Fig. 2: Correlation function.
From: Critical scaling of whole-brain resting-state dynamics
a Correlation function of fMRI signals as a function of the distance between nodes. Error bars indicate SEM. The correlation function of fMRI signals was approximately power-law, i.e., \(g(r) \sim {r}^{-\widetilde{\eta }}\). The power law was fitted in the distance interval \(r\in \left[10,\,90\right]\) mm. b Distribution of the estimated power exponent for single-subject scans (n = 1003). c Distribution of the relative estimation error of exponent \(\widetilde{\eta }\), i.e., \(\Delta \widetilde{\eta }/\widetilde{\eta }\), where \(\Delta \widetilde{\eta }\) is the least square estimation error of exponent \(\widetilde{\eta }\). Note that the average relative estimation error is <3%. d The power law fit was compared the one obtained using an exponential function by calculating the ratio between the explained variance of the competing regression models. Ratios larger than 1 favor the power law hypothesis. e, f When fitting the power law to \(g(r)\) in the distance interval \(r\in \left[{r}_{\min },\,{r}_{\max }\right]\), for several combinations of \({r}_{\min }\) and \({r}_{\max }\), we found a large region in the \(\left[{r}_{\min },\,{r}_{\max }\right]\) plane with high explained variance \({R}^{2}\) (e) yielding power exponents \(\widetilde{\eta }\, \sim \) 0.52 (f, the blue dotted line indicates the region for which \({R}^{2} > \) 0.95).
