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Normal Forms, Inner Products, and Maslov Indices of General Multimode Squeezings
Mathematical notes. 2014. Vol. 95. No. 5. P. 721–737.
Chebotarev A., Tlyachev T. V.
In this paper, we present a purely algebraic construction of the normal factorization of multimode squeezed states and calculate their inner products. This procedure allows one to orthonormalize bases generated by squeezed states. We calculate several correct representations of the normalizing constant for the normal factorization, discuss an analog of the Maslov index for squeezed states, and show that the Jordan decomposition is a useful mathematical tool for problems with degenerate Hamiltonians. As an application of this theory, we consider a nontrivial class of squeezing problems which are solvable in any dimension.
Publication based on the results of:
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
are found. One of the main tools is an improved asymptotics of sparkling saddle connections that
occur when a separatrix loop of a hyperbolic saddle breaks. Another main tool is a new topological
invariant of two arithmetic progressions, both perturbed and unperturbed, on the ...
Added: May 26, 2026
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| ...
Added: May 25, 2026
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 ...
Added: May 23, 2026
Kibkalo Vladislav, Chertopolokhov V., Mukhamedov A. 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 ...
Added: May 22, 2026
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 ...
Added: May 22, 2026
Селянин Ф. И., Journal of Dynamical and Control Systems 2026 Vol. 32 No. 2 P. 1–16
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 ...
Added: May 21, 2026
Ausubel L., Baranov O., Journal of Economic Theory 2026 Vol. 235 No. 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 ...
Added: May 20, 2026
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. ...
Added: May 19, 2026
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 ...
Added: May 18, 2026
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
intersections, dened on closed manifolds of dimension four. We show that for
such ows, the problem of complete topological classication can be reduced to
the combinatorial problem of distinguishing special framed graphs describing
the mutual arrangement of invariant manifolds and the action of the ow on a
wandering ...
Added: May 18, 2026
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 ...
Added: May 15, 2026
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, ...
Added: May 15, 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
Lebedev V., Journal of Mathematical Analysis and Applications 2026 Vol. 563 No. 2 Article 130787
It is known that for every continuous real-valued
function $f$ on the circle $\mathbb T=\mathbb R/2\pi\mathbb Z$ there exists a
change of variable, i.e., a self-homeomorphism $h$ of $\mathbb T$, such that
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 ...
Added: May 14, 2026
Blokh A., Oversteegen L., Selinger N. et al., Arnold Mathematical Journal 2026 Vol. 12 No. 1 P. 60–110
We describe a model for the boundary of the connectedness locus of the parameter space of cubic symmetric polynomials. We show that there exists a monotone continuous function from the connectedness locus to the model which is a homeomorphism if the former is locally connected. ...
Added: May 13, 2026
Vasilev A., Kapitanov A., Roman Solovyev et al., PeerJ Computer Science 2026 Vol. 12 Article 3724
This article introduces MinMAE, a novel activation calibration method for Post-Training Quantization (PTQ) that significantly reduces accuracy loss in Convolutional Neural Networks (CNN). Motivated by the need for high-fidelity quantization without costly retraining, MinMAE directly minimizes the Mean Absolute Error (MAE) between original and dequantized activations, making it robust to outliers that degrade standard methods. ...
Added: May 3, 2026
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 ...
Added: October 3, 2025
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 ...
Added: October 3, 2025
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 ...
Added: September 4, 2025
Galkina A. N., Экономика устойчивого развития 2023 № 4(56) С. 278–282
Purpose: the purpose of the article is on the basis of existing methods for assessing the achievement of integral indicators of the Sustainable Development Goals (SDGs) to develop a modified index considering the digitalization level, to conduct testing in relation to nuclear power development projects as one of global initiatives areas to achieve the SDGs, ...
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Lekili Y., Polishchuk A., Advances in Mathematics 2023 Vol. 418 Article 108942
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 ...
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Melville A. Y., Мальгин А. В., Mironyuk M. et al., Полис. Политические исследования 2023 № 5 С. 153–171
In recent decades, the expanding volume, diversity and coverage of data have created new or have transformed existing areas of research. They have also turned data into a key element of politics today. In this context, the status of empirical research that became the political science mainstream at the turn of the 20th - 21st ...
Added: September 29, 2023