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Аппроксимация функций с помощью нейронных сетей и нечетких систем
Проблемы управления. 2018. № 1. С. 21–29.
Shvedov A. S.
This paper surveys some parts of approximation theory for functions of one and several real variables. Approximation of functions by algebraic polynomials is a classical theory. The paper contains some results from this theory. First results on approximation of functions by neural networks and fuzzy systems have appeared as responses on practical requirements. It was necessary to know is it possible to approximate an arbitrary continuous function by such aggregates. Later, these fields were developed like the theory of approximation of functions by algebraic polynomials. In this paper we consider some results on approximation of functions by neural networks and fuzzy systems.
Taletskii D., / Series arXiv "math". 2026.
A vertex subset of a graph is called a \textit{distance-$k$ independent set} if the distance between any two of its distinct vertices is at least $k + 1$. For all $n,k \geq 1$, we determine the minimum possible number of inclusion-wise maximal distance-$k$ independent sets among all $n$-vertex trees. It equals~$n$ if $n \leq k ...
Added: May 1, 2026
Ovcharenko M., / Series arXiv "math". 2026.
We introduce an explicit class of tempered Laurent polynomials in the sense of Villegas and Doran--Kerr in n⩽4 variables including all Landau--Ginzburg models for smooth Fano threefolds with very ample anticanonical class. We check that it contains Landau--Ginzburg models for various Fano fourfolds which are complete intersections in smooth toric varieties and Grassmannians of planes, ...
Added: April 30, 2026
Ролинский С. О., Dvoynikova A., В кн.: Альманах научных работ молодых ученых Университета ИТМОТ. 2.: Университет ИТМО, 2022. С. 336–340.
В работе рассмотрены основные существующие подходы к автоматическому распознаванию речи, а также проводится сравнительный анализ открытых компьютерных систем распознавания речи. Для экспериментальных исследований эффективности работы рассматриваемых систем используется речевой корпус LibriSpeech. ...
Added: April 24, 2026
Dvoynikova A., Садикова А. А., В кн.: Сборник трудов X Конгресса молодых ученыхТ. 1.: Университет ИТМО, 2021.
В работе рассматривается применение различных планировщиков обучения (англ. scheduler) нейронных сетей для задачи текстонезависимой верификации дикторов. Для экспериментальных исследований использовалась база данных VoxCeleb1, которая содержит в себе различные речевые высказывания 1211 дикторов. В работе проводился анализ влияния различных планировщиков обучения нейронных сетей, представленных в библиотеке PyTorch языка программирования Python, а также 2 алгоритма планировщика, представленных ...
Added: April 24, 2026
Zlotnik Alexander, / Series arXiv "math". 2026. No. 2602.03481v1.
We deal with the global in time weak solutions to the 1D compressible Navier-Stokes system of equations for large discontinuous initial data and nonhomogeneous boundary conditions of three standard types. We prove the Lipschitz-type continuous dependence of the solution $(\eta,u,\theta)$, in a norm slightly stronger than $L^{2,\infty}(Q)\times L^2(Q)\times L^2(Q)$, on the initial data $(\eta^0,u^0,e^0)$ in a ...
Added: April 18, 2026
Efremov A., Portnoy S., Волошин А. Д., Первая миля 2025 № 8 С. 20–28
Выполнен комплексный обзор методов машинного обучения (ML), применяемых для повышения устойчивости сигнала к помехам в каналах связи. Бурное развитие поколений беспроводной связи, активная разработка концепции 6G предъявляют высокие требования к задержке, скорости и надежности передачи данных. Традиционные подходы к защите от помех, основанные на строгих аналитических моделях, зачастую не справляются с хаотичной природой плотных гетерогенных ...
Added: April 4, 2026
Medvedev V., / Series arXiv "math". 2026.
We investigate the interplay between the dimension of the space of static potentials and the geometric and topological structure of the underlying static three-manifold. A partial classification of boundaryless static manifolds is obtained in terms of this dimension. We also treat the case of static manifolds with boundary. In particular, we prove that if a ...
Added: April 3, 2026
Gabdullin N., Androsov I., / Series Computer Science "arxiv.org". 2026.
Label prediction in neural networks (NNs) has O(n) complexity proportional to the number of classes. This holds true for classification using fully connected layers and cosine similarity with some set of class prototypes. In this paper we show that if NN latent space (LS) geometry is known and possesses specific properties, label prediction complexity can ...
Added: April 2, 2026
Kolesnikov A., / Series arXiv "math". 2025.
We study Blaschke--Santal{ó}-type inequalities for N>=2 sets (functions) and a special class of cost functions. In particular, we prove new results about reduction of the maximization problem for the Blaschke--Santal{ó}-type functional to homogeneous case (functional inequalities on the sphere) and extend the symmetrization argument to the case of N>2 sets.
We also discuss links to the ...
Added: February 13, 2026
Sorokin K., Beketov M., Онучин А. et al., / arxiv.org. Серия cs.SI "Social and Information Networks ". 2025.
Community detection in complex networks is a fundamental problem, open to new approaches in various scientific settings. We introduce a novel community detection method, based on Ricci flow on graphs. Our technique iteratively updates edge weights (their metric lengths) according to their (combinatorial) Foster version of Ricci curvature computed from effective resistance distance between the ...
Added: January 15, 2026
Gaianov N., Parusnikova A., / Cornell University. Серия math "arxiv.org". 2025.
An algebraic q-difference equation is considered. A sufficient condition for the existence of a formal power-logarithmic expansion of a solution to such an equation in the neighborhood of zero is proposed. An example of applying this sufficient condition for constructing a formal expansion of a solution to a certain q-difference analogue of the fifth Painlevé equation ...
Added: December 25, 2025
Popov V., / Series arXiv "math". 2025. No. 2502.01539.
We prove that the variety of flexes of algebraic curves
of degree 3 in the projective plane is an ideal theoretic complete
intersection in the product of a two-dimensional and a nine-dimensional projective spaces. ...
Added: December 16, 2025
Gnetov F., Konakov V., / Series arXiv "math". 2025. No. 2512.04667.
We establish a central limit theorem, a local limit theorem, and a law of large numbers for a natural
random walk on a symmetric space M of non-compact type and rank one. This class of spaces, which
includes the complex and quaternionic hyperbolic spaces and the Cayley hyperbolic plane, generalizes
the real hyperbolic space Hn. Our approach introduces ...
Added: December 5, 2025
Kazakov A., Koryakin V., Safonov K. et al., / Series arXiv "math". 2025.
The Lorenz attractor is the first example of a robustly chaotic non-hyperbolic attractor. Each orbit of such an attractor has a positive top Lyapunov exponent, and this property persists under small perturbations despite possible bifurcations of the attractor. In this paper, we study the boundary of the Lorenz attractor existence region in the Shimizu-Morioka model. ...
Added: December 4, 2025
Bitter I., Konakov V., / Cornell University. Серия arXiv "math". 2025. № 2505.24548.
В работе приводится обобщение локальной предельной теоремы о сходимости неоднородных цепей Маркова к диффузионному пределу на случай, когда соответ- ствующие коэффициенты процессов удовлетворяют слабым условиям регулярности и совпадают лишь асимптотически. В частности, рассматриваемые нами коэффици- енты сноса могут быть неограниченными с не более чем линейным ростом, а оценки отражают перенос терминального состояния неограниченным трендом через ...
Added: December 3, 2025
Bogomolov F. A., Schrandt S., / Series arXiv "math". 2025.
We discuss phenomena of stabilization for direct images of line bundles over projective curves mapping onto the projective line, for maps of sufficiently big degree. ...
Added: December 1, 2025
Deviatov R., Baek S., / Series arXiv "math". 2025.
The torsion index of split simple groups has been extensively studied, notably by Totaro, who calculated the torsion indexes of the spin groups and $E_{8}$ in [5] and [6], respectively. The aim of this paper is to provide upper bounds for the torsion index of half-spin groups, the only remaining case in the calculation of ...
Added: December 1, 2025
Hessian-based lightweight neural network for brain vessel segmentation on a minimal training dataset
Меньшиков И. А., Бернадотт А. К., Elvimov N. S., / Series arXie "Statistical mechanics". 2025.
Accurate segmentation of blood vessels in brain magnetic resonance angiography (MRA) is essential for successful surgical procedures, such as aneurysm repair or bypass surgery. Currently, annotation is primarily performed through manual segmentation or classical methods, such as the Frangi filter, which often lack sufficient accuracy. Neural networks have emerged as powerful tools for medical image ...
Added: December 1, 2025
Prokhorov Y., / Series arXiv "math". 2025.
A $\mathbf{Q}$-conic bundle is a contraction $f: X\to Z$ of a three-dimensional algebraic variety $X$ to a surface~$Z$ such that the variety~$X$ has only terminal $\mathbf{Q}$-factorial singularities, the anticanonical divisor $-K_X$ is~$f$-ample, and $\uprho(X/Z)=1$. We provide an algorithm to transform a $\mathbf{Q}$-conic bundle to its standard form. ...
Added: December 1, 2025
Amerik E., Verbitsky M., Soldatenkov A., / Series arXiv "math". 2025.
Wierzba and Wisniewski proved that in dimension 4, every bimeromorphic map of hyperkahler manifolds is represented as a composition of Mukai flops. Hu and Yau conjectured that this result can be generalized to arbitrary dimension. They defined ``Mukai's elementary transformation'' as the blow-up of a subvariety ruled by complex projective spaces, composed with the contraction ...
Added: December 1, 2025
Kuznetsova A., / Series arXiv "math". 2025.
We study birational automorphisms of algebraic varieties of bounded growth, i.e. such that the norms of the inverse images ${(f^n)}^* \colon \mathrm{NS}(X)\to \mathrm{NS}(X)$ of the powers of the automorphism $f\in\mathrm{Bir}(X)$ are bounded above for $n\geqslant 0$. We prove that some power of an infinite order automorphism of a variety $X$ with such property factors either ...
Added: December 1, 2025
Cantat S., Amerik E., / Series arXiv "math". 2025.
Westudyparabolicautomorphismsofirreducibleholomorphi- cally symplectic manifolds with a lagrangian fibration. Such automorphisms are (possibly up to taking a power) fiberwise translations on smooth fibers, and their orbits in a general fiber are dense ([1]). We provide a simple proof that the associated Betti map is of maximal rank, in particular, the set of fibers where the induced ...
Added: December 1, 2025
Dzhanashia K., Aleksandr Fedosov, Oleg Evsutin, Sensors 2025 Vol. 25 No. 23 Article 7726
Using an attack-simulation module is a well-recognized approach to improving the robustness of end-to-end neural-network-based data-hiding schemes. However, most proposed attack simulators are limited in the types of attacks they cover, usually handling only a basic set of digital transformations. Real, in-demand use cases for data-hiding methods may involve modifications that cannot be modeled by ...
Added: November 28, 2025
O.A. Goryunov, Maslennikov O. V., Kiselev M. V. et al., Chaos, Solitons and Fractals 2026 Vol. 203 Article 117663
Training complex, biologically plausible Spiking Neural Networks (SNNs) with local learning rules is a significant challenge for theoretical analysis. Here we address this problem by developing a comprehensive analytical theory for the learning dynamics of CoLaNET, a recently proposed columnar SNN. In particular, we consider a simplified model that captures the core algorithmic logic of ...
Added: November 28, 2025