Fig. 4.
Matroids allow for parameter-free model discrimination and prediction. (A) Depiction of linear dependence and independence in a vector space (see main text for additional information). (B) Schematic representation of the matroids for Wnt models. Each species represented by a loop is determined from the parameters alone; groups of species represented on a point can be determined by measurement of one of the species; groups of species represented on a line can be determined by measurement of two species. For notation used see SI Appendix, Table S1. (C) Schematic of rank, which corresponds to “what-to-measure.” So, for rank 1, measure 1 species to determine all of the others, for rank 2, measure 2, etc. (D) Deletion is a matroid-theoretic operation which removes a species x from the ground set of the matroid and only considers dependencies of the original model that excluded x. Deleting T and gives a rank 4 matroid which can be visualized by planes in 3D space, as shown here.