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Замечания о дискретизации интегральных норм функций по значениям в точках
Труды Математического института им. В.А. Стеклова РАН. 2022. Т. 319. С. 202–212.
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
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
Petrov I., Автоматика и телемеханика 2026 № 6 С. 82–118
Системам связанных агентов и сетевому управлению посвящено большое число отечественных и зарубежных исследований. Исторически, наибольший интерес в теории управления возникал к усредняющим системам и, в частности, к задаче консенсуса. Однако сетевое взаимодействие может характеризоваться более специфическими функциями, отражающими зависимость от действий соседей по сети, что особенно явно проявляется в моделях стратегического взаимодействия на сети, которое ...
Added: May 12, 2026
М.: ООО «Макс Пресс», 2026.
В настоящем сборнике представлены тезисы докладов участников семинара "Интеграция основного и дополнительного физико-математического образования", проходившего 11 февраля 2026 года в ГБОУ Школа №2007 ФМШ г. москвы, а также другие публикации, посвящённые вопросам дополнительного физико-математического образования. ...
Added: May 11, 2026
Khestanov R., Suvalko A., Социологическое обозрение 2025 Т. 24 № 2 С. 164–189
The article examines the genesis of the concept of novelty and argues that modern difficulties in defining and identifying the new are a symptom of a semantic crisis, which is based on the loss of strategic normativity of novelty in modern culture. Three historical-semantic models of novelty are identified and analyzed: cyclical (characteristic of prehistoric ...
Added: June 29, 2025
Krichever I., A. Zabrodin, Physica D: Nonlinear Phenomena 2023 Vol. 453 Article 133827
We introduce a new integrable hierarchy of nonlinear differential-difference equations which is a subhierarchy of the 2D Toda lattice defined by imposing a constraint to the Lax operators of the latter. The 2D Toda lattice with the constraint can be regarded as a discretization of the BKP hierarchy. We construct its algebraic-geometrical solutions in terms ...
Added: November 30, 2023
Tikhonov E., Sneps-Sneppe M., International Journal of Open Information Technologies 2019 Vol. 7 No. 7 P. 13–26
The article introduces the theoretical foundations of the modern method of storing, transmitting and processing signals: digital processing. It’s a way to use relatively small number of values instead of continuous real signal.
For example, when transmitting information in telephony, speech is concentrated in the bandwidth up to 4 kHz. But we need doubled frequency 8 ...
Added: April 9, 2022
Высоцкий Л. И., Смирнов А. В., Тыртышников Е. Е., Lobachevskii Journal of Mathematics 2021 Vol. 42 P. 1608–1621
Numerical integration is a classical problem emerging in many fields of science. Multivariate integration cannot be approached with classical methods due to the exponential growth of the number of quadrature nodes. We propose a method to overcome this problem. Tensor-train decomposition of a tensor approximating the integrand is constructed and used to evaluate a multivariate ...
Added: October 31, 2021
Rulkov N., Hunt A. M., Rulkov P. et al., American Journal of Engineering and Applied Sciences 2016 Vol. 9 No. 4 P. 973–984
The discreet-time (map-based) approach to modeling nonlinear dynamics of spiking and spiking-bursting activity of neurons has demonstrated its very high efficiency in simulations of neuro-biologically realistic behavior both in large-scale network models for brain activity studies and in real-time operation of Central Pattern Generator network models for biomimetic robotics. This paper studies the next step ...
Added: January 15, 2017
Aksenov S. A., Bober S. A., Nikolaeva Y. A. et al., / ЦНИИмаш. 2015.
В работе предлагается методика расчета ограниченных орбит вокруг точки либрации L2 системы Солнце-Земля. Движение космического аппарата (КА) в окрестности точки либрации рассматривается как суперпозиция трех компонент: убывающей (устойчивой), возрастающей (неустойчивой) и ограниченной. Предлагаемая методика позволяет скорректировать вектор состояния КА, таким образом, чтобы нейтрализовать неустойчивую компоненту движения. На основе численных расчетов, выполненных с помощью данной методики, произведено ...
Added: October 12, 2015
Morozenko V. V., Pleshkova I. Y., Information Theories & Applications 2013 Vol. 20 No. 3 P. 252–262
It is shown that genetic algorithms can be used successfully in problems of definite integral calculation especially when an integrand has a primitive which can't be expressed analytically through elementary functions. A testing of the program, which uses the genetic algorithm developed by authors, showed that the best results are reached if the size of ...
Added: March 5, 2014
Ivanova E., М.: Московский государственный институт электроники и математики, 2012.
Составлено в соответствии с рабочей программой курса и содержит подробное изложение лекционного материала в объёме, достаточном для изучения студентами-бакалаврами данного направления в рамках дисциплины «Вычислительная математика». Включает разделы о теоретических основах численных методов, решении нелинейных, дифференциальных и интегральных уравнений, а также систем линейных, нелинейных и дифференциальных уравнений, приближенного вычисления производных и интегралов, аппроксимации функций, методах ...
Added: October 12, 2012