Large-scale cortical travelling waves predict localized future cortical signals - Fig 1

Schematic of analysis workflow A. Temporal relationships between predictor and predicted signal. The raw time-series is first analyzed using short-time-window Morlet wavelets to estimate the phase. The predictor and predicted phase are estimated from non-overlapping portions of the raw time-series. Since each phase estimate requires a window of the raw time-series (brackets), and this window is larger at low frequencies, this means the minimum temporal delay (milliseconds) between past and future phase estimates increases with decreasing frequency. The temporal delay was one cycle at the frequency of interest for the ECoG analysis, and two cycles for the MEG. B. Training stage. Principal components analysis (PCA) is used to empirically derive the spatio-temporal Fourier components. For a single subject, and for a single frequency, all the pairs past-future phase vectors available over all training trials were entered as cases into the PCA. The eigenvectors produced by the PCA were used as basis functions in the subsequent modelling. Each basis function was comprised of a past and future representation of the signal, by virtue of the structure of the paired input vectors. The site to be predicted was also chosen during the training stage, by finding the best predicted site from the future part of the model. For some analyzes, the training stage was performed again from scratch, save with the to-be-predicted site now omitted from the past part of the training vector. The most anterior site, most posterior, most superior and left-most site, are indicated by the letters A, P, S and L, respectively. C. Testing stage. A new past sample of phase (over all measurement sites, or possibly excluding the to-be-predicted site) from the test data set is used to estimate a set of model weights via regression onto the past part of the basis functions. These weights are then used to create a model representation of the future activity. The model phase at the to-be-predicted site is then compared to the actual phase that occurs at that site, forward in time. D. Fits of the past model and errors at the to-be-predicted future site. Left panel shows the fit of the past model to the past samples, averaged at each sample-within-trial; over trials (see Methods). The trial-averaged prediction error, for each sample, at the to-be-predicted future site is shown in the right panel (see methods). The critical feature to note is that each past sample is offset from its paired future sample by a delay that decreases with frequency, due to the requirement that phase be estimated from non-overlapping regions of the raw signal. Four equally spaced time-samples are indicated by ‘bins’ within the plot of past model fits, and their corresponding paired four future samples are likewise indicated within the plot of prediction errors. The paired samples have a corresponding representation in A, as the middle of the three frequencies shown. The relationship between frequency in the output plots (D) and the phase estimation windows for the raw time-series (A, brackets) is indicated by fine dashed lines. The second of the four paired past/future samples, at the middle frequency shown in A, is indicated by its position in the two output plots (D) via the half-circles brackets joined by bold dotted lines.