Elegant Geometry of Neural Computations

To try everything Brilliant has to offer—free—for a full 30 days, visit https://brilliant.org/ArtemKirsanov . You’ll also get 20% off an annual premium subscription Socials: X/Twitter: https://x.com/ArtemKRSV Patreon: https://patreon.com/artemkirsanov My name is Artem, I'm a graduate student at NYU Center for Neural Science and researcher at Flatiron Institute (Center for Computational Neuroscience). In this video, we explore how the internal dynamics of neurons give rise to their remarkable computational properties. Through geometric reasoning about phase portraits and bifurcations, we'll gain intuition behind various phenomena, such as excitability, bistability, hysteresis and resonant oscillations. Code for the video: https://github.com/ArtemKirsanov/Youtube-Videos/tree/main/2024/Elegant%20Geometry%20of%20Neural%20Computations Outline: 00:00 Introduction 01:26 Review of Hodgkin-Huxley equations 02:18 Deriving a 2-variable model 04:34 Phase Plane concepts 08:04 Excitability 12:14 Bistability and hysterisis 14:09 Saddle-Node Bifurcations 16:17 Andronov-Hopf Bifurcations 21:03 Integrators vs Resonators 22:26 Putting all together 25:15 Brilliant.org 26:17 Outro References: Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting by Eugene M. Izhikevich: https://mitpress.mit.edu/9780262514200/dynamical-systems-in-neuroscience/ This video was sponsored by Brilliant