Zachary Kilpatrick: Robust and adaptive collective dynamics of neurons and organisms

University of Colorado Boulder, Applied Mathematics

Title: Robust and adaptive collective dynamics of neurons and organisms

Abstract:

How do neural circuits and animal collectives maintain robust representations and make reliable decisions in the face of noise, bias, and environmental uncertainty? We present recent work developing asymptotic, spectral, and multiscale methods to characterize these challenges across two levels of organization. Localized persistent activity in neural circuits encodes continuous stimulus features in bumps whose stochastic drift shapes working memory error. We derive nonlinear Langevin equations characterizing how excitatory-inhibitory subpopulations wander under noise and how short-term plasticity couples activity to connectivity across timescales. A central new result is that astrocytic resource diffusion stabilizes bump position through a two-stage mechanism: diffusive redistribution smooths resource asymmetries created by small displacements, and local synaptic replenishment transfers this smoothing back to the neural layer, enlarging the parameter regime supporting persistent activity. We discuss extensions toward microscopic biophysical models of neurotransmitter recycling and glial uptake, and new dynamical regimes emerging when local and nonlocal astrocytic processes interact across scales. In the second part we turn to collective decision-making, where first passage time analysis and extreme value statistics characterize how groups accumulate evidence under bias and uncertainty. Fast deciders reflect prior bias regardless of the truth while slow deciders do not, and division of labor between explorers and foragers emerges as an optimal solution to tracking environmental change without central coordination.

 

Guests are welcome!

 

Organized by

Benjmin Lindner / Lisa Rosenbluhm