Lambda matrix

Another approach requires the use of Wilks lambda. This is a measure of the quality of the separation, computed as the determinant of the pooled within-class covariance matrix divided by the determinant of the covariance matrix for the whole set of samples. The smaller this is, the better and one selects variables in a stepwise way by including those that achieve the highest decrease of the criterion. 

Instead of the imivariate Fisher ratio, SLDA considers the ratio between the generalized within-category dispersion (the determinant of the pooled within-category covariance matrix) and total dispersion (the determinant of the generalized covariance matrix). This ratio is called Wilks lambda, and the smaller it is, the better the separation between categories. The selected variable is that that produces the maximum decrease of Wilks lambda, tested by a suitable F statistic for the input of a new variable or for the deletion of a previously selected one. 

Plasmid analysis is often used in recombinant DNA technology. Anew separation matrix, consisting of poly(A-isopropylacrylamide) (PNIPAM) polymer and mannitol as small molecule additive, was used for CE-based plasmid DNA separation. Supercoiled, linear, and nicked conformers of lambda plasmid were separated in 1% PNIPAM + 6% mannitol. The effect of the applied mannitol concentration on the separation quality is shown in Figure 6.6 [117]. 

The net result is that for each value of m, the Hamiltonian for our lambda-doubled molecule can be represented as a 2 x 2 matrix, similar to the ones above ... 

FIGURE 11.9 MALDI-TOF mass spectra of (a) 246-bp DMA amplified from pLBI29 and (b) 500-bp DMA amplified ftx>m bacteriophage lambda genome.The laser wavelength was 266 nm and the matrix HPA/3-HPA. (Reprinted with permission from reference 11). 

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