Moritz Helias, Tom Tetzlaff, Markus Diesmann
Correlations are employed in modern physics to explain microscopic and macroscopic phenomena, like the fractional quantum Hall effect and the Mott insulator state in high temperature superconductors and ultracold atoms. Simultaneously probed neurons in the intact brain reveal correlations between their activity and theoretical work illuminates the importance of correlation for information processing and for macroscopic measures of neural activity, like the EEG. Nevertheless networks of spiking neurons differ from most physical systems: The interaction between elements is directed, time delayed, is mediated by short pulses, and each neuron receives events from thousands of neurons and sends events to thousands of others. Even in the stationary state the network does not reach equilibrium in the sense of detailed balance. Here we develop a quantitative theory of pairwise correlations in finite sized random networks of spiking neurons. We show why the intuitive mean field description fails, how single action potentials reverberate in the network causing an apparent lag of inhibition with respect to excitation, and how global collective oscillations arise.
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http://arxiv.org/abs/1207.0298
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