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Here, ii represents the ith diagonal element of a matrix.
ij denotes the (i,j th element of a matrix.
Finally, denotes the element of a matrix in the th row and th column.
Al,k represents the (l,k th element of a matrix A. ∥x∥ denotes the ℓ2-norm of vector x.
Let the symbol (L_{i,j}) denote an element of a matrix, which is located at the (i -th row and (j)-th column.
stands for the Euclidean norm of a vector, denotes the cardinality of a set, refers to the th element of a matrix diagonal, and represents the complex space of dimensions.
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The inbreeding coefficient for each dog equals the diagonal element of the A matrix by subtracting one.
Therefore, in this application a pathway is inferred to be either up or down regulated if its targets have a correspondingly larger or smaller Z-score in elements of the A matrix relative to a random selection of genes.
For the SHAKE algorithm [ 64], only the diagonal elements of the A matrix are considered to reduce the complexity of the calculation, while for the MSHAKE algorithm [ 65] the whole matrix is solved with the LU decomposition.
(A) i,j and (a) i denote the (i,j -element of a matrix A and the ith element of a vector a. ∥·∥2 and ∥·∥ F denote the l 2 norm of a vector and the Frobenius norm of a matrix,j -elementely.
The function diag constructs a diagonal matrix by selecting the diagonal elements of a matrix.
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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