Y-scrambling

To avoid models with chance correlation, a check with different validation procedures must be adopted, such as, for example, cross-validation, y-scrambling and QUICK rule. A general validation procedure [Wold, 1991] would be the deletion of some objects before the selection of the variables applying the variable selection procedure and then predicting the responses for excluded objects. The whole procedure, including variable selection, is then repeated a number of times, depending on the adopted specific validation technique. 

Information about the validation of the model. This section describes how the model has been validated and reports the statistics obtained by techniques such as leave-one-out cross validation, leave-many-out cross validation, Y-scrambling, and external validation. The chemicals forming the test set are also listed in this section. 

To avoid models with chance correlation, a check with different validation procedures must be adopted, such as, for example, cross-validation, y-scrambling and QUICK rule. 

Because of the indistingiiishability of the electrons, the antisynnnetric component of any such orbital product must be fonned to obtain the proper mean-field wavefunction. To do so, one applies the so-called antisynnnetrizer operator [24] A= Y.p -lf p, where the pemuitation operator mns over all A pemuitations of the N electrons. Application of 4 to a product fiinction does not alter the occupancy of the fiinctions ( ). ] in it simply scrambles the order which the electrons occupy the ( ). ] and it causes the resultant fiinction... 

Fig. 14.6 Experimental and calculated enrichments or depletions of all possible ozone iso-topomers. The labels 6, 7 and 8 represent lsO, 170, and lsO respectively. Ozone (gray bars) was produced in well scrambled oxygen mixtures at about 90 mbar and room temperature (Mauersberger et al. Adv. Atomic Mol. Opt. Phys. 50, 1 (2005)). The calculated values (vide infra) are those of Gao, Y. Q. and Marcus, R. A., J. Chem. Phys. 116, 137 (2002) setting the parameter r = 1.18 (black bars) or r = 1.0 (white bars). A typical symbol, such as 668, denotes an ozone with the isotopic composition 160160180 and consists of a mixture of symmetric (160180160) and asymmetric (160160180) isotopomers (After Gao, Y. Q. and Marcus, R. A., Science 293, 259 (2001))...

Otsuka, H. Aotani, K. Higaki, Y Takahara, A. Polymer scrambling Macromolecular radical crossover reaction between the main chains of alkoxyamine-based dynamic covalent polymers. J. Am. Chem. Soc. 2003, 125, 4064 065. 

The O" ion is much more reactive than either OJ or OJ and the M=0 species reacts as O- when y- or photo-activated (see sections on reactivity in Ref. 7). Hydrogen reacts rapidly and irreversibly with O- even at low temperatures to form OH- groups on the surface and also with Ojc on some systems, but not with 02. Oxygen reacts with O- to form O3 on many different oxides in a reversible reaction (7). This reaction is thought to account for isotopic exchange reactions in which the isotopes can be scrambled among all three nuclei. 

Midlefort and Rose (95) used an isotope scrambling method to detect the rapid and reversible formation of a y-glutamyl phosphate adduct on the... 

Tsuji-Trost reaction (Scheme 11.12). xy -Disubstituted allyl derivatives can react with retention of the alkene geometry although y-monosubstituted allyl derivatives undergo geometrical scrambling typically to the extent of 10-15%. 

To add further credence to these critical assignments, the polarization-depen-dent OODR(Si) spectrum was recorded for the Ojj and 6j bands with implement of photoelastic modulator (PEM). This device alters the polarizations of the probe and pump beams with each laser pulse in a shot-by-shot fashion. For the 0q transition, the two beams would have parallel polarizations (pump and probe transition are both y (B2) polarized). For the 6j transition, the two photons would be perpendicularly polarized to each other, with y and z polarization, respectively. The temporal profiles of polarization-dependent OODR spectra in Figure 2.25 show the expected behavior, where the signals of the parallel and perpendicular polarizations for the S2(0°) < S [ (41) < S0(Oo) and S2(61) <— SjtT1) <— So(0o) are plotted against the delay time. The effects of reversing the polarizations is not too pronounced in these experiments, as the rotational coherence lifetimes are very short and the overall rotation of the molecule quickly scrambles the polarizations of the signals. At very short delay... 

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