Ran Levi - Bedlewo: Topological Analysis of Neural Networks

Explore topological analysis techniques applied to neural networks in this conference talk by Ran Levi. Delve into the challenges of obtaining connectivity data from biological brains and how artificial neural networks provide partial solutions. Learn about an ongoing collaborative project applying topological methods to study the brain, motivated by the Blue Brain Project's digital reconstruction of rat cortex. Discover how directed structural connectivity graphs are extracted and analyzed using novel ideas and basic algebraic topology. Examine the Flag Complex, abstract ordered simplicial complexes, and the directed flag complex of directed graphs. Investigate reciprocal connections and the Transmission-Response method for analyzing neural activity. Compare point vs. circle experiments and explore highway graphs and their relations through line digraphs. Gain insights into the intersection of topology, neuroscience, and artificial intelligence in this comprehensive presentation.

Intro
What can a topologist and a neuroscientist talk about?
Neurons in the cortex come in 55 distinct morphological types spread across 6 layers of the cortex.
55 morphological types of neurons, 6 Layers
The Flag Complex
Alstract ordered simplicial complexes and the directed flag complex of a directed graph
Reciprocal connections
Analysis of the Blue Brain Project Reconstruction
OK, so both a rat and a c-elegans have notrivial brains, topologically speaking, BUT
Activity: The Transmission-Response method
Point vs. Circle Experiment
"Applied" applied topology (?)
Highway graphs - some observations
Line digraphs and relations among highway graphs
Example 2