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