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Practical Guide to Persistent Homology

• Basics
  • Simplices
  • Filtration
  • Persistent Homology
  • Diagram Distances
  • Homologous Cycles
  • Representative Cycles
• Filtrations
  • Vietoris–Rips Complexes
  • Lower-star Filtrations
• Persistence
  • Omni-field Persistence
  • Cohomology Persistence
  • Zigzag Persistence
• Plotting
• Diagnostics

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