Berlin 2008 – wissenschaftliches Programm
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BP: Fachverband Biologische Physik
BP 3: Neuronal Systems
BP 3.9: Vortrag
Montag, 25. Februar 2008, 16:30–16:45, C 243
Statistical framework incorporating temporal and mutual correlations in a neural network ensemble. — •Tatjana Tchumatchenko1,2, Theo Geisel1,2, Stefan Treue3, and Fred Wolf1,2 — 1Max-Planck-Institute for Dynamics and Self-Organization, Göttingen — 2Bernstein Center for Computational Neuroscience (BCCN), Göttingen — 3Kognitive Neurowissenschaften, Deutsches Primaten Zentrum, Göttingen
We present a new class of parametric models for multiple impulse sequences correlated in time and between channels, which we call Gaussian Pseudo Potential Models (GPPMs). In our approach, correlated impulse sequences are defined by threshold crossings of temporally continuous random functions, called the Pseudo Potentials (PPs). Assuming Gaussian statistics of PPs, a correlated spike train ensemble is uniquely specified by the Matrix of cross- and auto-covariance functions of the PPs. Many spike train statistics, as e.g. firing rates, auto and cross conditional firing rates, can then be expressed in closed form [1]. In an ensemble of spike trains from a pair of neurons, we analyse the mapping between PP correlations and spike correlations. We show, that that for weak coupling strength the cross conditional rate is connected to the PP cross correlation function by a linear differential equation. The applicability of these differential equations is numerically confirmed for a simple set of model PP correlation functions. These and other exact results suggest that GPPMs provide a analytically very tractable parametric model of multiple correlated neuronal impulse sequences. [1] B. Naundorf et al. Nature, 440:1060--1063, 2006