Results 31 to 40 of about 416 (159)
Scalable Computation of Topological Abstractions for Scalar Data
Computer Graphics Forum, EarlyView.Abstract Topological data analysis has become an important tool for large scale scalar data analysis and visualization, efficiently extracting the inherent structure and features of interest of the data. However, with growing dataset sizes and complexity, it is increasingly becoming infeasible to compute topological abstractions of interest in serial ...
M. Will +6 more
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Some properties of hyperspaces of Cech closure spaces with Vietoris-like topologies [PDF]
Filomat, 2010 We study some topological properties of hyperspaces of Cech closure spaces endowed with Vietoris-like topologies. Some of these notions were introduced and considered in [9, 10] and [11], focussing on selection principles.
Andrijević, Dimitrije +2 more
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Some remarks on selectively highly divergent spaces
Applied General TopologyIn this paper, we study selectively highly divergent (SHD) spaces on hyperspaces with the Vietoris topology and the Pixley-Roy topology. Moreover, we show that they are preserved under quasi-perfect countable-to-one mappings and preserved inversely under
Luong Quoc Tuyen +2 more
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Selective Survey on Spaces of Closed Subgroups of Topological Groups
Axioms, 2018 We survey different topologizations of the set S ( G ) of closed subgroups of a topological group G and demonstrate some applications using Topological Groups, Model Theory, Geometric Group Theory, and Topological Dynamics.
Igor V. Protasov
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Topology‐Aware Machine Learning for High‐Throughput Screening of MOFs in C8 Aromatic Separation
Advanced Intelligent Discovery, Volume 2, Issue 4, August 2026.We screened 15,335 Computation‐Ready, Experimental Metal–Organic Frameworks (CoRE‐MOFs) using a topology‐aware machine learning (ML) model that integrates structural, chemical, pore‐size, and topological descriptors. Top‐performing MOFs exhibit aromatic‐enriched cavities and open metal sites that enable π–π and C–H···π interactions, serving as ...
Yu Li, Honglin Li, Jialu Li, Wan‐Lu Li
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Persistent sheaf Laplacian analysis of protein stability and solubility changes upon mutation
Protein Science, Volume 35, Issue 8, August 2026.Abstract Genetic mutations frequently disrupt protein structure, stability, and solubility, acting as primary drivers for a wide spectrum of diseases. Despite the critical importance of these molecular alterations, existing computational models often lack interpretability and fail to integrate essential physicochemical interactions.
Yiming Ren +4 more
wiley +1 more source
Journal of Scientific Research, 2016 In this article, we define the hyperspace of soft closed sets of a soft topological space (FA, ?). In addition, we define the Vietoris soft topology, ?v, by determining the soft base of this topology which has the form ?FH1, FH2,.....FHn?, where ?FH1, FH2,.....FHn? are soft open sets in (FA, ?).
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Vietoris-rips complexes also provide topologically correct reconstructions of sampled shapes [PDF]
Proceedings of the twenty-seventh annual symposium on Computational geometry, 2011 Given a point set that samples a shape, we formulate conditions under which the Rips complex of the point set at some scale reflects the homotopy type of the shape. For this, we associate with each compact set X of R^n two real-valued functions c"X and h"X defined on R"+ which provide two measures of how much the set X fails to be convex at a given ...
Attali, Dominique +2 more
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Topological Graph Neural Networks: A Novel Approach for Geometric Deep Learning
Applied AI Letters, Volume 7, Issue 2, June 2026.This graphical abstract illustrates the Topological Graph Neural Network (TopGNN) architecture. It demonstrates a parallel processing approach where an input graph is simultaneously analyzed by a standard GNN Encoder to capture local node features and by Persistent Homology to extract global topological features (like cycles and voids), visualized as a
Amarjeet +7 more
wiley +1 more source
Persistent entropy for separating topological features from noise in vietoris-rips complexes [PDF]
Journal of Intelligent Information Systems, 2017 Persistent homology studies the evolution of k-dimensional holes along a nested sequence of simplicial complexes (called a filtration). The set of bars (i.e. intervals) representing birth and death times of k-dimensional holes along such sequence is called the persistence barcode. k-Dimensional holes with short lifetimes are informally considered to be
Nieves Atienza +2 more
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