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The phrase "a function of the fraction of" is correct and usable in written English.
It can be used in mathematical, scientific, or analytical contexts to describe a relationship where one variable depends on the fraction of another variable.
Example: "The output of the system is a function of the fraction of resources allocated to each department."
Alternatives: "dependent on the proportion of" or "related to the ratio of".
Exact(43)
We also compute the cost to individual players and the social cost as a function of the fraction of highly-informed players when they receive perfectly accurate information.
The structure and the mechanical behaviour are reported for thin films as a function of the fraction of silica.
P-wave velocity changes almost linearly as a function of the fraction of pore space occupied by NAPL.
Similarity of subsampled correlation patterns to complete pattern as a function of the fraction of events sampled for 5, 10, 20, 30, or 50 events (blue, orange, yellow, purple, and green curves respectively).
The overall mean suspension viscosity is found as a function of the fraction of the drop surface area that is immobile or contaminated.
Using a coarse-grained structure-based model, we determined the diffusion coefficient, in reaction coordinate space, as a function of the fraction of native contacts formed Q for the cold shock protein (TmCSP).
Similar(17)
The differential equation in step 2 determines (except for dependence on an initial condition) the infected fraction i as a function of the susceptible fraction s.
The false-positive fraction is defined as the fraction of normal cases recalled as a function of the decision threshold.
The fact that banks are required to keep on hand only a fraction of the funds deposited with them is a function of the banking business.
Currently, we only understand the biological function of a fraction of human genes.
(B) A contour plot shows the fraction of simulations won by PCD+ as a function of disaster probability and migration.
More suggestions(16)
a function of the magnitude of
a function of the logarithm of
a function of the time of
a function of the number of
a function of the quality of
a function of the amount of
a function of the presence of
a function of the percentage of
a function of the volume of
a function of the degree of
a function of the rate of
a function of the nature of
a function of the age of
a function of the ratio of
a function of the concentration of
a function of the level of
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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