Extended Data Fig. 1: Exclusion of trials with potential inaccurate measurement of propagation direction due to spatial aliasing.

(A) Adequate spatial sampling when low-frequency oscillations propagate propagate across 3 widely spaced electrodes(left). Inadequate spatial sampling for higher-frequency oscillations propagating across 3 electrodes with the same spacing (middle). Arrows indicate two possible propagation direction measurements. Higher density electrode spacing would disambiguate the true propagation direction (right). (B) Combinations of oscillation frequencies and phase velocities where there is adequate and inadequate spatial sampling with 1 cm electrode spacing, determined by whether half the spatial wavelength of a propagating oscillation is less than 1 cm, shown in green and red, respectively. (C) Example 1 s of a trial with a traveling wave propagating in space across five adjacent electrodes of an alpha oscillation cluster in patient 34. (D) Time-lagged cross correlation for entire trial measured between adjacent electrodes (a) and (b) in oscillation cluster. Time of maximum coupling measured at -11 ms indicated by red star showing signal on electrode (b) leads electrode (a). (E) Correlation between time differences between electrodes (a) and (b) measured via phase differences with the time-lag measured from cross-correlation for unsuccessful encoding trial son the left and successful encoding trials on the right. Strong correlation along unity lines indicates alignment between the two measurements such that no trials were susceptible to spatial aliasing. (F) Correlation between phase-based time differences and correlation-based time differences for a beta oscillation cluster with 18% of trials showing an inconsistency between the two methods. Red time lags measured via cross-correlation indicate that the true lag between the signals on those trials was approximately a cycle forward or backwards indicating the potential for spatial aliasing when measuring only using phase. (G) When excluding trials with these inconsistencies across all clusters in the dataset, approximately 83% of trials were not susceptible to spatial aliasing (right) across all oscillation clusters (n=421). Error bars denote ± 1 SEM. (H) Percent of trials in which the correct direction could be measured using phase differences when perfect sinusoidal signals were shifted across five simulated electrodes (n=421). (I) Percent of trials in which the correct direction could be measured using phase differences when imperfect eeg signals were shifted across five simulated electrodes (n=421). (J) Percent of trials in which the correct direction could be measured using phase differences when real eeg signals were shifted across five simulated electrodes after excluding trials that were susceptible to spatial aliasing (n=421).