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Third, we investigated the best matrices obtained from our core gene sets with other two alternative core gene sets for the robustness of our DEPgenes selection: core gene sets based on best expression genes and candidate pathway genes.
Dairy products have been considered as the best matrices to deliver probiotics [ 1, 11].
We also thank Drs Nathan Vastesaeger, Gérard Trape and Cornelia R Allaart for thoughtful discussions about the ASPIRE and BeSt matrices.
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A best matrix approximation technique for updating the analytical model is developed using the known modal parameters.
Clay minerals provide one of the best matrix materials on which nanoparticles can be collected and aligned in that clay minerals are abundant, environmentally friendly and economical [13 18].
Thus, we selected matrix [2,1,1,8,1,1,7] as our final weight matrix for the seven data sources to calculate combined score for each candidate gene, which equals to (3, 1, 1.5, 4, 1, 1, 3.5) when multiplied the best matrix by preWeight.
Although Papac et al. reported that THAP was the best matrix in the analysis of sialylated glycans with MALDI-TOF [25], it was still impossible to identify sialylated glycans unambiguously from gel-separated proteomic level glycoproteins.
For positive selection detection, the Fixed Effect Likelihood model (FEL) implemented in HyPhy [36], [59] was used with the HKY85+G substitution model found to be the best matrix by HyPhy's model selection program.
According to relative entropy, our best matrix, MIQS (0.3004), is more diverse than BLOSUM62 (0.6979), even when compared with BLOSUM45 (0.3795).
The best matrix M, which gives the highest q value, is selected as the seed matrix for the next optimization step.
However, our finding that for so many alignments from cellular life, the best matrix was derived from viral sequences is surprising and the consequence is that ad hoc arguments for choice of matrix may not reasonable.
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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