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1
Intro
2
Acknowledgements
3
Problem statement
4
An abstracted methodology - Avoid specifying and committing to a high fidelity
5
Answering the challenge
6
Topology #topology
7
Simplicial complexes
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Tying in the physical model
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Link complex
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Interference complex
11
The two complexes are not the same
12
Persistence and model robustness
13
Network activation
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A sheaf is...
15
Wireless activation sheaf
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Sections of activation sheaves
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Region of influence
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Persistent homological invariant
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Interference filtration
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Simulation example
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Relative homological invariant
22
Results for a random network
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Lifting queues to switches
24
Categorification to the rescue?
25
Experimental setup . Using the ns 2 network simulator to generate traffic
26
Initial simulation
Description:
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.

Sheaf Based Modeling of Wireless Communications

Applied Algebraic Topology Network
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