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The phrase "adaptation of the underlying" is correct and usable in written English.
It can be used in contexts discussing changes or modifications made to a foundational concept, system, or structure.
Example: "The adaptation of the underlying framework was necessary to improve the overall performance of the software."
Alternatives: "modification of the base" or "adjustment of the core".
Exact(2)
The algorithm developed by Hovorka and colleagues has certain distinct features, such as real time adaptation of the underlying model to changing patient parameters implemented as a selection from several predefined models.
We strongly believe that the optimal and suboptimal solutions produced by our method provide a considerable benefit over heuristic solutions in that they allow for a sound evaluation and adaptation of the underlying model.
Similar(58)
In more traditional examples of visual adaptation (e.g. orientation) the impact of adaptation on the underlying neural mechanisms has commonly been observed in two main phenomena: selective changes in the sensitivity to the adapting stimulus, and perceptual bias aftereffects [e.g., 9].
Early microvasculature adaptations might be part of the underlying mechanisms for these associations.
"We still don't know about the exact nature of the underlying mutations that have allowed this adaptation to occur," Goddard says.
Rapid identification of the underlying disorder may improve the clinical management through reliable counseling of the parents and adaptation of the treatment.
Treatment is of the underlying disorder.
Again, treatment is of the underlying disorder.
Aspiring filmmakers should consider one of the underlying questions to emerge from a pair of ongoing discussions — one, about mumblecore and the other, here and elsewhere, about literary adaptations.
Monitor the color of the underlying skin.
In contrast, on P-5 × 5 × 5 actin only forms short fibers, which are concentrated on the edges and tops of the micro-pillars and demonstrate an adaptation of actin filament formation to the underlying surface topography [ 8].
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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