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Let be the adjacency matrix of and let be the number of neighbors of.
Let be the adjacency matrix of, and let be its eigenvalues.
For any matrix of and for any vector, consider the linear equation (3.1).
where and are the sample autocorrelation matrix of and the sample cross-correlation vector of and, respectively.
where is the covariance matrix of, and are the cross-covariance matrices of and, and is the covariance matrix of.
Next, let be the graph Laplacian matrix of which is defined as, where is the degree matrix of, and.
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Finally capable of grappling with the matrix of challenges and crises facing us in a way that was both effective and sustainable.
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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