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The same approximation used for processing the experimental datasets applies to simulation data, then the same assumptions are considered.
This is because the concrete form of the approximation used for a given particle depends on its position (which determines how FMM approximates each pair-wise force).
The background model used in this work models each pixel as a mixture of Gaussians with an on-line approximation used for updating the model.
The remaining filters use the same nonlinear forecast model but they introduce model error through different moment closure approximations and/or linear tangent approximation used for computing the second-order statistics of the augmented stochastic forecast model.
The nearly equal sign is used here only because of an approximation used for the modified Bessel function of the second kind present in the general solution and approximate knowledge of the fractal exponent and the percolation path length ratio.
As a first approximation, used for simplicity, this study considers all of the RDW to be protein, i.e. polypeptides.
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Depending on the methods and approximations used for breaking the ties, JFRP might require even more iterations.
The numerical algorithms, spatial and time discretizations, and approximations used for far-field acoustic simulation are presented.
The approximations used for (62) leads to a further reduction in convergence speed, while the algorithm described by (64) shows nearly an identical performance compared to using (62).
This rather low SNR was chosen to avoid using a regularization in the first two experiments that would otherwise obscure insights into the influence of the approximations used for the GFDAF algorithm.
This paper draws together some important recent results which are designed to improve: (a) the robustness of standard score tests; and (b) the reliability of the asymptotic approximations used for inferential purposes.
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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