Figure 10.

As we have pointed out previously, statistical stationarity, even multivariate stationary Gaussianity, can be richly inclusive of the types of time-varying multivariate behavior consistent with known brain responses to experimental tasks. Thus, the windowed connectivity states that a statistically stationary multivariate process moves through have every reason to resemble those of the real data upon which the process was tightly modeled (rows 1 and 2). However, it is also the case that short-timescale connectivity measurements from explicitly non-stationary processes (see “Statistically and Spectrally Non-stationary” regime in Section Empirical Data and Simulation Regimes) subjected to spectral and global covariance constraints drawn from the real data cluster in the same way (row 3) as both the real data and the stationary Gaussian simulation modeled upon it. This suggests that the short-timescale connectivity states and occupancies are driven more by auxiliary constraints on mean spectrum and mean covariance than by whether the underlying process is statistically stationary. As we have shown, statistical stationarity does not preclude a multivariate signal from passing through connectivity states resembling those potentially arising from FRBD in real data. But more importantly it passes through the same connectivity states in the same way as explicitly non-stationary processes subjected to the same auxiliary constraints and as such is not particularly useful as a null condition for detection relevant brain dynamics.