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

Self-Paced Multi-Task Learning

In this paper, we propose a novel multi-task learning (MTL) framework, called Self-Paced Multi-Task Learning (SPMTL). Different from previous works treating all tasks and instances equally when training, SPMTL attempts to jointly learn the tasks by taking into consideration the complexities of both tasks and instances. This is inspired by the cognitive process of human brain that often learns from the easy to the hard. We construct a compact SPMTL formulation by proposing a new task-oriented regularizer that can jointly prioritize the tasks and the instances. Thus it can be interpreted as a self-paced learner for MTL. A simple yet effective algorithm is designed for optimizing the proposed objective function. An error bound for a simplified formulation is also analyzed theoretically. Experimental results on toy and real-world datasets demonstrate the effectiveness of the proposed approach, compared to the state-of-the-art methods

Ultrathin Acoustic Parity-Time Symmetric Metasurface Cloak

Invisibility or unhearability cloaks have beenmade possible by using metamaterials enabling light or sound to flow around obstacle without the trace of reflections or shadows. Metamaterials are known for being flexible building units that can mimic a host of unusual and extreme material responses, which are essential when engineering artificial material properties to realize a coordinate transforming cloak. Bending and stretching the coordinate grid in space require stringent material parameters; therefore, small inaccuracies and inevitablematerial losses become sources for unwanted scattering that are decremental to the desired effect.These obstacles further limit the possibility of achieving a robust concealment of sizeable objects from either radar or sonar detection. By using an elaborate arrangement of gain and lossy acousticmedia respecting parity-time symmetry, we built a one-way unhearability cloak able to hide objects seven times larger than the acoustic wavelength. Generally speaking, our approach has no limits in terms of working frequency, shape, or size, specifically though we demonstrate how, in principle, an object of the size of a human can be hidden from audible sound

The Nullity of Bicyclic Signed Graphs

Let \Gamma be a signed graph and let A(\Gamma) be the adjacency matrix of \Gamma. The nullity of \Gamma is the multiplicity of eigenvalue zero in the spectrum of A(\Gamma). In this paper we characterize the signed graphs of order n with nullity n-2 or n-3, and introduce a graph transformation which preserves the nullity. As an application we determine the unbalanced bicyclic signed graphs of order n with nullity n-3 or n-4, and signed bicyclic signed graphs (including simple bicyclic graphs) of order n with nullity n-5