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- Andrew J. Blumberg, Itamar Gal, Michael A. Mandell, Matthew Pancia
- ArXiv
- 2012

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.

The classical isoperimetric inequality relates the lengths of curves to the areas that they bound. More specifically, we have that for a smooth, simple closed curve of length L bounding area A on a surface of constant curvature c, L2 ≥ 4πA− cA2 with equality holding only if the curve is a geodesic circle. We prove generalizations of the isoperimetric… (More)

- Andrew J. Blumberg, Itamar Gal, Michael A. Mandell, Matthew Pancia
- Foundations of Computational Mathematics
- 2014

We study distributions of persistent homology barcodes associated to taking subsamples of a fixed size from metric measure spaces. We show that such distributions provide robust invariants of metric measure spaces, and illustrate their use in hypothesis testing and providing confidence intervals for topological data analysis.

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