When the coding procedure of the quantized norms is over, the coefficients are normalized by the quantized norms, and then, the normalized spectral coefficients are lattice vector quantized according to the bit allocation which leads to different dynamic range in subbands.
(We have found that very little improvement in the policy is obtained by optimizing over the coefficients).
Our main result is to establish a necessary and sufficient condition over the coefficients of the system to get the exponential stability of the corresponding semigroup.
Specifically, we prove that under some conditions over the coefficients, the semigroup generated by the linear operator of the system is exponentially stable, and under other conditions we prove that for all the system is approximately controllable on.
as (conditional) priors for and, then it can be shown [7] that the marginal prior over the coefficients is a multidimensional Student's -distribution, which places most of its probability mass along the axial ridges of the space.
The author proved that in the Banach space where is the space of bounded uniformly continuous real valued functions on, if and are locally Lipshitz and under some conditions over the coefficients, and if then for all Moreover, and satisfy the system of ordinary differential equations.
The diagonal entries of Γ can be estimated from the data by first marginalizing over the coefficients β and then performing a type II maximum likelihood, which is equivalent to minimizing (8) where a flat hyper-prior is assumed for the diagonal entries of Γ.
If the evolutionary rates between the original (λ1) and duplicate (λ2) stay the same or change proportionally over time, the coefficient of rate correlation (rλ) between them will be 1.
We chose the intraclass correlation coefficient over the correlation coefficient, which has been typically used in prior RTOP studies (Sawada et al., 2002; Park et al., 2010; Budd et al., 2013), for two reasons (see Jones et al., 1983).
