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The phrase "additionally based on their" is correct and usable in written English.
It can be used when introducing an additional point that is contingent upon the information or criteria related to a specific subject.
Example: "The results of the study were significant, additionally based on their previous research findings."
Alternatives: "furthermore considering their" or "in addition to their".
Exact(1)
Additionally, based on their reported dairy product ingestion, over 90% of the participants consumed less than 1 g Ca/day.
Similar(59)
Additionally, based on the virtue approach to ethics, one need to will the good act [ 21, 48].
Additionally, based on the identified gene IDs, all but one oligonucleotides associated to the same gene were excluded from in silico localization.
Additionally, based on the reaction between PCl5 and 97 atom % 18O water, one would expect the maximum amount of oxygen-18 atoms to be 97%.
Additionally, based on a docking model of l-glutamate at the catalytic site, a one-step sequential mechanism was proposed for enzymatic catalysis.
Additionally, based on the normalized OTUs, alpha diversity was applied to analyse the complexity of species diversity for the samples.
Additionally, based on the current evidence, propose an algorithm for treatment of suspected macrosomia.
Additionally, based on the proposed concept, a design for a wing morphing application is introduced.
Additionally, based on Lipinski and other filters, the drug-likeness of compounds was assessed.
"Additionally, based on our review of the materials you provided, we do not believe there is any similarity between Apple's products and Mr Ross's applications," Lasker added.
Additionally based on the findings, a method to estimating the absorption constant of oxygen into the electrolyte is proposed.
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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