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Table 3 Comparison of maximal relative error under differing lumping inverses for the reduction of the E coli model via lumping in isolation

From: A combined model reduction algorithm for controlled biochemical systems

Dimensions Moore-Penrose Steady-state Average
6 6.67% 0.15% 0.18%
5 10.58% 0.55% 0.51%
4 13.99% 0.54% 1.26%
3 26.93% 4.78% 4.77%
2 78.36% 13.45% 12.88%
1 70.92% 75.56% 82.34%
  1. Each row represents a further level of dimensional reduction for the model, whilst the columns represent the different methods of lumping inverse. The ‘Moore-Penrose’ column contains values where the lumping inverse \(\bar {L}\) is the Moore-Penrose or pseudoinverse of the lumping matrix L. The ‘steady-state’ column contains values where the lumping inverse \(\bar {L}\) is selected to reconstruct the unperturbed steady-state values of the original system such that \(\boldsymbol {x}^{\ast }_{\boldsymbol {u}_{0}}=\bar {L}\tilde {\boldsymbol {x}}^{\ast }_{\boldsymbol {u}_{0}}\). The errors stated represent the maximal relative error between the original and reduced systems when simulated to steady-state under the introduction of 10μ M concentration of attractant ligand at t=0