Fig. 4.
Method to dissect networks into optimal and nonoptimal subnetworks. (A) Toy network configuration. Neurons 1–9 (blue) are optimal, and neuron 10 (pink) is located at random. Blue and pink links represent N and M connections each, respectively. (B) Position error for nonoptimal neuron 10 (red) and optimal neuron 7 (blue) as a function of the position of the nonoptimal neuron 10 (rest of neurons have vanishing error). Step 1 in the dissection method classifies neurons by their position error: neuron 10 is classified as the worst one when the red line is above the blue line (N > M and neuron 10 located sufficiently far from its center-of-mass position), then neuron 7, and then the rest. (C) Step 2 in the dissection method calculates the average position error ep in networks of decreasing size (from right to left) eliminating worst located neurons in the order determined in step 1 of the method. Minimum of the error located at size 9. (D) Same as C but for a network configuration with the C. elegans connectivity and with optimal and nonoptimal subnetworks (blue) and for a noisy network with neurons located at positions obtained adding to optimal positions noise following a uniform distribution of std = 8% (red). Plus signs indicate the point separating optimal and nonoptimal subnetworks. (E) Estimated size of the nonoptimal subnetwork (blue) and percentage of correctly estimated nonoptimal neurons (green). (F) Dissection method does not find a separation between optimal and nonoptimal components in noisy networks built without optimal and nonoptimal components.