Although many matrices were tested, the weight matrix used here evaluated a match (A-U, G-U, C-G) and with a score of 4, a mismatch (A-A, C-C, G-G, U-U, A-C, A-G, U-C) with a score of -20, and assessed a gap penalty of 100.
For amino acids, many matrices have been published, based on many rationales (Feng et al., 1984; Taylor, 1986), including the genetic code and amino acid physico-chemical properties.
In [16], Baraniuk et al. have been proved that many random matrices are good measurement matrices.
In [16], Baraniuk et al. have been proved that many random matrices are good measurement matrices, and some optimized methods can also be found in existing literatures, such as [17 22].
The user may provide the two parameters necessary for the calculation of the WLS statistic or they can be estimated by the program if many distance matrices are provided (again, in a separate file).
Finally, it is mentioned that, for many matrices which are not diagonally dominant, specially when the off-diagonal entries of each row have close values, one may make use of -matrices to obtain better lower bounds of determinant.
When many independent Vandermonde matrices are considered, the following relations hold.
In the prioritization procedures, too many weight matrices were obtained in the nine sets of parameters (φ = 0.8, 0.85, 0.9, and η = 3, 4, 5%), and we listed only those that met our selection criteria in Table 1.
Moreover, as shown in Table 2, many elements in the matrices are zeros for the KF tracking algorithm.
Many examples of optimal correlation matrices are given, both analytically and numerically.
