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In this work, we employ the $\bar{\partial}$-steepset descent method to study the Cauchy problem of the coupled dispersive AB system with initial conditions in weighted Sobolev space $H^{1,1}(\mathbb{R})$, \begin{align*} \left\{\begin{aligned} &A_{xt}-\alpha A-\beta AB=0,\\ &B_{x}+\frac{\gamma}{2}(|A|^2)_t=0,\\ &A(x,0)=A_0(x),~~~~B(x,0)=B_0(x)\in H^{1,1}(\mathbb{R}). \end{aligned}\right. \end{align*} Begin with the Lax pair of the coupled dispersive AB system, we successfully derive the solutions of the coupled dispersive AB system by constructing the basic Riemann-Hilbert problem. By using the $\bar{\partial}$-steepset descent method, the long-time asymptotic behaviors of the solutions for the coupled dispersive AB system are characterized without discrete spectrum. Our results demonstrate that compared with the previous results, we increase the accuracy of the long-time asymptotic solution from $O(t^{-1}\log t)$ to $O(t^{-1})$., Comment: 25 pages

Influence overlap is a universal phenomenon in influence spreading for social networks. In this paper, we argue that the redundant influence generated by influence overlap cause negative effect for maximizing spreading influence. Firstly, we present a theoretical method to calculate the influence overlap and record the redundant influence. Then in term of eliminating redundant influence, we present two algorithms, namely, Degree-Redundant-Influence (DRS) and Degree-Second-Neighborhood (DSN) for multiple spreaders identification. The experiments for four empirical social networks successfully verify the methods, and the spreaders selected by the DSN algorithm show smaller degree and k-core values., Comment: 20 pages, 6 figures

It was recently proposed that a giant flare of the blazar PKS B1424-418 at redshift $z=1.522$ is in association with a PeV-energy neutrino event detected by IceCube. Based on this association we here suggest that the flight time difference between the PeV neutrino and gamma-ray photons from blazar flares can be used to constrain the violations of equivalence principle (EP) and the Lorentz invariance for neutrinos. From the calculated Shapiro delay due to clusters or superclusters in the nearby universe, we find that violation of the equivalence principle for neutrinos and photons is constrained to an accuracy of at least $10^{-5}$, which is two orders of magnitude tighter than the constraint placed by MeV neutrinos from supernova 1987A. Lorentz invariance violation (LIV) arises in various quantum-gravity theories, which predicts an energy-dependent velocity of propagation in vacuum for photons and neutrinos. We find that the association of the PeV neutrino with the gamma-ray outburst set limits on the energy scale of possible LIV to $> 0.01 E_{pl}$ for linear LIV models and $>6\times 10^{-8} E_{pl}$ for quadratic order LIV models, where $E_{pl}$ is the Planck energy scale. These are the most stringent constraints on neutrino LIV for subluminal neutrinos., Comment: Accepted for publication in Physical Review Letters, 4 pages, no figures

Gamma-ray bursts (GRBs) are proposed as candidate sources of ultra-high energy cosmic rays (UHECRs). We study the possibility that the PeV neutrinos recently observed by IceCube are produced by GRB cosmic rays interacting with the interstellar gas in the host galaxies. By studying the relation between the X-ray absorption column density N_H and the surface star-formation rate of GRB host galaxies, we find that N_H is a good indicator of the surface gas density of the host galaxies. Then we are able to calculate the neutrino production efficiency of CRs for GRBs with known N_H. We collect a sample of GRBs that have both measurements of N_H and accurate gamma-ray fluence, and attempt to calculate the accumulated neutrino flux based on the current knowledge about GRBs and their host galaxies. When the CR intensity produced by GRBs is normalized with the observed UHECR flux above $10^{19}{\rm eV}$, the accumulated neutrino flux at PeV energies is estimated to be about $(0.3\pm0.2)\times10^{-8} \rm{GeV\ cm^{-2}\ s^{-1}\ sr^{-1}} $ (per flavor) under the assumption that GRB energy production rate follows the cosmic star-formation rate and the favorable assumption about the CR diffusion coefficient. This flux is insufficient to account for the IceCube observations, but the estimate suffers from some assumptions in the calculation and thus we can not rule out this scenario at present., Comment: 8 pages, 3 figures, 2 tables, to appear in ApJL