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We used correlation matrices rather than covariance matrices because we were interested in the relationship between indices independent of their absolute values.

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We have to willing to unplug from the Matrix, because we are being bilked.

Note that here we have a diffusion scalar rather than a matrix because we have only one slow variable.

We use the identity matrix as the amino acid similarity matrix, because we found that it works better than other similarity matrices (see Supplementary Material).

Carduus thistles were excluded from the community matrix, because we wanted to test for differences among the other community members in plots with and without thistles.

We call Π the preconditioning matrix, because, as it will be explained in Section  3.2, it is used to increase the convergence rate of the recursions (8).

We put the diagonal elements of both matrices to zero, because we shall not consider users who fly within the same airport basin or commuters who work in the same county of residence.

We built two-sex matrix projection models because we cannot identify sex of all fish.

We speculate that this was due to advances in analytical technique for small samples of serum and blood, making them the matrix of choice, because we found no reports showing substantial error of the measurements in urine.

In this paper, we assumed normal CPDFs with equal covariance matrices, because in many cases this choice provides a simple and robust method of discrimination, especially when many variables are available and have to be selected [ 17- 19].

The initial validity of the CCBQ was assessed using a principal components analysis (PCA) of a correlation matrix with Varimax rotation because we are simply transforming the original items into the new set of the principal components.

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