In the power, heterogeneous response, and runtime analysis benchmarks, the mean vector μ for each sample was calculated from the mean abundance of the first cell type in control samples (no effect) \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mu }_{0}$$\end{document}μ0, and the mean change in abundance of the first cell type between the two groups \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\mu ^{\prime}$$\end{document}μ′. All other cell types were modeled to be equally abundant, leading to \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{\boldsymbol{\mu }}}}}}=\,\log ({\mu }_{0},\frac{\bar{y}-{\mu }_{0}}{K-1},\frac{\bar{y}-{\mu }_{0}}{K-1},\ldots )$$\end{document}μ=log(μ0,ȳ−μ0K−1,ȳ−μ0K−1,…) for control samples, and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${{{{{\boldsymbol{\mu }}}}}}=\,\log ({\mu }_{0}+\mu ^{\prime} ,\frac{\bar{y}-({\mu }_{0}+\mu ^{\prime} )}{K-1},\frac{\bar{y}-({\mu }_{0}+\mu ^{\prime} )}{K-1},\ldots )$$\end{document}μ=log(μ0+μ′,ȳ−(μ0+μ′)K−1,ȳ−(μ0+μ′)K−1,…) for samples in the other group.
