標題: Titlebook: Mathematical Principles of Topological and Geometric Data Analysis; Parvaneh Joharinad,Jürgen Jost Textbook 2023 The Editor(s) (if applica [打印本頁] 作者: 爆裂 時間: 2025-3-21 17:45
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作者: Morbid 時間: 2025-3-21 22:59 作者: 厭食癥 時間: 2025-3-22 02:29 作者: 托運 時間: 2025-3-22 04:59 作者: cajole 時間: 2025-3-22 11:31
Mathematical Principles of Topological and Geometric Data Analysis978-3-031-33440-5Series ISSN 2731-4103 Series E-ISSN 2731-4111 作者: conformity 時間: 2025-3-22 16:31 作者: dictator 時間: 2025-3-22 19:27
Weighted Complexes, Cohomology and Laplace Operators,tors and their adjoints, Laplace type operators. The spectrum of a Laplace operator will encode important properties of the underlying geometric object, and therefore, in this chapter, we develop the spectral theory of such operators in an abstract manner.作者: 公豬 時間: 2025-3-22 22:18 作者: Thyroxine 時間: 2025-3-23 02:31
Metrics and Curvature, Our notion is very abstract and therefore also naturally applies to discrete metric spaces, as naturally emerging from data. We conclude by presenting a construction of a simplicial complex (typically infinite-dimensional) that as a topological object encodes all geometric properties of the metric that we want to represent.作者: 詢問 時間: 2025-3-23 08:57 作者: 心胸開闊 時間: 2025-3-23 11:22
Introduction,t in order to make distinctions without having to employ very high-dimensional spaces, a curved Riemannian manifold may work well. It is then a basic task of geometric data analysis to construct or approximate such a Riemannian manifold from finitely many data points.作者: GORGE 時間: 2025-3-23 17:11
Metric Spaces and Manifolds,ric in detail, including the exponential map and normal coordinates, sectional and Ricci curvatures, Jacobi fields and the Laplace-Beltrami operator. We conclude the chapter by discussing other important geometries and introducing the concept of largitude in order to quantify how much a metric space spreads out in different directions.作者: 碌碌之人 時間: 2025-3-23 20:14
Topological Foundations, Hypercomplexes and Homology,ures like (differentiable) manifolds, and from measure theory for quantifying sizes. Homology plays a fundamental role, as a scheme for assigning algebraic invariants to geometric objects by systematically using cancellations. This then also allows us to describe a powerful scheme of topological data analysis, persistent homology.作者: magenta 時間: 2025-3-24 01:00
Linear Methods: Kernels, Variations, and Averaging,Hilbert space that can be used for clustering data by embedding them into such a space. These are the ideas behind support vector machines (SVM). Averaging is the principle behind Laplace operators, and in this chapter, we both provide an abstract treatment and specific applications, for instance to image denoising.作者: 驚惶 時間: 2025-3-24 04:44 作者: nonplus 時間: 2025-3-24 07:07
Textbook 2023lysis of data. The underlying reason for this is that data are typically equipped with somekind of notion of distance, quantifying the differences between data points. Of course, to be successfully applied, the geometric tools usually need to be redefined, generalized, or extended appropriately..Pri作者: Expurgate 時間: 2025-3-24 14:31
Parvaneh Joharinad,Jürgen Josto that water-soluble compounds with an approximate molecular weight above 100 are largely prevented from directly entering the brain (Bradbury 1979). The functi978-3-540-11406-2978-3-642-68511-8Series ISSN 0171-9750 作者: 高興去去 時間: 2025-3-24 18:39 作者: NOMAD 時間: 2025-3-24 19:56
Mathematical Principles of Topological and Geometric Data Analysis作者: 不開心 時間: 2025-3-25 00:32 作者: 細頸瓶 時間: 2025-3-25 04:26
Parvaneh Joharinad,Jürgen Jostoss is increased under light loads, all the switches can achieve ZVS. The reduced switching loss can improve the overall efficiency. Finally, a 1.3?kW experimental prototype was built to verify the effectiveness of the converter and the modulation scheme, which demonstrates the ZVS performance and e作者: Vldl379 時間: 2025-3-25 07:35 作者: Genetics 時間: 2025-3-25 11:43 作者: initiate 時間: 2025-3-25 15:50
Parvaneh Joharinad,Jürgen Jostational one day strike over public sector pension provision and subsequently become a shop steward. His transition, from heavy manufacturing in a strong industrial working class community and overwhelmingly male working environment to the public service sector where he was now working with a predomi作者: MONY 時間: 2025-3-25 20:51
I’d be phoning them up moaning about things’ and she had subsequently become an Equality Representative. She defined herself as ’not really interested in the political side of things’, she did not believe that people should be defined in terms of class, had not voted at the last election and despite作者: HACK 時間: 2025-3-26 04:00
Introduction, exist various discrete geometric structures, like graphs, hypergraphs or simplicial complexes, for representing relations between data points. These will be very helpful tools, but as we shall argue, often continuous or smooth structures may better represent data and reveal their basic intrinsic st作者: 軍火 時間: 2025-3-26 07:29
Topological Foundations, Hypercomplexes and Homology,ta points, from category theory for organizing mathematical structures in an abstract manner, from topology for analyzing continuous and smooth structures like (differentiable) manifolds, and from measure theory for quantifying sizes. Homology plays a fundamental role, as a scheme for assigning alge作者: 記憶 時間: 2025-3-26 10:12
Weighted Complexes, Cohomology and Laplace Operators,ne coboundary operators and a cohomology theory. Since functions can be multiplied, this yields a ring structure on cohomology, making it richer than homology. When we introduce scalar products on function spaces, we also obtain adjoints of the coboundary operators and, by composing coboundary opera作者: Hemodialysis 時間: 2025-3-26 16:01
The Laplace Operator and the Geometry of Graphs,cts on vertex and edge functions, there are several versions of the Laplace operator. They include the algebraic Laplace operator that is usually studied in graph theory, and the normalized Laplacian that generates random walks on graphs. The spectra of these operators efficiently encode structural 作者: Heretical 時間: 2025-3-26 17:49
Metric Spaces and Manifolds, mathematical tool for data analysis. Metrics naturally induce other structures, like the qualitative structure of a topology. Differentiable manifolds describe smooth structures on which we can apply tools of calculus. On differentiable manifold, we can introduce a Riemannian metric. Riemannian man作者: Encoding 時間: 2025-3-26 23:54 作者: sterilization 時間: 2025-3-27 03:45 作者: FECT 時間: 2025-3-27 07:23 作者: FUSE 時間: 2025-3-27 10:12 作者: 燦爛 時間: 2025-3-27 15:52 作者: IDEAS 時間: 2025-3-27 21:51
Parvaneh Joharinad,Jürgen Jostfore the Council of Ministers of the European Communities has adopted on September 18, 1979 a Community legislation with respect to the notification of new chemicals. This is the so called sixth amendment of the Council directive of 27 June 1967 relating to the classification, packaging and labellin作者: 侵略主義 時間: 2025-3-28 00:31
fore the Council of Ministers of the European Communities has adopted on September 18, 1979 a Community legislation with respect to the notification of new chemicals. This is the so called sixth amendment of the Council directive of 27 June 1967 relating to the classification, packaging and labellin作者: 瑪瑙 時間: 2025-3-28 05:48 作者: FIR 時間: 2025-3-28 08:50
. What is it about this woman in her forties that made her become an activist and what does the term signify to her? Does the apparent absence of class consciousness or any other active social identity or consciousness reflect the paralysis of the British labour movement and its inability to play an作者: Nonthreatening 時間: 2025-3-28 13:59
Musings of Heidegger. Arts Education and , as a ‘Debased’ (Dreyfus) Work of Arts education context. Connecting such diverse categories as ., St. John the Baptist and J.R.R. Tolkien’s . with the theme of teacher authenticity, the article offers a fresh account of the challenges currently being faced within the broad field of arts education.作者: 救護車 時間: 2025-3-28 16:38
Nonlinear and Multisectoral Macrodynamics atherosclerosis in this setting (table 12–1). The lipoprotein abnormalities associated with nonuremic nephrotic syndrome and in the posttransplantation situation differ fundamentally from those in uremia, and will not be dealt with in this chapter.作者: 空氣 時間: 2025-3-28 22:21 作者: neolith 時間: 2025-3-28 23:41 作者: 感情 時間: 2025-3-29 06:14 作者: PHON 時間: 2025-3-29 09:55
Italy: After the Rewards of Growth, the Penalty of Debt,urvived, roads and railways were severely damaged, and the stock of houses, already badly in need of repair before the war, was severely depleted. Output was at a very low level, because of a lack of raw materials, a shortage of dollars and the general disorganization of the country, after a long pe作者: Esophagus 時間: 2025-3-29 11:24 作者: 珊瑚 時間: 2025-3-29 16:38
vide a detailed snapshot of a physiology, the ability to track such processes in real time has expanded the breadth of questions that can be interrogated in the laboratory. Intravital Microscopy (IVM) is a dynamic and powerful way to investigate both the homeostatic and host response to either thera
