Results 31 to 40 of about 1,043,448 (307)
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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Weighted persistent homology [PDF]
Rocky Mountain Journal of Mathematics, 2018 In this paper we develop the theory of weighted persistent homology. In 1990, Robert J. Dawson was the first to study in depth the homology of weighted simplicial complexes. We generalize the definitions of weighted simplicial complex and the homology of weighted simplicial complex to allow weights in an integral domain $R$. Then we study the resulting
Ren, Shiquan, Wu, Chengyuan, Wu, Jie
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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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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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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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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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A Framework for Fast and Stable Representations of Multiparameter Persistent Homology Decompositions [PDF]
Neural Information Processing Systems, 2023 Topological data analysis (TDA) is an area of data science that focuses on using invariants from algebraic topology to provide multiscale shape descriptors for geometric data sets such as point clouds.
David Loiseaux +2 more
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Photonic band structure design using persistent homology
APL Photonics, 2021 The machine learning technique of persistent homology classifies complex systems or datasets by computing their topological features over a range of characteristic scales. There is growing interest in applying persistent homology to characterize physical
Daniel Leykam, Dimitris G. Angelakis
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Persistent Homology Meets Object Unity: Object Recognition in Clutter [PDF]
IEEE Transactions on robotics, 2023 Recognition of occluded objects in unseen and unstructured indoor environments is a challenging problem for mobile robots. To address this challenge, we propose a new descriptor, Topological features Of Point cloud Slices (TOPS), for point clouds ...
Ekta U. Samani, A. Banerjee
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Stability and machine learning applications of persistent homology using the Delaunay-Rips complex [PDF]
Frontiers in Applied Mathematics and Statistics, 2023 Persistent homology (PH) is a robust method to compute multi-dimensional geometric and topological features of a dataset. Because these features are often stable under certain perturbations of the underlying data, are often discriminating, and can be ...
Amisha Mishra, Francis C. Motta
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