Critical capacity as a function of the basin size and the robustness parameter.

<p><b>A.</b> The red plot shows the critical capacity as a function of the size of the basins of attraction (<i>N</i> = 1001 neurons in the dense regime <i>f</i> = 0.5) when the strength of the external field is large (<i>γ</i> = 6) such that the ON and OFF neuronal populations are well separated. The points indicate 0.5 probability of successful storage at a given basin size, optimized over the robustness parameter <i>ϵ</i>. The error bars show the [0.95,0.05] probability interval for successful storage. The blue plot shows the performance of the Hopfield model with <i>N</i> = 1001 neurons. The maximal capacity at zero basin size (the Gardner bound) is equal to 2. <b>B.</b> To compare the result of simulation of our model with the analytical results, we plotted the critical capacity as a function of the robustness parameter <i>ϵ</i>. The dark red curve is the critical capacity versus <i>ϵ</i> for our model obtained form analytical calculations (see <a href="http://www.ploscompbiol.org/article/info:doi/10.1371/journal.pcbi.1004439#sec011" target="_blank">Materials and Methods</a>), the cyan line shows the result of simulations of our model, and the dark blue shows the Gardner bound for a network with no constraints on synaptic weights. The difference between the two theoretical curves is due to the constraints on the weights in our network.