26,095 research outputs found

    The zz-matching problem on bipartite graphs

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    The zz-matching problem on bipartite graphs is studied with a local algorithm. A zz-matching (z1z \ge 1) on a bipartite graph is a set of matched edges, in which each vertex of one type is adjacent to at most 11 matched edge and each vertex of the other type is adjacent to at most zz matched edges. The zz-matching problem on a given bipartite graph concerns finding zz-matchings with the maximum size. Our approach to this combinatorial optimization are of two folds. From an algorithmic perspective, we adopt a local algorithm as a linear approximate solver to find zz-matchings on general bipartite graphs, whose basic component is a generalized version of the greedy leaf removal procedure in graph theory. From an analytical perspective, in the case of random bipartite graphs with the same size of two types of vertices, we develop a mean-field theory for the percolation phenomenon underlying the local algorithm, leading to a theoretical estimation of zz-matching sizes on coreless graphs. We hope that our results can shed light on further study on algorithms and computational complexity of the optimization problem.Comment: 15 pages, 3 figure

    gap: Genetic Analysis Package

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    A preliminary attempt at collecting tools and utilities for genetic data as an R package called gap is described. Genomewide association is then described as a specific example, linking the work of Risch and Merikangas (1996), Long and Langley (1997) for family-based and population-based studies, and the counterpart for case-cohort design established by Cai and Zeng (2004). Analysis of staged design as outlined by Skol et al. (2006) and associate methods are discussed. The package is flexible, customizable, and should prove useful to researchers especially in its application to genomewide association studies.

    Understanding for flavor physics in the lepton sector

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    In this paper, we give a model for understanding flavor physics in the lepton sector--mass hierarchy among different generations and neutrino mixing pattern. The model is constructed in the framework of supersymmetry, with a family symmetry S4U(1)S4*U(1). There are two right-handed neutrinos introduced for seesaw mechanism, while some standard model(SM) gauge group singlet fields are included which transforms non-trivially under family symmetry. In the model, each order of contributions are suppressed by δ0.1\delta \sim 0.1 compared to the previous one. In order to reproduce the mass hierarchy, mτm_\tau and Δmatm2\sqrt{\Delta m_{atm}^2}, mμm_\mu and Δmsol2\sqrt{\Delta m_{sol}^2} are obtained at leading-order(LO) and next-to-leading-order(NLO) respectively, while electron can only get its mass through next-to-next-to-next-to-leading-order(NNNLO) contributions. For neutrino mixing angels, θ12,θ23,θ13\theta_{12}, \theta_{23}, \theta_{13} are 45,45,045^\circ, 45^\circ, 0 i.e. Bi-maximal mixing pattern as first approximation, while higher order contributions can make them consistent with experimental results. As corrections for θ12\theta_{12} and θ13\theta_{13} originate from the same contribution, there is a relation predicted for them sinθ13=1tanθ121+tanθ12\sin{\theta_{13}}=\displaystyle \frac{1-\tan{\theta_{12}}}{1+\tan{\theta_{12}}}. Besides, deviation from π4\displaystyle \frac{\pi}{4} for θ23\theta_{23} should have been as large as deviation from 0 for θ13\theta_{13} if it were not the former is suppressed by a factor 4 compared to the latter.Comment: version to appear in Phys. Rev.

    On the four-zero texture of quark mass matrices and its stability

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    We carry out a new study of quark mass matrices MuM^{}_{\rm u} (up-type) and MdM^{}_{\rm d} (down-type) which are Hermitian and have four zero entries, and find a new part of the parameter space which was missed in the previous works. We identify two more specific four-zero patterns of MuM^{}_{\rm u} and MdM^{}_{\rm d} with fewer free parameters, and present two toy flavor-symmetry models which can help realize such special and interesting quark flavor structures. We also show that the texture zeros of MuM^{}_{\rm u} and MdM^{}_{\rm d} are essentially stable against the evolution of energy scales in an analytical way by using the one-loop renormalization-group equations.Comment: 33 pages, 4 figures, minor comments added, version to appear in Nucl. Phys.
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