Tree loop graphs

Many problems involving DNA can be modeled by families of intervals. However, traditional interval graphs do not take into account the repeat structure of a DNA molecule. In the simplest case, one repeat with two copies, the underlying line can be seen as folded into a loop. We propose a new definition that respects repeats and define loop graphs as the intersection graphs of arcs of a loop. The class of loop graphs contains the class of interval graphs and the class of circular-arc graphs. Every loop graph has interval number 2. We characterize the trees that are loop graphs. The characterization yields a polynomial-time algorithm which given a tree decides whether it is a loop graph and, in the affirmative case, produces a loop representation for the tree.Facultad de Ciencias Exacta

Neutral Pion Electroproduction off Light Nuclei in Chiral Perturbation Theory

Threshold pion electroproduction on tri-nucleon systems is investigated in the framework of baryon Chiral Perturbation Theory (ChPT) at next-to-leading one-loop order O(q4) in the chiral expansion. To this order in small momenta, the production operator is a sum of one- and two-nucleon terms. While the one-nucleon terms resemble the impulse approximation, the two-nucleon contributions represent corrections due to the relevant nuclear interactions, e.g. pion-exchange interactions, which prove to be dominant, and due to recoil effects of the participating nucleons, which appear to be negligible. We calculate the expectation value of the production operator using chiral wave functions in a three-dimensional approach without partial wave expansion. The resulting integrals are evaluated using adaptive Monte Carlo integration, the VEGAS algorithm of Lepage. We obtain results for the threshold production multipoles E0+ and L0+ on 3He and 3H and comment on the sensitivity to the fundamental neutron amplitude Eπ0n0+.3He appears to be a particularly promising target to extract information about the neutron amplitude. This idea is usually invoked for spin-dependent quantities since the 3He wave function is strongly dominated by the principal S-state component which suggests that its spin is largely driven by the one of the neutron

Tree Loop Graphs

Many problems involving DNA can be modelled by interval families. However, traditional interval graphs do not take into account the repeat structures of a DNA molecule. We propose a new definition that respects repeats and define loop graphs as the intersection graphs of arcs of a loop. The class of loop graphs contains the class of interval graphs, and the class of circular-arc graphs. Every loop graph has interval number 2. We characterize the trees that are loop graphs. The characterization yields a polynomial-time algorithm which given a tree decides whether it is a loop graph and in the affirmative case, it produces a loop representation for the tree. © 2004 Elsevier B.V. All rights reserved.181723Lekkerkerker, C.G., Boland, J.C., Representation of a finite graph by a set of intervals on the real line (1962) Fund. Math., 51, pp. 45-64Setubal, J.C., Meidanis, J., (1997) Introduction to Computational Molecular Biology, , PWS, Boston. 0-534-95262-

Loop Graphs And Asteroidal Sets

[No abstract available]22179183Alcón, L., de Figueiredo, C.H., Cerioli, M., Gutierrez, M., Meidanis, J., Tree Loop Graphs (2004) Electronic Notes in Discrete Mathematics, 18, pp. 17-23. , Proceedings of LACGA 2004 Full paper accepted for publication in Discrete Applied Mathematics Series on Computational Molecular BiologyAlcón, L., de Figueiredo, C.H., Cerioli, M., Gutierrez, M., Meidanis, J., Loop Graphs with induced cycles (2005) Electronic Notes in Discrete Mathematics, 19, pp. 289-295. , Proceedings of GRACO 2005Setubal, J.C., Meidanis, J., (1997) Introduction to Computational Molecular Biology, , PWS, BostonWalter, J.R., Representations of Chordal Graphs as subtrees of a tree (1978) J. of Graph Theory, 2, pp. 265-26