## Group Schulthess

Group Description ```Biochemical networks from Pascal Schulthess, Inst. Pathology, Berlin Matrices from Pascal Schulthess, Institute for Pathology, Chariteplatz 1, 10117 Berlin, Germany. Three large biochemical networks (N_biocarta, N_pid, and N_reactome). These are stoichiometric matrices extracted from three biochemical databases (BioCarta, PID, and REACTOME) describing cell signaling pathways and protein-protein interaction networks. The goal is to find the left nullspace of the matrix; in MATLAB notation: N = null (Problem.A') ; The matrix (Problem.A')*N will thus be essentially zero. This can be done much more efficiently with the spqr_rank toolbox by Leslie Foster and Tim Davis, as: N = spqr_null (Problem.A') ; Results: The matrix A is transposed, then N = null (A) or N = spqr_null (A) is computed. The size statistic is the memory taken by N. spqr_null can compute either an explicit matrix N, or an implicit Householder-based representation. The latter takes less memory. Matrix: N_biocarta size: 1996 by 1922 (transposed) spqr_null stats: flag: 0 rank: 1023 tol: 3.5456e-12 est_sval_upper_bounds: [0.1689 3.4534e-15] est_sval_lower_bounds: [0.1203 0] sval_numbers_for_bounds: [1023 1024] est_norm_A_times_N: 2.4349e-15 spqr_null, implicit: 0.03 sec, norm(A*N) 9e-15 size: 0.08 MB spqr_null, explicit: 0.10 sec, norm(A*N) 9e-15 size: 0.11 MB MATLAB null: 3.31 sec, norm(A*N) 2e-13 size: 13.82 MB all report dim(N) of 899. Matrix: N_pid size: 3923 by 3625 (transposed) spqr_null stats: flag: 0 rank: 2048 tol: 1.3937e-11 est_sval_upper_bounds: [0.0922 5.1310e-15] est_sval_lower_bounds: [0.0585 0] sval_numbers_for_bounds: [2048 2049] est_norm_A_times_N: 1.6751e-15 spqr_null, implicit: 0.05 sec, norm(A*N) 4e-14 size: 0.21 MB spqr_null, explicit: 0.34 sec, norm(A*N) 4e-14 size: 1.32 MB MATLAB null: 24.86 sec, norm(A*N) 9e-13 size: 45.73 MB all report dim(N) of 1577 Matrix: N_reactome size: 16559 by 10204 (transposed) spqr_null stats: flag: 0 rank: 9025 tol: 1.1766e-10 est_sval_upper_bounds: [0.6722 1.3042e-14] est_sval_lower_bounds: [0.0106 0] sval_numbers_for_bounds: [9025 9026] est_norm_A_times_N: 9.4695e-15 spqr_null, implicit: 0.95 sec, norm(A*N) 2e-13 size: 7.5 MB spqr_null, explicit: 3.53 sec, norm(A*N) 2e-13 size: 25.2 MB MATLAB null: 904.54 sec, norm(A*N) 2e-10 size: 96.2 MB all report dim(N) of 1179.```
Displaying all 3 collection matrices
Id Name Group Rows Cols Nonzeros
2552 N_biocarta Schulthess 1,922 1,996 4,335
2553 N_pid Schulthess 3,625 3,923 8,054
2554 N_reactome Schulthess 10,204 16,559 43,816