Sentence examples for using the permutation matrix from inspiring English sources

The random-like nature of chaos is effectively spread into encrypted images by using the permutation matrix.

After exchanging the orientation using the permutation matrix P = ( 1 0 0 0 0 0 130 0 130 0 0 0 0 13), (13).

Therefore, in this paper, we use the solution for receive and transmit beamforming from [8, 19] and extend them to suit non-regenerative multi-way relaying by using the permutation matrix as explained above.

Although it can be realized using the permutation matrix (mathbf {P}) as (mathbf {M}'=mathbf {P}^{mathrm{T}}mathbf {M}mathbf {P}), this implementation is not efficient because the memory traffic increases and additional arithmetic operations are required compared to the COO format.

The numbers of reversals separating all genome pairs in these clades were estimated with MGR 2.03 (Bourque and Pevzner 2002) using the permutation matrix file generated by Mauve, which records the order and orientation of locally collinear blocks.

We use the permutation matrix P in order to bring the block of rows (G_{r}) and (f_{r}) at the bottom position if required.

Algorithm 1: A routine to find the adjoint matrix using the permutation technique.

Act10 with one single residue exchange only (D2E) is more distant, which reflects the scores in the permutation matrix used by the alignment program.

Using this order, we can make the permutation matrix P as follows: (3).

We use to denote the fact that the n × n real square matrix A = (a mk ) satisfies, m = 1,..., n; use A = diag(A1,..., A t ) to denote the fact that A is a block diagonal matrix with diagonal blocks A1,..., A t ; use σ(A) to denote the spectrum of A; use P (n) to denote the permutation matrix of order n the k th row of which is the (k + 1 th row of I n with the first row being (1, 0,..., 0).

Note that the SVD approach does not provide a numerically reliable and efficient way to determine the vectors of dependent and independent flux variables and in the following we use these in the form of the permutation matrix P found from the GJE approach: (8) which gives Equation (5b): (9) where Vindep is a regular f × f matrix.