other:Article Title: Integrating molecular, histopathological, neuroimaging and clinical neuroscience data with NeuroPM-box
Article Snippet: For each participant, the following optimization function is used in combination with MATLAB’s MultiStart algorithm : 12 \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\mathscr{L}}({{\varnothing }})={\mathop {\sum }\limits_{k=1}^{{N}_{t}}}{\mathop {\sum }\limits_{m=1}^{{N}_{{\mathrm{{factors}}}}}}{\mathop {\sum}\limits_{i=1}^{{N}_{{{\mathrm{{rois}}}}}}}{\left({S}_{i}^{m}\left({t}_{k}\right)-{\hat{S}}_{i}^{m}\left({t}_{k}{\rm{;}}{{\varnothing }}\right)\right)}^{2},$$\end{document} L ( ∅ ) = ∑ k = 1 N t ∑ m = 1 N factors ∑ i = 1 N rois S i m t k − S ^ i m t k ; ∅ 2 , where \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${N}_{t}$$\end{document} N t is the number of available longitudinal time points for the participant, \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${S}_{i}^{m}\left({t}_{k}\right)$$\end{document} S i m t k is the observed alteration level for factor m and brain region i , at the time point \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${t}_{k}$$\end{document} t k , and \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\hat{S}}_{i}^{m}\left({t}_{k};\varnothing \right)$$\end{document} S ^ i m t k ; ∅ is the corresponding estimated value for the set of model parameters \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\varnothing$$\end{document} ∅ .
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