Figure 5.

(i) Highest kurtosis applies in a signal with a transient high-amplitude high-frequency interval, more consistent with a motion or noise than with shifting CASE states; Φ is extremely low for this seeming artifact; (ii–iv) Much lower kurtosis in stylized signals with highly distinguishable temporal epochs are more consistent with FRBD; much higher in these strong FRBD candidates; (v) Lowest kurtosis in stylized signal with very strong and distinguishable temporal epochs; much higher Φ for this strong FRDB candidate. Positive univariate excess kurtosis indicates super-Gaussianity (and is not particularly useful for indicating functionally relevant dynamics). As such, kurtosis is high when there are a larger number of high-amplitude observations than should arise under the assumption of Gaussianity. Univariate kurtosis (transformed via equation (1) in the Technical Supplement) to distribute, assuming Gaussianity, as a standard normal random variable) is negative on each of the stylized examples (ii–v) that exhibit distinguishable temporal epochs consistent with functionally relevant brain dynamics. It is very large and positive only in the example containing a single high-amplitude, high-frequency “spike” (i). The behavior that appears in the upper tail of the kurtosis distribution is more consistent with motion artifacts or measurement error than anything previous imaging or EEG studies have found to be associated with experimental tasks. The metric, Φ, introduced in this work, is at least 2.8 times larger for examples (ii–v) that exhibit distinguishable temporal epochs consistent with functionally relevant brain dynamics than for the case (i) that features a single high-frequency high-amplitude “spike” embedded in an otherwise spectrally epochless signal. As such Φ exhibits the behavior we would expect, whereas kurtosis is not particularly useful for detecting behavior consistent with relevant brain dynamics for the examples shown above. Additionally, Φ successfully captured small changes in frequencies in several consecutive short term epochs as well (Supplementary Figure 2).