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A sizeable fraction of gamma-ray burst (GRB) time profiles consist of a temporal sequence of pulses. The nature of this stochastic process carries information on how GRB inner engines work. The so-called interpulse time defines the interval between adjacent pulses, excluding the long quiescence periods during which the signal drops to the background level. It was found by many authors in the past that interpulse times are lognormally distributed, at variance with the exponential case that is expected for a memoryless process. We investigated whether the simple hypothesis of a temporally uncorrelated sequence of pulses is really to be rejected, as a lognormal distribution necessarily implies. We selected and analysed a number of multi--peaked CGRO/BATSE GRBs and simulated similar time profiles, with the crucial difference that we assumed exponentially distributed interpulse times, as is expected for a memoryless stationary Poisson process. We then identified peaks in both data sets using a novel peak search algorithm, which is more efficient than others used in the past. We independently confirmed that the observed interpulse time distribution is approximately lognormal. However, we found the same results on the simulated profiles, in spite of the intrinsic exponential distribution. Although intrinsic lognormality cannot be ruled out, this shows that intrinsic interpulse time distribution in real data could still be exponential, while the observed lognormal could be ascribed to the low efficiency of peak search algorithms at short values combined with the limitations of a bin-integrated profile. Our result suggests that GRB engines may emit pulses after the fashion of nuclear radioactive decay, that is, as a memoryless process.
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Generative adversarial networks (GANs) represent a zero-sum game between two machine players, a generator and a discriminator, designed to learn the distribution of data. While GANs have achieved state-of-the-art performance in several benchmark learning tasks, GAN minimax optimization still poses great theoretical and empirical challenges. GANs trained using first-order optimization methods commonly fail to converge to a stable solution where the players cannot improve their objective, i.e., the Nash equilibrium of the underlying game. Such issues raise the question of the existence of Nash equilibrium solutions in the GAN zero-sum game. In this work, we show through several theoretical and numerical results that indeed GAN zero-sum games may not have any local Nash equilibria. To characterize an equilibrium notion applicable to GANs, we consider the equilibrium of a new zero-sum game with an objective function given by a proximal operator applied to the original objective, a solution we call the proximal equilibrium. Unlike the Nash equilibrium, the proximal equilibrium captures the sequential nature of GANs, in which the generator moves first followed by the discriminator. We prove that the optimal generative model in Wasserstein GAN problems provides a proximal equilibrium. Inspired by these results, we propose a new approach, which we call proximal training, for solving GAN problems. We discuss several numerical experiments demonstrating the existence of proximal equilibrium solutions in GAN minimax problems.
The performance of the nine RHESSI germanium detectors has been gradually deteriorating since its launch in 2002 because of radiation damage. To restore its former sensitivity, the spectrometer underwent an annealing procedure in November 2007. However, it changed the RHESSI response and affected gamma-ray burst measurements, e.g., the hardness ratios and the spectral capabilities below ~100keV.
A preponderance of evidence links long-duration, soft-spectrum gamma-ray bursts (GRBs) with the death of massive stars. The observations of the GRB-supernova (SN) connection present the most direct evidence of this physical link. We summarize 30 GRB-SN associations and focus on five ironclad cases, highlighting the subsequent insight into the progenitors enabled by detailed observations. We also address the SN association (or lack thereof) with several sub-classes of GRBs, finding that the X-ray Flash (XRF) population is likely associated with massive stellar death whereas short-duration events likely arise from an older population not readily capable of producing a SN concurrent with a GRB. Interestingly, a minority population of seemingly long-duration, soft-spectrum GRBs show no evidence for SN-like activity; this may be a natural consequence of the range of Ni-56 production expected in stellar deaths.
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 lightcurve allows a measurement of the jet opening angle and true energetics of GRBs. In this paper, we reinvestigate this problem using a large sample of GRBs that have an optical jet break which is consistent with being achromatic in the X-ray band. Our sample includes 99 GRBs from February 1997 to March 2015 that have optical and, for Swift GRBs, X-ray lightcurves that are consistent with the jet break interpretation. Out of 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. The 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. 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 {em Swfit era}, is most likely the source of scatter. If one limits the sample to jet breaks later than $10^4$ 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.
To date, the Burst Alert Telescope (BAT) onboard Swift has detected ~ 1000 gamma-ray bursts (GRBs), of which ~ 360 GRBs have redshift measurements, ranging from z = 0.03 to z = 9.38. We present the analyses of the BAT-detected GRBs for the past ~ 11 years up through GRB151027B. We report summaries of both the temporal and spectral analyses of the GRB characteristics using event data (i.e., data for each photon within approximately 250 s before and 950 s after the BAT trigger time), and discuss the instrumental sensitivity and selection effects of GRB detections. We also explore the GRB properties with redshift when possible. The result summaries and data products are available at http://swift.gsfc.nasa.gov/results/batgrbcat/index.html . In addition, we perform searches for GRB emissions before or after the event data using the BAT survey data. We estimate the false detection rate to be only one false detection in this sample. There are 15 ultra-long GRBs (~ 2% of the BAT GRBs) in this search with confirmed emission beyond ~ 1000 s of event data, and only two GRBs (GRB100316D and GRB101024A) with detections in the survey data prior to the starting of event data. (Some figures shown here are in lower resolution due to the size limit on arXiv. The full resolution version can be found at http://swift.gsfc.nasa.gov/results/batgrbcat/3rdBATcatalog.pdf )
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