Derived responses

The statistical techniques associated with response surface methodology are concerned primarily with two aspects of the experimentation process the construction of experimental designs that yield data to permit the efficient modeling of the response surfaces, and the analysis of the experimental data and derived response surfaces. 

Figure 6. Effect of orientation of substituent group at C-l on the stimulatory ability of a D-glucopyranosyl derivative. Responses are relative to the maximum sucrose response. Methyl a-n-glucopyranoside (9), methyl a-D-xylopyranoside (Y), a-o-glucose (A), fi-D-glucose (A) (both of these sugars freshly made), o-glu-cose (equilibrium mixture) (Q), methyl R-o-xylopyranoside (M), and methyl /3-d-...

Potentiometric titration curves normally are represented by a plot of the indicator-electrode potential as a function of volume of titrant, as indicated in Fig. 4.2. However, there are some advantages if the data are plotted as the first derivative of the indicator potential with respect to volume of titrant (or even as the second derivative). Such titration curves also are indicated in Figure 4.2, and illustrate that a more definite endpoint indication is provided by both differential curves than by the integrated form of the titration curve. Furthermore, titration by repetitive constant-volume increments allows the endpoint to be determined without a plot of the titration curve the endpoint coincides with the condition when the differential potentiometric response per volume increment is a maximum. Likewise, the endpoint can be determined by using the second derivative the latter has distinct advantages in that there is some indication of the approach of the endpoint as the second derivative approaches a positive maximum just prior to the equivalence point before passing through zero. Such a second-derivative response is particularly attractive for automated titration systems that stop at the equivalence point. 

Four experimental variables were assumed to influence the result and were studied by a two-level factorial design, see Table 14. In the original paper [70], the authors analyzed five derived responses which were calculated from the observed yields. The derived responses were analysed one at a time. 

Data extraction is the process of selecting and copying data fields to an external file. Data extraction procedures generally produce files that are simply a reflection of the database. The data can then be manipulated and/or transposed to achieve an optimal structure for analysis and reporting requirements. Additional fields can be derived, response values standardized or decoded, and variables labeled more clearly. 

The variables are specified in Table 12.12. The experimental design and yields obtained are given in Table 12.13. Two responses were measured The yield (%) of enamine, y, and the yield of by-product, 2- The reaction was monitored by GLC and the yields obtained after 4 h are given here. The derived response D is a desirability... 

Another common way of introducing colinearities is to use the measured responses to derive other responses, e.g. to obtain a measure of selectivity. It is often seen that ratios of sums of responses are used this way. This causes another problem The error distribution of such derived responses will rarely be approximated by the normal distribution. Hence, any attemps to evaluate the significance of the estimated effects by the t distribution or by the F distribution must be considered highly dubious. 

It is strongly recommended that such derived responses should be avoided in the evaluation of experiments. Sums and differences of responses are acceptable as long as they are not "normalized", but do not use ratios or products of responses. If possible, use the raw data directly as they are measured. 

In the original work[6] the authors analyzed five derived responses, calculated from the originally recorded yields. The derived responses were analyzed one at a time. We shall see that the important variables can be identified from the principal component score calculated from the original yields. 

A normal probability plot of the estimated coefficients is shown in Fig.17.2. It is seen that variables Xj and are significant, and that they also show a significant interaction effect. These are the same conclusions as were reached in the original report, where five derived responses were anaylzed one at a time. 

Fig. 9.8.5 Theoretical first derivative response at 30% concentration as particle size increases from 100 to 4900 nm in 200 nm increments.

C) Calcitriol is the major derivative responsible for increasing intestinal absorption of phosphate. 

Vitamin D increases serum calcium and phosphate, with calcitriol d.25rOH], vitamin D) being the major derivative responsible for promoting their intestinal absorption. Calciferol and calcitriol decrease renal excretion of calcium and phosphate. Parathyroid hormone, not vitamin D. acts via cAMP. The cause of Paget s disease is obscure. The answer is (C). 

Fig. 9-21, Typical control mode characteristics, (a) On-off response creates huntiuK action) ( ) proportional response (eliminates hunting but creates offset except on constant preset demand) (c) proportional and reset response (eliminates hunting and offset) (d) proportional plus rate or derivative response (reduces recovery time but maintains offset unless reset is also used).

Partial derivatives Response functions partial molar properties... 

Figure 10.3 Combination of stereoelectronic effects in propane-1,2-diol derivatives responsible for the reliable shielding effects in -0CH CH(R)0- moiety.

In prokaryotes, the initiating residue is not methionine itself, but Af-formylmetlnonine. Formylation occurs after esterification of the methionine residue with the tRNA, and it is catalysed by a formyltrans-ferase which transfers the formyl group from formyl-tetrahydrofohc acid. The complete tRNA derivative responsible for introduction of the first Af-lerminal residue is therefore fMet-tRNA (formylmethionyl-tRNA), where the subscript f indicates that tUs species of RNA carries a formylated methionine. 

It is important to note that the EPA s PAGs cannot be used directly to interpret environmental measurements. For this purpose, derived response levels (DRLs, another name for operational intervention levels) have been established for environmental survey instruments indicating when protective actions should be taken to meet the PAGs. The DRLs will be different for different types of releases and different times during the emergency. Default DRLs for nuclear power plant release are shown in Table 9.22. 

It should be pointed out that the quinoxalin-2-one/quinoxalin-2-ol tautomerism like 166 to H, when R = Aik, is impossible and therefore the isocyanate derivative responsible for the course of the rearrangement in the case of R = H cannot be... 

We have established that for a fully variational wavefunction we may calculate the molecular gradient from the zero-order response of the wavefunction (i.e., from the unperturbed wavefunction) and the molecular Hessian from the first-order response of the wavefunction. In general, the 2n + 1 rule is obeyed for fully variational wavefunctions, the derivatives (responses) of the wavefunction to order n determine the derivatives of the energy to order 2n -i- 1. This means, for instance, that we may calculate the energy to third order with a knowledge of the wavefunction to first order, but that the calculation of the energy to fourth order requires a knowledge of the wavefunction response to second order. These relationships are illustrated in Table 1. 

An empirical meta-analysis approach was applied in order to develop a quantitative review of the available data and their aggregation towards response laws (Sauvant, 1992). The definite strength of this approach lays in the robustness of the empirically derived response laws, with the limit that the derived laws depend on the physiological and nutritional conditions associated to the data used. Their application is defined by the range of validity of the meta-design. Outside this range of validity, the derived predictions have to be used with caution. 

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