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Sheaf Based Modeling of Wireless Communications

Applied Algebraic Topology Network via YouTube

Overview

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This course aims to teach students about sheaf-based modeling of wireless communications. The learning outcomes include understanding the concepts of simplicial complexes, network activation, interference complexes, and persistent homological invariants. Students will learn how to apply sheaf theory to wireless communication scenarios and analyze results using experimental setups. The course uses a combination of theoretical explanations, simulation examples, and experimental results to convey the material. The intended audience for this course includes students and professionals interested in advanced topics in wireless communications and algebraic topology.

Syllabus

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

Taught by

Applied Algebraic Topology Network

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