Table 1 Notations used in the models and optimization formulation.

n

Number of ROIs or the number of nodes in the brain graph.

p

Number of training subjects.

SC

Structural connectivity matrix.

SC^s

SC matrix for subject s.

D^s

Degree matrix for subject s; sum of edge weights for every region.

FC

Functional connectivity matrix.

FC^s

FC matrix for subject s.

\([{f}_{1}^{s},\cdots ,{f}_{n}^{s}]\)

W _n×n

Weighted adjacency matrix of a graph.

D _n×n

Degree matrix of a graph, computed by taking the sum of all weights on every node and diagonalizing the vector.

\({{\bf{L}}}_{n\times n}^{s}\)

Laplacian matrix of subject s.

\({{\rm{\Psi }}}_{n\times n}^{s}\)

Eigenvector matrix of the graph Laplacian of subject s.

\({{\rm{\Lambda }}}_{n\times n}^{s}\)

Eigenvalue matrix, diagonal matrix with increasing order of eigenvalues, of the graph Laplacian of subject s.

γ _i

A scale at which diffusion kernel is defined.

\({{\bf{H}}}_{i\,n\times n}^{s}\)

Diffusion kernel at scale γ _i for subject s.

m

Number of scales

\({{\bf{H}}}_{n\times mn}^{s}\)

Collection of all m diffusion kernels of a subject s. \([\begin{array}{ccc}{{\bf{H}}}_{1\,n\times n}^{s} & \cdots & {{\bf{H}}}_{m\,n\times n}^{s}\end{array}]\)

π_in×n

Interregional co-activations corresponding to scale γ _i .

Π _mn×n

Interregional co-activations collectively represented at all scales. \([\begin{array}{c}{\pi }_{1n\times n}\\ \vdots \\ {\pi }_{mn\times n}\end{array}]=[\begin{array}{ccc}{{{\rm{\Pi }}}^{1}}_{mn\times 1} & \cdots & {{{\rm{\Pi }}}^{n}}_{mn\times 1}\end{array}]\)

X _pn×mn

\([\begin{array}{c}{{\bf{H}}}^{1}\\ \vdots \\ {{\bf{H}}}^{p}\end{array}]\)

Y _pn×n

\([\begin{array}{c}{{{\rm{FC}}}^{1}}_{n\times n}\\ \vdots \\ {{{\rm{FC}}}^{p}}_{n\times n}\end{array}]=[\begin{array}{ccc}{f}_{1}^{1} & \cdots & {f}_{n}^{1}\\ & \vdots & \\ {f}_{1}^{p} & \cdots & {f}_{n}^{p}\end{array}]=[\begin{array}{ccc}{Y}_{1pn\times 1} & \cdots & {Y}_{npn\times 1}\end{array}]\)

\({{\bf{C}}}_{f}^{s}\)

Predicted FC \({\sum }_{i=1}^{m}{{\bf{H}}}_{i}^{s}{\pi }_{i}\)

\({{\bf{C}}}_{f}{|}_{{k}_{0}}\)

Functional connectivity FC when reaction only happens at k₀τ.