The image elements will be either 8-bit pixel values, in which case I = { 0, …, 255 }, or quantized JPEG DCT coefficients, I = { - 1, 024, …, 1, 023 }, arranged into an n1 × n2 matrix by replacing each 8 × 8 pixel block with the corresponding block of quantized coefficients.
A matrix-free method [ 17, 18] is proposed to avoid explicit calculation and storage of the large weight matrix by replacing it using matrix-vector products.
To assess the effect of differences in signal intensities within extracted ion chromatograms, the matrix of doubly-normalized intensities was transformed into a binary matrix by replacing all nonzero values with 1.
In such cases, it is possible to transform A into a nonsingular matrix by replacing its linearly dependent rows with vectors in its left null space (see Ref. 18 of [ 20]).
Considering the perturbation to the original transition matrix P, for each network state x, we compare the steady-state distributions π and (x) that correspond to P and the controlled transition matrix by replacing the row in P corresponding to the state x by the row that corresponds to the flipped state x c.
The matrix was transformed into a binary matrix by replacing the values of all correlations > 0.7 by 1, and assigning the others as 0. The resulting binary matrix induced the adjacency matrix of the coexpression network, in which genes form the nodes and two genes are connected by an edge if they are correlated above 0.7.
Following the construction in [17 19], GLD codes are defined using a sparse matrix constructed by replacing each row in a sparse parity-check matrix, which indeed defines an LDPC code, with rows including one copy of the parity-check matrix of the constituent code Here, is usually a block code of code length n and information bit length k, such as BCH code and Reed-Solomon (RS) code.
The i th power, Li, of a Latin square L is that matrix obtained by replacing each row permutation in L by its i th power.
end{aligned} (3.6) For (i = 1,ldots,n), let (A^{i}) be the matrix formed by replacing the ith column of A by the column vector b.
The impact resistance of concrete was typically improved using additives, specifically fibers, to the polymer matrix or by replacing aggregate with energy absorbent ones.
(3.10) Further, for (i = 1,ldots,n), let (B^{i}) be the matrix formed by replacing the ith row of B by the row vector (( mu_{n} mu_{n + 1} cdot cdot mu_{2n})).
