Assessing Percolation Threshold Based on High-Order Non-Backtracking Matrices

Percolation threshold of a network is the critical value such that when nodes or edges are randomly selected with probability below the value, the network is fragmented but when the probability is above the value, a giant component connecting large portion of the network would emerge. Assessing the percolation threshold of networks has wide applications in network reliability, information spread, epidemic control, etc. The theoretical approach so far to assess the percolation threshold is mainly based on spectral radius of adjacency matrix or non-backtracking matrix, which is limited to dense graphs or locally treelike graphs, and is less effective for sparse networks with non-negligible amount of triangles and loops. In this paper, we study high-order non-backtracking matrices and their application to assessing percolation threshold. We first define high-order non-backtracking matrices and study the properties of their spectral radii. Then we focus on 2nd-order non-backtracking matrix and demonstrate analytically that the reciprocal of its spectral radius gives a tighter lower bound than those of adjacency and standard non-backtracking matrices. We further build a smaller size matrix with the same largest eigenvalue as the 2nd-order non-backtracking matrix to improve computation efficiency. Finally, we use both synthetic networks and 42 real networks to illustrate that the use of 2nd-order non-backtracking matrix does give better lower bound for assessing percolation threshold than adjacency and standard non-backtracking matrices.Comment: to appear in proceedings of the 26th International World Wide Web Conference(WWW2017

Heavy Quark Effective Theory on the Light Front

The light-front heavy quark effective theory is derived to all orders in $1/m_Q$. In the limit $m_Q\rightarrow \infty$, the theory exhibits the familiar heavy quark spin-flavor symmetry. This new formalism permits a straightforward canonical quantization to all orders in $1/m_Q$; moreover, higher order terms have rather simple operator structures. The light-front heavy quark effective theory can serve as an useful framework for the study of non-perturbative QCD dynamics of heavy hadron bound states.Comment: 11 pages, revtex, no figure

The Possible JPCIG=2++2+J^{PC}I^G=2^{++}2^+ State X(1600)

The interesting state X(1600) with $J^{PC}I^G=2^{++}2^+$ can't be a conventional $q \bar q$ meson in the quark model. Using a mixed interpolating current with different color configurations, we investigate the possible existence of X(1600) in the framework of QCD finite energy sum rules. Our results indicate that both the "hidden color" and coupled channel effects may be quite important in the multiquark system. We propose several reactions to look for this state.Comment: axodraw.sty include