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This is a more complex version of distance estimation that necessitates path and road network files and could include directions, speed limits, barriers, type of road surface to produce a more accurate measurement.
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Luckily for me, I discovered early on that my science degree did not necessitate a path of pure research.
The coalition will continue despite the increasing fears of many Lib Dems and Tories that the trade-offs it necessitates represent the path to self-destruction.
This specific action needs to be determined before the first word is written and necessitates a clear path forward.
For every subset U ⊆ S â§¹ { r } and for each customer k ∈ R, an open arc from a facility in U toward j, necessitates a directed path from r towards U. Constraints (2) can be replaced by inequality in case that c ij ≥ 0, for all ij ∈ A R. Furthermore, the same optimization problem with continuous assignment variables x ij, for all ij ∈ A R, returns an optimal ConFL solution.
Forging my own path necessitated redefining the concept of failure in my mind.
Regardless, keeping in mind being an entrepreneur does not necessitate forging a path alone.
The United States' population is both vast and varied ― rather than minuscule and homogeneous ― necessitating an alternate path to make the fairy tale of gender equality approach reality.
Our ongoing public service career path progression necessitates the utilisation of sector-specific linguistic shorthand.
And with that we are on the path that necessitates an urgent renaissance of ideas related to the individual" [34, p 84].
It follows that the emerging best practice of using persistent identifiers (data-DOIs) to cite data within an article narrative or elsewhere necessitates a machine operable path from the persistent identifier to the data, particularly where data is made available on fully open terms.
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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