Figure 6

Coordinate systems used to describe bi-directional reactions. The schematics under the matrix equations shows how the two coordinate systems, [v^xch, v^net] and [v^←, v^{→, net}], are mapped to [v^←, v^→ ]. The former requires a conditional operator, which cannot be implemented using the null-space matrix. The prerequisite for the compactification transformation is that the black and grey arrows are overlapping.