Titlebook: Mathematical Principles of Topological and Geometric Data Analysis; Parvaneh Joharinad,Jürgen Jost Textbook 2023 The Editor(s) (if applica

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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

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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

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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

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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

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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

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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

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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

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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