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"A" is a vector with element ( A_{0} ) and "D" is a matrix with element ( D_{0} ).
To obtain the kernels the annihilation coordinates were voxelized into a 3D matrix with element size equal to the reconstructed image's voxel size and then normalised.
end{aligned} (2)Here, ({mathbf {W}} in {mathbb {R}}^{N_{theta } N_d times N^2}) is called the system matrix, with element (w_{ij}) equal to the contribution of pixel j to the measurement i.
We denote by D F M - 1 = I K ⊗ F M - 1 the KM × KM matrix where F M - 1 is the M × M inverse Fourier matrix with element [ F M - 1 ] m, k = 1 M exp ( j 2 π M ( m - 1 ) ( k - 1 ) ).
Therefore, the similarity for a pair of proteins is the sum of strengths of walks connecting them, which can be a generalization of Eq. (4) as (6) S = W + β W 2 + β 2 W 3, where W is a matrix with element (W) ij = D i, j).
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Letting GF q) be a finite field with q = ph elements, an n × r matrix with elements from the field is said to have the property Pt if any t rows are independent.
0 N c × N − N c is a N c × (N−N c ) matrix with elements of zeroes.
Therefore, ( denote the matrix with elements ) is nonnegative semi definite and (2.6) is valid for.
The Vandermonde matrix, with elements, is given by the following [13]: (5).
The block-interleaved mapping can be described by an matrix with elements (3).
Let D ∈ R n × n be a diagonal matrix with elements d1,1 > ⋯ > dn,n > 0.
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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