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MCMC were run sufficiently long to ensure stationarity and convergence.
If a minimal box size is used and the algorithm is run sufficiently long, DIRECT will perform an exhaustive grid search on an equidistant grid defined by the centers of the minimal size boxes.
In the experiments, we compare the accuracy and efficiency of the two-phase algorithms described above to the one-phase DIRECT algorithm used in by Ljungberg and colleagues, 26 which we denote by D. Note that, for the D and D-D algorithms, we are guaranteed to get a sufficiently accurate approximation of the local minimum if the algorithms are run sufficiently long.
Occupying this detached role as far as Brand's revolution is concerned is his friend Noel Gallagher, whose witheringly bewildered comments on the matter are sufficiently entertaining to be run almost in full.
Differences in the results of these two runs would indicate that the program has not been run for sufficiently long for Markov chains to converge.
The creep analysis was run for a sufficiently long time to achieve the steady state creep condition.
The fact they've given the nod indicates they now feel the way Chinese markets are run and regulated has sufficiently improved.
Chains were run for a default length of 1100 cycles, each cycle yielding a sufficiently decorrelated sample.
During the following winter, the trains had problems running through snowdrift unless they were running at a sufficiently high speed.
And Baggies assistant manager Michael Appleton admitted on Tuesday that time is running out for Dorrans to be sufficiently match fit to return during the current campaign.
We are running out of natural resources that we can extract at sufficiently low costs.
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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