Persistence and filtered complexes

These treatments share a subject; their labels distinguish the questions they answer.

• A hole appears and disappears — Mathematical lesson. When does a hole appear and disappear, and how can I read its interval?
• Finite encodings: recovering a module from finite data — Mathematical lesson. How can finite data recover a module over an infinite parameter domain?
• Persistence modules over posets — Mathematical lesson. How do vector spaces and compatible maps describe persistence?
• Why two parameters change the problem — Mathematical lesson. Why do two parameters require spaces and maps beyond a barcode?
• Choosing views and inspecting intervals — Library guide. Which view lets me investigate the mathematical object I have computed?
• From inputs to computed objects — Library guide. Which construction route should I choose, and what object will it return?
• Ordinary persistent homology — Library guide. Which ordinary persistence construction and retained output answer my question?
• Explain a distance through its matching — Task recipe. Which matched and unmatched intervals account for a computed diagram distance?
• Ordinary persistence: TamerOp and PHAT — Benchmark report. What does the scoped comparison with PHAT establish?
• Vietoris–Rips persistence: TamerOp and Ripser.py — Benchmark report. What does the fixed comparison with Ripser.py establish for ordinary Rips barcodes, cocycles and landmark workflows?

Explore all topics.