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Tangled Vines in a Vineyard of Persistence Diagrams
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Classroom Contents
Studying Fluid Flows with Persistent Homology - Rachel Levanger
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- 1 Intro
- 2 DYNAMICS
- 3 PATTERNS
- 4 2D Kolmogorov Flow
- 5 Sublevel Set Persistent Homology
- 6 Bottleneck Distance in per
- 7 Point Cloud Persistent Homology
- 8 Dealing with Multiple Time Scales
- 9 Algebraic Stability Theorem for Generalized Interleavings
- 10 2D Rayleigh-Bénard Convection : Spiral Defect Chaos
- 11 Lyapunov Vectors and SDC
- 12 Topological Defects + Canonical Pattern Classification
- 13 Critical Point Pairings and Persistent Homology
- 14 Persistent Homology Defects
- 15 Finding a Correspondence...
- 16 Tangled Vines in a Vineyard of Persistence Diagrams
- 17 Linear Interpolation vs. Actual Flow
- 18 BEYOND PERSISTENCE MODULES
- 19 3D Navier-Stokes: Fully-developed Turbulence
- 20 Diffusion Maps
- 21 Landscape Metric on per
- 22 Diffusion Map Embedding of 512 Vorticity Fields
- 23 RESULT:Uncovered a New Relationship
- 24 Tsurushima Mechanism for HCCI
- 25 Landscape l'Speed Profiles
- 26 Differentiating Chemical Species by Speed Profile
- 27 Reaction Profile: R1
