Results 21 to 30 of about 1,143,028 (268)
Discrete & Computational Geometry, 2022 AbstractThe alpha complex efficiently computes persistent homology of a point cloud $$X$$ X in Euclidean space when the dimension $$d$$ d is low. Given a subset $$A$$ A of $$X$$ X , relative Čech persistent homology
Nello Blaser, Morten Brun
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Stable Vectorization of Multiparameter Persistent Homology using Signed Barcodes as Measures [PDF]
Neural Information Processing Systems, 2023 Persistent homology (PH) provides topological descriptors for geometric data, such as weighted graphs, which are interpretable, stable to perturbations, and invariant under, e.g., relabeling.
David Loiseaux +4 more
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Flow estimation solely from image data through persistent homology analysis
Scientific Reports, 2021 Topological data analysis is an emerging concept of data analysis for characterizing shapes. A state-of-the-art tool in topological data analysis is persistent homology, which is expected to summarize quantified topological and geometric features ...
Anna Suzuki +6 more
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A cyclic perspective on transient gust encounters through the lens of persistent homology [PDF]
Journal of Fluid Mechanics, 2023 Large-amplitude gust encounters exhibit a range of separated flow phenomena, making them difficult to characterize using the traditional tools of aerodynamics.
Luke R. Smith +4 more
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On the Expressivity of Persistent Homology in Graph Learning [PDF]
LOG IN, 2023 Persistent homology, a technique from computational topology, has recently shown strong empirical performance in the context of graph classification. Being able to capture long range graph properties via higher-order topological features, such as cycles ...
Bastian Alexander Rieck
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Persistent homology in graph power filtrations [PDF]
Royal Society Open Science, 2016 The persistence of homological features in simplicial complex representations of big datasets in Rn resulting from Vietoris–Rips or Čech filtrations is commonly used to probe the topological structure of such datasets.
Allen D. Parks, David J. Marchette
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The persistent homology of genealogical networks
Applied Network Science, 2023 Genealogical networks (i.e. family trees) are of growing interest, with the largest known data sets now including well over one billion individuals. Interest in family history also supports an 8.5 billion dollar industry whose size is projected to double
Zachary M. Boyd +6 more
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Weighted persistent homology [PDF]
Involve, a Journal of Mathematics, 2019 We introduce weighted versions of the classical ech and Vietoris-Rips complexes. We show that a version of the Vietoris-Rips Lemma holds for these weighted complexes and that they enjoy appropriate stability properties. We also give some preliminary applications of these weighted complexes.
Bell, Gregory +4 more
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Adaptive Topological Feature via Persistent Homology: Filtration Learning for Point Clouds [PDF]
Neural Information Processing Systems, 2023 Machine learning for point clouds has been attracting much attention, with many applications in various fields, such as shape recognition and material science.
Naoki Nishikawa +2 more
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The persistent homology of mitochondrial ATP synthases
iScience, 2023 Summary: Relatively little is known about ATP synthase structure in protists, and the investigated ones exhibit divergent structures distinct from yeast or animals.
Savar D. Sinha, Jeremy G. Wideman
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