The resting state data used here was recorded for a test-retest reliability project. Details on data acquisition, preprocessing, and source reconstruction can be found in [

14]. Briefly, 4 min resting state eyes closed data from 16 healthy subjects (age 30.4 ± 5.8, ten female) were employed here. MEG recordings were acquired with an Elekta Neuromag

^{®} Vectorview system with 306 sensors (102 magnetometers and 204 planar gradiometers), inside a Vacuumschmelze

^{®} magnetically shielded room. Subjects’ heads were digitized with a Fastrak Polhemus, and four coils were attached to the forehead and mastoids so that the head position on the MEG helmet was continuously determined. Activity in electrooculogram channels was also recorded to keep track of ocular artifacts. Signals were sampled at 1000 Hz with an online filter of bandwidth 0.1–300 Hz.

SSS and tSSS were applied to the raw resting state data with Maxfilter (Version 2.2) and its default parameters (

${L}_{in}$ = 8,

${L}_{out}$ = 3, tSSS correlation window = 10 s, and tSSS correlation limit = 0.9). We note that, although the data presented in subsequent sections corresponds to the SSS-filtered dataset, we obtained similar results with tSSS. Bad channels were visually detected, and were not included in the SSS/tSSS estimation. Jump, muscle and ocular artefacts were detected using FieldTrip [

15], and non-overlapping artefact-free 6-s epochs were located. Data was bandpass filtered in [2–10] Hz with a finite impulse response (FIR) filter of order 1000.

Source and forward models were built individually after segmenting each subject’s T1-weighted MRI with Freesurfer (Version 5.1.0), [

16,

17], downsampling and realigning surfaces, and estimating leadfield matrices with MNE software [

7]. Linearly constrained minimum variance (LCMV) beamformer [

18] was used to perform source reconstruction. For each subject and source

$i$, we computed beamformer filters as:

where

${\mathit{L}}_{\mathit{i}}$ is the

${N}_{sensors}\times 3$ leadfield matrix between each sensor and the

$i$-th source for three brain current orientations (along Cartesian axes

$x$,

$y$ and

$z$).

$\mathit{C}$ is the

${N}_{sensors}\times {N}_{sensors}$ sensor covariance matrix and is estimated using all samples in the resting state clean trials.

${\mathit{C}}_{\mathit{i}\mathit{n}\mathit{v}}$ is an estimate of the inverse of

$\mathit{C}$:

where

$\mathit{I}$ is the identity matrix and λ > 0 is called the regularization factor. λ is a dimensionless magnitude and represents the fraction of

$\frac{trace\left(\mathit{C}\right)}{{N}_{sensors}}$, which is added to the diagonal of

$\mathit{C}$ in order to render it more robust to matrix inversion. This is a common convention in the literature [

19], and it is used in the popular FieldTrip toolbox [

15]. Regularizing is equivalent to adding uncorrelated noise to the sensor measurements, but it is necessary for the stability of the inversion of the covariance matrix

$\mathit{C}$. This is especially crucial after SSS, since SSS projects back only 60–80 inside coefficients, and yields rank-deficient covariance matrices. The robustness of the

${\mathit{C}}_{\mathit{i}\mathit{n}\mathit{v}}$ matrix inversion can be quantified through:

where cond refers to the 1-norm condition number, a dimensionless measure defined as

$\mathrm{cond}\left(A\right)=||A||\xb7||{A}^{-1}||$ [

20]. Matrices with condition numbers close to one are well conditioned with respect to inversion. Conversely, matrices with higher condition numbers are ill conditioned with respect to inversion; small changes in the original matrix

$A$ can lead to big changes in the estimate of the inverse matrix

${A}^{-1}$.

For each source location

$\mathit{i}$, the orientation

${\mathbf{\eta}}_{\mathit{i}}$ (1 × 3 row vector) of the source activity was determined as the one maximizing the source power

${{\mathit{W}}_{\mathit{i}}}^{\mathit{T}}\mathit{C}{\mathit{w}}_{\mathit{i}}$, and the beamforming filter was projected into this direction:

${\mathit{W}}_{\mathit{i},\mathbf{\eta}}={\mathbf{\eta}}_{\mathit{i}}{\mathit{W}}_{\mathit{i}}$. Finally, we derived source time series as: