Microscopic linear response calculations based on the Skyrme functional plus the pairing contribution

A self-consistent Quasiparticle-Random-Phase-Approximation (QRPA) model which employs the canonical Hartree-Fock-Bogoliubov (HFB) basis and an energy-density functional with a Skyrme mean field part and a density-dependent pairing, is used to study the monopole collective excitations of spherical even-even nuclei. The influence of the spurious state on the strength function of the isoscalar monopole excitations is clearly assessed. We compare the effect of different kinds of pairing forces (volume pairing, surface pairing and mixed pairing) on the monopole excitation strength function. The energy of the Isoscalar Giant Monopole Resonance (ISGMR), which is related to the nuclear incompressibility $K_{\infty}$, is calculated for tin isotopes and the results are discussed.Comment: Accepted for publication in Phys. Rev.

Solving the undirected feedback vertex set problem by local search

An undirected graph consists of a set of vertices and a set of undirected edges between vertices. Such a graph may contain an abundant number of cycles, then a feedback vertex set (FVS) is a set of vertices intersecting with each of these cycles. Constructing a FVS of cardinality approaching the global minimum value is a optimization problem in the nondeterministic polynomial-complete complexity class, therefore it might be extremely difficult for some large graph instances. In this paper we develop a simulated annealing local search algorithm for the undirected FVS problem. By defining an order for the vertices outside the FVS, we replace the global cycle constraints by a set of local vertex constraints on this order. Under these local constraints the cardinality of the focal FVS is then gradually reduced by the simulated annealing dynamical process. We test this heuristic algorithm on large instances of Er\"odos-Renyi random graph and regular random graph, and find that this algorithm is comparable in performance to the belief propagation-guided decimation algorithm.Comment: 6 page

BPS M2M2-branes in AdS4×Q1,1,1AdS_4\times Q^{1, 1, 1} Dual to Loop Operators

In this paper, we first compute the Killing spinors of $AdS_4\times Q^{1, 1, 1}$ and its certain orbifolds. Based on this, two classes of $M2$-brane solutions are found. The first class of solutions includes $M2$-branes dual to Wilson loops in the fundamental representation as special cases. The second class includes the candidates of the holographic description of vortex loops in the dual field theories.Comment: v6, typoes fixed, 14 pages, no figure