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Methods for coupling reaction and transport, such as sequential iteration approach (SIA) and predictor corrector approach are incorporated into the code to make the model versatile.
Two families of approaches exist to simulate reactive transport in groundwater: The Direct Substitution Approach (DSA), based on Newton Raphson and the Picard or Sequential Iteration Approach (SIA).
Algorithm 2 shows the proposed sequential iteration of the mean-field approximation in a 2D fully connected grid with distribution Q using the update sequence from bottom right to top left (Fig. 4 b).
Similar to this work, we develop a sequential iteration that updates a single variable in each step and therefore does not suffer from the same problems as the parallel scheme.
Although the sequential iteration is guaranteed to converge and minimize the KL-divergence, its result is biased with respect to the chosen update sequence due to the nature of the mean-field approximation (i.e., the result depends on the order in which variables are updated).
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This process was conducted for different calendar years for starting the measurement of duration in the S term of the equation above by sequentially deriving values for b for 5-year sequential iterations of specified calendar years and examining the goodness of fit for the resulting predicted incidence.
The first part is a fixed number of immigrants called 'basic number of immigrants' or BIN, and the second one varies in sequential iterations called 'variable number of immigrants' or VIN.
There is a trend to add genes in thematic blocks in more-or-less sequential iterations, as mentioned above for early addition of most clock genes to the network (see Additional file 1: mini-website of learned GRN at each iteration).
A selection of genes with well-characterized roles in regulation of plant responses to cold and salt-stress [ 30] were added to the network in nearly-sequential iterations and with connections to each other.
The convergence of the sequential iterative solution is achieved when the sum of the absolute differences of the solution variables between two successive iterations falls below a pre-specified small number, which was chosen as 1 × 10−5 in this study.
eThis sequential re-initialization process is stopped in case the best solution found for both problems does not improve for more than three consecutive iterations.
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