Molecular structure descriptor

Clearly, the constant can be included into threshold value B, so that the function /o(C) = 1 is not necessary. We must stress that in such form the probabilistic approach has no tuned parameters at all. Some tuning of naive Bayes classifier can be performed by selection of the molecular structure descriptors [or /(C)] set. This is a wonderful feature in contrast to QSAR methods, especially to Artificial Neural Networks. 

Calculate molecular structure descriptors for each molecule. The descriptors... 

Generation and storage of molecular structure descriptors from the topological or geometrical representations of the structures. 

These results show that pattern recognition can be used as an effective tool to characterize polycyclic aromatic hydrocarbon carcinogens. Using a set of only 28 molecular structure descriptors, linear discriminants can be found to correctly dichotomize 191 out of 200 randomly selected PAH s. This same set of 28 descriptors supports a linear discriminant function that has an average predictive ability of over ninety percent when subjected to randomized predictive ability tests. 

Mdosavljevic, S. and Radenkovic, S. (2003a) Graph energy a useful molecular structure-descriptor. Indian J. Chem., 42, 1309—1311. 

Li, X. and Gutman, I. (2006) Mathematical Aspects of Randic-Type Molecular Structure Descriptors, University of Kragujevac, Kragujevac, Serbia. 

Raevsky, O.A. (1999) Molecular structure descriptors in the computer-aided design of biologically active compounds. Russ. Chem. Rev., 68, 505-524. 

Toropoy A.A., Gutman, I. and Furtula, B. (2005) Graph of atomic orbitals and molecular structure descriptors based on it. J. Serb. Chem. Soc., 70, 669-674. 

F or the characterization of the charge distribution in a molecule, the numerically unitary integrated molecular transform (FTm), its analogous electronic (FTe) and charge (FTC) transforms, and the normalized molecular moment (Mn), its analogous electronic (AQ and charge (Mc) moment, have been developed as molecular structure descriptors [45,46]. Those descriptors have been applied successfully for the development of QSAR models for various physicochemical, pharmacological, and thermodynamic properties of compounds. 

The structures of compounds having a particular odor quality and compounds of similar structural classes that do not can be adequately represented by a set of molecular structure descriptors. 

Descriptor Generation. The most Important part of SAR studies is the development of molecular structure descriptors. 

ADAPT has a variety of pattern recognition and statistical methods available for use. The object of the analysis phase is to find discriminants that separate subsets of the data into the proper categories. That is, one is trying to find mathematical models that will classify compounds as belonging to the active or inactive subset based on the molecular structure descriptors available. This phase of SAR studies Is guided by the user in a highly interactive manner in order to search through the available descriptors for the best set. 

Flora, S. de, Koch, R. Strobel, K. and Nagel, M. (1985) A model based on molecular structure descriptors for predicting mutagenicity of organic compounds. Toxicol Environ. Chem., 10, 157-70. 

A general advantage of QSRR is that the equations derived allow the prediction of retention indices for compounds structurally similar to those used to develop the model but not represented in the initial data set. An essential condition for derivation of significant quantitative relationships between retention data and molecular structure descriptors is the precision and reliability of the chromatographic data used. Although there are several potential sources of errors in routinely determined GC retention indices, the correlations obtained are often very promising and meaningful. 

X. Li and I. Gutman, Mathematical aspects of Randic-type molecular structure descriptors. Mathematical Chemistry Monographs, MCM-1, University of Kragujevac and Faculty of Science, Kragujevac, Serbia, 2006. 

B. Lucid, S. Nikolid, N. Trinajstid, B. Zhou, and S. Ivanis Turk, Sum-connectivity index, in Novel molecular structure descriptors—Theory and application I, ed. I. Gutman and B. Furtula, University of Kragujevac, Kragujevac, Serbia, 2010, pp. 101-136. 

I. Gutman, Preface to a special issue entitled Graph-based molecular structure-descriptors— theory and applications, Ind. J. Chem. 42A (2003) 1197-1198. 

Last but not least, we may mention considerable activity in some mathematical circles interested in mathematical properties of molecular descriptors. Mathematical Aspects of Randic-Type Molecular Structure Descriptors is the title of one of two books on the mathematical properties of the connectivity index X, in which selected papers on these topics were presented [21,22]. Clearly, the connectivity index represents one successfully solved problem in the search for useful mathematical molecular descriptors. But a question can be raised Is there anything unsolved relating to the topic of the connectivity index Is there something that can still be improved We will come up with some answers to these questions later. 

The most widely used types of topological indices are molecular connectivity indices. They have been widely reported as molecular structure descriptors in SPR studies and in structure-activity (SAR) studies as well. Originally developed by Randic/ and later modified by Kier and Hall, ° these indices have been used in a variety of studies. These indices are based on a graph theoretical treatment of the molecular topology of the compounds, and encode information about the branching and size of the molecules. The general equation for calculating molecular connectivities of the nth order is... 

The QSRR study was performed in three stages (1) entry and storage of the structures and the associated retention indices, (2) generation of molecular structure descriptors, and (3) generation and testing of linear model equations. The compounds structures and associated retention indices were entered into computer files using the structure entry capabilities of the ADAPT software system.The study was limited to the 144 compounds listed in Table 1. 

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