Multiple topology method

For illustration, we shall consider here one of the nonlinear variable selection methods that adopts a k-Nearest Neighbor (kNN) principle to QSAR [kNN-QSAR (49)]. Formally, this method implements the active analog principle that lies in the foundation of the modern medicinal chemistry. The kNN-QSAR method employs multiple topological (2D) or topographical (3D) descriptors of chemical structures and predicts biological activity of any compound as the average activity of k most similar molecules. This method can be used to analyze the structure-activity relationships (SAR) of a large number of compounds where a nonlinear SAR may predominate. 

Topological Methods. The topological properties of the stirred-reactor equations (37) can be used to predict the occurrence of multiple states and to determine their stability. More sophisticated tediniques can be enqiloyed in determining the oscillatory nature and limit-cycle bdiaviour of such systems. The introduction of topological methods in the study of chemical reactors was made by Oavalas in 196S fixed-point methods were introduced in the study of thermodynamically... 

Most of the 2D QSAR methods are based on graph theoretic indices, which have been extensively studied by Randic [29] and Kier and Hall [30,31]. Although these structural indices represent different aspects of molecular structures, their physicochemical meaning is unclear. Successful applications of these topological indices combined with multiple linear regression (MLR) analysis are summarized in Ref. 31. On the other hand, parameters derived from various experiments through chemometric methods have also been used in the study of peptide QSAR, where partial least square (PLS) [32] analysis has been employed [33]. 

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