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where Γ m = diag γ 0 m, γ 1 m, …, γ 2 N − 1 m (32). is a diagonal matrix of variable leakage factors as determined by (28).
To capture the interactions of different types, we employ a payoff matrix of variable size and thus are able to accommodate an arbitrary number of mutations.
The size of the eigenvectors is equal to number of variables and the eigenvectors are orthogonal to each other, i.e. V 1 ¯ V ¯ 2 = 0. We have used R, rgl and lattice packages to compute the matrix of variable loadings, rotated data and to plot rotated variables.
(4) H X = 1 2 log 2 πe n C, (5) I X, Y = 1 2 log C X · C Y C X, Y, (6) I X, Y | Z = 1 2 log C X, Z · C Y, Z C Z · C X, Y, Z, where C is the covariance matrix of variable X, | C | is the determinant of matrix C, and n is the number of variables in C. A high MI value indicates that there is a close relationship between the variables, while a low MI value implies variable independence.
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He likes to build things, to solve things, and he often talks about slicing apples as an "equation" -- a matrix of "variables" and "commonalities" that may never be fully controlled but, with enough persistence, can be made adequately algorithmic.
The screens virtually eliminate the trial and error that goes into achieving complicated stitch patterns, displaying a matrix of variables that includes stitch width and length, thread tension, sewing speed and presser-foot pressure.
The correlation matrix of variables was generated and factors were extracted by the centroid method, rotated by Varimax.
Experiments according to the design matrix of variables in Table 1 were carried out, and the relevant results are shown in Table 2.
The whole matrix of variables of adaptive capacity (X ij ) and variables of exposure and sensitivity (Y ij ) appears as follows: X ij Y ij = X 11 + X 12 + ⋯ + X 2 n − Y 11 + Y 12 + ⋯ Y 2 n ⋅ X m 1 + X m 2 + ⋯ + X mn − Y m 1 + Y m 2 + ⋯ Y mn (3).
The Bartlett's sphericity test on the correlation matrix of variables demonstrates the calculated χ 2 = 2368.7, greater than the critical value of χ 2 = 59.30 (p = 0.0005 and 28 degrees of freedom), thereby indicating that PCA can accomplish a momentous reduction of the dimensionality of the original dataset.
(DOCX 19 KB) 40529_2013_98_MOESM7_ESM.docx Additional file 7: Table S7: Component matrix of variables and their contributions to principal components (Abbreviations: Number of polymorphic locus P, average number of allele A, average number of allele per polymorphic locus A P, genetic diversity He, temperature T, rainfall RA, humidity HU, altitude AL, latitude LA and longitude LN).
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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