Rules, hypergraphs, and probabilities: The three-level analysis of chemical reaction systems and other stochastic stoichiometric population processes
Fig 12
The Pythagorean theorem (50) in the linear-response regime where it is the ordinary Euclidean theorem.
Two irreducible flows f14 and f193 differ by a TKL trefoil current v° with magnitude 1. In the hierarchy ,
is the full graph from Fig 2, and
is the union of the supporting graphs for f14 and f193.
may be the supporting graph for either f14 or f193. Vertical solid arrow is square root of the integral
in Eq (50) from zero to
in
. Hypotenuse solid arrows are square roots of integrals
in Eq (50) in either graph
. Horizontal dashed arrows are square roots of integrals ∫dη′ in either direction of v° in Eq (50). Details of the final flow parameters and the functional dependence of
on v° are given in Table 4.