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We applied the model to data obtained from rigorous measurements and show, as examples, that MDA-MB-231 breast-cancer cells are at least 20 times less sensitive to gradients of EGF or CXCL12 than neutrophils are to formyl peptides; we then used this information to determine the extent to which gradient sensing increases the rate of boundary crossing relative to a random-motility control.
This would suggest a rate of boundary sliding for Cryptococcus introns of around 4 × 10-11 or 4 × 10-12 per year.
Given that for each such change both a true (unobserved) boundary change and a mutation knocking out the initial boundary are expected, the rate of mutations knocking out initial boundaries is expected to equal the true rate of boundary change, thus this scenario cannot explain the lack of observed change.
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The present results demonstrate that triple junction mobility is finite and can be sufficiently small to limit the rate of grain boundary migration.
According to this view, oblique-angle deposition on a mesoscopically rough surface eliminates or reduces condensation at and near grain boundaries, and therefore lowers the rate of adatom grain boundary attachment, resulting in reduction in the compressive component of the intrinsic stress.
We have monitored the grain boundary profile, triple junction angles and rate of grain boundary migration with and without triple junctions as a function of grain size, grain misorientation, direction of migration and temperature in a series of configurations designed to ensure steady-state migration.
It is evident from our work that the grain boundary structure and misorientation have a significant influence on the rate of grain boundary migration.
Given that this shift would need to be realised during the interval between 1961 90 and 2070 99, i.e. within 109 years, the rate of range boundary shift (V – km yr−1) was estimated by dividing the estimated range boundary shift by 109.
This drag limits the rate of grain boundary migration and leads to triple junction angles that differ substantially from their equilibrium value.
This eventually leads to the formation of dislocation-free grains, and reduction in the rate of grain boundary migration.
Using the results, we estimated the mean distance and direction of the potential spatial displacement of species' ranges, and also the mean rate of range boundary shift required to realise these potential range changes.
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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