Here dL is the descriptor value of molecule i, dav the average (or mean) value of the entire data set, the a standard deviation, and d( the scaled value of descriptor d for molecule i. This procedure ensures that all chosen descriptors have similar value ranges (i.e., that descriptor axes have comparable length) and thus prevents space distortions. [Pg.10]

Descriptor frequence values (cm )] are claimed to be helpful in predicting the direction of these rearrangements (96ZOK1742). These values were developed for oxazoles, 1,2,4-oxadiazoles, and furazanes. The calculated descriptor values [v sr(cm )] for the E- and Z-isomers of 4-aminofurazan 3-carboxamidoximes [E-I and Z-I, = (CH2)4, (013)2] and their rearranged 3-(substituted amino)furazan 4-carboxamidoximes [II, [Pg.206]

Target = Ideal descriptor values Ql Acceptable compounds Q Rejected compounds [Pg.213]

Thus, calculation of these descriptor values for a molecule involves the separate calculation of atomic charges and SAAs. [Pg.7]

Here n, and //, are the number of descriptor values for molecules i and /, respectively, and ny is the number of common values. />.,. is the distance between molecules i and j, D the average distance, and n the total number of molecules. [Pg.7]

For each molecule, calculation of n descriptor values produces an TV-dimensional coordinate vector in descriptor space that determines its position [Pg.5]

Fig. 7. Artificial neural network model. Bioactivities and descriptor values are the input and a final model is the output. Numerical values enter through the input layer, pass through the neurons, and are transformed into output values the connections (arrows) are the numerical weights. As the model is trained on the Training Set, the system-dependent variables of the neurons and the weights are determined. |

Korany et al. [28] used Fourier descriptors for the spectrophotometric identification of miconazole and 11 different benzenoid compounds. Fourier descriptor values computed from spectrophotometric measurements were used to compute a purity index. The Fourier descriptors calculated for a set of absorbencies are independent of concentration and is sensitive to the presence of interferents. Such condition was proven by calculating the Fourier descriptor for pure and degraded benzylpenicillin. Absorbance data were measured and recorded for miconazole and for all the 11 compounds. The calculated Fourier descriptor value for these compounds showed significant discrimination between them. Moreover, the reproducibility of the Fourier descriptors was tested by measurement over several successive days and the relative standard deviation obtained was less than 2%. [Pg.40]

Figure 6.19 Graphic representation of the distances in a simplified three-dimensional descriptor space (space B). Catalysts with descriptor values within the model are good candidates for optimization. Those outside the model space may lead to new discoveries. |

Figure 1. Simplified three-dimensional representation of the multi dimensional spaces containing the catalysts, the descriptor values, and the figures of merit. |

A point that is often not fully realized is that the chemical descriptors, as typically obtained with commercial software, are quite ambiguous because the exact mathematic equation used to get the descriptor value is not available, and different software or even different versions of the same software may produce different values for, apparently, the same descriptor. [Pg.191]

Because principal component analysis attempts to account for all of the variance within a molecular dataset, it can be negatively affected by outliers, i.e., compounds having at least some descriptor values that are very different from others. Therefore, it is advisable to scale principal component axes or, alternatively, pre-process compound collections using statistical filters to identify and remove such outliers prior to the calculation of principal components. [Pg.287]

Chemical descriptors are in most of the cases obtained with equations that are not known. Even if the references to certain general equations are given, in practice, it is difficult to replicate the results obtained with chemical descriptors. As we have discussed, chemical descriptors based on tridimensional structures are subject to manual optimization, and this may change the descriptor values. But even in the case of other simpler descriptors, we found that using software from two different commercial sources, the results may be different. Even the use of two different versions of the same software may provide different results for the same descriptor. Even descriptors, which seem simple, such as number of double bonds, or of aromatic rings, are critical because they depend on how tautomers and aromaticity are considered in the different software, or are sensitive to the structure format that is used. [Pg.198]

The multiple linear regression (MLR) method was historically the first and, until now, the most popular method used for building QSPR models. In MLR, a property is represented as a weighted linear combination of descriptor values F=ATX, where F is a column vector of property to be predicted, X is a matrix of descriptor values, and A is a column vector of adjustable coefficients calculated as A = (XTX) XTY. The latter equation can be applied only if the matrix XTX can be inverted, which requires linear independence of the descriptors ( multicollinearity problem ). If this is not the case, special techniques (e.g., singular value decomposition (SVD)26) should be applied. [Pg.325]

By dividing the problem this way, we translate it from an abstract problem in catalysis to one of relating one multi dimensional space to another. This is still an abstract problem, but the advantage is that we can now quantify the relationship between spaces B and C using QSAR and QSPR models. Note that space B contains molecular descriptor values, rather than structures. These values, however, are directly related to the structures (8). [Pg.263]

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