  The functional significance of correlations between action potentials of
neurons is still a matter of vivid debates. In particular it is presently
unclear how much synchrony is caused by afferent synchronized events and how
much is intrinsic due to the connectivity structure of cortex. The available
analytical approaches based on the diffusion approximation do not allow to
model spike synchrony, preventing a thorough analysis. Here we theoretically
investigate to what extent common synaptic afferents and synchronized inputs
each contribute to closely time-locked spiking activity of pairs of neurons. We
employ direct simulation and extend earlier analytical methods based on the
diffusion approximation to pulse-coupling, allowing us to introduce precisely
timed correlations in the spiking activity of the synaptic afferents. We
investigate the transmission of correlated synaptic input currents by pairs of
integrate-and-fire model neurons, so that the same input covariance can be
realized by common inputs or by spiking synchrony. We identify two distinct
regimes: In the limit of low correlation linear perturbation theory accurately
determines the correlation transmission coefficient, which is typically smaller
than unity, but increases sensitively even for weakly synchronous inputs. In
the limit of high afferent correlation, in the presence of synchrony a
qualitatively new picture arises. As the non-linear neuronal response becomes
dominant, the output correlation becomes higher than the total correlation in
the input. This transmission coefficient larger unity is a direct consequence
of non-linear neural processing in the presence of noise, elucidating how
synchrony-coded signals benefit from these generic properties present in
cortical networks.
