We ran 10 network initializations for the same 3 parameter combinations used throughout the paper (subcritical A,B, critical C,D, supercritical E,F). For each run we binned the trials in 32 bins based on the pre-stimulus phase at -5 ms, and computed the PLF at 150 ms for each bin. (A,C,E). Each individual colored line corresponds to the PLF distribution across phases for one of the 10 simulations. The black line represents the average across all 10 simulations. As shown before, the pre-stimulus phase regulates the post-stimulus response only for critical networks. For each simulation run, we highlighted the phase bin showing the highest PLF with a red rectangle, and the phase bin showing the lowest PLF with a blue rectangle. The bins with highest/lowest PLF are roughly the same across trials for critical networks (C), but highly spread out for sub/supercritical networks (A,E). (B,D,F) The pre-stimulus phase is calculated on the signal filtered using a one-way filter, which induces a phase shift of 125 ms. To resolve the phase of the oscillation right before the stimulation, we computed, for each of the 10 simulations, the average of the network signal (unfiltered), across trials belonging to the phase bin with the highest PLF (red) and the phase bin with the lowest PLF (blue). We included in our analysis stimulation trials from all 10 simulations. To isolate variation in pre-stimulus phase from the baseline level of activity, which differs between sub/super/critical networks, we standardized the data. We subtracted from the average across simulation runs, the mean of activity calculated between -50 and 0 ms, and then we divided by the standard deviation of the activity from the same time interval. For critical networks (D), there is a clear differentiation: on trials where the phase-locking response is strongest (red), the stimulus arrives half-way through the rising side of the alpha oscillation (where the phase is approximately 0). On trials where the phase-locking is weakest (blue), on the other hand, the stimulus arrives half-way through the falling side of the alpha oscillation (where the phase is approximately ). Subcritical and supercritical networks do not show such a clear differentiation, thereby illustrating that pre-stimulus phase regulation of stimulus response requires critical-state dynamics.