The proposed algorithm works backward by computing the equilibrium from the last possible deadline of the bargaining to the initial time point and by applying at each time point the actions prescribed by the choice rule whose conditions are satisfied.
As mentioned before, the right eigenvector centrality is equivalent to the backward linkages computed with the eigenvector method described in Dietzenbacher (1992) where linkages are the right principal eigenvector of the direct input coefficients matrix.
Another example are backward linkages computed with the eigenvector method that are equivalent to the eigenvector centrality which is the largest eigenvector of the matrix that represents the structure of the system.
Precompute signals at loops: In this mode, the algorithm firstly finds cycle-forming backward edges, computes their signals, and updates their target node values.
The analogue of the forward-backward algorithm for computing these expectations is the inside-outside algorithm.
For T-helper and dendritic cell networks, the combined model takes marginally more time than the asynchronous model but this might be attributed to the fact that there is a fixed overhead involved in computing the backward reachable set in Line 8 of Algorithm 2 that is not compensated by the small run time difference between the synchronous and the asynchronous model.
Before the 12th dynasty, plausible dates for the 11th can be computed backward, but for earlier times dates are approximate.
A backward filter then computes the estimates operating on the inverse dynamics of the forward filter.
Forward and backward rates were computed to be 0.3 and 146 μs−1, respectively, which resulted in a calculated equilibrium constant of Keq = 1.9 × 10−3.
An example is offered by the right panel of Figure 3, illustrating the estimated daily deaths b-AN x, t and f-AN x, t attributable to heat, computed backward and forward for the first summer in the time series for Rome, with related temperature trend.
