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The phrase "are substantially determined" is correct and usable in written English.
It can be used when discussing factors or conditions that significantly influence or shape a particular outcome or situation.
Example: "The results of the experiment are substantially determined by the temperature at which the reactions occur."
Alternatives: "are largely influenced" or "are significantly shaped".
Exact(4)
Biological effects of cortisol are substantially determined by protein binding of the hormone.
But these are substantially determined by state policy, and that that will influence how people with different levels of education, their health, their behavior, their longevity.
Photophysical properties of this dye are substantially determined by the methyl group at N5 atom of benzothiazole ring [28], [30].
We adjusted for nondietary confounding factors such as smoking and other lifestyle factors, but we did not adjust the main analyses for any other aspects of diet or for BMI, because differences between groups in nutrient intake and BMI are substantially determined by diet group.
Similar(56)
Clearly, the robustness of a BLSS subjected to stress will be substantially determined by the robustness of the plant components of the phototrophic unit.
The force applied on ECBG is substantially determined by both the wheel-rail force (external factor) and the transmission rate of track structure (internal factor).
Meritocracy, "while highly democratic in its intentions, has turned out to be colossally undemocratic in its results" because of "the steep decline of opportunity for those Americans who must live outside the magic circle of meritocratic validation". Entrance into that circle often is substantially determined by higher education, especially at elite institutions.
Just as the trajectory for climate change at the moment is substantially determined by emissions of greenhouse gases emitted in decades past, prospects for climate legislation or a new international treaty are largely determined by bigger political and diplomatic realities shaped over generations.
In a groundbreaking study, Johns Hopkins University researchers followed nearly 800 Baltimore school children for a quarter of a century, and discovered that their fates were substantially determined by the family they were born into.
In a groundbreaking study, Johns Hopkins University researchers followed nearly 800 Baltimore schoolchildren for a quarter of a century, and discovered that their fates were substantially determined by the family they were born into.
Data are presented in table 4. In summary, the analyses confirmed that BPF is substantially determined by both the patients' age (p<0.001) and EDSS (p<0.001).
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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