Manuela Pavan

Structure/response correlations and similarity/diversity analysis by GETAWAY descriptors. 1. Theory of the novel 3d Molecular descriptors

Novel molecular descriptors based on a leverage matrix similar to that defined in statistics and usually used for regression diagnostics are presented. This leverage matrix, called Molecular Influence Matrix (MIM), is here proposed as a new molecular representation easily calculated from the spatial coordinates of the molecule atoms in a chosen conformation. The proposed molecular descriptors are called GETAWAY (GEometry, Topology, and Atom-Weights AssemblY) as they try to match 3D-molecular geometry provided by the molecular influence matrix and atom relatedness by molecular topology, with chemical information by using different atomic weightings (atomic mass, polarizability, van der Waals volume, and electronegativity, together with unit weights). A first set of molecular descriptors, called H-GETAWAY, is derived by using only the information provided by the molecular influence matrix, while a second set, called R-GETAWAY, combines this information with geometric interatomic distances in the molecule. The prediction ability in structure-property correlations of the new descriptors was tested by analyzing regressions of these descriptors for selected properties of octanes.

Structure/Response Correlations and Similarity/Diversity Analysis by GETAWAY Descriptors. 2. Application of the Novel 3D Molecular Descriptors to QSAR/QSPR Studies

In a previous paper the theory of the new molecular descriptors called GETAWAY (GEometry, Topology, and Atom-Weights AssemblY) was explained. These descriptors have been proposed with the aim of matching 3D-molecular geometry, atom relatedness, and chemical information. In this paper prediction ability in structure-property correlations of GETAWAY descriptors has been tested extensively by analyzing the regressions of these descriptors for selected properties of some reference compound classes. Moreover, the general performance of the new descriptors in QSAR/QSPR has been evaluated with respect to other well-known sets of molecular descriptors.

Prediction of aromatic amines mutagenicity from theoretical molecular descriptors

In the present research the mutagenicity data (Ames tests TA98 and TA100) for various aromatic and heteroaromatic amines, a data set extensively studied by other quantitative structure–activity relationship (QSAR)-authors, have been modeled by a wide set of theoretical molecular descriptors using linear multivariate regression (MLR) and genetic algorithm–variable subset selection (GA–VSS). The models have been calculated on a subset of compounds selected by a D-optimal experimental design. Moreover, they have been validated by both internal and external validation procedures showing satisfactory predictive performance. The models proposed here can be useful in predicting data and setting a testing priority for those compounds for which experimental data are not available or are not yet synthesized.

Scientific data ranking methods : theory and applications

Publisher Summary The statistical analysis based on the distribution of the ranks (order of the experimental values) has had an increasing development. Outcomes associated with an experiment may be numerical in nature, such as quantity in an analytical sample. The types of measurements are usually called “measurement scales” and are, from the weakest to the strongest, nominal, ordinal, interval and ratio scale. This chapter describes procedures that can be used with data in nominal scale. It presents statistical methods, which is the most powerful for data in ordinal scale—they are the test of ranks. The tests of ranks are valid for data with continuous, discrete or both continuous and discrete distributions. The chapter discusses order in graphs and optimization problems. Graphs are highly versatile models for analyzing many practical problems in which points and connections between them have some physical or conceptual meaning. Optimization refers to finding one or more feasible solutions that correspond to extreme values of one or more objectives or criteria. When an optimization problem involves only one objective, the task of finding the optimal solution is called “single-objective optimization,” whereas if the problem involves more than one objective, it is known as “multi-objective optimization.”

Chapter 2 Total-Order Ranking Methods

Publisher Summary This chapter describes the theory of the mostly known total-order ranking techniques. Total-order ranking methods are multicriteria decision making (MCDM) techniques used for the ranking of various alternatives on the basis of more than one criterion. The chapter reviews a number of total-order ranking methods that have been widely used to facilitate the structuring and understanding of the perceived decision problem. The chapter presents the simplest approaches, like the Pareto optimality and the simple additive ranking (SAR) approach followed by the approaches belonging to the so-called multiattribute value theory—that is, utility, desirability, and dominance functions. In these models, numerical scores are constructed to represent the degree to which an alternative may be preferred to another. These scores are developed initially for each criterion and aggregated into a higher level of preference models.

Multicriteria Decision-Making Methods

Multi-criteria decision making (MCDM) deals with decisions involving the choice of the best alternative among several potential candidates in a decision. Every decision requires the balancing of multiple factors, the criteria, which is done sometimes explicitly, sometimes without conscious consideration. Decision might be a simple choice between two or more well-defined alternatives; however, often, decision problems are rather complex problems covering information of complex and conflicting nature reflecting differing perspectives. It is under these conditions that the tools and methods presented in this chapter come into play. We reviewed a number of methods that have been widely used to facilitate the structuring and understanding of the perceived decision problem. We started with the simplest approaches, such as the Pareto optimality and the simple additive ranking approach followed by the approaches belonging to the so-called multiattribute value theory, that is, utility, desirability, and dominance functions. In these models, numerical scores are constructed to represent the degree to which an alternative may be preferred to another. These scores are developed initially for each criterion and are aggregated into a higher level of preference models. The outranking model category, which includes PROMETHEE, ELECTRE, and ORESTE (Organisation, Rangement Et Synthese de donnees relaTionElles) methods, is then presented. In these methods, alternatives are compared pairwise, initially in terms of each criterion and then the preference information is aggregated across all the criteria. These methods attempt to set up the strength of evidence in favor of one alternative over the others. A fairly detailed description of the methods ELECTRE I, II, and III is provided to illustrate its evolution from a simple method to a quite sophisticated method. The Hasse diagram technique is illustrated as an example of partial order ranking (POR) methods, which are vectorial approaches that recognize that different criteria are not always in agreement, but can be conflicting, which means that not all the alternatives can be directly compared with others. This approach not only ranks alternatives but also identifies contradictions in the criteria used for ranking, allowing the so-called incomparable condition where some residual order remains. The chapter also provides a short overview of the goal programming approach. The theoretical background of each of these models is presented together with the practical implementation of some of these methods provided as an illustrative example.

New QSAR Modelling Approach Based on Ranking Models by Genetic Algorithms - Variable Subset Selection (GA-VSS)

Partial and total order ranking strategies, which from a mathematical point of view are based on elementary methods of Discrete Mathematics, appear as an attractive and simple tool to perform data analysis. Moreover order ranking strategies seem to be a very useful tool not only to perform data exploration but also to develop order-ranking models, being a possible alternative to conventional QSAR methods. In fact, when data material is characterised by uncertainties, order methods can be used as alternative to statistical methods such as multiple linear regression (MLR), since they do not require specific functional relationship between the independent variables and the dependent variables (responses).

Chapter 9 The DART (Decision Analysis by Ranking Techniques) Software

Publisher Summary Decision analysis by ranking techniques (DART) is a toolbox designed to import and pre-process data and to obtain a ranking of the dataset thus gaining useful information on decision-making. The DART software is able to perform a ranking analysis by means of several total-ranking methods and a partial ranking method that leads to a chart known as “Hasse diagram.” It also allows the user to improve the quality of the analysis by performing pre-processing methods, such as principal component analysis (PCA) and cluster analysis. It is important to underline that in the workflow of the application, the management and pre-processing of data is a relevant issue, as this part of the software allows the user to have great flexibility on the analysis and to apply his or her knowledge of the meaning of data.