Using problem-specific background knowledge, computer programs developed within the framework of Inductive Logic Programming (ILP) have been used to construct restricted first-order logic solutions to scientific problems. However, their approach to the analysis of data with substantial numerical content has been largely limited to constructing clauses that: (a) provide qualitative descriptions ("high", "low" etc.) of the values of response variables; and (b) contain simple inequalities restricting the ranges of predictor variables. This has precluded the application of such techniques to scientific and engineering problems requiring a more sophisticated approach. A number of specialised methods have been suggested to remedy this. In contrast, we have chosen to take advantage of the fact that the existing theoretical framework for ILP places very few restrictions of the nature of the background knowledge. We describe two issues of implementation that make it possible to use background predicates that implement well-established statistical and numerical analysis procedures. Any improvements in analytical sophistication that result are evaluated empirically using artificial and real-life data. Experiments utilising artificial data are concerned with extracting constraints for response variables in the text-book problem of balancing a pole on a cart. They illustrate the use of clausal definitions of arithmetic and trigonometric functions, inequalities, multiple linear regression, and numerical derivatives. A non-trivial problem concerning the prediction of mutagenic activity of nitroaromatic molecules is also examined. In this case, expert chemists have been unable to devise a model for explaining the data. The result demonstrates the combined use by an ILP program of logical and numerical capabilities to achieve an analysis that includes linear modelling, clustering and classification. In all experiments, the predictions obtained compare favourably against benchmarks set by more traditional methods of quantitative methods, namely, regression and neural-network.

A systematic survey was carried out in an unbiased sample of 815 protein chains with a maximum of 20% homology selected from the Protein Data Bank, whose structures were solved at a resolution higher than 1.6 Å and with a R‐factor lower than 25%. A set of 5556 subsequences with α‐helix or 310‐helix motifs was extracted from the protein chains considered. Global and local propensities were then calculated for all possible amino acid pairs of the type (i, i + 1), (i, i + 2), (i, i + 3), and (i, i + 4), starting at the relevant helical positions N1, N2, N3, C3, C2, C1, and N‐int (interior positions), and also at the first nonhelical positions in both termini of the helices, namely, N‐cap and C‐cap. The statistical analysis of the propensity values has shown that pairing is significantly dependent on the type of the amino acids and on the position of the pair. A few sequences of three and four amino acids were selected and their high prevalence in helices is outlined in this work. The Glu‐Lys‐Tyr‐Pro sequence shows a peculiar distribution in proteins, which may suggest a relevant structural role in α‐helices when Pro is located at the C‐cap position. A bioinformatics tool was developed, which updates automatically and periodically the results and makes them available in a web site. Proteins 2008. © 2007 Wiley‐Liss, Inc.

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