Noise Suppression and Surplus Synchrony by Coincidence Detection
Figure 9
Mechanistic model of enhanced correlation transmission by synchronous input events.
A The detailed model discussed in the results section is simplified two-fold. 1) We consider binary neurons with a static non-linearity . 2) We distinguish two representative scenarios with different models for the common input:
: Gaussian white noise with variance
, representing the case without synchrony, or
: a binary stochastic process
with constant amplitude
, mimicking the synchronous arrival of synaptic events. In both scenarios in addition each neuron receives independent Gaussian input. B Marginal distribution of the total input
to a single neuron for input
(gray) and
(black) and for
. In input
the binary process
alternates between
(with probability
) and
(with probability
), resulting in a bimodal marginal distribution. The mean activity of one single neuron is given by the probability mass above threshold
. We choose the variances
and
of the disjoint Gaussian fluctuating input such that the mean activity is the same in both scenarios. C Output correlation
as a function of the input correlation
(see A) between the total inputs
and
. Probability
is chosen such that inputs
and
result in the same input correlation
. The four points marked by circles correspond to the panels D–G. D–G Joint probability density of the inputs
,
to both neurons. For two different values of
the lower row (E,G) shows the scenario
, the upper row (D,F) the scenario
. Note that panel B is the projection of the joint densities in F and G to one axis. Brighter gray levels indicate higher probability density; same gray scale for all four panels.