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The phrase "improved both by" is correct and usable in written English
It can be used when discussing enhancements or benefits that come from two different sources or methods. Example: "The project was improved both by the new software and by the team's collaborative efforts."
Exact(7)
Ancestral reconstructions can be improved both by data selection and by model improvements.
Geometric quality of DWI1 was poor, but improved both by optimization of acquisition (DWI2) and by post-processing.
For example, to reduce the operational cost and to offer a competitive price to customers, the utilisation of wagons and trains must be improved, both by advance and proper planning and by improving the technical aspects.
Staffing can be improved both by creating new posts and transferring existing staff.
The initial stability of joint replacements can be improved both by systemic and local bisphosphonates.
Selection of targets for genome editing can be improved both by increasing the accuracy of enhancer predictions and by generating empirical evidence of activity in the higher throughput (but context independent) assays.
Similar(53)
Tasimelteon was shown to "restore the sleep-wake cycle by improving both the ability to initiate and to maintain sleep".
The profit motive can play a part by improving both the quantity and the quality of care on offer.
Figure 5 shows that our proposed system has better performance than [16], by improving both diversity and coding gains.
It also aims improving both Dewulf exergetic analyses by considering a more analytical differentiation of energy dissipations during service.
Furthermore, it better addresses the cycling stability and rate performance issues of Co3O4 by improving both ion and electron transportation.
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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