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Lambdas were between 0 and 1 for all models, and were significantly different from the two bounds, indicating that the evolution of all the traits depended on their phylogenetic history (not random), but might not strictly follow the Brownian model.
Also for the 1996 birth cohort (32 cases) and the 1996/1997 birth cohort (25 cases) the differences between the K-functions of cases and controls are well above the upper confidence bounds, indicating strong spatial clustering of BSE cases for these birth cohorts.
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These efficiency variance bounds indicate that the propensity score is ancillary for the "verify-in-sample" case, but is not ancillary for the "verify-out-of-sample" case.
Comparison of the analytical bulk and shear moduli with the Hashin Shtrikman bounds indicates that the mechanical properties of the SI-square honeycomb are relatively close to being optimal.
For the PPMI data, the 95% confidence interval bounds indicate that the increase in reliability was statistically significant.
However it did increase our uncertainty, as the more extreme lower and upper bounds indicated that the true effect of treatment could likely be higher or lower than indicated by the original analysis.
We set labeling efficiency as 82% but also modeled a range of labeling efficiency from 51% to 100% as lower and upper bounds (indicated as 'Low L' and 'High limitsits).
The fits to even the simplest diffusion model (with flat bounds) indicate that the conversion from motion to accumulated evidence (e.g., drift rate) did not change consistently in the two regimes.
Using recent estimates of the human base substitution mutation rate [ 21], the central value between the bounds indicated in Figure 2 gives a gene conversion rate between the two CMT1A-REPs of 1.3 × 10-4 per generation for the HI994 model, and 5.1 × 10-5 per generation for the B2000 model.
An outgroup species used for detecting a conversion in a primary species helps to establish the upper bound, indicating that the conversion occurred after the separation of the primary and outgroup species.
The lower bound is a signature of the response of the materials that do not change its shape and the upper bound indicates that the volume is unchanged.
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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