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Cтатистические веса и процедура слияния для рациональной семивершинной SOS модели
Записки научных семинаров ПОМИ РАН. 2023. Т. 520. С. 17–49.
Антоненко П. В., Валиневич П. А.
We consider seven-vertex two-dimensional integrable statistical model. With the help of intertwining vector method we construct its counterpart integrable model of SOS type. More general models of both types are constructed by means of fusion procedure. For SOS models we calculate the Boltzmann weights in terms of terminating hypergeometric series 9F8. Then using the similarity transformation for R-operators we construct a new family of vertex models containing the 11-vertex model as the simplest representative. For this new set of models the vertex-SOS correspondence is constructed: we find the intertwining vectors, show that they do not depend on spectral parameter and the SOS statistical weights are similar to those obtained from the 7-vertex model.
Qian X., Deng Y., Shchur L. et al., Physica A: Statistical Mechanics and its Applications 2026 Vol. 696 P. 1–13
We perform a Monte Carlo analysis of the Ising model on many three-dimensional lattices. By means of finite-size scaling we obtain the critical points and determine the scaling dimensions. As expected, the critical exponents agree with the three-dimensional Ising universality class for all models. The irrelevant field, as revealed by the correction-to-scaling amplitudes, appears to ...
Added: May 24, 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
Melentiev P. N., Калмыков А. С., Гритченко А. С. et al., Успехи физических наук 2024 Т. 194 № 11 С. 1130–1145
Представлен краткий обзор достигнутого уровня оптических методов детектирования единичных молекул в биомедицинских приложениях. Показано, что регистрация флуоресценции единичных молекул красителей, ковалентно связанных с антителами (биомолекулами), совместно с использованием современных методов нанофотоники может быть применена для решения различных задач в биологии и медицине: визуализации биомолекул, токсинов, вирусных частиц, определения ультранизких концентраций аналитов напрямую во взятой пробе, ...
Added: May 21, 2026
Antsiferov P.S., Stepanov L.V., Matiukhin N. D., Review of Scientific Instruments 2025 Vol. 96 No. 12 Article 123506
The article presents the discharge plasma based source of extreme ultraviolet (EUV) radiation. The discharge circuit has been driven by means of stripe line storage with working voltage 10.5 kV. The main feature of the proposed source is that plasma electrons acquire the energy, necessary for the production of multiply charged ions with ionization potentials ...
Added: May 20, 2026
Анциферов П. С., Степанов Л. В., Матюхин Н. Д., Оптика и спектроскопия 2026 Т. 134 № 2 С. 214–218
Сообщено о разработке системы регистрации спектров на ПЗС-линейке для уникального ВУФ спектрометра, построенного на основе сферической дифракционной решетки с радиусом 6.65 m. Была использована линейка HAMAMATSU S11156-2048-02, которая устанавливалась по касательной к окружности Роуланда с возможностью механического перемещения для сканирования спектра. Были получены спектрограммы в диапазоне длин волн 2130-2270 Angstrem. Описана методика сшивки регистрируемых спектральных ...
Added: May 20, 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
Shipilov F., Barnyakov A., Ivanov A. et al., / Series Physics "arxiv.org". 2026.
A fast simulation of the detector response is a vital task in high-energy physics (HEP). Traditional Monte-Carlo methods form the backbone of modern particle physics simulation software but are computationally expensive. We present a machine-learning-based approach to fast simulation of the Focusing Aerogel Ring Imaging Cherenkov (FARICH) detector response. Given a particle track and momentum, ...
Added: May 19, 2026
Malinovsky A. M., Пилипенко С. В., Mikhalchenko A. O. et al., Astronomy Reports 2026 Vol. 70 P. 1–6
Radiation from rotational transitions of CO molecules in distant galaxies creates a chaotic background with an intensity reaching 1000 Jy/sr at a wavelength of approximately 1 mm. This background will pose a serious problem, when measuring spectral distortions of the cosmic microwave background, in particular, the mu-distortion, which presumably has an intensity of less than ...
Added: May 19, 2026
Kaveev A. K., Fedorov V. V., Pavlov A. V. et al., Journal of Materials Chemistry C 2026 Vol. 14 No. 7 P. 2697–2705
Bismuth nanostructures represent a promising material platform for semiconductor nanooptoelectronics and colorimetry owing to the multi-colored light reflection and quantum confinement. In this work, we study the photoluminescent properties of bismuth nanostructures grown using molecular beam epitaxy on the planar CaF2/Si(111) surface. We demonstrate the different surface morphologies of Bi, ranging from planar films obtained ...
Added: May 19, 2026
Pavlova T., V.M. Shevlyuga (Шевлюга В. М., Applied Surface Science 2026 Vol. 736 P. 166813–166813
The objective of miniaturizing doped areas in silicon, with the ultimate goal of achieving atomic-precision doping, requires a fundamental understanding of the dopant incorporation process at the atomic level. We present a combined scanning tunneling microscopy (STM) and density functional theory (DFT) investigation of single phosphorus atom incorporation into the Si(100) surface. Phosphorus was supplied ...
Added: May 19, 2026
Pasternak D., Romshin A., Khmelnitsky Р. et al., Carbon 2026 Vol. 256 Article 121655
A single-photon source (SPS) is a key component required for quantum communication devices. We report the
discovery of bright diamond-based SPS created by nature. It is shown that narrow (≤2 nm) lines observed in the
500-800 nm range in photoluminescence (PL) spectra of the surface layer of untreated Yakut diamonds rich in
nitrogen and hydrogen are linked to ...
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
Alfimov M., Kurakin A., Nuclear Physics B 2024 Vol. 998 Article 116418
We present the way to continue the bosonic Thirring model or betagamma-system with quartic interaction to Minkowski signature, based on the symmetries of this model. It is shown that the considered Minkowski version of the model is one-loop renormalizable. Based on this, we find the amplitudes of the scattering of the excitations corresponding to the ...
Added: December 26, 2023
Povolotsky A. M., Pyatov P. N., Tribe R. et al., Annales de l'institut Henri Poincare (B) Probability and Statistics 2025 Vol. 61 No. 2 P. 967–1020
Many continuous reaction-diffusion models on Z (annihilating or coalescing random walks, exclusion processes, voter
models) admit a rich set of Markov duality functions which determine the single time distribution. A common feature of these models is that their generators are given by sums of two-site idempotent operators. In this paper, we classify all continuous time Markov ...
Added: December 20, 2023
Vasilyev M, Zabrodin A., Zotov A., Journal of Physics A: Mathematical and Theoretical 2020 Vol. 53 No. 49 Article 494002
We extend duality between the quantum integrable Gaudin models with boundary and the classical Calogero-Moser systems associated with root systems of classical Lie algebras B-N, C-N, D-N to the case of supersymmetric gl(m|n) Gaudin models with m + n = 2. Namely, we show that the spectra of quantum Hamiltonians for all such magnets being ...
Added: September 7, 2021
Bychkov B., Kazakov A., Talalaev D., Symmetry, Integrability and Geometry: Methods and Applications (SIGMA) 2021 Vol. 17 Article 35
We explore several types of functional relations on the family of multivariate Tutte polynomials: the Biggs formula and the star-triangle (Y−ΔY−Δ) transformation at the critical point n=2n=2. We deduce the theorem of Matiyasevich and its inverse from the Biggs formula, and we apply this relation to construct the recursion on the parameter nn. We provide two different ...
Added: July 7, 2021
Levin A., Olshanetsky M., Zotov A., Journal of Physics A: Mathematical and Theoretical 2016 Vol. 49 No. 1 P. 14003–14021
We consider Yang–Baxter equations arising from its associative analog and study the corresponding exchange relations. They generate finite-dimensional quantum algebras which have the form of coupled &${\rm{GL}}(N)$; Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter–Belavin quantum R-matrix to the case &${\rm{Mat}}{(N,{\mathbb{C}})}^{\otimes 2}\otimes {\rm{Mat}}{(M,{\mathbb{C}})}^{\otimes 2}.$; It can be viewed as symmetric ...
Added: April 13, 2016
Levin A., Olshanetsky M., Zotov A., / Series math "arxiv.org". 2015.
We consider Yang-Baxter equations arising from its associative analog and study corresponding exchange relations. They generate finite-dimensional quantum algebras which have form of coupled GL(N) Sklyanin elliptic algebras. Then we proceed to a natural generalization of the Baxter-Belavin quantum R-matrix to the case Mat(N, C) ⊗ Mat(N, C) ⊗Mat(M, C) ⊗ Mat(M, C) . It can be ...
Added: November 19, 2015
A.I. Zobnin, Mathematical Models and Computer Simulations 2014 Vol. 26 No. 11 P. 51–56
Abstract. Associative Yang-Baxter equation arises in different areas of algebra, e.g.,
when studying double quadratic Poisson brackets, non-abelian quadratic Poisson brack ets, or associative algebras with cyclic 2-cocycle (anti-Frobenius algebras). Precisely,
faithful representations of anti-Frobenius algebras (up to isomorphism) are in one-to-one
correspondence with skew-symmetric solutions of associative Yang-Baxter equation (up
to equivalence). Following the work of Odesskii, Rubtsov and ...
Added: October 1, 2014