Complete data matrix

SeqMan II and SeqEdit (LaserGene System Software, DNAStar Inc.), and consensus sequences for each gene were input and manually ahgned in SeAI (Rambaut, 1996). The complete data matrix is available in the acompanying CD (Appendix 17.1). 

The complete principal component decomposition of the data matrix X into a score matrix P and a loading matrix P is given by... 

Completion of missing data. The proceeding of completion depends on the character of the incomplete data set. In conventional data lists of random character such as a nxm data list (data matrix) which contain results of several analytes (m) in diverse samples (n), missing data are frequently substituted by the mean of the respective analyte over all the samples. 

Spectra taken during the Auger sputter profile were transformed into a data matrix and treated by the PHI-MATLAB , version 4.0, software. Each element was treated separately, that is the number of matrices was the same as the number of significant elements, and each matrix was completely independent of the others. The number of factors used for reconstruction was the one predicted by the minimum of the indicator function (IND). Unless specified, no mathematical treatment was performed on the data (differentiation, smoothing). 

Table 2.40 shows a complete design matrix by the method of random balance original data taken from normal population y0 y synthesized response to which values of effects were added and the phases of factor screening with corrected response y1 y11 ym and ylv and their standard deviations. 

The tubulin-bound conformation of DDM in solution has been determined from tr-NOE data [112], Sample conditions were similar to those used previously to determine the bioactive conformation of EpoA. Distance restraints were obtained from a series of tr-NOE spectra recorded at several mixing times and were used in the structure calculation based on the complete relaxation matrix methodology [37], The NMR-derived bioactive conformation is quite similar to the crystal structure except for the conformation of the 8 lactone ring, that is close to a flattened chair in solution but a twisted boat in the crystal (Fig. 18). 

The population parameters 2 and [x completely specify the properties of a multivariate distribution. Usually it is impossible determine the population parameters therefore, one usually tries to estimate them from a small finite sample of size n, where n is the number of observations, The population mean vector, p, is approximated by the sample mean vector, x, which is simply the mean of each column in the data matrix X shown in Figure 3.4. As n becomes large, the approximation in Equation 3.31 becomes better. 

The singular-value decomposition (SVD) is a computational method for simultaneously calculating the complete set of column-mode eigenvectors, row-mode eigenvectors, and singular values of any real data matrix. These eigenvectors and singular values can be used to build a principal component model of a data set. 

Both PCA and MCR-ALS can be easily extended to complex data arrays ordered in more than two ways or modes, giving three-way data arrays (data cubes or parallelepipeds) or multiway data arrays. In PCA and MCR-ALS, the multiway data set is unfolded prior to data analysis to give an augmented two-way data matrix. After analysis is complete, the resolved two-way profiles can be regrouped to recover the profiles in the three modes. The current state of the art in multiway data analysis includes, however, other methods where the structure of the multiway data array is explicitly built into the model and fixed during the resolution process. Among these... 

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