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These matrix elements were calculated using the pure electronic wave functions obtained by the energy level calculations for 4f and 5d configurations.
The energy-integrated inelastic transition matrix elements were calculated using the method of sum rules inversion [17].
Composition of secondary structural elements and frequency of hydrogen bonds mediated by residues in secondary structural elements were calculated using custom Perl scripts.
The contents of the elements were calculated using standard samples: BIL-1 (Baikal silt), 1633A (fly ash, National Bureau of Standards, USA), soil-7 (IAEA standard).
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The concentration of the surface elements was calculated using the system database after subtracting the background counts.
The mixing enthalpy ΔHmix x) of body-centered cubic (BCC) β-Ti with transition elements was calculated using first-principles methods based on density functional theory (DFT).
Assessment values for lowest-level elements are calculated using a series algorithm that relates composite scores uniquely to the scoring scale.
The predicted concentration vector ŷ for the volume elements is calculated using the corresponding measured spectra X according to the prediction model: begin{aligned} hat{y} = Xhat{b} end{aligned} (5 where (hat{b}) is the calculated regression vector from the calibration model.
The overall percentage of reads corresponding to known repetitive elements was calculated using BLAT (minimum sequence identity = 70%) to determine the number of reads that hit the Viridiplantae repeat sequences downloaded from the Repbase Update release 15.07 database [ 52].
Intensity and background data for each element were calculated using Imagene 5.5 (BioDiscovery Inc., Australia).
Expression scores (RPKM) for each TE element were calculated using custom scripts in which each score was divided by the total length (in kb) of each annotated TE and this value was normalized to the total mapped reads (in millions) in that sample (instead of normalizing to just the reads which map to TE elements).
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