12,869 research outputs found
Delayed Onset and Fast Rise of Prompt Optical-UV Emission from Gamma-Ray Bursts in Molecular Clouds
Observations imply that long \gamma-ray bursts (GRBs) are originated from
explosions of massive stars, therefore they may occur in the molecular clouds
where their progenitors were born. We show here that the prompt optical-UV
emission from GRBs may be delayed due to the dust extinction, which can well
explain the observed optical delayed onset and fast rise in GRB 080319B. The
density and the size of the molecular cloud around GRB 080319B are roughly
constrained to be \sim10^3cm^{-3} and \sim 8pc, respectively. We also
investigate the other GRBs with prompt optical-UV data, and find similar values
of the densities and sizes of the local molecular clouds. The future
observations of prompt optical-UV emission from GRBs in subsecond timescale,
e.g., by UFFO-Pathfinder and SVOM-GWAC, will provide more evidence and probes
of the local GRB environments.Comment: 15 pages, 5 figures, RAA 13 (2013) 57-70, typo correctio
Gradient Hard Thresholding Pursuit for Sparsity-Constrained Optimization
Hard Thresholding Pursuit (HTP) is an iterative greedy selection procedure
for finding sparse solutions of underdetermined linear systems. This method has
been shown to have strong theoretical guarantee and impressive numerical
performance. In this paper, we generalize HTP from compressive sensing to a
generic problem setup of sparsity-constrained convex optimization. The proposed
algorithm iterates between a standard gradient descent step and a hard
thresholding step with or without debiasing. We prove that our method enjoys
the strong guarantees analogous to HTP in terms of rate of convergence and
parameter estimation accuracy. Numerical evidences show that our method is
superior to the state-of-the-art greedy selection methods in sparse logistic
regression and sparse precision matrix estimation tasks
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