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The model is based on a working practical approximation in that the total start-up time is reduced by one third.
For apertured beams, the results show that the method fails to capture near aperture effects due to a violation of the paraxial approximation in that region.
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Of course, this reduction comes at the price of a low-rank approximation in (7b) that entails some negative effects and requires extra measures.
As discussed in Section 2.1.3, the maximum weighted matching is time-consuming and therefore we propose an approximation solution in that section.
In practical applications, one is normally more interested in sequential implementation of the Monte Carlo approximation in (6), that is, to represent (p({x_k}|{z_{1 k}})) using (p({x_{k-1}}|{z_{1 {k-1}} {k-1}}
We shall show (in "Low confinement: the linear-noise approximation" in "Results") that the ACF may become negative due to oscillations, which may make Eq. (4) unsuitable as a measure of a correlation time.
The previous assumption is reasonable here since otherwise a linear approximation of f in that interval would yield a very inaccurate approximation.
The approximation is remarkable in that simultaneously: (i) it has an extremely simple final form; (ii) in situations for which it is designed it is typically much more accurate than is the large sample normal approximation; and (iii) it is able to capture most of those stylized facts that characterize lack of identification and weak instrument scenarios.
It is seen that the approximation is satisfactory in that case, but clearly it is not appropriate for α=1. Figure 4 Simulation results for trembling aspen (see the legend of Figure3).
Specifically, the gamma approximation is conservative in that it tends to overestimate extremely small P-values, leading to false-negative results, which is due to the fact that the discrete rank products take values of 1, 2,…, n m, whereas the continuous chi-squared distribution uses positive, real numbers.
The sodium channel is sufficiently fast that we make the standard approximation in Equation 3a that takes the value m, NaF ∞.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com