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These can use an alternating square-diamond rolling principle on horizontal and vertical rolls, as shown in B in the figure, or a series of oval-to-round passes, as illustrated in C in the figure.
Similarly, we use an alternating strategy to minimize problem (21) with respect to each component separately: {mathbf{F}}^{k+1}= argkern0.24em underset{mathbf{F}}{min}mathrm{mathcal{L}}left(mathbf{F},{mathbf{B}}^k,{mathbf{Y}}^kright) (23) {mathbf{B}}^{k+1}= argkern0.24em underset{mathbf{B}}{min}mathrm{mathcal{L}}left(mathbf{B},{mathbf{F}}^{k+1},{mathbf{Y}}^kright) (24).
In our implementation, we use an alternating proximal algorithm [ 26], which provides an approximation of the exact solution with a controlled error.
In QmmRAxML we use an alternating scheme to optimize parameters in the class frequency mixture model, including branch-lengths, the among-sites rate variation parameter and the weights (wc) of class frequency vectors.
We then use an alternating minimization algorithm where each iteration consists of the following two steps: (using the superscript (i) to denote the ith step) (9) { X (i ) = arg min X ‖ HX − Y ‖ F 2 + α 1 ‖ X − U (i − 1 ) ‖ F 2 U (i ) = arg min U α 1 ‖ X (i ) − U ‖ F 2 + α 2 ‖ U ‖ TV.
Similar(55)
Mr. Karliner, who said that Mr. Woods had wanted the juror to continue and had not wanted to use an alternate juror, requested a mistrial.
We use an alternate view.
Thus we use an alternate method to prove the result.
Whenever a path breaks, the algorithm should try to use an alternate path, instead of initiating a new route discovery.
In the meantime, we recommend you use an alternate means of transportation and we will refund pre-paid passes for any missed rides.
However, in this study, we use an alternate method in which (sigma _{text {R}} z)) is first estimated from the observed data in the area of interest.
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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