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Yayın Discovering cis-regulatory modules by optimizing barbecues(Elsevier Science Bv, 2009-05-28) Mosig, Axel; Bıyıkoğlu, Türker; Prohaska, Sonja J.; Stadler, Peter F.Gene expression in eukaryotic cells is regulated by a complex network of interactions, in which transcription factors and their binding sites on the genomic DNA play a determining role. As transcription factors rarely, if ever, act in isolation, binding sites of interacting factors are typically arranged in close proximity forming so-called cis-regulatory modules. Even when the individual binding sites are known, module discovery remains a hard combinatorial problem, which we formalize here as the Best Barbecue Problem. It asks for simultaneously stabbing a maximum number of differently colored intervals from K arrangements of colored intervals. This geometric problem turns out to be an elementary, yet previously unstudied combinatorial optimization problem of detecting common edges in a family of hypergraphs, a decision version of which we show here to be NP-complete. Due to its relevance in biological applications, we propose algorithmic variations that are suitable for the analysis of real data sets comprising either many sequences or many binding sites. Being based on set systems induced by interval arrangements, our problem setting generalizes to discovering patterns of co-localized itemsets in non-sequential objects that consist of corresponding arrangements or induce set systems of co-localized items. In fact, our optimization problem is a generalization of the popular concept of frequent itemset mining.Yayın Coupled quintic nonlinear Schrodinger equations in a generalized elastic solid(IOP Publishing Ltd, 2004-10-08) Hacınlıyan, Irma; Erbay, SaadetIn the present study, the nonlinear modulation of transverse waves propagating in a cubically nonlinear dispersive elastic medium is studied using a multiscale expansion of wave solutions. It is found that the propagation of quasimonochromatic transverse waves is described by a pair of coupled nonlinear Schrodinger (CNLS) equations. In the process of deriving the amplitude equations, it is observed that for a specific choice of material constants and wavenumber, the coefficient of nonlinear terms becomes zero, and the CNLS equations are no longer valid for describing the behaviour of transverse waves. In order to balance the nonlinear effects with the dispersive effects, by intensifying the nonlinearity, a new perturbation expansion is used near the critical wavenumber. It is found that the long time behaviour of the transverse waves about the critical wavenumber is given by a pair of coupled quintic nonlinear Schrodinger (CQNLS) equations. In the absence of one of the transverse waves, the CQNLS equations reduce to the single quintic nonlinear Schrodinger (QNLS) equation which has already been obtained in the context of water waves. By using a modified form of the so-called tanh method, some travelling wave solutions of the CQNLS equations are presented.
