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The phrase "shown to influence" is grammatically correct and commonly used in written English.
It is typically used when one thing has been demonstrated or proven to have an impact on another thing. Example: Scientific studies have shown that a person's diet can greatly influence their overall health and well-being.
Exact(60)
The type and order of search rankings was shown to influence voters in India in double-blind trials.
This has been shown to influence bony union positively [15].
Network complexity has been shown to influence global population differentiation.
Alternative behavioral assumptions are shown to influence the optimal hedge.
Not only has the priming effect been shown to influence our thoughts and feelings, it can also influence our behavior.
Psychological variables have also been shown to influence functional levels following ACLR [4, 5, 6, 7].
Differences in climate have been shown to influence the nutrient availability in manure.
Volatile matter content has also been shown to influence the thermal behaviour of solid fuels [15].
The size distribution of various nanoparticulate carriers has already been shown to influence their applications.
The elastic mismatch is shown to influence the growth rate variation around the interface.
Staff communication has been shown to influence overall nursing home (NH) performance.
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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