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Each of these matrices comes with a list of singular values.
The POD method is then applied to each of these matrices to construct a basis for projection.
Similarly, we generate a new matrix of market similarity for each year from 2008-2011, in which the new elements of each of these matrices are given by the difference between the market similarity between two corporations in a given year S i j ( t ) and their market similarity in the previous year S i j ( t − 1 ).
From each of these matrices an objective Oij can be computed to represent the relationship between every gene pair.
For each of these matrices, we conducted analyses of complete plastomes (non-coding and protein coding) and protein-coding sequence (cds).
Both matrix A and G were fitted in the model simultaneously in order to estimate the fraction of the genetic variance captured by each of these matrices.
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This proposed technique is based on the information provided by the arithmetic mean of the number of zeros in each column of these matrices.
Based on subsection 2.2, we can know each element of these matrices is replaced by the length of the VLI code of its corresponding DCT coefficient at the same position.
Each entry in one of these matrices is a vector with a variable number of elements that is constant for each column of a matrix.
Each of these two matrices was analyzed in RAxML with an unpartitioned GTR-GAMMA model, with 1000 bootstrap replicates.
Upon implementing the RMA algorithm, the probe-set level data from each of these three matrices were subjected to further QC by inspecting pair-wise M vs. A plots of replicate GeneChips and examining correlation matrices among replicate GeneChips (minimum mean r for a given species by time point combination across all three of the RMA expression matrices = 0.989).
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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