Correlations in a network of three populations as illustrated in Figure 2 in dependence of the size of the external population.

<p>Each neuron in population receives randomly drawn excitatory inputs with weight , randomly drawn inhibitory inputs of weight and external inputs of weight (homogeneous random network with fixed in-degree, connection probability ). <b>A</b> Correlations averaged over pairs of neurons within the local network (22). Dots indicate results of direct simulation over averaged over pairs of neurons. Curves show the analytical result (24). The point <b>“</b>DC<b>”</b> shows the correlation structure emerging if the drive from the external population is replaced by a constant value , which provides the same mean input as the original external drive. <b>B</b> Correlations between neurons within the local network and the external population averaged over pairs of neurons (same labeling as in A). <b>C</b> Correlation between the inputs to a pair of cells in the network decomposed into the contributions due to shared inputs (gray, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003428#pcbi.1003428.e409" target="_blank">eq. 25</a>) and due to correlations in the presynaptic activity (light gray, <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1003428#pcbi.1003428.e410" target="_blank">eq. 26</a>). Dashed curves and St. Andrew's Crosses show the contribution due to external inputs, solid curves and dots show the contribution from local inputs. The sum of all components is shown by black dots and curve. Curves are theoretical results based on (24), (25), and (26), symbols are obtained from simulation. <b>D</b> Probability distribution of the fluctuating input to a single neuron in the excitatory population. Dots show the histogram obtained from simulation binned over the interval with a bin size of . The gray curve is the prediction of a Gaussian distribution obtained from mean-field theory neglecting correlations, with mean and variance given by (4) and (6), respectively. The black curve takes correlations in the afferent signals into account and has a variance given by (13). Other parameters: simulation resolution , synaptic delay , activity measurement in intervals of . Threshold of the neurons , time constant of inter-update intervals . The average activity in the network is .