Threshold-Linear Networks, Attractor Moduli Spaces, and Oriented Matroids

Explore threshold-linear networks (TLNs) as computational models in theoretical neuroscience through this Coxeter Lecture Series presentation by Professor Carina Curto from Brown University. Discover how these simple, recurrently-connected networks exhibit rich nonlinear dynamics including multistability, limit cycles, quasiperiodic attractors, and chaos despite their straightforward structure. Learn about the surprising phenomenon where identical dynamic attractors can emerge in multiple TLNs with completely different architectures and dynamics, and understand how these attractors remain stable across extensive regions of the TLN parameter space. Examine the application of oriented matroid theory to analyze TLN bifurcation behavior, gaining insights into the fundamental relationships between network architecture and resulting dynamics. Understand how these mathematical frameworks provide valuable tools for modeling neural activity and computation in the brain, bridging theoretical mathematics with computational neuroscience applications.