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Discover LudwigSuggestions(5)
The phrase "are shown to depend" is correct and usable in written English.
It can be used when discussing findings or conclusions that indicate a reliance or relationship between two or more factors.
Example: "The results of the study are shown to depend on the sample size and the methodology used."
Alternatives: "are demonstrated to rely" or "are indicated to be contingent".
Exact(40)
The optimal lending technology and collateral asset are shown to depend on the project quality and bank-borrower distance.
These bounds are shown to depend only on the function mapping the control input to the performance variable.
These effects are shown to depend, each on the envelope ratio, an overall geometry factor, and thus are interdependent.
The sensitivity patterns are shown to depend on the nature of both the perturbed parameter and the variable investigated.
The thermal stability and the magnetic properties of the as-synthesized alloy nanoparticles are shown to depend on the composition.
The optical properties of these materials are shown to depend on their dimensions, composition and the presence of other molecules attached to their surface.
Similar(20)
These transitions were shown to depend on protein concentrations.
Indeed, directly optogenetically driven seizures have been shown to depend critically on cell type26.
Rc is shown to depend on the pore geometry.
The triple junction mobility is shown to depend upon the direction of triple junction migration.
Their cellular uptake was shown to depend on the mitochondrial (Δψm) and plasma membrane (Δψp) potentials.
More suggestions(18)
are shown to lie
are suggested to depend
are shown to rely
are indicated to depend
are shown to require
are shown to consist
are shown to determine
are shown to correspond
are shown to differ
are shown to derive
are shown to vary
are shown to function
are observed to depend
are shown to develop
are shown to improve
are shown to support
are shown to correlate
are shown to increase
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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