Sheaf Based Modeling of Wireless Communications

Explore the application of sheaf theory to wireless communications modeling in this 57-minute lecture by Michael Robinson. Delve into an abstracted methodology that avoids high-fidelity specifications, and discover how topology, simplicial complexes, and persistence concepts tie into physical models. Learn about link and interference complexes, network activation, and the wireless activation sheaf. Examine sections of activation sheaves, regions of influence, and persistent homological invariants. Investigate interference filtration through a simulation example and analyze results for random networks. Conclude with insights on lifting queues to switches, categorification, and an experimental setup using the ns-2 network simulator to generate traffic.

Intro
Acknowledgements
Problem statement
An abstracted methodology - Avoid specifying and committing to a high fidelity
Answering the challenge
Topology #topology
Simplicial complexes
Tying in the physical model
Link complex
Interference complex
The two complexes are not the same
Persistence and model robustness
Network activation
A sheaf is...
Wireless activation sheaf
Sections of activation sheaves
Region of influence
Persistent homological invariant
Interference filtration
Simulation example
Relative homological invariant
Results for a random network
Lifting queues to switches
Categorification to the rescue?
Experimental setup . Using the ns 2 network simulator to generate traffic
Initial simulation