Results 91 to 100 of about 521,410 (206)
Butterfly points and hyperspace selections
Applied General TopologyIf f is a continuous selection for the Vietoris hyperspace ℱ(X) of the nonempty closed subsets of a space X, then the point f(X)∊ X is not as arbitrary as it might seem at first glance. In this paper, we will characterise these points by local properties
Valentin Gutev
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A topological approach for protein classification
, 2015 Protein function and dynamics are closely related to its sequence and structure. However prediction of protein function and dynamics from its sequence and structure is still a fundamental challenge in molecular biology.
Cang, Zixuan +5 more
core +1 more source
Complexity, Volume 2025, Issue 1, 2025.The present paper employs topological data analysis methods to reveal ‘holes’ (stable persistent homologies) in the semantic spaces of words, bigrams, and trigrams of the English and Russian languages, and to ascertain their boundaries. Furthermore, the paper selects those holes that belong to the large‐scale (coarse‐grained) structure of the language ...
Vasilii A. Gromov +3 more
wiley +1 more source
Topology-controlled Laplace–Beltrami operator on point clouds based on persistent homology
Graphical ModelsComputing the Laplace–Beltrami operator on point clouds is essential for tasks such as smoothing and shape analysis. Unlike meshes, determining the Laplace–Beltrami operator on point clouds requires establishing neighbors for each point.
Ao Zhang +3 more
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Contributions to Persistence Theory
Annals of the West University of Timisoara: Mathematics and Computer Science, 2014 Persistence theory discussed in this paper is an application of algebraic topology (Morse Theory [29]) to Data Analysis, precisely to qualitative understanding of point cloud data, or PCD for short.
Du Dong
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The Euler Characteristic of the Fiber Product of Morse Functions on Grassmannians
International Journal of Mathematics and Mathematical Sciences, Volume 2025, Issue 1, 2025.For F=R, C, or H, let GkFn denote the Grassmannian of k‐planes in Fn. For a well‐known Morse function f:GkFn⟶R, we denote by C(f) the fiber product of two copies of f. We prove a formula which describes χ(C(f)).
Yasuhiko Kamiyama, Muhammad Ahsan
wiley +1 more source
Eilenberg–Mac Lane Spaces for Topological Groups
Axioms, 2019 In this paper, we establish a topological version of the notion of an Eilenberg−Mac Lane space. If X is a pointed topological space, π 1 ( X ) has a natural topology coming from the compact-open topology on the space of maps S
Ged Corob Cook
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Partition complexes, duality and integral tree representations
, 2004 We show that the poset of non-trivial partitions of 1,2,...,n has a fundamental homology class with coefficients in a Lie superalgebra. Homological duality then rapidly yields a range of known results concerning the integral representations of the ...
Alan Robinson +5 more
core +1 more source
Weak Convergence of Probability Measures on Hyperspaces with the Upper Fell-Topology [PDF]
Bulletin of the Iranian Mathematical SocietyLet E be a locally compact second countable Hausdorff space and F\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\
Dietmar Ferger
semanticscholar +1 more source
Topology and its Applications, 2022 We show that if $L$ is a topological vector lattice, $u \colon L \to L$ is the function $u(x) = x \vee 0$, $C \subset L$ is convex, and $D = u(C)$ is metrizable, then $D$ is an ANR and $u|_C \colon C \to D$ is a homotopy equivalence and thus an AR.
openaire +2 more sources