Then, using Rutledge's formulation, this "capacity" could be decomposed into two complementary terms as,
where the first summation represents the coherence between the ai and the bj, and the second on the remaining dissonance between the distributions.
The genius of Rutledge et al. (1976) was to identify p(at) and p(bj with the com-partmental distributions of inputs and outputs, respectively. That is, if Ttj represents the quantity of flow from compartment i to j, and T.. represents the sum of all the flows (a dot in place of a subscript means summation over that index), then
Substituting these estimates into the decomposition equation yields,
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