No. 2 Article 84
High-dimensional tabular data are common in biomedical and clinical research, yet conventional machine learning methods often struggle in such settings due to data scarcity, feature redundancy, and limited generalization. In this study, we systematically evaluate Synolitic Graph Neural Networks (SGNNs), a framework that transforms high-dimensional samples into sample-specific graphs by training ensembles of low-dimensional pairwise ...
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Chertopolokhov V., Mukhamedov A., Bugriy G. et al., IEEE Access 2026 Vol. 14 P. 14369–14392
This study presents on-the-fly identification and multi-step prediction of nonlinear systems with delayed inputs using a dynamic neural network combined with a smooth projection onto ellipsoids. The projection enforces parameter constraints that guarantee stability, while a Lyapunov–Krasovskii analysis yields computable ultimate error bounds. Riccati-type matrix inequalities are derived, providing an efficient vectorization–projection–devectorization implementation suitable for ...
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Морозов С. В., Calcolo 2026 Vol. 63 No. 2 Article 23
The approximation of tensors in a low-para metric format is a crucial component in many mathematical modelling and data analysis tasks. Among the widely used low-parametric representations, the canonical polyadic (CP) decomposition is known to be very efficient. Nowadays, most algorithms for CP approximation aim to construct the approximation in the Frobenius norm; however, some ...
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Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 Article 18
A B-facet is a lattice -dimensional polytope in the positive octant with a positive normal covector, such that every -dimensional simplex with vertices in it is a B-simplex (i.e., a pyramid of height one with base on a coordinate hyperplane). B-facets were introduced in [2] in the context of the monodromy conjecture. In this paper, we complete the ...
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Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 Article 106192
The Vickrey-Clarke-Groves (VCG) mechanism is one of the most compelling constructs in mechanism design, but the presence of complementary goods creates the possibility of non-core and even zero-revenue outcomes. In this article, we show that joint feasibility constraints on allocations offer a second pathway to ill-behaved outcomes in the VCG mechanism, even when all bidders ...
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Denis Seliutskii, Russian Journal of Mathematical Physics 2025 Vol. 32 No. 2 P. 399–407
In this paper, we find an upper bound for the first Steklov eigenvalue for a surface of revolution with boundary consisting of two spheres of different radii. Moreover, we prove that, in some cases, this boundary is sharp. ...
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Жакупов О. Б., European Journal of Mathematics 2025 Vol. 11 Article 84
We provide examples of smooth three-dimensional Fano complete intersections of degree 2, 4, 6, and 8 that have absolute coregularity 0. Considering the main theorem of Avilov, Loginov, and Przyjalkowski (CNTP 18:506–577, 2024) on the remaining 101 families of smooth Fano threefolds, our result implies that each family of smooth Fano threefolds has an element of absolute ...
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Gurevich E., Saraev I., Известия РАН. Серия математическая 2026 Т. 90 № 3 С. 19–56
In this paper, we consider a class of gradient-like ows without heteroclinic
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Gonchenko S., Lerman L., Turaev D., Regular and Chaotic Dynamics 2026 Vol. 31 No. 3 P. 349–369
We show that bifurcations of four-dimensional symplectic diffeomorphisms with a quadratic homoclinic tangency to a saddle periodic orbit with real multipliers produce 2-elliptic periodic orbits if the tangency is not partially hyperbolic. We show that a normal form for the rescaled first-return maps near such tangency is given by a four-dimensional symplectic H´enonlike map and study bifurcations of the ...
Added: May 15, 2026
Aleskerov F. T., Khutorskaya O., Stepochkina A. et al., Springer, 2026.
The book contains new models of bibliometric analysis based on centrality measures in network analysis, pattern analysis and stability analysis. A distinctive feature of these centrality measures is that they account for the parameters of vertices and group influence of vertices to a vertex. This reveals specific groups of publications, authors, terms, journals and affiliations ...
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Kuptsov P., Panyushev A., Stankevich N., Chaos 2026 Vol. 36 No. 5 Article 053138
We develop a machine-learning approach to reproduce the behavior of two versions of the van der Pol oscillator exhibiting a subcritical Andronov–Hopf bifurcation, with or without a codimension-2 Bautin point. We construct a neural-network model that functions as a recur rent map and train it on short segments of oscillator trajectories. The results show that, ...
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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. ...
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Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
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the superposition $f\circ h$ is in the Sobolev space $W_2^{1/2}(\mathbb T)$.
We obtain new results on simultaneous improvement of functions by a single
change of variable in relation ...
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Yusupov V., Rakhuba M., Frolov E., , in: CIKM '25: Proceedings of the 34rd ACM International Conference on Information and Knowledge Management.: ACM, 2025. Ch. 1 P. 5469–5473.
In this work, we present a fast and effective Linear approach for updating recommendations in a scalable graph-based recommender system UltraGCN. Solving this task is extremely important to maintain the relevance of the recommendations under the conditions of a large amount of new data and changing user preferences. To address this issue, we adapt the ...
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Yusupov V., Rakhuba M., Frolov E., , in: RecSys '25: Proceedings of the Nineteenth ACM Conference on Recommender Systems.: ACM, 2025. Ch. 1 P. 1217–1221.
Recent studies have demonstrated the potential of hyperbolic geometry for capturing complex patterns from interaction data in recommender systems. In this work, we introduce a novel hyperbolic recommendation model that uses geometrical insights to improve representation learning and increase computational stability at the same time. We reformulate the notion of hyperbolic distances to unlock additional ...
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Grishina E., Gorbunov M., Rakhuba M., , in: Findings of the Association for Computational Linguistics: ACL 2025.: Association for Computational Linguistics, 2025. P. 26937–26949.
Large language models (LLMs) demonstrate impressive results in natural language processing tasks but require a significant amount of computational and memory resources. Structured matrix representations are a promising way for reducing the number of parameters of these models. However, it seems unrealistic to expect that weight matrices of pretrained models can be accurately represented by ...
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Polishchuk A., Varolgunes U., / Series arXiv "math". 2021.
We consider Takahashi's categorical interpretation of the Berglund-Hubsch mirror symmetry conjecture for invertible polynomials in the case of chain polynomials. Our strategy is based on a stronger claim that the relevant categories satisfy a recursion of directed A∞-categories, which may be of independent interest. We give a full proof of this claim on the B-side. On ...
Added: November 28, 2021
Polishchuk A., Lekili Y., / Series arXiv "math". 2021.
For an appropriate choice of a ℤ-grading structure, we prove that the wrapped Fukaya category of the symmetric square of a (k+3)-punctured sphere, i.e. the Weinstein manifold given as the complement of (k+3) generic lines in ℂP2 is quasi-equivalent to the derived category of coherent sheaves on a singular surface Z2,k constructed as the boundary of a toric Landau-Ginzburg model (X2,k,w2,k). We do this ...
Added: November 28, 2021
Pavlov A., Mathematische Zeitschrift 2021 No. 297 P. 223–254
We show that for maximal Cohen–Macaulay modules over the homogeneous coordinate ring of a smooth Calabi–Yau varieties X, the computation of Betti numbers can be reduced to computations of dimensions of certain HomHom spaces in the bounded derived category Db(X). In the simplest case of a smooth elliptic curve E embedded in P2 as a smooth cubic, we get explicit values for Betti ...
Added: October 31, 2020