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3 questions
3
votes
1
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Why is the Vietoris–Rips complex $\operatorname{VR}(S, \epsilon)$ a subset of the Čech complex $\operatorname{Čech}(S, \epsilon\sqrt{2})$?
$\DeclareMathOperator\Cech{Čech}\DeclareMathOperator\VR{VR}$I am reading Fasy, Lecci, Rinaldo, Wasserman, Balakrishnan, and Singh - Confidence sets for persistence diagrams (see here for a version of ...
2
votes
0
answers
53
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Facet counting argument for polytopes
Consider a pair of piecewise-linear cobordant $n$ dimensional polyhedra $P_1, P_2$ sitting in $\mathbb{R}^{n+2}$ (with some fixed orientation).
Let $O$ be an $n+1$ dimensional piecewise-linear ...
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5
votes
1
answer
237
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Triangulation of the surface determined by sampling two of its cross-sections
I have a data set that essentially looks like the picture below, i.e., it's given by sets of points in $\mathbb{R}^3$ that sample the cross-sections of a certain surface that in principle I do not ...
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