Complex Contagions and Hybrid Phase Transitions

on YouTube ↗01h 08m

" summary

Adapts infectious-disease methods to produce closed-form dynamical equations for the Watts threshold model on configuration-model and triangle-based clustered networks, using a test-node probability argument, cobweb-style maps and edge-based compartmental ideas. Derives explicit criteria when arbitrarily small seeding still triggers global cascades in clustered graphs, and predicts hybrid phase transitions where tiny seeds fail but larger seeds jump the system to a very different final size. Equations reproduce simulations showing bistability and sudden jumps.

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" chapters (10)

1. 0:00Introduction to contagions
2. 3:20Cobweb diagrams
3. 6:30Defining contagion models
4. 12:40The Watts threshold model
5. 21:25Configuration model networks
6. 26:30Clustered random networks
7. 29:25Mathematical modeling framework
8. 40:20Phase transitions and dynamics
9. 48:50First-order phase transitions
10. 1:00:00Global cascades and conclusion