Complexity and phase transitions in a holographic QCD model

Applying the "Complexity=Action" conjecture, we study the holographic complexity close to crossover/phase transition in a holographic QCD model proposed by Gubser et al. This model can realize three types of phase transition, crossover or first and second order, depending on the parameters of the dilaton potential. The re-scaled late-time growth rate of holographic complexity density for the three cases is calculated. Our results show that it experiences a fast drop/jump close to the critical point while approaching constants far beyond the critical temperature. Moreover, close to the critical temperature, it shows a behavior characterizing the type of the transition. These features suggest that the growth rate of the holographic complexity may be used as a good parameter to characterize the phase transition. The Lloyd's bound is always satisfied for the cases we considered but only saturated for the conformal case.Comment: v1: 14 pages, 2 figures; v2: refs added, minor modifications. arXiv admin note: substantial text overlap with arXiv:1608.03072; v3: More details on the Lloyd's bound, matching the published versio

Holographic entanglement entropy close to crossover/phase transition in strongly coupled systems

We investigate the behavior of entanglement entropy in the holographic QCD model proposed by Gubser et al. By choosing suitable parameters of the scalar self-interaction potential, this model can exhibit various types of phase structures: crossover, first order and second order phase transitions. We use entanglement entropy to probe the crossover/phase transition, and find that it drops quickly/suddenly when the temperature approaches the critical point which can be seen as a signal of confinement. Moreover, the critical behavior of the entanglement entropy suggests that we may use it to characterize the corresponding phase structures.Comment: v1:19 pages, 5 figures; v2: refs added; v3: 20 pages, high-temperature behaviors of holographic entanglement entropy are given, accecpted for publication by NP

A simple iterative algorithm for maxcut

We propose a simple iterative (SI) algorithm for the maxcut problem through fully using an equivalent continuous formulation. It does not need rounding at all and has advantages that all subproblems have explicit analytic solutions, the cut values are monotonically updated and the iteration points converge to a local optima in finite steps via an appropriate subgradient selection. Numerical experiments on G-set demonstrate the performance. In particular, the ratios between the best cut values achieved by SI and the best known ones are at least $0.986$ and can be further improved to at least $0.997$ by a preliminary attempt to break out of local optima.Comment: 30 pages, 1 figure. Subgradient selection, cost analysis and local breakout are adde

A Bayesian Framework to Constrain the Photon Mass with a Catalog of Fast Radio Bursts

A hypothetical photon mass, $m_\gamma$, gives an energy-dependent light speed in a Lorentz-invariant theory. Such a modification causes an additional time delay between photons of different energies when they travel through a fixed distance. Fast radio bursts (FRBs), with their short time duration and cosmological propagation distance, are excellent astrophysical objects to constrain $m_\gamma$. Here for the first time we develop a Bayesian framework to study this problem with a catalog of FRBs. Those FRBs with and without redshift measurement are both useful in this framework, and can be combined in a Bayesian way. A catalog of 21 FRBs (including 20 FRBs without redshift measurement, and one, FRB 121102, with a measured redshift $z=0.19273 \pm 0.00008$) give a combined limit $m_\gamma \leq 8.7 \times 10^{-51}\, {\rm kg}$, or equivalently $m_\gamma \leq 4.9 \times 10^{-15}\, {\rm eV}/c^2$ ($m_\gamma \leq 1.5\times10^{-50} \, {\rm kg}$, or equivalently $m_\gamma \leq 8.4 \times 10^{-15} \,{\rm eV}/c^2$) at 68% (95%) confidence level, which represents the best limit that comes purely from kinematics. The framework proposed here will be valuable when FRBs are observed daily in the future. Increment in the number of FRBs, and refinement in the knowledge about the electron distributions in the Milky Way, the host galaxies of FRBs, and the intergalactic median, will further tighten the constraint.Comment: 10 pages, 6 figures; Physical Review D, in pres

On the Coverage Bound Problem of Empirical Likelihood Methods For Time Series

The upper bounds on the coverage probabilities of the confidence regions based on blockwise empirical likelihood [Kitamura (1997)] and nonstandard expansive empirical likelihood [Nordman et al. (2013)] methods for time series data are investigated via studying the probability for the violation of the convex hull constraint. The large sample bounds are derived on the basis of the pivotal limit of the blockwise empirical log-likelihood ratio obtained under the fixed-b asymptotics, which has been recently shown to provide a more accurate approximation to the finite sample distribution than the conventional chi-square approximation. Our theoretical and numerical findings suggest that both the finite sample and large sample upper bounds for coverage probabilities are strictly less than one and the blockwise empirical likelihood confidence region can exhibit serious undercoverage when (i) the dimension of moment conditions is moderate or large; (ii) the time series dependence is positively strong; or (iii) the block size is large relative to sample size. A similar finite sample coverage problem occurs for the nonstandard expansive empirical likelihood. To alleviate the coverage bound problem, we propose to penalize both empirical likelihood methods by relaxing the convex hull constraint. Numerical simulations and data illustration demonstrate the effectiveness of our proposed remedies in terms of delivering confidence sets with more accurate coverage