An Application of Neighborhoods in Directed Graphs in the Classification of Binary Dynamics

Explore the application of neighborhoods in directed graphs for classifying binary dynamics in this 55-minute lecture by Ran Levi from the Applied Algebraic Topology Network. Delve into the concept of binary states on graphs, focusing on their relevance to encoding spiking neuron networks. Discover a topological and graph-theoretic method for extracting information from binary dynamics using vertex neighborhoods. Follow the speaker's demonstration of this method applied to binary dynamics arising from sample activity in the Blue Brain Project's reconstruction of rat cortical tissue. Gain insights into synaptic connections, neuronal activity encoding, and the creation of topological spaces from brain data. Learn about tournaments, graph and topological invariants, and the process of classifying binary dynamics from subgraphs. Examine the function classification experiment, methodology, and results, concluding with further validation using NEST.

Intro
Motivation
Synaptic Connections
A few neurons forming a small network
Encoding neuronal activity
The Blue Brain Reconstruction
Binary Dynamics on digraphs
Make a topological space out of the brain
Some familiar concepts
Tournaments
Application - BBP simulation data
Classifying binary dynamics from subgraphs
Function classification experiment
Neighbourhoods
Graph and topological invariants
Method
Results
Conclusion
Further Validation - NEST