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In this survey we motivate studies of the invariants from the title. A graph drawing in the plane is called an almost embedding if the images of any two non-adjacent simplices (i.e. vertices or edges) are disjoint. We introduce integer invariants of almost embeddings: winding number, cyclic and triodic Wu numbers. We prove some relations between the invariants. We demonstrate connection of these relations to homology of the deleted product of a graph. We construct almost embeddings realizing some values of these invariants. This paper is accessible to mathematicians not specialized in the area (and to students). All the necessary definitions are recalled. We present some ideas of algebraic and geometric topology in a language accessible to non-topologists. However elementary, this paper is motivated by frontline of research; there are some conjectures and an open problem., Comment: 27 pages, many figures, in Russian. The paper belongs to math.AT because the invariants are special cases of the degree; to math.GT because the most closely related papers are 1805.10237 [math.GT], 2205.01013 [math.GT], and almost embeddings are studied in 2303.14503 (math.CO math.GT), 2008.02523 (math.GT math.AT), 1703.06305 (math.GT), 1904.02404 (math.AT math.GT), 2206.13486 (math.GT math.CO)

In this paper, we consider the simplest version of a linear neural network (LNN). Assuming that for training (constructing an optimal weight matrix $Q$) we have a set of training pairs, i.e. we know the input data \begin{equation} G=\left\{g^{\left(1\right)},g^{\left(2\right)},\cdots,g^{\left(K\right)}\right\}, \end{equation} as well as the correct answers to these input data \begin{equation} H=\left\{h^{\left(1\right)},h^{\left(2\right)},\cdots,h^{\left(K\right)}\right\}. \end{equation} We will study the possibilities of constructing a weight matrix $Q$ of a neural network that will give correct answers to arbitrary input data based on the connection of the specified problem with a system of linear algebraic equations (SLAE). Consider a class of neural networks in which each neuron has only one output signal and performs linear operations. We will show how such LNEs are reduced to SLAEs. Since the questions $G$ and the correct answers $H$ are known to us, the desired weight matrix $Q$ must satisfy the equations \begin{equation} Qg^{\left(k\right)}=h^{\left(k\right)}, k=1,2,\cdots,K. \end{equation} It is required to restore $Q$. In the general case, the matrix $Q$ is rectangular $Q=Q_{MN}=\left\{q_{mn}\right\}$, $m$ is the row number, and $g^{\left(k\right)}\in\mathbb{R}^N$, $h^{\left(k\right)}\in\mathbb{R}^M$. Let $G_{NK}$ be a matrix composed of columns $g^{\left(1\right)}, g^{\left(2\right)},\cdots,g^{\left(k\right)}$, and $H_{MK}$ be a matrix composed of columns $h^{\left(1\right)},h^{\left(2\right)},\cdots,h^{\left(k\right)}$. Then, with respect to $Q_{MN}$, we obtain a matrix SLAE. \begin{equation} Q_{MN}G_{NK}=H_{MK}. \end{equation} This paper will present methods for regularizing the constructed system., Comment: in Russian language

The paper studies a regularization of the quantum (effective) action for a scalar field theory in a general position on a compact smooth Riemannian manifold. As the main method, we propose the use of a special averaging operator, which leads to a quasi-locality and is a natural generalization of a cutoff regularization in the coordinate representation in the case of a curved metric. It is proved that the regularization method is consistent with a process of gluing of manifolds and partition functions, that is, with the transition from submanifolds to the main manifold using an additional functional integration. It is shown that the method extends to other models, and is also consistent with the process of multiplicative renormalization. Additionally, we discuss issues related to the correct introduction of regularization and the locality., Comment: LaTeX, 30 pages, 1 figure. Firstly appeared in Russian, November 15, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-11.html

Practically relevant problems of quadratic optimization often contain multidimensional arrays of variables interconnected by linear constraints, such as equalities and inequalities. The values of each variable depend on its specific meaning and can be binary, integer, discrete, and continuous. These circumstances make it technically difficult to reduce the original problem statement to the QUBO form. The paper identifies and considers three main transformations of the original problem statement, namely, the transition from a multidimensional to a one-dimensional array of variables, the transition in mixed problems to binary variables, and the inclusion of linear constraints in the objective function in the form of quadratic penalties. Convenient formulas for calculations are presented and proven, simplifying the implementation of these transformations. In particular, the formulas for the transition in the problem statement from a multidimensional to a one-dimensional array of variables are based on the use of the Kronecker product of matrices. The considered transformations are illustrated by numerous examples., Comment: 26 pages, 3 figures; in Russian

This paper introduces a novel methodology for modeling stationary shock waves in porous materials, which employs the recently developed moving window technique. The core of this method is the iterative adjustment of the reference frame to the boundary conditions that regulate the entry and exit of Lagrangian particles from a fixed computational domain, which are used to model the flow of a compressible medium. A Godunov-type smoothed particle hydrodynamics (SPH) method with reconstruction of values at the contact is employed for the purposes of modeling. Kernel gradient correction for this method is proposed to enhance the precision of the approximation. The shock Hugoniot of porous copper is calculated, and the structure of the compacting wave and elastic precursor in porous copper at shock amplitude near the yield strength of solid copper is studied., Comment: Accepted in "VANT" (in Russian)

In countries with a growing number of elderly and a shrinking workforce, one of which is Russia, it becomes impossible to maintain a solidary pension system and a need to switch to a more stable funded system appears. This paper analyzes various scenarios of Russia's transition to such a system. This is the first study on the Russian economy in which an Overlapping Generations Model is used to simulate the pension transition. It is demonstrated that in the long term, the transition to a funded system slightly reduces the welfare of pensioners, and during the transition, the situation of pensioners deteriorates strongly. However, it is also important to emphasize that the transition imposes a heavy burden on all generations living during the reform, they are forced to consume less and greatly change their savings, while also often starting to work more. Such conclusions are made concerning average population cohorts, and the results may not be the same for different groups of individuals within these cohorts. In different scenarios, the pension system transition can cause both economic growth and economic recession, as well as a corresponding increase or decrease in wages and consumption., Comment: Comments: 23 pages, in Russian

In this paper, we study a two-dimensional Lorentzian problem on the anti-de Sitter plane. Using methods of geometric control theory and differential geometry, it was possible to construct an orthonormal frame, calculate extremal trajectories, describe the reachable set, construct an optimal synthesis, and describe the Lorentzian distance., Comment: In Russian

Multiple magnetic and kinetic solar wind plasma parameters are used to detect coronal mass ejections (CMEs) as they travel through the heliosphere. There are various interplanetary CME (ICME) catalogues, but due to differences between their ICME identification criteria they can significantly vary. In this paper we analyze Richardson and Cane and CCMC CME Scoreboard ICME catalogues and the SRI RAS solar wind types catalogue, and propose an algorithm of merging them. A unified catalogue is constructed for 2010 to 2022. The resulting catalogue is completed with data from the OMNI database. Analysis of the unified catalogue demonstrated high accuracy when merging events present in multiple catalogues and a tendency of events defined in all three initial catalogues to demonstrate greater duration, speed and geoeffectiveness. The catalog is presented on the SINP MSU Space Weather Exchange website: https://swx.sinp.msu.ru/tools/icme_list.php, Comment: 22 pages, in Russian language, 4 figures

In 1957, Nemytskii proved the following fact: if in a locally compact or in an Abelian connected group there is a neighborhood of the identity in which some identity holds, then it holds in the entire group. The following question was also posed there: Let G be a connected topological group. In some neighborhood of the identity of the group G the identity $x^3=1$ holds. Is it true that then the identity $x^3=1$ holds in the entire group $G$? The same question is posed for the identity $gx^2 = x^2g$, where $g$ is a fixed element of the group. Platonov formulated the following generalized formulation of the Mytselsky problem: for a topological connected group, is it true that if the identity holds in a neighborhood of the identity, then the identity holds everywhere? In this paper, a negative answer to Platonov's question is given, the following theorem is proven: if $n > 1010$ is odd, then there exists a connected topological group in which the identity $x^n=1$ holds in some neighborhood of unity, but not in the entire group., Comment: in russian

It is well known that whenever a class of structures $\mathcal{K}_1$ is interpretable in a class of structures $\mathcal{K}_2$, then the hereditary undecidability of (a fragment of) the theory of $\mathcal{K}_1$ implies the hereditary undecidability of (a suitable fragment of) the theory of $\mathcal{K}_2$. In the present paper, we construct a $\Sigma_1$-interpretation of the class of all finite bipartite graphs in the class of all pairs of equivalence relations on the same finite domain; from this we obtain the hereditary undecidability of the $\Sigma_2$-theory of the second class. Next, we construct a $\Sigma_1$-interpretation of the class of all pairs of equivalence relations on the same finite domain in the class of all pairs consisting of a linear ordering and an equivalence relation on the same finite domain; this gives us the hereditary undecidability of the $\Sigma_2$-theory of the second class. The corresponding results are, in a sense, optimal, since the $\Pi_2$-theories of the classes under consideration are decidable. Keywords: undecidability, elementary theories, prefix fragments, Comment: in Russian language

In this paper we study holomorphically homogeneous model submanifolds CR-type (1, 3) complex space $\mathbb C^4$. One finds moduli space of five-dimensional model surfaces Bloom-Graham type ((2, 1), (3, 1), (4, 1)). It is shown that there exists unique model surface of this type with property of holomorphical homogeneous, which is equivalent to tube surface $\mathcal C$ with affin homogeneous base. One describes and classifies with respect to model surfaces the orbits relative to the group of holomorhical automorphisms of $\mathcal C$, Comment: in Russian language

The paper studies the quantum action for the five-dimensional real $\phi^3$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The explicit form of the first three coefficients for the renormalization constants is presented. The absence of non-local singular contributions and partial results for the fourth correction are discussed., Comment: LaTeX, 20 pages, 5 figures. Firstly appeared in Russian, April 9, 2024, see https://www.pdmi.ras.ru/preprint/2024/24-05.html

This paper presents the experience of developing and utilizing computer simulations for student laboratory assignments in atomic physics, specifically focusing on emission atomic spectra. The fundamental component of each laboratory assignment is a computer simulator of a spectrograph, which displays atomic line spectra on the monitor screen. The simulator operates by converting the wavelength of radiation into an RGB triplet. Calibration of the spectrograph is conducted using the atomic spectrum of mercury. The configuration of setup parameters and experimental conditions is unique to each student conducting the laboratory assignment using the simulator. Individualized parameters, stored in Google Sheets, are transferred to the HTML template of the laboratory assignment via the Google Apps Scripts service. This individualization of simulator parameters serves to encourage students to engage in independent work., Comment: 17 pages, in Russian, 9 figures

The paper discusses an applicability criterion for a cutoff regularization in the coordinate representation in the Euclidean space with a dimension larger than two. It is shown that the set of functions satisfying the criterion is not empty. As an example, an explicit function is presented. It is proved by explicit construction that there are functions satisfying the criterion in a stronger formulation., Comment: LaTeX, 8 pages, 1 figure. Firstly appeared in Russian, March 5, 2024. Compared to the Russian version, some comments and minor corrections have been added. The forgotten imaginary unit in the Fourier transform has also been restored. See https://www.pdmi.ras.ru/preprint/2024/24-04.html

The paper presents various modifications of the Frank-Wolfe algorithm in the equilibrium traffic assignment problem. The Beckman model is used as a model for experiments. In this article, first of all, attention is paid to the choice of the direction of the basic step of the Frank-Wolfe algorithm. Algorithms will be presented: Conjugate Frank-Wolfe (CFW), Bi -conjugate Frank-Wolfe (BFW), Fukushima Frank-Wolfe (FFW). Each modification corresponds to different approaches to the choice of this direction. Some of these modifications are described in previous works of the authors. In this article, following algorithms will be proposed: N-conjugate Frank-Wolfe (NFW), Weighted Fukushima Frank-Wolfe (WFFW). These algorithms are some ideological continuation of the BFW and FFW algorithms. Thus, if the first algorithm used at each iteration the last two directions of the previous iterations to select the next direction conjugate to them, then the proposed algorithm NFW is using more than N previous directions. In the case of Fukushima Frank-Wolfe, the average of several previous directions is taken as the next direction. According to this algorithm, a modification WFFW is proposed, which uses a exponential smoothing from previous directions. Experiments with various modifications were carried out on several datasets representing urban structures and taken from publicly available sources. The relative gap value was taken as the quality metric. The experimental results showed the advantage of algorithms using the previous directions for step selection over the classic Frank-Wolfe algorithm. In addition, an improvement in efficiency was revealed when using more than two conjugate directions. For example, on various datasets, the modification 3FW showed the best convergence. In addition, the proposed modification WFFW often overtook FFW and CFW, although performed worse than NFW., Comment: 14 pages, in Russian language, 8 figures

The paper tests the validity of the critique of the fiscal theory of the price level. A stochastic general equilibrium model with continuous time is constructed. An active fiscal policy and a passive monetary policy have been set. Monetary policy manages the interest rate through the Taylor rule. The stochastic default factor in the special form is introduced. A complete definite system of equations is obtained for the detection of equilibrium. It is asserted that the peculiarities of the approach to modeling are of critical importance for verifying the presence of certain hypotheses and formulating conclusions. The results of this work are in support of the fiscal theory of the price level., Comment: Master Thesis, in Russian. Supervisor: Sergey E. Pekarski

The paper studies the quantum action for the four-dimensional real $\phi^4$-theory in the case of a general formulation using the background field method. The three-loop renormalization is performed with the usage of a cutoff regularization in the coordinate representation. The absence of non-local singular contributions and the correctness of the renormalization $\mathcal{R}$-operation on the example of separate three-loop diagrams are also discussed. The explicit form of the first three coefficients for the renormalization constants and for the $\beta$-function is presented. Consistency with previously known results is shown., Comment: LaTeX, 71 pages, 8 figures. Firstly appeared in Russian, February 6, 2024, see https://www.pdmi.ras.ru/preprint/2024/pr2024.html

This paper presents the experimental results on research of growth processes of GaAs layers on silicon substrates by molecular beam epitaxy. The formation of buffer Si layer in a single growth process has been found to significantly improve the crystalline quality of the GaAs layers formed on its surface, as well as to prevent the formation of anti-phase domains both on offcutted towards the [110] direction and on singular Si(100) substrates. It has been demonstrated that the use of cyclic thermal annealing at temperatures 350-660{\deg}C in the flow of arsenic atoms makes it possible to reduce the number of threading dislocations and increase the smoothness of the GaAs layers surface. At the same time, the article considers possible mechanisms that lead to an improvement in the quality of the surface layers of GaAs. It is shown that the thus obtained GaAs layers of submicron thickness on the singular Si(100) substrates have a mean square value of surface roughness 1.9 nm. The principal possibility of using thin GaAs layers on silicon as templates for forming on them light-emitting semiconductor heterostructures with active area based on self-organizing InAs quantum dots and InGaAs quantum well is presented. They are shown to exhibit photoluminescence at 1.2 um at room temperature., Comment: 18 pages, in Russian language, 6 figures

We study solutions of parabolic equations with a discontinuous hysteresis operator, described by a free interface boundary. It is established that for spatially transverse initial data from the space $W^{2-2/q}_q$ with $q > 3$, there exists a solution in the space $W^{2,1}_q$, where the interface boundary exhibits Holder continuity with an exponent $1/2$. Furthermore for initial data from the space $W^2_\infty$, it is proven that the interface boundary satisfies the Lipschitz condition. It is shown that for non-transversal initial data, solutions with an interface boundary do not exist., Comment: 31 pages, in Russian

For a poset $(P,\leqslant)$ we consider the first-order theory, that is defined by set $P$ and relation $\leqslant$. The problem of undecidability of combinatorial theories attracts significant attention. Recently A. Wires proved the undecidability of the elementary theory of Young lattice and also established the maximal definability property of this theory. The purpose of this article is to obtain the same results for another graded lattice, which has much in common with Young lattice: Young--Fibonacci lattice. As Wires does for Young lattice, for the proof of undecidability we define Arithmetic into this theory., Comment: 20 pages, in Russian

We describe Martin boundary of the path space of $r$-differential version of Young--Fibonacci graph. Also we establish ergodicity of the corresponding measures., Comment: 23 pages, in Russian

This study presents the development of a part-of-speech (POS) tagging model to extract the skeletal structure of sentences using transfer learning with the BERT architecture for token classification. The model, fine-tuned on Russian text, demonstrating its effectiveness. The approach offers potential applications in enhancing natural language processing tasks, such as improving machine translation. Keywords: part of speech tagging, morphological analysis, natural language processing, BERT., Comment: in Russian language. Conference: Automated control systems and information technologies https://asuit.pstu.ru/ Section: IT and automated systems

The study aimed at detecting cartel collusion involved analyzing decisions of the Russian Federal Antimonopoly Service and data on auctions. As a result, a machine learning model was developed that predicts with 91% accuracy the signs of collusion between bidders based on their history after dividing 40 auctions into test and training samples in a 30/70 ratio. Decomposition of the model using the Shepley vector allowed the interpretation of the decision-making process. The behavior of honest companies in auctions was also studied, confirmed by independent simulation validation., Comment: 22 pages, 9 figures. in Russian language

Various technologies, including computer vision models, are employed for the automatic monitoring of manual assembly processes in production. These models detect and classify events such as the presence of components in an assembly area or the connection of components. A major challenge with detection and classification algorithms is their susceptibility to variations in environmental conditions and unpredictable behavior when processing objects that are not included in the training dataset. As it is impractical to add all possible subjects in the training sample, an alternative solution is necessary. This study proposes a model that simultaneously performs classification and anomaly detection, employing metric learning to generate vector representations of images in a multidimensional space, followed by classification using cross-entropy. For experimentation, a dataset of over 327,000 images was prepared. Experiments were conducted with various computer vision model architectures, and the outcomes of each approach were compared., Comment: 19 pages, in Russian

The influence of growth regimes of the silicon capping layer on the optical properties of heterostructures with submonolayer InAs quantum dots embedded in a silicon matrix has been studied. The photoluminescence signal at 1650 nm from submonolayer quantum dots at low temperatures up to 120 K was obtained. It was established that the use of a two-stage method of silicon overgrowing InAs nanoislands makes it possible to increase the photoluminescence intensity by improving the crystalline quality of heterostructures. Analysis of the temperature dependence allowed us to calculate an activation energy for electrons confined in the quantum dots potential well at the level of the thermal energy at room temperature., Comment: 22 pages, in Russian language, 4 figures

The author proposed an elementary derivation of the formula of Yu.V. Nesterenko expansion in continued fraction of a number 2*$\zeta(3)$., Comment: in Russian language

Author-made translation of the book published in Russian in 1982. Chapter 1. Channeling of High-Energy Particles in Crystals. Chapter 2. A Channeled Fast Particle as a 2D (1D) Relativistic Atom. Chapter 3. The Foundations of the Theory of $\gamma$-quanta Emission in Crystals under Channeling Conditions. Chapter 4. The Influence of $\gamma$-quanta Refraction and Diffraction on Angular and Spectral Characteristics of Radiation Produced by Particles in Crystals. Chapter 5. Classical Theory of Radiation Formation by Particles in a Medium. Chapter 6. Scattering and Radiation in Crystals Exposed to Variable Fields. Chapter 7. Interference of Independently Generated Beams of $\gamma$-quanta. Chapter 8. Theory of Measurement of Nuclear Reaction Times Using Shadow Effect. Yield of Reactions Induced by High-energy Particles in Crystals. Chapter 9. Spin Rotation and Radiative Self-Polarization of Particles Moving in Bent Crystals. Chapter 10. The Influence of Radiative Transitions on Channeling of Charged Particles in Crystals., Comment: Author-made translation of the book published in Russian in 1982, 232 pages, 10 chapters

In this study, we investigate the contribution of millisecond pulsars (MSPs) to the gamma-ray excess observed in the Galactic Center by analyzing data from high-resolution direct N-body simulations of six globular clusters (GCs) that experience close encounters with the nuclear star cluster. Using the {\phi}-GPU code, we tracked the orbits of individual neutron stars (NSs) formed during the simulations, assuming a fraction of these NSs evolve into MSPs. Our model includes state-of-the-art single stellar evolution code including prescription for neutron star formation. We estimated the gamma-ray flux from these MSPs, considering known values for their gamma-ray emission. Our results show that MSPs originating from the six modeled GCs contribute a small but non-negligible fraction of the observed gamma-ray flux. This finding suggests that the actual gamma-ray flux from MSPs could be much higher when considering the entire population of GCs, potentially significantly contributing to the gamma-ray excess. This study highlights the importance of considering MSPs in the Galactic Center, originating from nearby globular clusters, as a potential source of the observed gamma-ray excess. Future work will involve more sophisticated simulations incorporating binary stellar evolution and comparing the fraction of MSPs in observed GCs to refine our models and improve the accuracy of our estimates., Comment: in Russian language

The effect of violation of $T$-invariance, provided that $P$-parity is preserved, is given by the total cross section of the interaction of a vector-polarized particle with a tensor-polarized target. A formalism for calculating this effect developed previously and based on the spin-dependent Glauber theory of elastic $pd$ scattering is used here to calculate the effect under discussion in the range of collision energies corresponding to the invariant mass of the $pN$ system $\sqrt{s_{pN}}=5$--$30$ GeV. The spin-dependent amplitudes of elastic $pN$ scattering required for this calculation are taken from existing phenomenological models for $pN$ scattering in the energy region considered., Comment: 8 pages, 1 figure;in Russian, presented at Scientific session of Nuclear Physics section of Physics Division of RAS, submitted to PEPAN

The article contributes to the theory of infinitesimal bendings of smooth surfaces in Euclidean 3-space. We derive a certain linear differential equation of the first order, which previously did not appear in the literature and which is satisfied by any Darboux rotation field of a smooth surface. We show that, for some surfaces, this additional equation is functionally independent of the three standard equations that the Darboux rotation field satisfies (and by which it is determined). As a consequence of this additional equation, we prove the maximum principle for the components of the Darboux rotation field for disk-homeomorphic surfaces with strictly positive Gaussian curvature., Comment: 11 pages, in Russian

We discuss the stochastic interpretation of a control system determined by a system of differential equations on a tree. For example, such a system on a finite tree arises after replacing the coefficients of the equation on an interval with stochastic processes in discrete time and with finitely many states. The countable number of states will correspond to a more complicated and, at the same time, more general case of an infinite tree, which is under consideration., Comment: 5 pages, in Russian language