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The implications from the first two matrices to the last one are well documented.
where I is a γ-size identity matrix, and W results from multiplication of the first two matrices in the above equation.
We used a partial Mantel's test to control for phylogenetic proximity, i.e., remove the phylogenetic signal while still testing the correlation between the first two matrices (phenotypic and genetic distances).
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Most of the spoofing is at the expense of movies like "Signs," "The Ring" and the first two "Matrix" movies.
For example, one day the kids wondered about sequels: would a Netflix user who liked the first two "Matrix" movies be just as likely to enjoy the third one, even though it was widely considered to be pretty dreadful?
Anyone who hasn't seen "Signs," "The Ring" or the first two "Matrix" films may be baffled by much of "Scary Movie 3," the third installment of the comedy franchise whose jokes derive largely from references to recent hit films.
We compute the fourth-order cumulant array of { x ̄ [ f ] } and choose the first three matrix slices in order to build a three-way array.
The first array of dimension (N × N × 3) is built by choosing the first three matrix slices from the fourth-order cumulant array, while the second array of dimension (N × N× N) is built using the first N matrix slices.
We first constructed two matrices that each represented a main effects design and together represented the full factorial design (2 × 2 × 2 design).
The difference between the first eigenvector of two matrices explains most of the variation in the orientation of the matrix [ 15, 61].
We used a PCA matrix (first two vectors) and the IBD matrix to correct for population stratification.
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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