Homological Percolation: The Formation of Giant Cycles

Homological Percolation: The Formation of Giant Cycles

Applied Algebraic Topology Network via YouTube Direct link

MAIN RESULT

10 of 21

10 of 21

MAIN RESULT

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Homological Percolation: The Formation of Giant Cycles

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  1. 1 Intro
  2. 2 PERSISTENT HOMOLOGY
  3. 3 THE MAXIMAL PERSISTENCE OF NOISE
  4. 4 TYPICAL BEHAVIOR
  5. 5 CROSSING PROBABILITIES
  6. 6 CONT. PERC. IN A BOX - SETUP
  7. 7 CONT. PERC. - GIANT COMPONENTS
  8. 8 "GIANT" K-CYCLES
  9. 9 HOMOLOGICAL PERCOLATION
  10. 10 MAIN RESULT
  11. 11 SIGNAL VS. NOISE
  12. 12 H, PERCOLATION
  13. 13 DUALITY - PROOF
  14. 14 H.- -PERCOLATION
  15. 15 BIG PICTURE?
  16. 16 EULER CHARACTERISTIC
  17. 17 EC & PERCOLATION?
  18. 18 SIMULATIONS
  19. 19 PERMUTAHEDRAL SITE-PERCOLATION
  20. 20 GAUSSIAN RANDOM FIELDS
  21. 21 SUMMARY & FUTURE WORK

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