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We derive a relationship between a PRBS design parameters and the maximum eigenvalue of the parameter error covariance matrix, which yields useful guidelines for the design.
We derive a relationship between the PRBS design parameters and the maximum eigenvalue of the parameter error covariance matrix, which yields some useful insights and design guidelines.
MNMF estimates the spatial mixing system, whereas ICA-based BSS techniques optimize the demixing matrix, which yields a more stable and efficient algorithm than MNMF.
By making use of a recently introduced block tridiagonal partitioning of the collocation matrix, which yields faster rates of convergence, and its associated modified red-black ordering of unknowns and equations, we succeeded to increase the scalability of the problem.
Hence, the time-varying area moments of inertia of the cracked section are employed in formulating the periodic finite element stiffness matrix which yields a linear time-periodic system.
PC are obtained through an eigenvalue decomposition of a covariance or correlation matrix, which yields its eigenvectors and corresponding eigenvalues.
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Importantly, while some Model 3b outcomes indicate that rat eradication does have a very limited potential to bring about population increases, the matrices which yield these results all include substantially lower than average bycatch rates; thus reduced bycatch is ultimately responsible for even these small gains (Figure 5B).
Likewise, we generate dissimilarity matrix (Delta^{ y)}=[delta ^{ y)}_{ij}]_{ntimes n}) by comparing the columns of B. Finally, the dissimilarity between row object i and column object j is defined by a monotonic transformation of the entries in matrix B, which yields a cross-class dissimilarity matrix (Delta^{(xy)}=[delta ^{(xy)}_{ij}]_{mtimes n}).
Using the (CK1) relation with the fact that w i is a sink, one shows easily that the set of N i 2 elements { α β ∗ | α, β ∈ Path ( E ), r = r = w i } is a set of matrix units, which yields that I ( w i ) ≅ M N i ( K ).
It means that we can find K + 1 sub-matrices of A which yields a set of dependent columns, so that k A ″ < K + 1.
The two systems differ in the deterministic perturbation: del Molino et al. include self-coupling (their deterministic matrix is rank one), which yields trivial deterministic dynamics without a driving current (in the sense of Example 1.2); thus, they do not see the dynamics described here.
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