Figure 3

Applying our method to a larger network of \(N_{c}=50\) neurons. As coupling strength increases (red → green → cyan → purple), performance worsens. (A) The absolute value of the error of our method with the Monte Carlo simulations as a function of time. Each Average Absolute Error time point is averaged over the entire set of statistics (i.e., for the mean and variances the average is over all 50, for covariances the average is over \(1225=49*25\)). (A) Left: the average for the mean activity \(X_{j}\) (solid) and mean firing \(F(X_{j})=\nu_{j}\) (dot-dashed); with the progression of colors (red to purple) representing stronger (i.e., larger) coupling values \(G_{j,k}\). (A) Middle: Error of covariances (thinner lines, \(j\neq k\)) and variances (thicker lines, \(j=k\)) of activity \(X_{j}\). (A) Right: Error of covariances (thinner lines, \(j\neq k\)) and variances (thicker lines, \(j=k\)) of firing \(F(X_{j})=\nu_{j}\). (B) Representative comparisons of our method with the Monte Carlo simulations. (B) Left: although the average error increases with coupling magnitude, the discrepancies are not noticeable for mean activity and firing (not shown). (B) Middle: the method is visibly worse for the variance of activity as coupling magnitude increases. (B) Right: the method is visibly worse as coupling magnitude increases – note that the weakest coupling (red) is between green (second weakest) and purple (strongest)