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However, when we varied the initial condition, only the ER model accurately approximated the full deterministic model (Fig. 5 b).
Our method requires that the reduced deterministic system is accurately approximated the full deterministic system over a range of initial conditions that includes all plausible values of the fast species.
We therefore approximated the full 3D point spread function (PSF) with a 2D PSF, neglecting one lateral component (along the rotation axis), and processed each plane orthogonal to the rotation axis independently (Fig. 1a).
Most XFEL diffraction data processing approaches reported to date have approximated the full intensity by the so-called "Monte Carlo" method, in which thousands of partial intensity observations of a given reflection are summed and normalized by the number of observations, which assumes that these observations sample the full 3D Bragg volume.
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At the Grand Ballroom the Last Shadow Puppets merged a rock band with a dozen strings and a horn section, approximating the full production of their album, "The Age of the Understatement" (Domino).
These non-linearities are made susceptible to analysis by first approximating the full equation by one in which the most significant non-linear term is retained.
The proposed joint allocation scheme approximates the full search scheme [25] while the computational complexity is greatly reduced.
In [19], a probability hypothesis density (PHD) filter is used in the context of visual tracking, which approximates the full posterior distribution by its first-order moment.
A recent human study, however, suggests that for critically ill patients clinical outcome might be better if T > MIC approximates the full 100% [8].
We show that the geometric method approximates the full data posterior distribution better than its competitors across diverse simulations and reproduces known results when applied to a movie ratings database.
Most authors have payed more attention to the first family, designing local adaptive random-walk algorithms [9, 10], due to the difficulty of approximating the full target distribution by non-parametric schemes with any degree of generality.
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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