${\mathbf{G}}_{\mathbf{q}}\in {\mathbb{R}}^{g\times m}$	Input query gene expression matrix, prior to scaling.
${\mathbf{G}}_{\mathbf{qs}}\in {\mathbb{R}}^{g\times m}$	Query gene expression matrix, scaled by reference gene means $\mathbf{\mu }$ and standard deviations $\mathbf{\sigma }$.
${\mathbf{X}}_{\mathbf{q}}\in {\left\{0,1\right\}}^{c\times m}$	Design matrix assigning query cells (cols) to query batches (rows).
${\mathbf{Z}}_{\mathbf{q}}={\mathbf{\Sigma }}_{\mathbf{q}}{\mathbf{V}}_{\mathbf{q}}^{\mathbf{T}}\in {\mathbb{R}}^{d\times m}$	Query cell locations in original (pre-harmonized) reference PC embedding.
${\widehat{\mathbf{Z}}}_{\mathbf{q}}\in {\mathbb{R}}^{d\times m}$	Approximate query cell locations in integrated embedding (hPC space). Output of Symphony reference mapping.
${\mathbf{R}}_{\mathbf{q}}\in {\left[0,1\right]}^{k\times m}$	Soft cluster assignment of query cells (cols) to clusters (rows). Each column is a probability distribution that sums to 1.
${\mathbf{B}}_{\mathbf{q}}\in {\mathbb{R}}^{k\times \left(1+c\right)\times d}$	3D tensor of the estimated parameters (betas and intercepts) of the linear mixture model for each of $k$ clusters.