In mathematical terms, the preferential disruption of hub nodes is given by multiplying 1/gy factor to the coupling strength 8 in eqs (2) and (3) (see Materials and Methods).

For 7/ = 1, the network becomes homogeneous with the coupling strength 8 for a node normalized by its degree: 8/ g. Otherwise, if 7/ >1, the coupling term S/gY will be smaller for a node with high degree producing a larger perturbation effect for such a node.

Fig 4A and 4C clearly demonstrate a negative correlation between node degree and dPLI (Spearman correlation coefficient = - 0.61, p< 0.01) and positive correlation between node degree and amplitude of oscillators (Spearman correlation coefficient = 0.92, p<0.01) at coupling strength 8 = 3.

We first ran 78 coupled Stuart-Landau models on a scale-free model network [37, 38]—that is, a network with a degree distribution following a power law—where coupling strength 8 between nodes can be varied as the control parameter.

The natural frequency of each node was randomly drawn from a Gaussian distribution with the mean at 10 Hz and standard deviation of 1 Hz, simulating the alpha bandwidth (8-13HZ) of human EEG, and we systematically varied the coupling strength 8 from 0 to 50.

When the coupling strength 8 is large enough, we observed distinct patterns for each group.

The interaction hamiltonian or the energy function of the system in terms the contact variables can be written as whereas Ii]- is the coupling strength between the one atom on a receptor and another one on a ligand.

The coupling strength Iij between the two atoms can have variety of values.

Wherel is the average coupling strength and A]2 is the variance.

The Hamiltonian or energy function for the interactions between ligands and receptors can be described by the collections of contact interactions between the atom pairs E = 21-]- Iij 01-], where 01-]- is the contact variable between atoms i andj with certain distance cutoff and the Il-j is the coupling strength for specific contact pair between i and j.

This forms a distribution for the coupling strength I.

2) The inferred coupling strength is strongly correlated with the true amplitudes of synaptic inputs.

These recordings provide a link between properties of synaptic connections typically measured in intracellular experiments in vitro, such as PSC amplitude, and estimates of connectivity made from in vivo extracellular recordings, such as inferred functional connectivity and coupling strength .

Here we use the kernel mean over the first 25ms to summarize the coupling strength in Model 2 (see Methods).