Foundations of Mathematical Neuroscience Bard Ermentrout

Stochastic Neuroscience

Stochastic Network Models in Neuroscience: A Festschrift for Jack Cowan. Introduction to the Special Issue.

Jack Cowan's remarkable career has spanned, and molded, the development of neuroscience as a quantitative and mathematical discipline combining deep theoretical contributions, rigorous mathematical work and groundbreaking biological insights. The Banff International Research Station hosted a workshop in his honor, on Stochastic Network Models of Neocortex, July 17-24, 2014. This accompanying Fe...

Mathematical neuroscience: from neurons to circuits to systems.

Applications of mathematics and computational techniques to our understanding of neuronal systems are provided. Reduction of membrane models to simplified canonical models demonstrates how neuronal spike-time statistics follow from simple properties of neurons. Averaging over space allows one to derive a simple model for the whisker barrel circuit and use this to explain and suggest several exp...

Multiple Rhythmic States in a Model of the Respiratory Central Pattern Generator

Jonathan E. Rubin, Natalia A. Shevtsova, G. Bard Ermentrout, Jeffrey C. Smith, and Ilya A. Rybak Department of Mathematics, University of Pittsburgh, Pittsburgh; Department of Neurobiology and Anatomy, Drexel University College of Medicine, Philadelphia, Pennsylvania; Cellular and Systems Neurobiology Section, Porter Neuroscience Research Center, National Institute of Neurological Disorders and...

Pre-referee eprint Forthcoming in Philosophy of Science Dynamical Models and Explanation in Neuroscience

Kaplan and Craver claim that all explanations in neuroscience appeal to mechanisms. They extend this view to the use of mathematical models in neuroscience and propose a constraint such models must meet in order to be explanatory. I analyze a mathematical model used to provide explanations in dynamical systems neuroscience and indicate how this explanation cannot be accommodated by the mechanis...