Chromatogram from random numbers

A statistical analysis of the peak counts obtained from the simulated chromatograms was made as follows. We changed the random number sequence, by means of the seed change previously described, to generate random changes In component retention times and amplitudes while holding constant component number, zone width, and peak capacity. This procedure. In essence, mimicked the Injection of different samples with the same component number and zone width onto a column. A mean peak count and standard deviation at each of the different peak capacities were calculated. The means and standard deviations of the peak counts were fit by a least squares analysis to Equation 11 with a proper transformation of the standard deviations from an exponential to a linear function (5). From the value of the least squares slope and Intercept, an estimated component number was calculated. 

Consequently, several hidden quantities can be estimated on the basis of the SMO approach. The procedure based on Equation 4.13 can be simply extended even to 2D separations as described in Fig. 4.7. In practice, the 2D pattern, in terms of spot positions and abundances, is divided into several strips. Each strip is transformed into a ID line chromatogram and the procedure described in Fig. 4.7 is then applied. Equation 4.13 is employed to calculate the m value of each strip from which the total m value is obtained. Applications to this procedure will be reported in Section 4.5. At this point, the reader s attention is drawn to the fact that the procedure of transforming 2D strips into ID chromatograms (see Fig. 4.7) once more corresponds to the overlapping mechanisms described in Fig. 4.2 and has been evocated in comparing Fig. 4.4 with Fig. 4.3. In this way, if random structures (e.g., such as those marked in Fig. 4.1b) are present, their memory is lost and the 2D pattern is reduced to a Poissonian ID one. Therefore, the number of SCs can be correctly estimated, even if the 2D pattern was not Poissonian. 

A series of computer-simulated chromatograms has been generated to test the validity of a procedure derived from the statistical model for calculating the number of randomly distributed components when many of them are obscured by overlap. Plots of the logarithm of the peak count versus reciprocal peak capacity are used for this purposTI TRese plots are shown to provide reasonable estimates of the total number of components In the synthetic chromatograms. 

---