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Request resources for mathematical foundations of higher-order topological dynamics in networks

Wolfram Resources for Higher-Order Topological Dynamics

I'm looking for Wolfram resources to study the following topics. Any guidance would be greatly appreciated as I've tried Notebook Assistant and OpenAI Wolfram ChatGPTs without success.

Algebraic Topology

  • Simplicial complexes
  • Homology theory
  • Betti numbers
  • Persistent homology

Discrete Exterior Calculus

  • Boundary operators
  • Hodge theory
  • Hodge Laplacians

Dynamical Systems on Higher-Order Networks

  • Synchronization
  • Topological Kuramoto model
  • Topological pattern formation

Quantum-Inspired Mathematical Formalism

  • Topological spinors
  • Topological Dirac operator
  • Triadic interactions
POSTED BY: Amin Cheikhi
3 Replies

Thank you so much!

POSTED BY: Amin Cheikhi
POSTED BY: Wolfram U

Also PersistantHomology in the Wolfram Function Repository might be relevant.

POSTED BY: Daniel Lichtblau
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