In addition, ranking of prioritized gene sets generated by the ten matrices were highly correlated with each other (mean correlation coefficients was 0.92), suggesting that the DEPgenes selected for depression by the current gene prioritization system are effective (see Supplementary Table S4).
However, the E vdW and E SF of peptide-MHC and peptide-TCR interfaces are calculated by the four matrices of PPI and iMatrix, respectively, in this study.
The probability that two different trajectories (Pa and Pb) coincide in connections between cells can be calculated by
Therefore, the sequence { X n } is monotone decreasing and bounded from below by the zero matrix.
Throughout this paper we denote by the set of all matrices with positive elements, by the zero matrix, and by the identity matrix.
If is an integer, the space of all matrices is denoted by, the zero matrix by, and the identity matrix by. is a lattice under the canonical ordering defined by what follows: means that for every,, where and.
Similarly, we can prove that F has a minimal element in (D_{1}), noting that F is bounded below by the zero matrix.
Since the rest (M - K) columns of U in (12) are multiplied by the zero matrix in (17), then the eigenvector matrix ( U ̄ ) and the matrix A span the same signal subspace, and we have A = U ̄ ϒ (22).
Denote by A ⊙ B the element-by-element multiplication of the two matrices A and B, and by A ⊘ B the element-by-element division of the two matrices.
Unlike the methods available, it constructs two matrices from the scaling sequences, and the associated multiwavelet can be obtained by means of the two matrices along with the eigenvalues and eigenvectors of the matrices concerned.
