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Reconstruction of manifold embeddings into Euclidean spaces via intrinsic distances
ESAIM - Control, Optimisation and Calculus of Variations. 2024. Vol. 30. Article 3.
We consider the problem of reconstructing an embedding of a compact connected Riemannian manifold in a Euclidean space up to an almost isometry, given the information on intrinsic distances between points from its “sufficiently large” subset. This is one of the classical manifold learning problems. It happens that the most popular methods to deal with such a problem, with a long history in data science, namely, the classical Multidimensional scaling (MDS) and the Maximum variance unfolding (MVU), actually miss the point and may provide results very far from an isometry; moreover, they may even give no bi-Lipshitz embedding. We will provide an easy variational formulation of this problem, which leads to an algorithm always providing an almost isometric embedding with the distortion of original distances as small as desired (the parameter regulating the upper bound for the desired distortion is an input parameter of this algorithm).
Prokofev V., Zabrodin A., Journal of Physics A: Mathematical and Theoretical 2021 Vol. 54
We consider solutions of the Kadomtsev–Petviashvili hierarchy which are elliptic functions of x = t1. It is known that their poles as functions of t2 move as particles of the elliptic Calogero–Moser model. We extend this correspondence to the level of hierarchies and find the Hamiltonian Hk of the elliptic Calogero–Moser model which governs the dynamics of poles with respect to the kth ...
Added: July 14, 2026
Prokofev V., Zabrodin A., Theoretical and Mathematical Physics 2021 Vol. 208 P. 1093–115
We consider solutions of the 2D Toda lattice hierarchy which are elliptic functions of the zeroth time t_0=x. It is known that their poles as functions of t_1 move as particles of the elliptic Ruijsenaars-Schneider model. The goal of this paper is to extend this correspondence to the level of hierarchies. We show that the ...
Added: July 14, 2026
Prokofev V., Zabrodin A., Теоретическая и математическая физика 2023 Т. 217 № 2 С. 299–316
We continue the study of the B-Toda hierarchy (the Toda lattice with the constraint of type B), which can be regarded as a discretization of the BKP hierarchy. We introduce the tau function of the B-Toda hierarchy and obtain bilinear equations for it. Examples of soliton tau functions are presented in explicit form. ...
Added: July 14, 2026
Silakov D., Системный администратор 2026 № 5 С. 46–51
В предыдущей статье про Open Source в КНР [1] мы рассказали про Alibaba – крупную корпорацию, занимающую тридцатое место в рейтинге самых значимых мировых брэндов за 2025 год [2]. Место почетное, но не первое среди китайских компаний – на тринадцатом месте расположилась Tencent, разработчик WeChat и ряда других продуктов, широко используемых нашими восточными соседями. Tencent ...
Added: July 14, 2026
IEEE, 2026.
Added: July 13, 2026
Switzerland: Springer, 2026.
This volume contains the refereed proceedings of the 25th International Conference on Mathematical Optimization Theory and Operations Research (MOTOR 2026) 1 held during July 6–11 in a picturesque place near Lake Baikal, Irkutsk, Russia. The MOTOR conference is a direct successor and scientific inheritor of several prominent events on mathematical programming, combinatorial and stochastic optimization, ...
Added: July 12, 2026
Шиманогов И. Н., Vyalyi M., Дискретный анализ и исследование операций 2025 Т. 32 № 4 С. 213–230
A well-studied class of algorithmic problems is that of regular realizability: checking the non-emptiness of the intersection of a regular language with a given language. This problem has a natural algebraic interpretation: verifying whether an element of a Boolean algebra belongs to the kernel of a certain homomorphism. This motivates the consideration of an analogous ...
Added: July 12, 2026
Rybakov M., Annals of Pure and Applied Logic 2026 Vol. 177 Article 103811
The paper presents a solution to the question about the decidability of the two-variable fragment of the superintuitionistic predicate logic QLC defined by the class of linear Kripke frames, which is also the ‘superintuitionistic’ fragment of the modal predicate logic QS4.3, under the Gödel translation. We prove that the fragment is undecidable. The result remains true for the ...
Added: July 11, 2026
Panov V., Ryabchenko A., / Series arXiv "stat.ME". 2026. No. 2607.05048.
This paper investigates the problem of statistical inference for a mixture distribution consisting of a discrete and a continuous component, with a particular focus on the class of rational-infinitely divisible distributions. We consider non-parametric estimation of both components of the mixture as well as the quasi-L{é}vy measure, assuming that the mixture belongs to the class ...
Added: July 9, 2026
Surkov A., Ignatenko V., Koltcov Sergei, Computers, Materials and Continua 2026
Large language models have recently demonstrated promising capabilities in mathematical reasoning; however, their performance on tasks requiring strict symbolic manipulation, such as solving differential equations, remains limited, especially for compact models. In this work, we investigate whether activation steering combined with reinforcement learning can improve the quality of solutions generated by pretrained language models without ...
Added: July 8, 2026
Springer, 2027.
The series Lecture Notes in Computer Science (LNCS), including its subseries Lecture Notes in Artificial Intelligence (LNAI) and Lecture Notes in Bioinformatics (LNBI), has established itself as a medium for the publication of new developments in computer science and information technology research, teaching, and education. LNCS enjoys close cooperation with the computer science R & ...
Added: July 8, 2026
IEEE, 2026.
The purpose of the 2026 IEEE Ural-Siberian Conference on Biomedical Engineering, Radioelectronics and Information Technology (USBEREIT) is to bring together researchers and practitioners from multiple areas of radio science, including biomedical engineering, radioelectronics, microelectronics, information technology, smart energy, information security and others. ...
Added: July 8, 2026
Маликов М. А., Монахова Э. А., Rzaev E. et al., Ученые записки Казанского университета. Серия: Физико-математические науки 2026 Т. 168 № 2 С. 269–286
This article examines series of families of two-dimensional circulant networks with rectangular
L -shapes, optimal in diameter, as network-on-chip topologies with a minimal number of crossings
between the links and a bounded length of the maximum link that does not depend on the network
size. New network-on-chip routing algorithms, which use the coordinates of three adjacent zeros in
the ...
Added: July 8, 2026
Pilé I., Shchur L., Deng Y., Physical Review B: Condensed Matter and Materials Physics 2026 Vol. 114 Article 014101
We investigate the spatial overlap of successive spin configurations in Markov chain Monte Carlo simulations using the local Metropolis algorithm and the Swendsen-Wang and Wolff cluster algorithms. We examine the dynamics of these algorithms for models in different universality classes: Ising model, Potts model with three components, and four-state Potts model. The overlap of two ...
Added: July 6, 2026
Irkutsk: ISDCT SB RAS, 2026.
We study a model problem on the filtration of a conducting fluid through a
porous layer. A porous medium is presented as an assemblage of identical spherical
cells. Each cell consists of a porous core and liquid shell. We derive apriori estimates
for flow characteristics which show the specific behavior of the fluid. Our estimates
are validated numerically. ...
Added: July 5, 2026
М.: Наука и технологии, 2026.
«Телекоммуникации» ежемесячный рецензируемый производственный, информационно-аналитический и учебно-методический журнал выходит в свет с июля 2000 г.
Для руководителей и работников промышленности, научно-исследовательских и проектно-конструкторских институтов, высших учебных заведений, аспирантов и студентов, а также для специалистов, разрабатывающих, выпускающих и эксплуатирующих средства телекоммуникаций.
Новости разработок и производства, прогнозы развития, защита информации, Нормативные, справочные, аналитические и учебно-методические материалы.
Переход к глобальному информационному ...
Added: July 4, 2026
МФТИ, 2025.
абота редакции научного журнала «Труды Московского физико-технического института» (кратко «Труды МФТИ»), редакционной коллегии и редакционного совета осуществляется в соответствии с Положением, утвержденным ректором института. В состав редакционной коллегии входят руководители института, факультетов, институтских и факультетских кафедр. Главный редактор журнала —президент МФТИ, член-корр. РАН Кудрявцев Н.Н.
Журнал «Труды МФТИ» входит в базу данных РИНЦ (Российский Индекс Научного Цитирования) и доступен в электронной ...
Added: July 4, 2026
Kachan O., Yanovich Y., Abramov E., Uchenye Zapiski Kazanskogo Universiteta. Seriya Fiziko-Matematicheskie Nauki 2018 Vol. 160 No. 2 P. 300–308
According to the manifold hypothesis, high-dimensional data can be viewed and meaning- fully represented as a lower-dimensional manifold embedded in a higher dimensional feature space. Manifold learning is a part of machine learning where an intrinsic data representation is uncovered based on the manifold hypothesis.
Many manifold learning algorithms were developed. The one called Grassmann&Stiefel eigenmaps ...
Added: January 21, 2026
Марченко И. А., Ronko R., В кн.: Исследования по славянской диалектологии. Выпуск 25Т. 25.: М.: Институт славяноведения РАН, 2025. Гл. 5 С. 236–260.
This paper presents a classification of Russian dialects based on data from the Dialectological Atlas of the Russian Language, using the method of multidimensional scaling. The main outcome of the study is a map of the Russian dialectal space, which identifies six zones (three western and three eastern) and corresponding sets of dialectal features. The ...
Added: December 7, 2025
Kroshnin A., Eugene Stepanov, Trevisan D., ESAIM - Control, Optimisation and Calculus of Variations 2022 Vol. 28 Article 58
For a given metric measure space (X, d, μ) we consider finite samples of points, calculate the matrix of distances between them and then reconstruct the points in some finite-dimensional space using the multidimensional scaling (MDS) algorithm with this distance matrix as an input. We show that this procedure gives a natural limit as the number ...
Added: November 15, 2022
Puchkin N., Spokoiny V., Journal of Machine Learning Research 2022 Vol. 23 No. 40 P. 1–62
We consider a problem of manifold estimation from noisy observations. Many manifold learning procedures locally approximate a manifold by a weighted average over a small neighborhood. However, in the presence of large noise, the assigned weights become so corrupted that the averaged estimate shows very poor performance. We suggest a structure-adaptive procedure, which simultaneously reconstructs ...
Added: February 3, 2022
Alanov A., Kochurov M., Volkhonskiy D. et al., , in: Proceedings of the 15th International Joint Conference on Computer Vision, Imaging and Computer Graphics Theory and Applications (VISAPP 2020)Vol. 4.: SciTePress, 2020. P. 214–221.
We propose a novel multi-texture synthesis model based on generative adversarial networks (GANs) with a user-controllable mechanism. The user control ability allows to explicitly specify the texture which should be generated by the model. This property follows from using an encoder part which learns a latent representation for each texture from the dataset. To ensure ...
Added: November 8, 2020
Kachan O. N., Yanovich Y., Abramov E., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 300–308
According to the manifold hypothesis, high-dimensional data can be viewed and meaningfully represented as a lower-dimensional manifold embedded in a higher dimensional feature space. Manifold learning is a part of machine learning where an intrinsic data representation is uncovered based on the manifold hypothesis.
Many manifold learning algorithms were developed. The one called Grassmann & Stiefel eigenmaps (GSE) ...
Added: October 29, 2020
Abramov E., Yanovich Y., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 220–228
Real data are usually characterized by high dimensionality. However, real data obtained from real sources, due to the presence of various dependencies between data points and limitations on their possible values, form, as a rule, form a small part of the high-dimensional space of observations. The most common model is based on the hypothesis that ...
Added: October 29, 2020