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The phrase "a given update" is correct and usable in written English.
It can be used when referring to a specific update that has been provided or is understood in the context of a discussion.
Example: "In order to proceed with the project, we need to review a given update from the last meeting."
Alternatives: "a specific update" or "an assigned update".
Exact(5)
We present an explicit design algorithm that achieves minimal center storage for a given update communication constraint.
It's not big cats, or places in California, or alphabetical dessert foods, but at least there'll be no confusion about when exactly a given update was released….
One of PageLever's key features is the ability to track how a given update on a Facebook Page fares over time — did that status update about a new deal fade quickly, or were people still commenting on it a day after it was posted?
Moreover, the shelf-life of a given update is short.
The locations within the grid had different relevances to the objects on a given update, which we define below (cf. Hedge & Leonards, 2013), along with their frequency of occurrence.
Similar(55)
On a given updating step n, the arrow stimulus leads to modulation of the priority profile in the attentional priority map through two routes, one mediated through perceptual attention processes, the other mediated through attentional processes in WM.
The simulations were run for a given number of update steps with asynchronous updating.
A Twitter feed — @usfoodsworkers — is giving updates on the progress of the picketers.
In Alexei Ratmansky's Cinderella, the fairytale is a given a witty update to 20th-century Russia.
System parses the file stored in a given directory and updates the database accordingly.
Its staff have given an update to this week's biennial Ocean Sciences meeting.
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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