SLT-Resolution for the Well-Founded Semantics

Global SLS-resolution and SLG-resolution are two representative mechanisms for top-down evaluation of the well-founded semantics of general logic programs. Global SLS-resolution is linear for query evaluation but suffers from infinite loops and redundant computations. In contrast, SLG-resolution resolves infinite loops and redundant computations by means of tabling, but it is not linear. The principal disadvantage of a non-linear approach is that it cannot be implemented using a simple, efficient stack-based memory structure nor can it be easily extended to handle some strictly sequential operators such as cuts in Prolog. In this paper, we present a linear tabling method, called SLT-resolution, for top-down evaluation of the well-founded semantics. SLT-resolution is a substantial extension of SLDNF-resolution with tabling. Its main features include: (1) It resolves infinite loops and redundant computations while preserving the linearity. (2) It is terminating, and sound and complete w.r.t. the well-founded semantics for programs with the bounded-term-size property with non-floundering queries. Its time complexity is comparable with SLG-resolution and polynomial for function-free logic programs. (3) Because of its linearity for query evaluation, SLT-resolution bridges the gap between the well-founded semantics and standard Prolog implementation techniques. It can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: Slight modificatio

Central engine afterglow of Gamma-ray Bursts

Before 2004, nearly all GRB afterglow data could be understood in the context of the external shocks model. This situation has changed in the past two years, when it became clear that some afterglow components should be attributed to the activity of the central engine; i.e., the {\it central engine afterglow}. We review here the afterglow emission that is directly related to the GRB central engine. Such an interpretation proposed by Katz, Piran & Sari, peculiar in pre-{\it Swift} era, has become generally accepted now.Comment: 4 pages including 1 figure. Presented at the conference "Astrophysics of Compact Objects" (July 1-7, 2007; Huangshan, China

Linear Tabulated Resolution Based on Prolog Control Strategy

Infinite loops and redundant computations are long recognized open problems in Prolog. Two ways have been explored to resolve these problems: loop checking and tabling. Loop checking can cut infinite loops, but it cannot be both sound and complete even for function-free logic programs. Tabling seems to be an effective way to resolve infinite loops and redundant computations. However, existing tabulated resolutions, such as OLDT-resolution, SLG- resolution, and Tabulated SLS-resolution, are non-linear because they rely on the solution-lookup mode in formulating tabling. The principal disadvantage of non-linear resolutions is that they cannot be implemented using a simple stack-based memory structure like that in Prolog. Moreover, some strictly sequential operators such as cuts may not be handled as easily as in Prolog. In this paper, we propose a hybrid method to resolve infinite loops and redundant computations. We combine the ideas of loop checking and tabling to establish a linear tabulated resolution called TP-resolution. TP-resolution has two distinctive features: (1) It makes linear tabulated derivations in the same way as Prolog except that infinite loops are broken and redundant computations are reduced. It handles cuts as effectively as Prolog. (2) It is sound and complete for positive logic programs with the bounded-term-size property. The underlying algorithm can be implemented by an extension to any existing Prolog abstract machines such as WAM or ATOAM.Comment: To appear as the first accepted paper in Theory and Practice of Logic Programming (http://www.cwi.nl/projects/alp/TPLP

Revisiting B_s\to\mu^+\mu^- and B\to K^{(*)}\mu^+\mu^- decays in the MSSM with and without R-parity

The rare decays B_s -> \mu^+\mu^- and B -> K^{(*)}\mu^+\mu^- are sensitive to new particles and couplings via their interferences with the standard model contributions. Recently, the upper bound on B(B_s -> \mu^+\mu^-) has been improved significantly by the CMS, LHCb, CDF, and D{\O} experiments. Combining with the measurements of B(B-> K^{(*)}\mu^+\mu^-), we derive constraints on the relevant parameters of minimal supersymmetic standard model with and without R-parity, and examine their contributions to the dimuon forward-backward asymmetry in B-> K^{*}\mu^+\mu^- decay. We find that (i) the contribution of R-parity violating coupling products \lambda^{\prime}_{2i2}\lambda^{\prime*}_{2i3} due to squark exchange is comparable with the theoretical uncertainties in B-> K \mu^+\mu^- decay, but still could be significant in B-> K^{*}\mu^+\mu^- decay and could account for the forward-backward asymmetry in all dimuon invariant mass regions; (ii) the constrained mass insertion (\delta^{u}_{LL})_{23} could have significant contribution to dA_{FB}(B-> K^{*}\mu^+\mu^-)/ds, and such effects are favored by thr recent results of the Belle, CDF, and LHCb experiments.Comment: 20 pages, 9 figures, published versio

Half Metallic Bilayer Graphene

Charge neutral bilayer graphene has a gapped ground state as transport experiments demonstrate. One of the plausible such ground states is layered antiferromagnetic spin density wave (LAF) state, where the spins in top and bottom layers have same magnitude with opposite directions. We propose that lightly charged bilayer graphene in an electric field perpendicular to the graphene plane may be a half metal as a consequence of the inversion and particle-hole symmetry broken in the LAF state. We show this explicitly by using a mean field theory on a 2-layer Hubbard model for the bilayer graphene.Comment: 4+ pages, 4 figure