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Discover Ludwig"empirically obtained" is a correct and usable phrase in written English.
It is used to describe information or data that was gathered through observation or experimentation, rather than speculation or theory. Example: The results of the study were based on empirically obtained data, providing concrete evidence for the researchers' claims.
Exact(43)
For Subjects 4 7, z-tests (model data vs. empirical data) indicated that the ABM predicted empirically obtained 24-hr mediator values 67% (2/3; p<0.05) of the times for markers that were considered "valid," as described shortly, and 44% (4/9; p<0.05) of the time for markers that were considered "pre-inflamed and/or non-responsive" (see Materials and Methods).
where m n and p are empirically obtained exponent factors, one of them always being zero.
Empirically obtained deposition models for the used symmetrical plasma reactor are given.
This MTF was empirically obtained to make the 1D frequency spectrum appear more like an in-situ buoy [7].
However, only a few results based on empirically obtained data which can validate the aforementioned channel models are available.
Based on backscattered light characteristics (empirically obtained) they presented a visibility recovery approach which also yields a rough estimate of the 3D scene structure.
Similar(17)
It is noted that our algorithm provides a method to empirically obtain these rings.
We design a heuristic algorithm based on genetic algorithms to empirically obtain the Nash equilibrium.
The rates of inbreeding were calculated using a first-order approximation, by empirically obtaining the probabilities of co-selection of relatives.
For the control teams one empirically obtains rΔG = 0.53.
The method uses sample permutation test [ Equation (2)] to empirically obtain the null distribution of the test statistic.
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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