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Of the 664 loci considered, with the optimal constant of translation applied, 662 had a close match of the translated Pacific Islander genotypes to the HGDP-CEPH genotypes, with gc*,2 > 0.773.
Indeed any translation applied to such a state (V_{0}) gives another solution, thanks to the translational invariance.
Then the full system of connections, local and long-range, keeps translation invariance: any planar translation applied to a pattern yields another one, up to periodicity.
This paper illustrates the potential for such change by presenting conceptual models and case studies of research translation applied to urban and transport planning and urban design.
In the following, we consider b = t the translation applied to each t time point, and the frequency linked to the scale parameter α, ; thus C s (f, t) ≈ C s (a, b).
Among the 659 loci, with the optimal constant of translation applied, 656 had gc*,2 = 1, indicating perfect agreement, and the other three had gc*,2 < 0.990.
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Cribb uses the term translation metaphorically to investigate whether translation applies as well in ethics as it does in biomedical research.
The first 6 modes corresponding to self rotations and translations applied to the whole system, were not taken into account further.
For the above search, the following translations apply.
We followed a sequential forward and backward translation approach (applied in patient group 1) (see figure 1).[ 20] Two translators independently translated the English interviewer administered CRQ (CRQ-IA) and self-administered CRQ (CRQ-SA) as well as the individual and standardised dyspnoea items into German.
The missing ingredient was a fuller understanding of language itselfThe earliest method, "direct translation", is applied strictly to a single pair of languages, usually in just one direction (say, from Japanese to English only).
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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