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A given translation-invariant quasifree Hamiltonian is ℛ-symmetric (i.e. [ R, H ] = 0 ) iff the coefficient matrix is restricted to be real.
The Lp-class (p>0) of optimality criteria, which includes D-optimality, A-optimality and E-optimality as special cases, is considered in a regression setting where the experimental errors are uncorrelated with unequal variances and the design matrix is restricted to have row Euclidean norms bounded above by constants.
In addition, the necessary condition for obtaining the optimal scale matrix is restricted to the diagonal matrix (e.g., Eq. (36)), where the off-diagonal elements are simply deleted in every iteration step thereby leading to solutions that do not ensure a true global minimum for the trace of the error matrix.
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When the sources and the mixing matrix are restricted to be non-negative, the problem can be seen as a non-negative matrix factorization (NMF) problem for which many algorithms have been developed[15].
Unlike the present method, in the previous methods of this third category codon exchangeabilities for nonsynonymous changes were assumed to be proportional to the corresponding amino acid exchangeability [23], or a codon substitution matrix was restricted to yield amino acid exchangeabilities equal to empirically-derived ones [21].
To keep the transmitted power unchanged after precoding, the precoder matrices are restricted as: mathsf{tr}left{mathbf{P}_{i}mathbf{R}_{x_{i}}mathbf{P}_{i}^{H}right}leq mathsf{tr}left{mathbf{R}_{x_{i}}right}, ; i=0,ldots,N-1, (16).
Since active matrix remodeling is restricted to the vicinity of living cells, such an effect can only be accounted for by the mechanical properties of the network.
While this approach has successfully identified a number of organic matrix proteins, this technique is restricted to related proteins, providing little latitude for novel matrix protein detection.
Although the Weighted Total Least Squares (WTLS) technique has been introduced into coordinate transformations as the measured points are heteroscedastic and correlated, the Variance-Covariance Matrix (VCM) of observations is restricted by a particular structure, namely, only the correlations of each points are taken into account.
Since H−1 is orthonormal, it is restricted to a permutation matrix.
It is restricted by the conditions that in the Matrix all elements are nonnegative.
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Justyna Jupowicz-Kozak
CEO of Professional Science Editing for Scientists @ prosciediting.com