320 - canonization similarity measure

The traditional view of molecular bonds is that they are due to an increased probability of finding electrons between two nuclei, as compared to a sum of the contributions of the pure atomic orbitals. The canonical MOs are delocalized over the whole molecule and do not readily reflect this. There is, furthermore, little similarity between MOs for systems which by chemical measures should be similar, such as a series of alkanes. The canonical MOs therefore do not reflect the concept of functional groups. 

As just described, the most precise measurements of masses come from double neutron star systems. There are currently five such systems known, three of which will coalesce due to gravitational radiation in less than the age of the universe, 1010 yr (Taylor 1994). These three systems in particular allow very precise measurements of the masses of the components, which are between 1.33 M and 1.45 M0 (Thorsett Chakrabarty 1999). The other two double neutron star systems also have component masses consistent with a canonical 1.4 M . It has been suggested that the tight grouping of masses implies that the maximum mass of a neutron star is 1.5 M0 (Bethe Brown 1995). However, it is important to remember that double neutron star systems all have the same evolutionary pathway and thus the similar masses may simply be the result of a narrow selection of systems. 

Relationships between the individual LOE can be examined via principal components analysis (PCA). Correlations among principal components for individual LOE indicate concordance or agreement. Relationships between different SQT LOE can also be assessed using other methods including Mantel s test (Legendre and Fortin, 1989) coupled with a measure of similarity or ordination canonical discriminant (or correspondence) analyses multidimensional scaling (MDS). 

Correlation coefficients ranged from 0.6 or lower to 0.7, depending on the reference compound that was used. With only a few exceptions, similar results were obtained for the other descriptors. Since the biodata and the shape descriptors in this study are both multivariate, canonical correlation analysis was selected to provide a single overall measure of correlation between molecular shape and biological activity, for comparison of the various shape descriptors. In canonical correlation analysis, the combination of the predictor variables is found, which correlates highest with any possible combination of the response variables (23). A similar approach is taken in Partial Least Squares (PLS) analysis (24). 

Canonical covariance provides a quantitative measure of how similar two sets of coordinate systems are in the scale of covariance. Here, the method is explained in terms of two sets of variance-covariance matrices, C(t) and C(t+x). First, C is decomposed into a matrix X as, C = XX. Then, the level of similarity is measured... 

Fingerprint methods are pretty uncorrelated. This is a disadvantage in some respect because the field of molecular modeling could use a more canonical measure of similarity and has been criticized as such [26]. However, it can also be seen as an advantage. Fusing methods based on significance scores do not appear to improve performance on traditional retrospective tests, at least... 

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