5,440 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 (z≥1z \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

    Inducing Effect on the Percolation Transition in Complex Networks

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    Percolation theory concerns the emergence of connected clusters that percolate through a networked system. Previous studies ignored the effect that a node outside the percolating cluster may actively induce its inside neighbours to exit the percolating cluster. Here we study this inducing effect on the classical site percolation and K-core percolation, showing that the inducing effect always causes a discontinuous percolation transition. We precisely predict the percolation threshold and core size for uncorrelated random networks with arbitrary degree distributions. For low-dimensional lattices the percolation threshold fluctuates considerably over realizations, yet we can still predict the core size once the percolation occurs. The core sizes of real-world networks can also be well predicted using degree distribution as the only input. Our work therefore provides a theoretical framework for quantitatively understanding discontinuous breakdown phenomena in various complex systems.Comment: Main text and appendices. Title has been change

    Probing GeV-scale MSSM neutralino dark matter in collider and direct detection experiments

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    Given the recent constraints from the dark matter (DM) direct detections, we examine a light GeV-scale (2-30 GeV) neutralino DM in the alignment limit of the Minimal Supersymmetric Standard Model (MSSM). In this limit without decoupling, the heavy CP-even scalar HH plays the role of the Standard Model (SM) Higgs boson while the other scalar hh can be rather light so that the DM can annihilate through the hh resonance or into a pair of hh to achieve the observed relic density. With the current collider and cosmological constraints, we find that such a light neutralino DM above 6 GeV can be excluded by the XENON-1T (2017) limits while the survivied parameter space below 6 GeV can be fully covered by the future germanium-based light dark matter detections (such as CDEX), by the Higgs coupling precison measurements or by the production process e+e−→hAe^+e^- \to hA at an electron-positron collider (Higgs factory).Comment: 15 pages, 5 figures. Discussions and references added, version accepted by PL

    Nuclear superfluidity for antimagnetic rotation in 105^{105}Cd and 106^{106}Cd

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    The effect of nuclear superfluidity on antimagnetic rotation bands in 105^{105}Cd and 106^{106}Cd are investigated by the cranked shell model with the pairing correlations and the blocking effects treated by a particle-number conserving method. The experimental moments of inertia and the reduced B(E2)B(E2) transition values are excellently reproduced. The nuclear superfluidity is essential to reproduce the experimental moments of inertia. The two-shears-like mechanism for the antimagnetic rotation is investigated by examining the shears angle, i.e., the closing of the two proton hole angular momenta, and its sensitive dependence on the nuclear superfluidity is revealed.Comment: 14 pages, 4 figure
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