Dynamic attractors in inhibition-dominated neural networks
Many networks in the brain possess an abundance of inhibition, which serves to shape and stabilize neural dynamics. The neurons in such networks exhibit intricate patterns of connectivity whose structure controls the allowed patterns of neural activity. To investigate how connectivity shapes activity, we examine inhibitory threshold-linear networks (TLNs) whose dynamics are constrained by an underlying directed graph. In this talk, I will quickly review some older results (graph rules) that enable us to predict fixed points and attractors from the graph, and then shift attention to newer *gluing rules* that enable us to infer dynamic properties of large networks as a function of smaller building blocks. The mathematical results will be illustrated with various examples and applications. If time permits, connections to oriented matroids of hyperplane arrangements will also be discussed.
Pennsylvania State University
Carina Curto is a Professor of Mathematics at Penn State University. She received an A.B. in Physics from Harvard U. in 2000 and a Ph.D. in Mathematics from Duke U. in 2005. During her postdoctoral years at Rutgers and NYU, she transitioned to research in theoretical and computational neuroscience. Her research focuses on theory and analysis of neural networks and neural codes, motivated by questions of learning, memory, and sequence generation in cortical and hippocampal circuits. Curto's work uses and develops tools in applied algebra, geometry, topology, and dynamical systems. Her honors include a Sloan Research Fellowship (2011), a Simons Fellowship (2021), and a Faculty Scholar Medal (2020), in addition to numerous NSF and NIH research awards.
About the Wu Tsai Neuro MBCT Seminar Series The Stanford Center for Mind, Brain, Computation and Technology Seminars (MBCT) explores ways in which computational and technical approaches are being used to advance the frontiers of neuroscience. It features speakers from other institutions, Stanford faculty and senior training program trainees.
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