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Persistent Homology-based Projection Pursuit
P. 3744–3751.
Dimensionality reduction problem is stated as finding a mapping f:X ∈ R m → Z ∈ R n , where ≪ m while preserving some relevant properties of the data. We formulate topology-preserving dimensionality reduction as finding the optimal orthogonal projection to the lower-dimensional subspace which minimizes discrepancy between persistent diagrams of the original data and the projection. This generalizes the classic projection pursuit algorithm which was originally designed to preserve the number of clusters, i.e. the 0-order topological invariant of the data. Our approach further allows to preserve k-th order invariants within the principled framework. We further pose the resulting optimization problem as the Riemannian optimization problem which allows for a natural and efficient solution.
Lukacheva S., Zakharova E., Makhaneva A. et al., Journal of Solid State Chemistry 2025 Vol. 345 Article 125223
A new gallium-rich intermetallic Ti2-xNi3Ga9 was synthesized by high-temperature techniques as bulk samples and single crystals. The composition and structure of the compound were established by a combination of single-crystal and powder X-ray analysis and energy-dispersive X-ray spectroscopy. The obtained intermetallic compound crystallizes in its own structure type and has a narrow homogeneous region of ...
Added: February 23, 2026
Дюканов П. А., Kozhukhov M., Popov D. et al., Успехи прикладной физики 2024 Т. 12 № 4 С. 334–342
The paper considers options for the design of an n-channel junction-gate field-effect transistor, integrated into a high-voltage complementary bipolar technological process with isolation by a reverse-biased p-n junction. Criteria for the selection of transistor models according to electrophysical parameters are formulated. Taking into account the criteria, the instrument-technological modeling on bulk silicon substrates was carried ...
Added: September 12, 2024
Mikhail Yu. Romashikhin, , in: Proceedings 2024 International Russian Smart Industry Conference (SmartIndustryCon), 25-29 March 2024.: Sochi: IEEE, 2024. P. 104–108.
This article describes the implementation of regular topologies for networks-on-chip. The complexity of network development and its main parameters depend on the choice of topology. The rationale for the influence of topology on network bandwidth is given. Software that automates the generation of configuration files (bitstream) for the implementation of networks-on-chip with different topologies and ...
Added: May 13, 2024
Krenke A., Sandlerskiy R., Baibar A. et al., Известия РАН. Серия биологическая 2023 № 7 С. 93–108
A brief review of the main models for emergence of boundaries and, in a particular case, integrity, arising from the theory of nonlinear volumetric systems. Based on the fundamental value of Kotelnikov’s reference and, accordingly, the general theory of awareness about identifying a characteristic border feature, as frequency of sampling functions in incidence along with ...
Added: December 9, 2023
Gogoleva N., Zorina-Tikhonova E., Khapaeva P. et al., Journal of Molecular Structure 2022 Vol. 1256 Article 132532
A series of cobalt(II) and cadmium(II) compounds comprising dimethylmalonate anions combined with potassium and barium ions have been synthesized. The compounds obtained are coordination polymers with 3D structure (1) or 2D structure (2–4). It has been shown that, depending on the nature of heterometals, the type of coordination of dimethylmalonic acid by d-metal atoms changes: from ...
Added: January 24, 2023
A. N. Krenke, R. B. Sandlersky, A. S. Baybar et al., Известия РАН. Серия биологическая. 2023 Vol. 50 No. 1 P. S85–S99
Four main models of the appearance of boundaries (in a particular case, integrity), arising from the theory of nonlinear dynamic systems, are considered briefly. On the basis of Kotelnikov’s fundamental sampling theorem and, accordingly, general information theory, the character of a distinguished boundary as a function of the sampling frequency in a spatial series with a ...
Added: December 2, 2022
Antonina A. Arkhipova, Ivanov S., Zhuravitskii S. et al., Nanophotonics 2022 Vol. 11 No. 16 P. 3653–3661
We report the experimental observation of the periodic switching of topological edge states between two dimerized fs-laser written waveguide arrays. Switching occurs due to the overlap of the modal fields of the edge states from topological forbidden gap, when they are simultaneously present in two arrays brought into close proximity. We found that the phenomenon ...
Added: October 17, 2022
Letellier C., Stankevich N., Rössler O., International Journal of Bifurcation and Chaos in Applied Sciences and Engineering 2022 Vol. 32 No. 2 Article 2230004
Characterizing accurately chaotic behaviors is not a trivial problem and must allow to determine the properties that two given chaotic invariant sets share or not. The underlying problem is the classification of chaotic regimes, and their labeling. Addressing these problems corresponds to the development of a dynamical taxonomy, exhibiting the key properties discriminating the variety ...
Added: February 24, 2022
Polotovskiy G., В кн.: Классическая и современная геометрия. Материалы Международной конференции, посвященной 100-летию со дня рождения Л.С. Атанасяна (Москва, 1–4 ноября 2021 г.).: М.: МПГУ, 2021. С. 125–126.
Очерк истории топологического образования в Нижнем Новгороде ...
Added: October 31, 2021
Rzaev E., Romanov A., , in: 2021 International Russian Automation Conference (RusAutoCon).: IEEE, 2021. P. 421–425.
Added: September 25, 2021
Glazov M., Поддубный А. Н., Physical Review Letters 2019 Vol. 123 P. 126801
We theoretically study Rydberg excitons in one-dimensional chains of traps in Cu2O coupled via the van der Waals interaction. The triplet of optically active p-shell states acts as an effective spin 1, and the interactions between the excitons are strongly spin dependent. We predict that the system has the topological Haldane phase with the diluted antiferromagnetic ...
Added: January 13, 2021
Romanov A., Starykh V., Heliyon 2020 Vol. 6 No. 7 P. 1–7
In this paper we propose and analyze various approaches to organizing routing in a triple loop circulant topologies as applied to networks-on-chip: static routing based on universal graph search algorithms, such as Dijkstra’s algorithm and a possible implementation using Table routing; algorithms created analytically based on an engineering approach with taking into account the structural ...
Added: July 21, 2020
Romanov A.Yu., Sidorenko M.V., Lezhnev E.V., , in: 2019 International Russian Automation Conference (RusAutoCon).: IEEE, 2019. P. 1–6.
The paper presents the implementation of a dynamic routing algorithm intended for use in networks-on-chip with a circulant topology with three generatrices of type C(N; s1, s2, s3) for finding the shortest routes between any two network nodes. The algorithm can be implemented as a RTL state machine in routers for NoCs. The proposed algorithm ...
Added: October 23, 2019
Stepanov E., Buttazzo G., Pratelli A. et al., Berlin: Springer, 2009.
Recently much attention has been devoted to the optimization of transportation networks in a given geographic area. One assumes the distributions of population and of services/workplaces (i.e. the network's sources and sinks) are known, as well as the costs of movement with/without the network, and the cost of constructing/maintaining it. Both the long-term optimization and ...
Added: December 12, 2018
Aleskerov F. T., Shvydun S., , in: Studies in Computational Intelligence* 1. Vol. 812: Complex Networks and Their Applications VII.: Springer, 2019. P. 94–103.
We propose a model that evaluates how much a network has changed over time in terms of its structure and a set of central elements. The difference of structure is evaluated in terms of node-to-node influence using known nodes correspondence models. To analyze the changes in nodes centralities we adapt an idea of interval orders ...
Added: December 4, 2018
Gavrilovich M., / Series arxiv "math.CT". 2017.
We illustrate the generative power of the lifting property (orthogonality of morphisms in a category) as means of defining natural elementary mathematical concepts by giving a number of examples in various categories, in particular showing that many standard elementary notions of abstract topology can be defined by applying the lifting property to simple morphisms of ...
Added: July 21, 2017
Paramonov A. A., Философский журнал 2016 Т. 9 № 4 С. 63–79
This article investigates the problem of the status spacial images and drawings may have in a philosophical text. The source of the present study are the recently published preparatory notes for the lectures on Proust held by Merab Mamardashvili in 1981-82. Mamardashvili papers abound in schematic sketches which graphically convey spatial images. In his interpretation, ...
Added: June 30, 2017
Shalaeva A., SocioTime (Социальное время) 2015 № 4 С. 50–59
The paper is devoted to the concept of mythological thinking and its special characteristic – mythological space. The category of space is considered as ontological and stated in mythological history and order. We introduce the topological method as a method for studying the mythological space, partly borrowed from the branch of mathematics – topology, partly ...
Added: October 20, 2015
Gavrilovich M., The De Morgan Gazette 2014 Vol. 5 No. 4 P. 23–32
We observe that some natural mathematical definitions are lifting properties relative to simplest counterexamples, namely the definitions of surjectivity and injectivity of maps, as well as of being connected, separation axioms T0 and T1 in topology, having dense image, induced (pullback) topology, and every real-valued function being bounded (on a connected domain). We also offer ...
Added: October 20, 2015
Starovoytenko E. B., Мир психологии. Научно-методический журнал 2013 Т. 76 № 4 С. 189–203
The problem from the area of Personology of Self, being the most important part of general personology, is studied in this paper. The paper offers the model of basic features and abilities of Self. The role of ability of Self to be its own ability, the ability which integrates many intentions of “I can” type ...
Added: November 15, 2013
Potapova T. A., Молотков С. Н., Письма в Журнал экспериментальной и теоретической физики 2013 Т. 97 № 6 С. 384–391
The symmetry nature of the appearance of specific surface (edge) states at the boundaries of low_dimension structures with the symmetry of ribbons (borders) invariant with respect to time reversal is discussed. Symmetry reasons for the stability of such states against the elastic scattering from nonmagnetic impurities have been revealed. ...
Added: October 11, 2013
Potapova T. A., Молотков С. Н., Письма в Журнал экспериментальной и теоретической физики 2013 Т. 98 № 5 С. 336–341
A new type of massless Dirac fermions in crystalline three_dimensional topological insulators (three_dimen_sional two_dimensional situation) has been predicted. The spectrum has fourfold degeneracy at the top of the two_dimensional Brillouin zone (M point) and twofold degeneracy near the M point. Crystal symmetry along with the time reversal invariance in three_dimensional topological insulators allows fourfold degenerate ...
Added: October 11, 2013