Department of Applied Mathematics
University of Colorado Boulder
Boulder, CO 80309-0526
Dr. Kilpatrick received his PhD in mathematics from the University of Utah in 2010. His research in mathematical neuroscience has covered spatiotemporal pattern formation in continuum models of neural networks, stochastic and nonlinear dynamics of both spike and rate-based models, information transfer in models of working memory, and stochastic models of evidence accumulation and decision making. One of his primary interests is understanding how the architecture of large-scale neural circuits engenders robust neural computation in various space-related cognitive tasks, including spatial working memory and spatial navigation. Mathematical models developed are amenable to asymptotic analysis that accurately characterize how neural architecture shapes information transfer. Another ongoing project focuses on how humans and non-human animals integrate observations in changing environments, in order to make decisions and learn the underlying statistics of the environment. To this end, he is working with several experimental collaborators who are interested in the behavior and underlying neural computations of animals performing decision making tasks in dynamic environments.
DB Poll, K Nguyen, and ZP Kilpatrick (2016). Sensory feedback in a bump attractor model of path integration J Comput. Neurosci. 40, pp. 137-155.
A Veliz-Cuba, ZP Kilpatrick, K Josic (2016). Stochastic models of evidence accumulation in changing environments SIAM Rev. 58, pp. 264–289.
A Veliz-Cuba, HZ Shouval, K Josic, ZP Kilpatrick (2015). Networks that learn the precise timing of event sequences. J Comput. Neurosci. 39, pp. 235-254.
ZP Kilpatrick (2015). Stochastic synchronization of neural activity waves. Phys. Rev. E 91, 040701(R).
ZP Kilpatrick, B Ermentrout, and B Doiron (2013). Optimizing working memory with heterogeneity of recurrent cortical excitation. J Neurosci., 33, pp. 18999-19011.