Eigenvalues descriptors

Electronic Eigenvalue descriptors = EEVA descriptors —> EVA descriptors... 

EVA descriptors were proposed by Ferguson et al. [Ah, 47]. The EVA descriptor (EigenVAlue) extracts structural information from infrared spectra. The eigenva-... 

The BCUT descriptors (Buiden-CAS-University of Texas eigenvalues) [52], are commonly used, are eigenvalue-based, and include 3D information also. 

Linear representations are by far the most frequently used descriptor type. Apart from the already mentioned structural keys and hashed fingerprints, other types of information are stored. For example, the topological distance between pharmacophoric points can be stored [179, 180], auto- and cross-correlation vectors over 2-D or 3-D information can be created [185, 186], or so-called BCUT [187] values can be extracted from an eigenvalue analysis of the molecular adjacency matrix. 

The methodology of nD-QSAR adds to the 3D-QSAR methodology by incorporating unique physical characteristics, or a set of characteristics, to the descriptor pool available for the creation of the models. The methods of Eigenvalue Analysis (40) (EVA) and 4D-QSAR (5) are examples of using unique physical characteristics in the creation of a QSAR model. 4D-QSAR uses an ensemble of molecular conformations to aid in the creation of a QSAR. The EVA-QSAR method uses infrared spectra to extract descriptors for the creation of the QSAR model. 

In order to characterize the interaction between different clusters, it is necessary to consider the mechanism of cluster identification during the process of the DA algorithm. As the temperature (Tk) is reduced after every iteration, the system undergoes a series of phase transitions (see (18) for details). In this annealing process, at high temperatures that are above a pre-computable critical value, all the lead compounds are located at the centroid of the entire descriptor space, thereby there is only one distinct location for the lead compounds. As the temperature is decreased, a critical temperature value is reached where a phase transition occurs, which results in a greater number of distinct locations for lead compounds and consequently finer clusters are formed. This provides us with a tool to control the number of clusters we want in our final selection. It is shown (18) for a square Euclidean distance d(xi,rj) = x, — rj that a cluster Rj splits at a critical temperature Tc when twice the maximum eigenvalue of the posterior covariance matrix, defined by Cx rj =... 

Table 11.3 displays a variety of geometrical descriptors for each fluid (extending results presented in Sidebar 11.3 for a monatomic ideal gas). These descriptors include the lengths of various thermodynamic vectors ( T, P, S, V ), 0Sy coupling angle (=0TP cf. Fig. 11.2), Gramian M, and minor eigenvalue e2 of the metric M. Sidebar 11.5 describes numerical evaluation of e2. 

Determinants and Eigenvalues of A and D Several molecular descriptors are defined from determinants or eigenvalues of A, D, and A + D. The interested reader is referred elsewhere [20,21],... 

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