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This is a convex least squares task which is the same as the optimization of (15) with fixed bases w k and can be solved in the by using the update rule just for h i j, i.e., Equation (17).
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We now suggest another iterative method by using the updated value of the solution.
Firstly, the search range is automatically reduced, by using the updated information of the current design, at each iteration.
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An elastoplastic tangent stiffness matrix of three-dimensional beam element is derived by using the updated Lagrangian formulation, in which the isotropic hardening model, the Von-Mises yield criterion and the Prandtl Reuss flow relations are applied to this study.
The LMS implementation of the MCBER detector can be obtained straightforwardly by using the updating rule of (11) combined with the gradient expressions reported in the following (mathematical details are omitted for the sake of brevity): (15).
(4) Based on data made available to base stations at the termination of step k-1, each residual BS-i calculates the weight metric β(i) at step k by using the updated parameters ratio(i), Pmin(i) and P″max(i).
Additional file 2: RMP genes with a PEXEL motif as identified by using the updated HMM algorithm ExportPred v2.0.
By using the updated recommendations for the OARSI Osteoarthritis Histopathology Assessment System [ 42], measures of the lesion depth, width, and volume were assessed by using ImageJ [ 43].
In this study, we also wanted to examine the improved methods for predicting the current GO annotations of protein sequences by using the updated databases.
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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