Gamma-Ray Burst Jet Breaks Revisited

Gamma-ray Burst (GRB) collimation has been inferred with the observations of achromatic steepening in GRB light curves, known as jet breaks. Identifying a jet break from a GRB afterglow light curve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we re-investigate this problem using a large sample of GRBs that have an optical jet break that is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from 1997 February to 2015 March that have optical and, for Swift GRBs, X-ray light curves that are consistent with the jet break interpretation. Out of the 99 GRBs we have studied, 55 GRBs are found to have temporal and spectral behaviors both before and after the break, consistent with the theoretical predictions of the jet break models, respectively. These include 53 long/soft (Type II) and 2 short/hard (Type I) GRBs. Only 1 GRB is classified as the candidate of a jet break with energy injection. Another 41 and 3 GRBs are classified as the candidates with the lower and upper limits of the jet break time, respectively. Most jet breaks occur at 90 ks, with a typical opening angle θj = (2.5 ± 1.0)°. This gives a typical beaming correction factor ${f}_{b}^{-1}\sim 1000$ for Type II GRBs, suggesting an even higher total GRB event rate density in the universe. Both isotropic and jet-corrected energies have a wide span in their distributions: log(Eγ,iso/erg) = 53.11 with σ = 0.84; log(EK,iso/erg) = 54.82 with σ = 0.56; log(Eγ/erg) = 49.54 with σ = 1.29; and log(EK/erg) = 51.33 with σ = 0.58. We also investigate several empirical correlations (Amati, Frail, Ghirlanda, and Liang–Zhang) previously discussed in the literature. We find that in general most of these relations are less tight than before. The existence of early jet breaks and hence small opening angle jets, which were detected in the Swfit era, is most likely the source of scatter. If one limits the sample to jet breaks later than 104 s, the Liang–Zhang relation remains tight and the Ghirlanda relation still exists. These relations are derived from Type II GRBs, and Type I GRBs usually deviate from them

Semi-supervised Deep Generative Modelling of Incomplete Multi-Modality Emotional Data

There are threefold challenges in emotion recognition. First, it is difficult to recognize human's emotional states only considering a single modality. Second, it is expensive to manually annotate the emotional data. Third, emotional data often suffers from missing modalities due to unforeseeable sensor malfunction or configuration issues. In this paper, we address all these problems under a novel multi-view deep generative framework. Specifically, we propose to model the statistical relationships of multi-modality emotional data using multiple modality-specific generative networks with a shared latent space. By imposing a Gaussian mixture assumption on the posterior approximation of the shared latent variables, our framework can learn the joint deep representation from multiple modalities and evaluate the importance of each modality simultaneously. To solve the labeled-data-scarcity problem, we extend our multi-view model to semi-supervised learning scenario by casting the semi-supervised classification problem as a specialized missing data imputation task. To address the missing-modality problem, we further extend our semi-supervised multi-view model to deal with incomplete data, where a missing view is treated as a latent variable and integrated out during inference. This way, the proposed overall framework can utilize all available (both labeled and unlabeled, as well as both complete and incomplete) data to improve its generalization ability. The experiments conducted on two real multi-modal emotion datasets demonstrated the superiority of our framework.Comment: arXiv admin note: text overlap with arXiv:1704.07548, 2018 ACM Multimedia Conference (MM'18