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Perhaps his most startling thesis (built on elementary mathematics) was the "impossibility theorem" (or "Arrow's theorem"), which holds that, under certain conditions of rationality and equality, it is impossible to guarantee that a ranking of societal preferences will correspond to rankings of individual preferences when more than two individuals and alternative choices are involved.
However, combined with the comparable high correlation coefficients between the PharmDock predicted binding energies and the experimentally measured binding affinities, this result suggests that a good prediction in the overall correlation does not guarantee a good ranking power for the ligands bound with the same protein.
Overall, SRC-VLS outperformed the "random picking" baseline (as expected); however it was unable to guarantee a systematic ranking of true binders among the first hits.
Ireland produced a brilliant seven-try display to hammer Argentina and guarantee a crucial top-eight ranking ahead of the 2015 World Cup draw.
To guarantee the existence of a rank detection result, we also need to consider the case that there is no element in (mathcal {I}), i.e., (mathcal {I}=emptyset ).
Diversity workshops may have failed to move the needle, but here's a guarantee: an algorithm designed to rank skill sets will never assume the Asian guy is better at math.
This guarantees that D is a rank-1 matrix, and thus the reconstructed stimulus belongs to a small subset of ({mathcal {H}}_{2}).
To guarantee a balanced BMI distribution between the groups (FBV or placebo), we conducted stratification via BMI rank statistics.
A well-positioned and top-ranked ligand in docking does not guarantee its good ranking during VS, and vice versa.
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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