Overview
Syllabus
Intro
How does connectivity shape activity?
Combinatorial Threshold-Linear Networks (CTLNs)
A diversity of dynamical behaviour
Dynamic attractors "live around fixed points"
Graph structure and CTLN fixed points
Nerves: divide and conquer
Directional graphs Agraph G is directional there is a partition of its nodes V
DAG decompositions
Directional graphs and feed-forward networks
Directional covers and their nerves
Basic examples
Theorem (DAG decomposition)
5-clique chain example Graph G
Theorem (cycle nerve)
Grid graph
Network engineering: Grid as a nerve
Dynamical prediction
Summary
Thank you for listening
Iterating the construction
Taught by
Applied Algebraic Topology Network