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Chunk #15 — Methods — Computation of the 1st and 2nd derivatives of the time series of phase differences

Source
LORETA EEG phase reset of the default mode network.
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PR is composed of two events: (1) a phase shift of a finite duration (SD) and (2) followed by an extended period of phase locking as measured by the phase lock duration (LD) and PR = SD + LD. Phase Shift duration (SD) is the interval of time from the onset of a phase shift to the termination of phase shift (5° threshold) where the termination is defined by two conditions: (1) a peak in the 1st derivative (i.e., 1st derivative changes sign from positive to zero to negative) and (2) a peak in the 2nd derivative or inflection on the declining side of the time series of first derivatives. The peak of the 2nd derivative marked the end of the phase shift period. Phase shift duration is the difference in time between phase shift onset and phase shift offset or SD(t) = S(t)onset − S(t)offset. Phase lock duration (LD) was defined as the interval of time between the end of a significant phase shift (i.e., peak of the 2nd derivative) and the beginning of a subsequent significant phase shift,