## 4 Discussion
At least a partial explanation of this may be the apparent tendency of the unnormalized KL-MI to find higher PAC values at low phase frequencies, which can be observed from the concentration of the PAC peaks in the left parts of the windows in Figure 11A-FJ (in contrast to Figure 11G,H for the normalized indices). Being apparently unspecific to a particular dataset, thistendency may also be present in the surrogate comodulograms and thus be removed by the normalization. In line with this tendency is the observation of significantly lower average peak phase frequencies for the (unnormalized) 'basic' and 'Butterworth' methods than for the 'normalized MVL' method, although these algorithms differ not only in the normalization but also in the PAC measure (KL-MI in the 'basic' and 'Butterworth' methods). Overall, the possible systematic biases of PAC calculation methods towards higher or lower PAC for different frequency ranges need further investigation, including theory and simulations, because the identification of a PAC maximum requires an unbiased comparison between PAC values at different frequencies. The PAC peak frequencies for EEG showed absolute variability that was comparable to that in the benchmark LFP data for the phase frequency (mean change 0.6-1.9 Hz), but larger variability in the amplitude frequency (8.2-15 Hz). Crucially, their relative reliability measured by the ICC was found to be poor, as the ICCs did not differ significantly from zero (the only result with uncorrected \(p<0.05\) was \(p=0.04\) for the ICC of the amplitude frequency in the 'eegiltnew' algorithm, which cannot be considered reliable in view of the number of tests performed). Taken together, these results demonstrate poor reproducibility of the comodulograms and their peaks for all the considered methods applied to EEG during the 3-back task. With all the ICCs being non-significant, the results do not point to any of the algorithms as producing the most reliable results. That said, in the present sample, the highest ICC estimates were obtained for the 'eegfiltnew' algorithm (0.2 and 0.5 for phase and amplitude), making it a promising starting point for further methodological exploration on independent datasets. The unreliability of the TGC peak frequencies presents a substantial challenge to the validity of using them for personalizing neuromodulation protocols in the considered setting. Indeed, this use relies on the TGC measurement procedure for capturing the individual deviations from the population mean that are stable at least during the time period of the study. The statistical insignificance of the ICCs suggests that even if such deviations do exist, their presence cannot be reliably inferred from the data due to the high trial-to-trial variability. There are several possible directions that one could investigate aimed at improving this situation. First, the range of algorithms for PAC computation can be further expanded. We mainly varied one aspect of the algorithm at a time while keeping the remaining aspects as in the 'basic' method (taken from the scripts deposited by [PERSON] et al.). However, every option in every step can be combined with any choice in the other steps. This creates a vast space of algorithms, and it is possible that some combinations are better at extracting the stable parts of PAC patterns. Second, the length of the recording can be increased. The authors of the study [23] suggest that \"each laboratory should perform its own control analysis to assess the minimal data length providing a reliable measurement\". However, increasing data length may or may not make the frequencies more stable, because prolonged sessions can induce fatigue effects, while merging data from different occasions may introduce heterogeneities due to temporal effects such as time of day. Third, one can vary the cognitive task or eliminate it (i.e., investigate the resting state). In the latter case, with eyes closed, the study [18] found between-session reproducibility comparable to our results for the n-back task.