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This index enables one to diagnose whether a distance matrix is compatible with a tree and to modify the biased distances until they satisfy orthogonality, that is, with a zero value for the index.
We know from the analyses of expected covariance matrices (see above, Table 2) that the rank 1 C covariance matrix is compatible with Ph->E transmission.
When a distance matrix is compatible with a tree structure, sequences are expressed by the composites of branch vectors that are orthogonal among others.
However, we note that an ADE model, notably with a rank 1 D covariance matrix, is compatible with Ph->E transmission with a negative parameter βk.
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Attenuated total reflectance Fourier transform infrared spectra demonstrated that the sheath polymer and core matrix were compatible with KET owing to hydrogen bonding.
The resulting matrices are compatible with direct factorization using SuperLU_dist.
As RCW is a weighting of an existing matrix, it is compatible with all matrix-based methods.
Note that while S' is not the only stoichiometric matrix which is compatible with the reduced REs (any matrix of the form S s + A S f where A is some general matrix will do), it is the matrix which is uniquely selected by adiabatic elimination of the concentration fluctuations of the fast species.
This reformulation is necessary in order to obtain an appropriate sensing matrix that is compatible with the employed recovery algorithm.
Lemma 2 also indicates that the k '-rank ofA θ andF ϕ are related to the structure of their sub-matrices, which is compatible with the multipath structure of sources.
Hunley and Long [2] and Hunley et al. [14] applied a test of treeness developed by Cavalli-Sforza and Piazza [16] to decide if a matrix of genetic distances is compatible with a language tree.
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