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Fundamental theorem of discrete Morse theory Letf be a discrete Morse function on a cell complex K.
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Classroom Contents
Ulrich Bauer: Ripser - Efficient Computation of Vietoris–Rips Persistence Barcodes
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- 1 Intro
- 2 Vietoris-Rips filtrations
- 3 Demo: Ripser
- 4 Ripser A software for computing Vietoris-flips persistence barcodes - about 1000 lines of C++ code, no external dependencies
- 5 Design goals
- 6 The four special ingredients
- 7 Matrix reduction algorithm Setting: finite metric space X, points
- 8 Compatible basis cycles For a reduced boundary matrix R-D. V, call
- 9 Persistent cohomology
- 10 Counting cohomology column reductions
- 11 Observations
- 12 Implicit matrix reduction Standard approach
- 13 Oblivious matrix reduction
- 14 Natural filtration settings
- 15 Fundamental theorem of discrete Morse theory Letf be a discrete Morse function on a cell complex K.
- 16 Morse pairs and persistence pairs
- 17 Apparent pairs
- 18 From Morse theory to persistence and back
- 19 Ripser Live: users from 156 different cities
