Wavelength selection optimization functions

Two different measures of selectivity from the literature were chosen as optimization functions for K-matrix analysis. The first is an estimator of overall 

A commonly used measure of quality for a P-matrix analysis is the predicted residual sum of squares (PRESS) value computed by 

The PRESS value is determined by leave-one-out cross-validation [15]. Basically, one spectrum at a time is removed from the set of calibration spectra, a calibration model is built from the remaining spectra, and the concentration for the excluded spectrum is estimated as The squared differences between these values and their respective known concentrations c j are summed up as PRESS. The set of wavelengths that minimizes the PRESS value is deemed best. 

If a sufficient number of calibration spectra are available, it is possible to split the spectra pool into a calibration set and one or more independent prediction set(s). The best set of wavelengths would then be the one that minimizes the standard error of prediction (SEP) defined as 

SEP evaluation over PRESS is the time factor. To compute a single PRESS value, as many PLS models have to be formed as there are calibration samples. Conversely, only one PLS model is needed for SEP regardless of the number of spectra considered for calibration and prediction. In order to obtain a statistically valid SEP, it is crucial that the prediction set truly represents future prediction samples. 

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The observation of luminescence from laser dyes by ECL methods offers the possibility of using this approach to create dye lasers. A laser operating by ECL would not require an additional pump laser, and enhanced power, tunability, and wavelength selection are additional factors. While the pumping rate achieved by ECL previously has been two orders of magnitude lower than the optimal, Horiuchi et al. have reported a device structure designed to enhance the ECL efficiency and realize laser action driven by ECL [67], This experiment is illustrated in Fig. 14. A pair of sputter-deposited platinum film electrodes were positioned facing each other 2 to 7 microns apart. One electrode functioned... 

Initial applications of SA were related to combinatorial optimization problems, for example, wavelength selection in multicomponent analysis (cf. Applications for Multicomponent Analysis Section). However, continuous functions can also be optimized. Thus, the parameters in a nonlinear model can be found by SA if the objective function is defined in analogy to the criterion in nonlinear regression analysis (Eq. (6.110)). 

The function of the monochromator in AES is to isolate the determinant spectral wavelength of interest from the emission from all concomitant matrix emitting elemental or molecular species. This frequently means that a narrow spectral bandpass must be selected. It is however generally slightly easier to make sure in AES than in AAS that the optimal wavelength is being employed since emission spectra often may be scanned directly. 

Kowalczyk et al. [121] have investigated the basis set dependence of calculated ORs at four different wavelengths, and of the lowest six states in the ECD spectrum, for (S)-2-chloropropionitrile optimized at the B3LYP/6-311++G(d,p) level of theory. The ORD was calculated at 633, 589, 436, and 355 nm. Six basis sets were selected to calculate the specific rotation with an origin-invariant GIAO approach aug-cc-pVDZ, aug-cc-pVTZ, aug-cc-pVQZ, d-aug-cc-pVDZ, d-aug-cc-pVTZ, and Sadlej-pVDZ (155, 326, 588, 207, 426, and 174 basis functions, respectively). All TDDFT calculations used the B3LYP functional. No solvation models were employed in the calculations. Experimental gas phase measurement... 

Computed the digitalized data are stored and the derivative is calculated direct deriv.itive as a function of wavelength original spectrum is not lost use of various algorithms optimization of the selected parameters necessity for an integrated computer or data station... 

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