?
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).
Kh. Kh. Abdullin, D. B. Mokeev, D. S. Taletskii, Mathematical notes 2026 Vol. 119 No. 1 P. 3–7
By the Ramsey number R(K1,s,Pt) one means the least positive integer n such that, for every n-vertex graph G, the following condition holds: either G contains a vertex of degree at least s or the complement of G contains a simple t-path. In this paper, we fi nd precise values of R(K1,s,Pt) for certain values ...
Added: June 10, 2026
Sorokin D., Kostin A., Savchenko L. et al., Knowledge-Based Systems 2026 Vol. 348 Article 116258
A convenient approach to optimally solving combinatorial optimization tasks is the Branch-and-Bound method.
Its branching heuristic can be learned to solve a large set of similar tasks. The promising results here are
achieved by the recently appeared on-policy reinforcement learning method based on the tree Markov Decision
Process. To overcome its main disadvantages, namely, very large training time ...
Added: June 10, 2026
Namsaraev Z., Kozlova A., Toshchakov S., Scientific Reports 2026 Vol. 16 No. 17769
Distilled fermented milk beverages are rare in food technology, despite the global prevalence of plant-based spirits. Currently, the production of distilled strong alcoholic beverages from fermented milk using traditional technologies is known only among Mongolic-speaking peoples and their Siberian neighbors. This study provides the first interdisciplinary analysis of darasun, a traditional Buryat spirit made from fermented ...
Added: June 10, 2026
Hushchyn M., Butorova A., Bobakov V. et al., European Physical Journal: Special Topics 2026 P. 1–19
This paper presents a review of artificial intelligence (AI) methods for failure prediction in data center cooling systems, with a focus on the integration of digital twins (DTs), physics-informed learning, and graph-based models. Positioned within complex network science, this review addresses a limitation of conventional graph approaches—their reliance on pairwise connectivity—whereas real-world failures often arise ...
Added: June 10, 2026
Springer, 2026.
The book presents the proceedings of the 13th International Conference on Frontiers of Intelligent Computing: Theory and Applications (FICTA 2024), held at Intelligent Systems Research Group (ISRG), London Metropolitan University, London, United Kingdom, during June 6–7, 2025. Researchers, scientists, engineers and practitioners exchange new ideas and experiences in the domain of intelligent computing theories with ...
Added: June 8, 2026
Flamarion M. V., Pelinovsky E., Nonlinear Dynamics 2026 Vol. 114 Article 784
In this article, we investigate wave packet and solitary wave dynamics in the Whitham–Ostrovsky (WO) equation. By means of a multiple-scales expansion, we formally derive a nonlinear Schrödinger (NLS) equation governing the envelope evolution.The corresponding modulational stability diagram is then obtained using the Lighthill criterion. We show that sufficiently large values of the low-frequency dispersive term render ...
Added: June 5, 2026
Medvedev T. V., Pochinka O., Chaos 2026 Vol. 36 No. 6 Article 063107
We consider 3-diffeomorphisms with source–sink dynamics where Smale solenoids play the role of the source and the sink (NSSS-diffeomorphisms). It is known that such diffeomorphisms exist only on lens spaces. On the 3-sphere, every NSSS-diffeomorphism is associated with an exchangeable braid. An exchangeable braid with the strand number n was constructed for each n 3 in such a way ...
Added: June 4, 2026
Seul: PMLR, 2026.
Added: June 4, 2026
Kazakov A., Mints D., Petrova I. et al., Chaos 2026 Vol. 36 No. 6 Article 063112
We study hyperbolic chaotic dynamics for maps of a two-dimensional torus. We introduce a two-parameter family of diffeomorphisms which, as we show, demonstrates all types of hyperbolic chaotic dynamics that can appear in the two-dimensional case. In addition, we describe all the bifurcations responsible for the transitions between these chaotic regimes. ...
Added: June 4, 2026
Nozdrinova E., Pochinka O., Shmukler V., Математический сборник 2026 Т. 217 № 6 С. 71–89
Гомеоморфизмы топологических пространств называются эквивалентными по надстройке, если надстройки над ними топологически эквивалентны. В частности, топологически сопряженные гомеоморфизмы эквивалентны по надстройке. Известно, что для гомологически неприводимых гомеоморфизмов их топологическая сопряженность является необходимым и достаточным условием их эквивалентности по надстройке. Тогда как инварианты топологической сопряженности гомологически приводимых гомеоморфизмов во многих случаях являются избыточными для эквивалентности по ...
Added: June 3, 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
Kuleshov A. P., Bernstein A. V., Yanovich Y., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 327–338
The problem of unknown high-dimensional density estimation has been considered. It has been suggested that the support of its measure is a low-dimensional data manifold. This problem arises in many data mining tasks. The paper proposes a new geometrically motivated solution to the problem in the framework of manifold learning, including estimation of an unknown ...
Added: October 28, 2020
Kuleshov A. P., Bernstein A. V., Yanovich Y., Ученые записки Казанского университета. Серия: Физико-математические науки 2018 Vol. 160 No. 2 P. 327–338
The problem of unknown high-dimensional density estimation has been considered. It has been suggested that the support of its measure is a low-dimensional data manifold. This problem arises in many data mining tasks. The paper proposes a new geometrically motivated solution to the problem in the framework of manifold learning, including estimation of an unknown ...
Added: October 28, 2020
Bernstein A., Kuleshov A. P., International Journal of Software and Informatics 2013 No. 7(3) P. 359–390
One of the ultimate goals of Manifold Learning (ML) is to reconstruct an unknown nonlinear low-dimensional Data Manifold (DM) embedded in a high-dimensional observation space from a given set of data points sampled from the manifold. We derive asymptotic expansion and local lower and upper bounds for the maximum reconstruction error in a small neighborhood ...
Added: November 21, 2014