Direct application of these findings to diffusion in the direction of shrinkage leads to predictions of th product distribution from competitive, consecutive reactions.
where e (r)i c is the expenditure elasticity (conditional) for item i within the r th product group and e (r) uc the income elasticity for the r th product group (unconditional).
As income is defined to be equal to expenditure (equation 4), the term in thesquare bracket is the marginal rate of substitution between expenditure and thej th product characteristics.
According to Lancaster's random utility theory (Lancaster [1966]), the utility of the i th consumer U i (i = 1,.,I) derived from the j th product alternative (out of a choice set of C) is a function of the selected attributes of alternative j: U ij = β x ij + ε ij (1).
where ε r ij H, c is the conditional Marshallian price elasticity for item i and j, w (r)j the budget share of item j within the r th product category, and ε rr M,uc the uncompensated Hicksian own-price elasticity of product category r.
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k m, s i and k m, p i denote the dissociation constants for the i-th substrate and i-th product, respectively.
Formally, the reaction α→ β between the α-th (reactant) and the β-th (product) complexes defines a directed edge with tail vertex being the α-th complex and head vertex being the β-th complex.
To associate quantitative measurements of protein and metabolite levels with metabolic fluxes, we used the following Michaelis Menten-like rate equation to estimate the flux in a reaction transforming a set of substrates S to a set of products P: (3) where S i and P i denote the concentrations for the i-th substrate and i-th product, respectively, and e denotes the enzyme concentration.
Compared to other cells in the innate immune system, ILCs are unique in that they may produce and secrete cytokines that were classically regarded as CD4+ Th cell products (Eberl et al., 2015b).
