PSU Mark
Eberly College of Science Mathematics Department

Meeting Details

For more information about this meeting, contact Kris Jenssen, Yuxi Zheng.

Title:Fokker-Planck Description for Noisy Neuronal Network Dynamics
Seminar:Computational and Applied Mathematics Colloquium
Speaker:Gregor Kovacic, Rensselaer Polytechnic Institute
Abstract:
Kinetic theory provides a coarse-grained alternative to the integrate- and-fire neuronal network description. In the limit of infinitely short conductance responses, a Boltzmann-type differential- difference equation can be derived for the probability density function of the neuronal voltage. A Fokker-Planck and a mean-field equation can be derived in the limit of small and vanishing conductance fluctuations, respectively. The talk will present detailed solutions to these equations, describing both the steady asynchronous and synchronously-oscillating states of the network, and will also discuss the effects of the network architecture. The mean- field provides exact solutions for the steady asynchronous state. For scale-free neuronal networks, it can be used to argue that the distributions of the firing rates and neuronal activity correlations are also scale free. The steady asynchronous state is also described by asymptotic solutions of the Fokker-Planck equation, using the size of the neuronal conductance fluctuations as the small parameter. in addition, the Fokker-Planck equation can also be used to describe the likelihood and temporal period of synchronous network oscillations, in which all the neurons fire in unison. The likelihood of synchrony is computed combinatorially using the network oscillation period and the voltage probability distribution. The oscillation period is found from a first-passage-time problem described by a Fokker-Planck equation, which is solved analyticaly via an eigenfunction expansion. The voltage probability distribution is found using a Central-Limit-Theorem-type argument via a calculation of the voltage cumulants. Differences between oscillations in all-to- all coupled and scale-free networks will also be discussed.

Room Reservation Information

Room Number:MB106
Date:09 / 25 / 2009
Time:03:35pm - 04:25pm