The SEM was fitted using Bayesian methods that fit a multi-trait mixed model in software Bayz 2.1 [ 22], where causal parents (e.g., Y1 is causal parent of Y2 in Y1 → Y2) of a given trait were considered as covariates in the equations assigned to this trait, and a diagonal residual (co variance matrix was imposed.
When some symmetries on the transition matrices or on the root distribution are imposed, one obtains the substitution matrices of the corresponding Jukes-Cantor and Kimura (2 and 3 parameters) models among others (([ 10], § 4.2), [ 12], see Methods section).
Desired matrix properties including satisfaction of characteristic equation, symmetry, positive semidefiniteness, and sparsity are imposed as side constraints to form the optimal matrix pencil approximation problem.
Taxes are imposed on businesses.
A matrix G was imposed for the condition of controllability [7] which is required due to the dynamics of the system where the algorithm is being applied.
This leads one to speculate on the possibility that the weave pattern of the undenatured bone matrix could be imposed upon the plasma membranes of competent or preprogrammed cell populations, which then synthesize relatively large quantities of alkaline phosphatase, and other enzymes associated with deposition of calcifiable matrix [ 10].
Furthermore, with this approach penalties on additional covariance matrices can easily be imposed, provided appropriate tuning factors are available.
Due to the well-known ambiguity between the scatter matrix and the density generator of any CES distribution, a constraint on the scatter matrix needs to be imposed.
In contrast to the framework of parallel distributed compensation for T S fuzzy system, the proposed method does not rely on the existence of common matrix P which is imposed in stability conditions.
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