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Figure 2 R matrix of the original 3D MIMO codeword.
Illustration of the R matrix of the original 3D MIMO codeword given in (9) in quasi-static channel.
We denote the reduced network with the minimum number of links to preserve synchronizability (eigenratio of the Laplacian matrix) of the original network as the synchronization backbone.
Therefore, the new axes are the eigenvectors of the correlation matrix of the original variables, which captures the similarities of the original variables based on how data samples are projected onto them.
The result is a matrix of the original type, only its dimension decreased by 3. Repeat these reduction steps until the size of the matrix is reduced to =5.
The multiple CS tasks are produced via simply circular-shifting the columns of the measurement matrix of the original CS model, which corresponds to circular-shifting the elements in the original signal vector and creates signals that have overlapping clusters, or equivalently speaking, correlated signals.
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The method does not require generation and storage of stiffness and mass matrices of the original structure.
Fig. 1 Conceptual illustration of non-negative matrix factorization (NMF) decomposition of a matrix consisting of m words in n documents into two non-negative matrices of the original m words by k topics and those same k topics by the n original documents.
The extension of the method to variable shapes, for example by setting a constraint on the particle volume, or to a non uniform background, by computing it on sub-matrices of the original frame, can be easily obtained.
Biclustering methods [ 37, 38] are designed to cluster in two dimensions simultaneously to produce sub-matrices of the original data that behave consistently in both dimensions.
Figure 6 shows the adjacency matrices of the original communities (a,b) and those of the respective most similar networks (c,d) obtained by considering the topological properties at each node.
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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