Description:

The brain accomplishes perceptual, motor, and cognitive function through interconnected
neurons wired in precise functional circuits, and the resulting patterns of activity are often 
distributed across brain areas. The brain thus relies on communication between cortical areas to achieve complex cognitive tasks. To understand this ability, we need a deeper understanding of the underlying circuit mechanisms that give rise to the observed patterns of activity, and of the mechanisms of information transfer across cortical areas. In neuroscience, the leading hypotheses for interareal communication contend that communication is modulated either via coherent oscillatory  activity,  or  via  the  alignment  of  low-dimensional  “communication subspaces” (CS) of population activity. In this talk, I will show how we can reconcile these two mechanisms of communication through a spectral decomposition of CS, and how its dimensionality is influenced by coherence. I will develop an analytical theory of communication for circuits described by stochastic dynamical systems exhibiting fixed-point solutions and propose experimentally-testable 
predictions while advancing a new hypothesis for the functional role of oscillatory activity in the brain. I will also discuss how different choices of circuit models influence these predictions. My main focus will be on a new class of dynamical circuit models implementing divisive normalization exactly called ORGaNICs.

Finally, if time allows it, I will discuss the problem of basin volume estimation and present a 
powerful numerical technique for its computation that scales to O(1000) dimensions, and I will speculate on how it may enable us to predict stability of cognitive states in models of the brain, and even achieve nonlinear control of neural network dynamics.