This is quite remarkable taking the often much larger scatter of main diagonal data into account.
For that purpose, we introduce the X transmitted diagonal data matrix, where each element x k corresponds to the desired symbol transmitted over the k th subcarrier X = diag x 0, x 1, …, x K − 1 (64).
A much smaller degree of commonality was observed between the Shared- and LPS-responsive genes where many of the diagonal data points seen in the BCR vs Shared comparison migrated closer to the axes.
The data for the diagonal components (Z xx and Z yy ) are not shown in Fig. 3 because their amplitudes are (for the most part) minor in comparison with those for the off-diagonal data (see Fig. 2), but also because these data-points have relatively large associated error bars.
The ROC analysis of the immune responses to fibrils in early / late PD patients vs controls gave the AUC values not greater than 0.5 and ROC curves close to diagonals (data not shown).
From inspection of individual off-diagonal data points, we learned that error in peak identification was the major cause of irreproducibility (data not shown).
Based on the limit cycle data, a diagonal TITO transfer function model of the system dynamics are obtained.
{mathcal C}^{N_{c} times 1}}) and ({{mathbf z}_{d} != [!z(n_{1}), cdots !,} z(n_{N_{c}})]^{T} in {mathcal C}^{N_{c} times 1}) are received coded data symbols and AWGN, respectively, X d =diag(x d ) is a diagonal matrix with the precoded data vector x d on its main diagonal, and (textbf {h}_{d} = [h(n_{1}), dots, h(n_{N_{c}})]^{T} in mathcal {C}^{N_{c} times 1}).
We define the matrix (A.5 where R is a diagonal matrix containing the missing data indicator of Y.
Having obtained these fitted outcome vectors, we define our first Q matrix as (2 where t denotes matrix transpose, R i is a diagonal matrix containing the missing data indicator of ; the jth entry of the leading diagonal of R i is equal to one if is observed and is zero if is missing.
