Table 1.

Notations used in the models and optimization formulation.

Object	Description
n	Number of ROIs or the number of nodes in the brain graph.
p	Number of training subjects.
SC	Structural connectivity matrix.
SCs	SC matrix for subject s.
Ds	Degree matrix for subject s; sum of edge weights for every region.
FC	Functional connectivity matrix.
FCs	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.
${\mathbf{L}}_{n\times n}^s$	Laplacian matrix of subject s.
${\mathrm{\Psi }}_{n\times n}^s$	Eigenvector matrix of the graph Laplacian of subject s.
${\mathrm{\Lambda }}_{n\times n}^s$	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.
${\mathbf{H}}_{in\times n}^s$	Diffusion kernel at scale γi for subject s.
m	Number of scales
${\mathbf{H}}_{n\times mn}^s$	Collection of all m diffusion kernels of a subject s. $\left[\begin{array}{ccc}{\mathbf{H}}_{1n\times n}^s& \cdots & {\mathbf{H}}_{mn\times n}^s\end{array}\right]$
πin×n	Interregional co-activations corresponding to scale γi.
Π mn×n	Interregional co-activations collectively represented at all scales. $\left[\begin{array}{c}{\pi }_{1n\times n}\\ ⋮\\ {\pi }_{mn\times n}\end{array}\right]=[\begin{array}{ccc}{{\mathrm{\Pi }}^1}_{mn\times 1}& \cdots & {{\mathrm{\Pi }}^n}_{mn\times 1}\end{array}]$
X pn×mn	$\left[\begin{array}{c}{\mathbf{H}}^1\\ ⋮\\ {\mathbf{H}}^p\end{array}\right]$
Y pn×n	$\left[\begin{array}{c}{{\mathrm{FC}}^1}_{n\times n}\\ ⋮\\ {{\mathrm{FC}}^p}_{n\times n}\end{array}\right]=\left[\begin{array}{ccc}{f}_1^1& \cdots & f_n^1\\ & ⋮& \\ f_1^p& \cdots & f_n^p\end{array}\right]=\left[\begin{array}{ccc}{Y}_{1pn\times 1}& \cdots & Y_{npn\times 1}\end{array}\right]$
${\mathbf{C}}_f^s$	Predicted FC ${\sum }_{i=1}^m{\mathbf{H}}_i^s{\pi }_i$
${\mathbf{C}}_f{|}_{k_0}$	Functional connectivity FC when reaction only happens at k0τ.