A query algebra is presented that expresses searches on structured text. In addition to traditional fulltext boolean queries that search a pre-defined collection of documents, the algebra permits queries that harness document structure. The algebra manipulates arbitrary intervals of text, which are recognized in the text from implicit or explicit markup. The algebra has seven operators, which combined intervals to yield new ones: containing, not containing, contained in, not contained in, one of, both of, followed by. The ultimate result of a query is the set of intervals that satisfy it. An implementation framework is given based on four primitive access functions. Each access function finds the solution to a query nearest to a given position in the database. Recursive definitions for the seven operators are given in terms of these access functions. Search time is at worst proportional to the time required to evaluate the access functions for occurrences of the elementary terms in a query.

The first part of this paper briefly describes a mathematical framework (called the containment model) that provides the operations and data structures for a text dominated database with a hierarchical structure. The database is considered to be a hierarchical collection of contiguous extents each extent being a word, word phrase, text element or non-text element.The filter operations making up a search command are expressed in terms of containment criteria that specify whether a contiguous extent will be selected or rejected during a search. This formalism, comprised of the mathematical framework and its associated language, defines a conceptual layer upon which we can construct a well-defined higher level layer, specifically the user interface that serves to provide a level of functionality that is closer to the needs of the user and the application domain.

Background The inverse-QSAR problem seeks to find a new molecular descriptor from which one can recover the structure of a molecule that possess a desired activity or property. Surprisingly, there are very few papers providing solutions to this problem. It is a difficult problem because the molecular descriptors involved with the inverse-QSAR algorithm must adequately address the forward QSAR problem for a given biological activity if the subsequent recovery phase is to be meaningful. In addition, one should be able to construct a feasible molecule from such a descriptor. The difficulty of recovering the molecule from its descriptor is the major limitation of most inverse-QSAR methods.Results In this paper, we describe the reversibility of our previously reported descriptor, the vector space model molecular descriptor (VSMMD) based on a vector space model that is suitable for kernel studies in QSAR modeling. Our inverse-QSAR approach can be described using five steps: (1) generate the VSMMD for the compounds in the training set; (2) map the VSMMD in the input space to the kernel feature space using an appropriate kernel function; (3) design or generate a new point in the kernel feature space using a kernel feature space algorithm; (4) map the feature space point back to the input space of descriptors using a pre-image approximation algorithm; (5) build the molecular structure template using our VSMMD molecule recovery algorithm.Conclusion The empirical results reported in this paper show that our strategy of using kernel methodology for an inverse-Quantitative Structure-Activity Relationship is sufficiently powerful to find a meaningful solution for practical problems.Electronic supplementary materialThe online version of this article (doi:10.1186/1758-2946-1-4) contains supplementary material, which is available to authorized users.

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D etermination of a protein's structure can facilitate an understanding of how the structure changes when that protein combines with other proteins or smaller molecules. In this paper we study a semidefinite programming (SDP) relaxation of the (NP-hard) side chain positioning problem presented in Chazelle et al [Chazelle B, Kingsford C, Singh M (2004) A semidefinite programming approach to side chain positioning with new rounding strategies. INFORMS J. Comput. 16:380-392].We show that the Slater constraint qualification (strict feasibility) fails for the SDP relaxation. We then show the advantages of using facial reduction to regularize the SDP. In fact, after applying facial reduction, we have a smaller problem that is more stable both in theory and in practice. We include cutting planes to improve the rounded SDP approximate solutions.