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The parameters for the dynamic simulation were estimated using the function implemented neural network.
Test statistics were recomputed on windows of one-hundred base pairs length with a step size of two using the function implemented in DnaSP [ 49].
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For the cubic spline interpolation, we used the functions implemented in the SciPy library [19].
PCA was performed using the procedure implemented in the R function ' prcomp'.
The variance was not homogeneous and changed with the predictor 'size overlap', thus the GLS model allowed us to work with a normal error distribution and taking into account the variance structure by using the function 'varFixed', implemented in the nlme package (Zuur et al. 2009).
To circumvent the problem of model overfitting, we assessed the significance of individual terms in the ANCOVA using the "step" function implemented in R, which uses Akaike's information criterion (AIC) to remove terms that do not significantly improve model fit that is, models that increase the AIC value resulting in the set of minimal adequate models discussed below.
Relative protein intensities in each biological replicate were subjected to global statistical analysis (ANOVA, p < 0.05) to reveal significant differences in between the different groups using the corresponding function implemented in the software.
Principal component analysis (PCA) was performed to visualize the various branching types (e.g., apical vs. basal branching) within the SAM association mapping population using the pca function implemented in the FactoMineR package ver. 1.16 [ 34] available in the R statistical computing language (ver. 3.1.0) [ 35].
The model was fitted to each of the 1,500 sub-datasets using the lsqcurvefit function implemented in MATLAB R2012a [ 89] under the criterion of the LSE of t, and the parameter estimation was constrained so that all parameters were greater than zero.
A correspondence analysis of amino acid composition was performed using the 'dudi.coa' function implemented in the ADE-4 package [ 46] under the R statistical computing environment.
Primers covering all exons were designed automatically using the ExonPrimer function implemented in the UCSC database [ 29] and the online Primer3 software package to cover the putative promoter sequence [ 30].
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