Fig. 1.

Method pipeline. a Structural connectome (SC) between $N=360$ atlas regions, displayed in logarithmic scale. b SC eigendecomposition leads to structural harmonics with increasing spatial frequency $k$. c Brain activity at every time point $t$ (${\mathbf{s}}_t$) is written as a linear combination of harmonics (by using coefficients ${\widehat{\mathbf{s}}}_t$). The median-split criterium on the activity energy spectral density $\xi$ (inset) is used to split the spectrum and decompose brain activity into coupled/decoupled portions ${\mathbf{s}}_t^{\mathrm{C}}$ and ${\mathbf{s}}_t^{\mathrm{D}}$ (using low/high-frequency harmonics, respectively; $\lambda$ = harmonic frequency). The ratio between decoupled/coupled signal norms is defined as structural-decoupling index. d Surrogate functional signals are generated with/without knowledge of SC, by spectral coefficient randomization. Average functional connectomes (FC) obtained from correlating pairs of empirical/surrogate functional signals are compared