The Topological Dirac Operator and the Dynamics of Topological Signals

The Topological Dirac Operator and the Dynamics of Topological Signals

Applied Algebraic Topology Network via YouTube Direct link

Intro

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1 of 25

Intro

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The Topological Dirac Operator and the Dynamics of Topological Signals

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  1. 1 Intro
  2. 2 Simplicial complex data
  3. 3 The boundary of a boundary is null
  4. 4 Square d-dimensional lattice
  5. 5 Apollonian and pseudo-fractal hyperbolic simplicial complexes
  6. 6 Network Geometry with Flavor GROWTH
  7. 7 Hausdorff and spectral dimension
  8. 8 Spectral dimension of Apollonian networks and effect of randomness
  9. 9 Higher-order spectral dimension
  10. 10 Spectral dimension of the up-higher-order Laplacian
  11. 11 Higher-order Diffusion
  12. 12 Topological Dirac operator on a network
  13. 13 Sketch of the derivation
  14. 14 Topological Dirac equation on simplicial complexes
  15. 15 Directional Dirac operator on lattices
  16. 16 3-dimensional lattice
  17. 17 Directional Dirac operators on
  18. 18 Synchronization is a fundamental dynamical process
  19. 19 Synchronization transition
  20. 20 Order parameters using the n-dimensional phases
  21. 21 Synchronization of uncoupled topological signals • The uncoupled dynamics of nodes and links of a network
  22. 22 Phase diagram of topological synchronisation
  23. 23 Rhythmic phase
  24. 24 Conclusions
  25. 25 References and collaborators

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