title: Mathematical neuroscience: from neurons to circuits to systems.
abstract: 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 experiments. Spatio-temporal pattern formation methods are applied to explain the patterns seen in the early stages of drug-induced visual hallucinations.
authors.affiliation: Division of Biology and Medicine, Department of Neuroscience, Brown University, Providence, RI, USA.
authors.forename: Boris
authors.initials: B
authors.lastname: Gutkin
authors.forename: David
authors.initials: D
authors.lastname: Pinto
authors.forename: Bard
authors.initials: B
authors.lastname: Ermentrout
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000818:Animals; D006212:Hallucinations / Q000503:physiopathology; D006801:Humans; D008433:Mathematics; D016571:Neural Networks, Computer; D009474:Neurons / Q000502:physiology*; D009488:Neurosciences / Q000379:methods*; D010775:Photic Stimulation / Q000379:methods