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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.
Aleksei Samarin, Nazarenko A., Nazarenko D. et al., Machine Learning and Knowledge Extraction 2026 Vol. 8 No. 10 Article 330
Automated microscopic image analysis is essential for quantitative microbiology, yet manual acquisition and generic recognition models struggle with morphological variability and scene artifacts. We address both ends of this pipeline. First, we present a low-cost, open-source acquisition system, based on an Arduino UNO R3 microcontroller and NEMA 17 stepper motors, that automates focusing, magnification, and ...
Added: October 14, 2026
Parkhomenko V., Kulikova S., Buzmakov A. V., Lobachevskii Journal of Mathematics 2026 Vol. 47 No. 6 P. 2979–2992
The stability of formal concepts and its generalization as robustness are considered in the paper. We use an approximation of stability in the form of Δ-measure for fast calculations. A computationally efficient method for calculating robustness based on subcontexts is presented. We also present a new method to analytically evaluate the number of preimages for ...
Added: October 14, 2026
Kuznetsov A. P., Sedova Y. V., Sataev I. R. et al., Mathematics and Computers in Simulation 2027 Vol. 2 P. 574–592
Universal bifurcation structures on the parameter plane of nonlinear systems, known as shrimps, are discussed. An overview of numerous examples from various fields of science is given. Shrimps are typical for both maps of different dimensions and flows. The varieties of shrimp are discussed and relevant examples are given. The similarity property on the parameter ...
Added: October 14, 2026
Dmitriev A., Kornilov V., Batienkov R., Lecture Notes in Civil Engineering 2026 Vol. 886 P. 249–255
Numerous studies have provided compelling evidence that the probability distribution of avalanche sizes follows a power law, and that 1/f noise is present in the stochastic dynamics of landslides. We present a theoretical explanation of these phenomena within the framework of self-organized criticality theory, proposing a discrete-time model in the form of a sandpile cellular ...
Added: October 13, 2026
Dmitriev A., Shulman I., Lebedev A., Studies in Computational Intelligence 2026 Vol. 1265 P. 266–273
A discrete-time model is presented for the self-organization of the X/Twitter social network to the edge of a phase transition, characterized by avalanche-like propagation of information in the network. The model is based on the analogy between the critical dynamics of the X social network and sandpile cellular automata with Manna rule on the Chung-Lu ...
Added: October 13, 2026
Arutyunov K., Kharitonov I. A., Petrosyants K. O., JETP Letters 2026 Vol. 124 No. 6 P. 1–16
Superconducting properties of metallic micro- and nanowires can be entirely different from those of bulk superconductors. Of particular interest is the nonequilibrium current-induced state of a quasi-one-dimensional superconducting channel. The most interesting phenomenon here is the stepped I–V characteristic, explained by a process known as phase slip center activation. If the origin of such step-like ...
Added: October 13, 2026
Makarov D. M., Kalikin N., Fashchevsky K. A. et al., Electrochimica Acta 2026 Vol. 579 Article 150159
Machine learning (ML) has become a powerful tool for accelerating the development of carbon-based supercapacitors;
however, most published models assume that a single predictive framework can describe both conventional
porous carbons and hybrid carbon electrodes. Here, we test this assumption using a comprehensive
benchmark dataset and an extended literature-curated dataset enriched with synthesis- and electrolyte-related
descriptors. Three ML algorithms ...
Added: October 13, 2026
Gusein-Zade S., Campillo A., Delgado F., Mathematische Zeitschrift 2026 Vol. 314 No. 1 P. 1–22
For a subfield $\K$ of the field $\C$ of complex numbers, we consider curve and divisorial valuations on the algebra $\K[[x,y]]$ of formal power series in two variables with the coefficients in $\K$. We compute the semigroup Poincar\'e series and the classical Poincar\'e series of a (discrete, rank one) valuation on it. ...
Added: October 13, 2026
Махлуф М., Ozhegov R., Elezov M. et al., Фотоника 2026 Vol. 20 No. 6 P. 414–423
This paper compares the ranging precision of direct time-of-flight (dToF) and non-line-of-sight (NLOS) LiDAR architectures, both using a superconducting nanowire single-photon detector (SNSPD). Both systems operate at 1550 nm with a 50 ps pulsed laser and time-correlated single-photon counting (TCSPC). The dToF configuration achieved approximately 100 µm precision at 10 m, while the NLOS configuration achieved 500 µm precision for ...
Added: October 12, 2026
Pyatov P. N., Pivovarov P. A., / Series math "arxiv.org". 2026. No. 2609.06274.
We investigate a special ansats that allows for an iterative solution of the constant Yang-Baxter equation. Testing this ansatz, we construct four sequences of the constant R-matrices. In each sequence the R-matrices act on the tensor squares of vector spaces of linearly growing dimensions. Each R-matrix also depends on a single complex parameter.
By analyzing the ...
Added: September 24, 2026
Bychkov A., Nekrasov B., Physical Review D - Particles, Fields, Gravitation and Cosmology 2026 Vol. 113 No. 6 Article 066007
We continue to explore the previously suggested dual regime of Yang-Baxter (YB) deformed $\OO(2N)$ sigma models, which is a new one-parametric deformation of the $\OO(2N)$ model. It can be obtained from the conventional YB deformed $\OO(2N+2)$ sigma model by freezing two isometries. The scattering matrix in the non-deformed $\OO(n)$ model is known coincide with the ...
Added: October 14, 2025
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