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The phrase "a function of the scale of" is correct and usable in written English.
It can be used when discussing how one variable or outcome is influenced by the size or extent of another variable.
Example: "The effectiveness of the marketing campaign is a function of the scale of the budget allocated."
Alternatives: "dependent on the size of" or "related to the extent of".
Exact(3)
Two categories of landslide early warning systems (LEWSs) can be defined as a function of the scale of analysis.
The dependence of both dynamic and time-averaged behavior on the column scale is considered to be closely related to the different macroscopic flow structure, which is a function of the scale of the column.
Several critical differences exist between CWs and IWs, which can be understood primarily as a function of the scale of water body of interest.
Similar(57)
"That partly is a function of the sheer scale of the problem.
This decay scale as a function of the angle is found analytically and numerically.
Those "human" qualities are obviously a function of scale, age, and the imprint of hand labor, though perhaps not merely.
Economies function at the scale of the region3.
3D printing is a function of scale and resolution.
Figure 12 BER as a function of amplitude scaling.
Figure 2: Cavity performance as a function of scaling.
There's no stipulation of distance in this etymology, however: remoteness is a function of separateness, rather than of scale.
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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