Average descriptor deviation

The next step is to calculate the difference between each descriptor g ir) and the average descriptor g r). This value is defined by the average descriptor deviation 6g for an individual descriptor i with the components j,... 

The sum of all average descriptor deviations divided by the number of descriptors L leads to the average diversity A ... 

Average Descriptor Deviation is a statistical measure for the deviation between descriptors in a data set and the average descriptor. 

Table 4.6. Geometries and NBO descriptors 0/MH2 and MH3 metal hydrides of the third transition series of various spin multiplicities (IS + I), illustrating the correlations of metal charge (Qu) with metal hybrid d character (%d, taken as the average of a and 3 hybrids for open-shell species), bond length (Ruw) and angle (9hmh)> and average absolute deviation (Dev. = average %mh — 90" ), from idealized covalent geometry...

Values for hydrocarbons other than alkynes and alkadienes can be predicted by the method of Suzuki et al. The best model includes the descriptors T, P, the parachor, the molecular surface area (which can be approximated by the van der Waals area), and the zero-order connectivity index. Excluding alkynes and alkadienes, a studv for 58 alkanes, aromatics, and cycloalkanes showed an average deviation from experimental values of about 30 K. 

Here y is the average and cr is the standard deviation of the Euclidean distances of the k nearest neighbors of each compound in the training set in the chemical descriptor space, and Z is an empirical parameter to control the significance level, with the default value of 0.5. If the distance from an external compound to its nearest neighbor in the training set is above Dc, we label its prediction unreliable. 

A linear solvation energy relationship (LSER) has been developed to predict the water-supercritical CO2 partition coefficients for a published collection of data. The independent variables in the model are empirically determined descriptors of the solute and solvent molecules. The LSER approach provides an average absolute relative deviation of 22% in the prediction of the water-supercritical CO2 partition coefficients for the six solutes considered. Results suggest that other types of equilibrium processes in supercritical fluids may be modeled using a LSER approach (Lagalante and Bruno, 1998). 

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. 

In the following we will thus present some basic statistical methods useful for determining turbulence quantities from experimental data, and show how these measurements of turbulence can be put into the statistical model framework. Usually, this involves separating the turbulent from the non-turhulent parts of the flow, followed by averaging to provide the statistical descriptor. We will survey some of the basic methods of statistics, including the mean, variance, standard deviation, covariance, and correlation (e.g., [66], chap 1 [154], chap 2 [156]). 

Table n. Average and Maximum Standard Deviation and F-value Descriptors with Senecionine as Reference (maximum in parentheses)... 

Statistical control applies to all parts of the analytical system - sampling process, the calibration, the blank, and the measurement. Statistical control is attained by the quality control of the entire system and Involves maintenance of realistic tolerances for all critical operations. A system of control charts is the best way to demonstrate attainment of statistical control and to evaluate the appropriate standard deviations. In the simplest form, the results of measurement of a stable check sample, obtained over a period of time, are plotted. Statistical control is demonstrated when the values are randomly distributed around their average value." Control limits are often taken as 2 or 3 standard deviation units of these replicates. Dr. Taylor also adds, "Even the ranges of duplicate measurements of the actual samples tested can be plotted in a similar manner to demonstrate a stable standard deviation. In either case, the statistics of the control charts are the best descriptors of the variability of the measurement process."... 

The descriptor of the protein requirements of a class of similar individuals is the safe level of intake, an amount that will meet or exceed the requirements of practically all the individuals in the group, explicitly taking into account individual variation in requirement. Following the lead of the 1971 Committee, the safe level is defined as the average +2 standard deviations (SD). 

In each case, the second descriptor listed was shuffled 10 times, and the netw ks were trained as for the original data. Values own are averages for the 10 trials ranges indicate standard deviations. 

Here, y is the average Euclidean distance between each compound and its fc-nearest neighbors in the training set fc is optimized in the course of QSAR modeling, and the distances are calculated using descriptors selected by the optimized (model only), a is the standard deviation of these Euclidean distances, and Z is an arbitrary cutoff parameter defined by a user (de Cerqueira et al. 2006 Hsieh et al. 2008 Kovatcheva et al. 2005 Zhang et al. 2008). We set the default value of this parameter Z at 0.5, which formally places the allowed distance threshold at the mean plus one-half of the standard deviation. We also define the AD in the entire... 

VAMP calculates chemical shifts for neutral compounds and cations calculated with AM1 or PM3 using a neural net technique that uses atomic multipoles, bond orders and angles as descriptors. C chemical shifts are calculated as part of the default output from VAMP and require no additional keywords. The average deviation from experiment for an extended test set is of the order of 7 ppm and the maximum deviation is 21 ppm using AMI and slightly worse for PM3. 

Figure 4 shows a few descriptor histograms of a chemical library of nowadays typical size, i.e., containing more than a million compounds.It is immediately apparent that any statistical technique that depends on a normal distribution cannot be generally applied it would be inappropriate, for example, to use the average value of the number of aromatic bonds to characterize a representative for a set of compounds. Any metric of descriptor variability based on a normal distribution such as a standard deviation is also... 

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