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The algorithm runs for 237 iterations until the relative gap and the relative pace value falls below 0.0001 and 0.01, respectively.
The "x" is replaced by the excess traffic ( (x_{a}^{(i)} - C_{a} ) ) and the slope of the delay function (( {text{d}}t/{text{d}}x )) is replaced by the slope of the inflated travel time minus the pace value normalized by the value of the capacity ( (hat{t}_{a}^{(i)} - hat{t}_{a,C}^{(i)} )/C_{a} ).
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As can be seen, the pace values rapidly converge to zero.
Variations of the pace values over successive iterations are depicted in Fig. 6b.
In this figure, the maximum of the pace values (in absolute value) across the toll/subsidy roads are plotted.
Consequently, the algorithm does not terminate unless both criteria the relative gap and the relative pace values are met.
Given the gradual buildup of the initial-beta, a convergence criterion can be defined as pace values falling below a trivial value (denoted by ( varepsilon )): mathop {hbox{max} }limits_{a} |nabla b_{a}^{(i)} /hat{t}_{a} |,, le,varepsilon.
The formulation provided in Eq. (20) follows the spirit of marginal cost (i.e., ( x_{a} cdotpartial t_{a} (x_{a} )/partial x_{a} )) to update the pace values.
In contrast, following pacing in group II, the hemodynamics were not significantly different from pre-pacing values.
In this group the average post-pacing threshold was 0.162 ± 0.026 mA (p = NS compared to pre-pacing values).
And yet Atlanta, in my experience, does remain distinctly Southern, Southern in its manners and language, Southern in its culture and history, Southern in its pace and values.
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Since I tried Ludwig back in 2017, I have been constantly using it in both editing and translation. Ever since, I suggest it to my translators at ProSciEditing.

Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com