Ran Levi- Topological Analysis of Neural Networks

Explore the intersection of topology and neural networks in this lecture from the Hausdorff Trimester Program on Applied and Computational Algebraic Topology. Delve into the fundamentals of topology and its application to neuroscience, starting with simple organisms like C. elegans and progressing to complex brain models. Discover surprising findings, including prize-winning research, and examine topological reconstructions, activity experiments, and time series analyses. Learn about characterization theorems for line graphs and diffusion processes, gaining insights into how topological analysis can enhance our understanding of neural networks and brain function.

Intro
What is topology
Neurons
C elegans
Brain of C elegans
Blue Brain Project
Connection
Formal definition
Complex of injective words
First surprising discovery
First prize
Results
Topological reconstruction
sanity check
activity
experiments
time series
Statistical test
What next
Example
Theorem for line graphs
Characterization theorem for line graphs
Diffusion
Characterization Theorem
Topology