## 2 Materials and Methods
### Reproducibility between Measurements: Characteristics and Statistical Tests  
The general approach that we used in studying reproducibility consists in dividing an EEG (or LFP) session into two parts of equal length (half-sessions), computing the PAC measures for each of the half-sessions, and comparing the resulting comodulograms in terms of the overall similarity and the stability of the point of maximal theta-gamma coupling. The half-sessions can be considered as two smaller sessions performed one immediately after another. Such treatment of half-sessions as consecutive measurements has been used in EEG analysis in various contexts [56; 57; 58; 59]. Repeatability between such measurements can be considered as the minimum requirement, indicating that the frequencies of maximal coupling are stable at least at the time scale of the session, and could be meaningfully used to guide neuromodulation performed shortly after the EEG measurement. Other applications may require stability at longer time scales. To visualize the degree of general similarity of the comodulograms between the half-sessions, we used scatter plots where each point corresponds to a pair of frequency bands, and its coordinates are the values of PAC between these bands in the two half-sessions. In the case of exact reproducibility, these points will lie on the line \"y = x\". The similarity of two comodulograms was measured by the sample Spearman correlation coefficient (denoted by \(\rho\)) of all the PAC values in them. This metric has been used to compare comodulograms between methods in [60]. It must be stressed, however, that this context of using Spearman correlation differs from its usual application to a sample of realizations of independent, identically distributed (i.i.d.) random variables. In our situation, all PAC values in a comodulogram are computed from the same signals, and thus, generally speaking, they are dependent. This precludes running the usual statistical tests on \(\rho\) while not invalidating its use as a similarity measure. To test whether the similarity of comodulograms between half-sessions differed on average from zero, we applied [PERSON]'s signed-rank test to the values of \(\rho\) obtained in each subject. Here, in contrast to the previous discussion, the values are taken from different subjects and hence do form an i.i.d. sample. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Letter in Figures** & \begin{tabular}{c} **Short** \\ **Algorithm** \\ **Name** \\ \end{tabular}  & **Channels** & \begin{tabular}{c} **Extraction of** \\ **Oscillations** \\ \end{tabular}  & \begin{tabular}{c} **Width Parameters** \\ **(Phase, Amplitude)** \\ \end{tabular}  & \begin{tabular}{c} **Epoch Selection** \\ **(from Stimulus** \\ **Onset)** \\ \end{tabular}  & \ \begin{tabular}{c} **PAC** \\ **Measure** \\ \end{tabular}  & **Normalization** \\ \hline A & basic & Fz-Pz & two-way FIR filter & 4, 20 Hz & 1250–2250 ms & KL-MI & no \\ B & Butterworth & Fz-Pz & two-way & 4, 20 Hz & 1250–2250 ms & KL-MI & no \\ C & no buffer & Fz-Pz & Butterworth filter & 4, 20 Hz & 500–3000 ms & KL-MI & no \\ C & no buffer & Fz-Pz & delay-corrected & 4, 20 Hz & 1250–2250 ms & KL-MI & no \\ D & eegfiltnew & Fz-Pz & one-way FIR filter & 4, 20 Hz & 1250–2250 ms & KL-MI & no \\ E & wavelet & Fz-Pz & Morlet wavelet & 6, 4 cycles & 1250–2250 ms & KL-MI & no \\ F & no epochs & Fz-Pz & delay-corrected & 4, 20 Hz & no (all cleaned & KL-MI & no \\ G & normalized & Fz-Pz & two-way FIR filter & 4, 20 Hz & 1250–2250 ms & KL-MI &
\begin{tabular}{c} 200 ‘split-swap’ \\ surrogatesThe similarity between the comodulograms from half-sessions of a given individual can be due to specific reproducible features of the coupling pattern in this subject. However, it can also be unspecific, so that all the comodulograms calculated by a particular method are similar, regardless of whether they are obtained from the same or different subjects.