Correlations from theory and simulations for a two-population binary network with asymmetric connectivity.

<p><b>A</b> Average pairwise cross-covariances from simulations (solid curves) and <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004490#pcbi.1004490.e117" target="_blank">Eq (55)</a> (dashed curves). <b>B</b> Naive scaling with <i>J</i> ∝ 1/<i>K</i> but without adjustment of the external drive changes the correlation structure. <b>C</b> With an appropriate adjustment of the external drive (<i>σ</i>_ex = 53.4, <i>σ</i>_ix = 17.7), scaling synaptic weights as <i>J</i> ∝ 1/<i>K</i> is able to preserve correlation structure as long as <i>N</i> and <i>K</i> are reduced by comparable factors. <b>D</b> The same holds for </p><p></p><p></p><p><mi>J</mi><mo>∝</mo><mn>1</mn><mo>/</mo></p><p><mi>K</mi></p><p></p><p></p><p></p> (<i>μ</i>_ex = 43.3, <i>μ</i>_ix = 34.6, <i>σ</i>_ex = 46.2, <i>σ</i>_ix = 15.3), but the susceptibility <i>S</i> is increased by about 20% already for <i>N</i> = 0.75 <i>N</i>₀ in this case. In <b>B</b>, <b>C</b>, and <b>D</b>, results of simulations are shown. The curves in <b>C</b> and <b>D</b> are identical because internal inputs, the standard deviation of the external drive, and the distance to threshold due to the DC component of the drive in <b>D</b> are exactly <p></p><p></p><p></p><p></p><p><mi>K</mi></p><p><mi>K</mi><mn>0</mn></p><p></p><p></p><p></p><p></p><p></p> times those in <b>C</b>. Hence, identical realizations of the random numbers for the connectivity and the Gaussian external drive cause the total inputs to the neurons to exceed the threshold at exactly the same points in time in the two simulations. The simulated time is 30 s, and the population activity is sampled at a resolution of 0.3 ms.<p>