Fig. 1

Averaging time-series with spatial and temporal variability. (A) Synthetic two-peaked signals generated with a Gaussian function. (B) Generating signals of equal length via padding NaNs at the end of the signal. Resulting mean profile and standard deviations (SD) are shown by the red line and the shaded band around the mean, respectively. (C) Normalizing data by resampling the time-series to equalize number of samples for all signals. Resulting mean and standard deviation (SD) are shown by the red line and the shaded band around the mean, respectively. (D) Example of time-warping a single signal. The original signal is shown with a dashed line, and the warped signal with a solid line. (E) Temporal remapping of original time to warped time γ(t). After the time normalization, both have units of percent. (F) Mean and SD after time-normalizing and aligning the ensemble of signals shown in panel A via time-warping. (G) Warping functions that emerged with the alignments. Each time of a signal before alignment (%) is mapped into its time after alignment γ(t) (%).