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The coastline shown in Fig. 2 serves as an approximate reference only and is of low resolution, such that some data plotted offshore.
Theorem 1 and Lemma 1 suggest the definition of an approximate reference prior inspired by priors π r 1 and π r 2 that has the same value for the hyperparameter a=1 and share their tail behavior with respect to p. We define such an approximate reference prior in Definition 1.
In addition to the two formally obtained reference priors, we propose an approximate reference prior that shares the same tail behavior but is much more straightforward to implement in practice.
This dataset can thus serve as an approximate reference for the kind of spread in apparent mRNA-specific translation efficiencies that is falsely generated by noise in the underlying studies.
Regarding the validity of the estimates of nutrients consumed for the food-frequency information assessed in this study, both antioxidant [ 26] and phytoestrogen (Horn-Ross, P. et al., Am J Epidemiol, in review, 2005) nutrients estimates closely approximate reference values in previous studies.
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The array weights for each frequency bin within the working frequency band are designed to insure that the array patterns approximate the reference ones.
Second, we approximate the reference contour using a Gaussian mixture model (GMM) continuous optimization algorithm followed by an order-preserved foot-point detection method used to extract the feature points that correspond to the feature points of the floating contours.
The approximate time reference for the MMR estimate was the year 1999, eight years before the interviews.
Qualitatively, we can see that except for algorithm RA, the distribution curves tend to approximate the reference curve as we increase the time limit.
Here, we use the geometric mean to approximate the reference state as follows, (3) where N is the number of samplings and X and Y represent two sampled proteins with the same lengths as S and T, respectively.
An approximate clinical reference range of 1,500 to 3,500 pg/mL was established by analyzing multiple CSF samples from early AD patients both at an MRD of six and treated with Tween-20 (data not shown).
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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