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The phrase "and given the narrow" is not complete on its own but can be correct and usable in written English when part of a larger sentence.
You can use it when introducing a condition or context that relates to something being limited or restricted.
Example: "And given the narrow scope of the project, we need to focus on the most critical tasks."
Alternatives: "considering the limited" or "taking into account the restricted".
Exact(3)
And, given the narrow margin of victory, Mr Hewlett has every right to have a court take a close look.
If that is the case it is totally unacceptable and given the narrow margin of the win I believe the result should be reversed".
This suggests that a transient agent may be involved in aetiology and – given the narrow age range – that exposure to this agent arose shortly before diagnosis.
Similar(57)
Regarding vesicles in the PV and vesicle fusion in the absence of SNAREs etc.: If these vesicles were present in the PV only transiently and given the very narrow lumen of the PV it would be exceedingly difficult to capture images of such vesicles by electron microscopy unless their fusion were inhibited by some means.
Working solutions that involve both the high-tech community and the San Francisco community are highly unlikely, given the narrow nature and interests of people in tech. Louis Gudema Newton, Mass.
Even during the day, you have to be careful given the narrow and slippery paths –you can easily fall in the dirty water".
Brian Feeney, a spokesman for the National Park Service, said, "The sculptor, Fr?ric Bartholdi, never intended for people to climb to the top of the Statue of Liberty," adding that the issue was safety, not security, given the narrow staircase and the 364 steps to the top.
This was appropriate given the narrow transitions and consequently limited number of hybrid localities across transects (see Results).
"These results are on such a knife edge," explains Boon, "that assuming that just one or two extra former Conservative or Lib Dem voters will 'go home' on Thursday could have dragged Labour down to 34%, and given the Tories the narrowest of leads".
This represents a particular challenge given the narrow glucose reference range and risk of hypoglycemia during pregnancy.
Given the narrow range of the data, the minimum and maximum values are selected empirically (0.940 and 0.999, respectively).
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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