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A better solution was to find different ways to perform the same calculation.
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In speed and accuracy, the prototype rivals existing electronic-only computing processors that are programmed to perform the same calculations, but it provides substantial computational cost savings.
Instead of being lost in a lab notebook, the data are available for students to perform the same calculations that the authors used (including applying the gas law, something every science student learns but rarely uses in context) and generate a data figure similar to those published in Science.
Nevertheless, the rΔ value computed for the mRNA abundance data remained significant (rΔ = −0.05, P = 1.1 × 10−2), so we used it to perform the same calculations (supplementary table S4, Supplementary Material online).
Expected values were calculated by scrambling 5-hmC gains over the genome and performing the same calculation.
Using data from 2015 provided by the Census Bureau, we performed the same calculation as above.
It then considers another investment level and performs the same calculation.
We also performed the same calculation using only the stars with superflares having a total bolometric flare energy larger than 2·1034 erg (Table 2).
This method performs the same calculation as mytsearch above, but only on those pixels inside the bounding box of the polygon.
In his book, "The United States as a Debtor Nation", published last year, William Cline, of the Institute for International Economics, performed the same calculation, backing out the value of America's net foreign assets from the income they generate.
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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