Fig. 6

Group-based analysis of neural activity patterns (\(S_1/N, S_2, \sigma _A, \rho _1\)) as a function of T for all patients and controls in the low \(r_2\) scenario described in Fig. 5. The first line presents the unnormalized model, while the second line shows the rescaled model using \(T/\langle W\rangle\). The third line displays the results for the normalized model. Brown lines represent patients at \(t_1\) (3 months post-stroke, \(n=54\)), and green lines represent patients at \(t_2\) (12 months post-stroke, \(n=59\)). Thin solid curves indicate individual stroke patients, whereas thick dashed lines represent the group average. The blue dashed line depicts the average across control subjects. Group-level neural patterns exhibit significant differences between the unnormalized and normalized models. In the unnormalized model, the critical point is influenced by individual differences in brain networks³. The second largest cluster shows a peak around \(T=0.02\) for healthy controls, but this peak is absent for patients at both time points. When the threshold is rescaled using \(T/\langle W\rangle\), a collapse of the neural patterns is observed³. This collapse is particularly noticeable in \(\langle S_1\rangle /N\), \(\sigma _A\) and \(\rho _1\), although it is less pronounced in the second cluster, where patient peaks are absent at both time points. Conversely, a clear trend toward normalization is evident from \(t_1\) to \(t_2\) in the second largest cluster of the normalized model. Additionally, the variability of activity and the first autocorrelation coefficient are significantly lower compared to the normalized model. The horizontal dashed line in the \(\rho _1\) graph illustrates this effect, indicating that the peak of \(\rho _1\) in the normalized model exceeds that of the unnormalized model.