AATRN Watch Party: Computing the Topology of Directed Networks

Directed networks provide a natural representation of interactions in neural and other complex systems. Persistent homology can reveal their structure across scales, but its computation often involves very large complexes. I will present local criteria for simplifying directed filtered graphs through vertex and edge collapses while preserving the persistent homology of their associated complexes. These reductions operate directly on the graph and reduce the time and memory required for computation. I will then discuss applications to spiking neural systems, where transfer entropy is used to construct weighted directed networks from neural activity. Their directed persistent homology reveals differences associated with task complexity, stimulus structure, and behavioural conditions.