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The phrase "are presented based on" is correct and usable in written English.
It can be used when describing how information or data is organized or displayed according to certain criteria or foundations.
Example: "The results of the study are presented based on the participants' responses to the survey questions."
Alternatives: "are shown according to" or "are displayed based on".
Exact(60)
Initially, some extended Wirtinger׳s inequalities are presented based on the classic scalar Wirtinger׳s ones.
Results are presented based on percent change in least-squares means (Table 3).
Gradient computations are presented based on adjoint sensitivity analysis.
Numerical solutions are presented based on a finite-difference approximation.
Then, the selection principles of different subbands are presented based on the corresponding activity measures.
Quantitative results are presented based on performance observed in a large scale heterogeneous multi-user environment.
Seismic microzonation maps for Skopje (Macedonia) are presented based on the Uniform-Hazard-Spectrum (UHS) methodology.
Illustrative design examples are presented based on the recommended design methods.
Finally, the findings of the research are presented based on the investigation and analysis.
Examples are presented based on the Galerkin method for discussing the applicability of this approach.
The significant constructs of safe work behavior are presented based on the sensitivity analysis.
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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