(A) The consistent problem in Eq. (2), where the intersection set C0 is nonempty. The circle is the initial solution. The thick black point is the consistent solution in the intersection of two sets for gene expression and GO constraints, respectively. POCS ensures that the initial solution will converge to the consistent solution after enough projections represented by the arrows. (B) The inconsistent problem in Eq. (4), where the intersection set C0 is empty. After enough simultaneous projections represented by the arrows, the thick black dot is the approximate solution such that a weighted set distance from gene expression and GO constraints is minimized.