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We introduce weighted versions of the classical \v{C}ech and Vietoris-Rips complexes.
An introduction to algebraic topology
J. J. Rotman · 1988
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Algebraic topology
A. Hatcher · 2002
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Lectures on Discrete Geometry
J. Matoušek · 2002
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Computing persistent homology
A. Zomorodian and G. Carlsson · 2005
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Stability of persistence diagrams
D. Cohen-Steiner, H. Edelsbrunner, and J. Harer · 2007
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Coverage in sensor networks via persistent homology
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Computational topology
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Persistent homology analysis of brain artery trees
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Efficient and robust persistent homology for measures
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Further Properties and Applications of Weighted Persistent Homology
S. Ren, C. Wu, and J. Wu · 2017
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Weighted Persistent Homology
S. Ren, C. Wu, and J. Wu · 2017
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