Difficult control is related to instability in biologically inspired Boolean networks
Fig 4
A correction that incorporates the number of isolated fixed points leads to better predictions of control kernel sizes.
(A and B) The simple prediction that the mean control kernel size within each network is equal to the logarithm of the number of attractors r (Eq 1) works well for most networks, but there are a number of outlier networks that are much harder to control than expected. We mark networks as outliers (triangles) when their mean control kernel size is more than 3σ away from the expected value of log2r, where σ is the standard deviation of the residuals 〈|CK|〉 − log2r. These outlier networks all have isolated fixed points (highlighted with a darker color). (C and D) A correction that assumes isolated fixed points have control kernel of size nc (Eq 2) leads to better predictions. For the biological networks, the RMSE is 0.93 when using Eq 1 and reduces to 0.60 when using Eq 2. For the random networks, the RMSE reduces from 1.3 to 0.68.