By Renato Bruni (auth.), Renato Bruni (eds.)

Many difficulties bobbing up in organic, chemical and scientific study, which may no longer be solved long ago because of their measurement and complexity, are these days tackled through computerized elaboration, therefore growing the rising box of Bioinformatics. in spite of the fact that, the luck of such ways relies not just on brute computational power of the pcs on which the answer methods run, but in addition, and infrequently significantly, at the mathematical caliber of the types and of the algorithms underlying these resolution strategies. the current quantity deals a close assessment of a few of the main fascinating mathematical techniques to series research and different series comparable difficulties. certain emphasis is dedicated to difficulties in regards to the such a lot proper biopolymers (proteins and genetic sequences), however the exposition isn't constrained to them. the objective viewers contains researchers from many parts of Bioinformatics attracted to series research difficulties both from a theoretical and mathematical viewpoint, akin to mathematicians and desktop scientists, or for extra applicative and production-oriented purposes, equivalent to biologists and scientific researchers or practitioners operating for chemical or pharmaceutical businesses. The e-book should still furthermore be of use to arithmetic scholars studying computational biology, or to biology scholars studying bioinformatics.

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**Extra info for Mathematical Approaches to Polymer Sequence Analysis and Related Problems**

**Example text**

To reduce variability, multiple cross-validation rounds are performed by interchanging training and test sets, and the results obtained are averaged over the number of rounds. A proper evaluation (or cross-validation) of prediction methods needs to meet one fundamental requirement: the test set must not contain examples too much similar to those contained in the training set. When testing prediction methods for protein features (such as secondary structure or inter-residue contacts), this requirement transduces in having test and training sets compiled from proteins that share no significant pairwise sequence identity (typically <25%).

H. Kleine B¨uning and T. Lettman. Propositional Logic: Deduction and Algorithms. Cambridge University Press, Cambridge (1999) 19. D. Lee. Fast atom bombardment and secondary ion mass spectrometry of peptides and proteins. E. Shively (editor) 403–441, Humana Press, NJ (1986) 20. G. P. Lattimer (editors). Mass Spectrometry of Polymers. CRC Press, Boca Raton (2001) 21. L. A. Wolsey. Integer and Combinatorial Optimization. Wiley, New York (1988) 22. S. S. V. P. Swaminathan. On finding solutions for extended horn formulas.

Such problem is of basic relevance in biological and medical research, but is difficult to model and computationally hard to solve. Data obtained from the mass spectrometry analysis of a generic polymeric compound, constituted, according to specific chemical rules, by a sequence of components, are here used to build a propositional logic formula. The models of this formula represent coherent interpretations of the set of data and are used to generate all possible correct results of the analysis itself.