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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).
Piontkovski D., / Series arXiv "math". 2026.
A noncommutative projective variety is defined, following Artin and Zhang, by a graded coherent algebra 𝐴. The category of coherent sheaves is then the quotient qgr(𝐴) of the category of finitely presented graded modules by the subcategory of torsion modules. We consider the categorical and polynomial entropies of the Serre twist, that is, of the ...
Added: June 23, 2026
Piontkovski D., / Series arXiv "math". 2025.
If a symmetric multilinear algebra is weakly nil, then it is Engel. This result may be regarded as an infinite-dimensional analogue of the well-known Jacobian theorem, which states that if a polynomial mapping has a polynomial inverse, then its Jacobian matrix is invertible. This refines a theorem of Gerstenhaber and partially answers a question posed ...
Added: June 23, 2026
Atlasov B., Selskiy A., Russian Journal of Information Technology in Sports 2025 Vol. 2 No. 1 P. 13–21
The article examines the current state of the global virtual and augmented reality (VR/AR) technology market in sports, noting its growth, although slower than previously expected. Special attention is paid to the Russian market, where the development of VR technologies in sports lags behind world leaders such as the United States, EU countries and China, ...
Added: June 23, 2026
IEEE, 2026.
The 9th International Scientific Conference on Information, Control, and Communication Technologies (ICCT-2025) had been held October 7-11, 2025 in Gomel, Belarus. The main technical areas and applications covered by the proceedings are optoelectronics, acousto-optic, microwave technology, antenna systems, measuring technology, metamaterials, nanostructures, nanofilms, photonic crystals, biology and medicine, biophotonics, bioengineering, neural networks in communication technologies; ...
Added: June 23, 2026
Buzaev F., Mullakhmetov R., Bogachev R. et al., Association for Computational Linguistics, 2026.
Playlist generation based on textual queries using large language models (LLMs) is becoming an important interaction paradigm for music streaming platforms. User queries span a wide spectrum from highly personalized intent to essentially catalog-style requests. Existing systems typically rely on non-personalized retrieval/ranking or apply a fixed level of preference conditioning to every query, which can ...
Added: June 22, 2026
Herbert A., Cherednichenko O., Lybrand T. et al., International Journal of Molecular Sciences 2025 Vol. 26 No. 6 Article 2422
The double-stranded RNA editing enzyme ADAR1 connects two forms of genetic programming, one based on codons and the other on flipons. ADAR1 recodes codons in pre-mRNA by deaminating adenosine to form inosine, which is translated as guanosine. ADAR1 also plays essential roles in the immune defense against viruses and cancers by recognizing left-handed Z-DNA and ...
Added: June 22, 2026
Калужский печатный двор, 2026.
Conference Proceedings INTERNATIONAL CONFERENCE
“Mathematical Ideas of Academician
P.L. Chebyshev, Their Applications in Natural
Sciences and Artificial Intelligence Technologies”
dedicated to the 205th anniversary of his birth ...
Added: June 20, 2026
Джанбекова А. Р., Shvedov A. S., Математическое моделирование 2026 Т. 38 № 3 С. 159–176
Boundary value problems for the Black–Scholes partial differential equation, which describes the value of a financial instrument, may contain a free boundary condition if the financial instrument allows for early exercise. This article considers free boundary value problems for the Black–Scholes equation and the convection diffusion equation. For the convection diffusion equation, a finite difference ...
Added: June 20, 2026
Stognieva O., Чеснокова Н. Е., Отечественная и зарубежная педагогика 2026 Т. 1 № 3 (115) С. 123–131
Integration of generative artificial intelligence tools into educational practice highlights the need for pedagogically grounded approaches to their use in the creation of educational video content, which is increasingly applied in language and professionally oriented instruction.
The purpose of this article is to conduct a comparative analysis of educational video content created using generative AI tools ...
Added: June 20, 2026
Buryak A., Tessler R., Troshkin M., Journal of Geometry and Physics 2026 Vol. 223 Article 105783
We give a natural definition of open Hurwitz numbers, where the weight of each ramified covering includes an integer parameter N taken to the power that is equal to the number of boundary components of a Riemann surface with boundary mapping to . We prove that the resulting sequence of partition functions, depending on , is a tau-sequence of ...
Added: June 19, 2026
Buryak A., Rossi P., Communications in Mathematical Physics 2025 Vol. 406 Article 205
Of the two approaches to integrable systems associated to semisimple cohomological field theories (CohFTs), the one suggested by Dubrovin and Zhang and the more recent one using the geometry of the double ramification (DR) cycle, the second has the advantage of being very explicit. The Poisson operator of the DR hierarchy is , where is the metric ...
Added: June 19, 2026
Cherednichenko O., Herbert A., Poptsova M., Computational and Structural Biotechnology Journal 2025 Vol. 27 P. 992–1000
Large language models (LLMs) in genomics have successfully predicted various functional genomic elements. While their performance is typically evaluated using genomic benchmark datasets, it remains unclear which LLM is best suited for specific downstream tasks, particularly for generating whole-genome annotations. Current LLMs in genomics fall into three main categories: transformer-based models, long convolution-based models, and state-space models ...
Added: June 19, 2026
Poptsova M., Briefings in Bioinformatics 2025 Vol. 26 No. 2 P. 1–11
Kolmogorov–Arnold networks (KANs) emerged as a promising alternative for multilayer perceptrons (MLPs) in dense fully connected networks. Multiple attempts have been made to integrate KANs into various deep learning architectures in the domains of computer vision and natural language processing. Integrating KANs into deep learning models for genomic tasks has not been explored. Here, we ...
Added: June 19, 2026
Анненков А. Н., Nesterov R., Моделирование и анализ информационных систем 2026 Т. 33 № 2 С. 176–205
Declarative process models are widely used in process mining to describe flexible process behavior through sets of constraints. However, models discovered automatically from event logs may contain inconsistent constraints, which can make them difficult to interpret and unusable for execution, conformance checking, or further analysis. Existing methods for consistency analysis either rely on automata-based constructions ...
Added: June 18, 2026
Cham: Springer Publishing Company, 2026.
The four-volume set LNCS 16483-16486 constitutes the refereed conference proceedings of the 48th European Conference on Information Retrieval, ECIR 2026, held in Delft, The Netherlands, during March 29–April 2, 2026.
The 46 full papers and 37 short papers presented together with 10 findings papers, 9 reproducibility papers, 17 resource papers, 11 workshop papers, 7 tutorial papers, ...
Added: June 18, 2026
Poddiakov A., Троицкий вариант. Наука 2026 № 12 С. 24–25
В научно-популярной заметке представлен обзор содержания поста филдсовского медалиста Тимоти Гауэрса о возможностях ИИ в математике и содержания комментариев под постом. Обзор сделан в основном чат-ботом DeepSeek. В заключение обсуждается возможность не только решения задач искусственным интеллектом, но и их постановки. ...
Added: June 18, 2026
Beznosikov A., Kormakov G., Grigorievskiy A. et al., Journal of Optimization Theory and Applications 2026 Vol. 209 Article 18
The objective of Vertical Federated Learning (VFL) is to collectively train a model using features available on different devices while sharing the same users. This paper focuses on the saddle point reformulation of the VFL problem via the classical Lagrangian function. We first demonstrate how this formulation can be solved using deterministic methods.More importantly, we explore various stochastic modifications to ...
Added: June 17, 2026
Garzón J., Mora Rodríguez J., Moreno-Franco H. A., Applied Mathematics and Optimization 2026 Vol. 94 No. 10 P. 1–43
We study an optimal extraction problem where the agent’s actions in the spot market exert an additive proportional negative impact on the commodity price. The commodity price dynamics, prior to any activity by the agent, evolve according to a drifted Brownian motion with jumps. The agent’s primary aim is to identify an optimal extraction strategy ...
Added: June 17, 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