(revised February 2013)

My current research tries to advance the understanding of single neurons and interactions of populations of neurons using ideas from stochastic dynamics. One theme is that interactions of excitatory and inhibitory populations produce oscillations which are sustained by noise. Analysis of the corresponding stochastic process yields information about the pattern of bursts of various frequencies in local field potential data. Another theme is that subthreshold oscillations are produced by dynamics of e.g. Morris Lecar, Fitzhugh Nagumo, or Hodgkin Huxley neuron models near the fixed point. The stochastic dynamics of the corresponding stochastic models yields sustained oscillations at a frequency which, in stelate neurons, for instance, can be identified with theta oscillations. These appear prominently in the first few subthreshold oscillations after each firing. The population effect, combined with synchronization, is theta rhythm of firing in a population.

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