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The phrase "across various instances" is correct and usable in written English.
It can be used to refer to multiple occurrences or examples of something happening in different situations or contexts.
Example: "The results of the study were consistent across various instances, indicating a strong correlation."
Alternatives: "in different cases" or "throughout several examples".
Exact(1)
Notably, the fact that anti-Westernism and strong unacceptance of the West's criticism is present in Putin's and absent in Nazarbayev's foreign policies across various instances correlates well with their approaches to domestic protests: while Putin is known for never conceding at any price, Nazarbayev is more attentive to public opinion (Jarosiewicz, 2016: p. 29).
Similar(59)
It tackles various instances across three periods in the 20th-century when history has been called on to construct a heroic Persian identity – such as from 1925 to 1941, under the Pahlavi dynasty, when monumental mausoleums drew on ancient forms to honour historic national heroes, while simultaneously using the formal language of modern construction to project into the future.
Figure 4 demonstrates oil saturation across the reservoir at various instances in time.
There is a general evolutionary association between the number of precloacal and caudal vertebrae in snakes; however, there are various instances across the phylogenetic diversity of this group where this pattern is contradicted [ 30].
In this article, we examined the dynamic interactions (i.e., changing cohesiveness) between specific domain-general networks across time while participants experienced various instances of sadness, fear, and anger.
Gives various instances of this renewed hope.
Trump, at various instances, failed to correct that misapprehension.
Make a chart comparing and contrasting various instances of current military occupation around the world.
The writer tells of various instances when people believed they saw one.
Dr. Phillips, who from 1999 to 2002 led the agency of the Department of Education that administers the national assessment, likened the methodology to what economists do when they convert international currencies into dollars to compare poverty levels across various countries, for instance.
While analytics companies want to monitor social media in real time — gauging customer sentiment about specific brands during the Super Bowl, for instance — academic researchers across various fields wanted to "go back and study things" over almost a decade of historical data, said Chris Moody, Twitter's vice president of data strategy.
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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