In each sub-problem we diagonalize the weighting matrix and perform the outer vector product operation followed by vectorization.
(affiliation 1), H.-M.T., C.-M.K., C.-T.C. and A.W.N. performed the materials and biointerfaces characterizations; Y.J. developed the photoresponse analysis matrix and performed the COMSOL simulation; Y.J., X.L., B.L. and B.T. wrote the paper, and received comments and edits from all authors; B.T. and G.M.G.S. mentored the research.
Coatings formed by adding Si into the Zr N matrix and performing annealing at 600 °C in a 1% O2 99% Ar atmosphere showed notably high oxidation resistance because Si Zr O oxide scales formed on the surfaces.
For symmetric structures with multiple self-stress modes, two efficient methods, respectively applying singular value decomposition on the constrained equilibrium matrix and performing eigenvalue analysis without manual classifications of member types, are proposed to compute the independent states of self-stress retaining full symmetry.
After obtaining the equivalent channels (in total N × M) of all UEs, eNodeB can construct an equivalent MIMO channel matrix and perform MIMO detection to detect the data packets of M UEs.
We then calculated a Euclidean distance matrix and performed hierarchical clustering on this matrix and calculated FD as the total branch lengths connecting community members together [24].
To estimate the age of early divergences in Microhylidae and Natatanura, we combined both clades in a single data matrix and performed relaxed molecular clock analyses using two independent methods and multiple combinations of calibration points [12].
In order to investigate any possible population structure or cryptic relatedness among our study subjects, we selected a subset of genotyped SNPs to produce a kinship matrix and perform Principal Component Analysis (PCA).
The ensemble method consists of multiple procedures: weighting an adjacency matrix, applying multiple base partitioning algorithms to the weighted matrix, and performing principal component analysis to find the consensus clusters calculated by the base clustering methods, thereby enabling finding biologically-significant clusters.
To make the TF binding scores and motif scores directly comparable, we combine the TF binding matrix and motif-matching matrix, and perform quantile normalization to normalize them.
