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Students often make mistakes in their introductory programming assignments as part of their learning process. Unfortunately, providing custom repairs for these mistakes can require a substantial amount of time and effort from class instructors. Automated program repair (APR) techniques can be used to synthesize such fixes. Prior work has explored the use of symbolic and neural techniques for APR in the education domain. Both types of approaches require either substantial engineering efforts or large amounts of data and training. We propose to use a large language model trained on code, such as Codex (a version of GPT), to build an APR system -- PyDex -- for introductory Python programming assignments. Our system can fix both syntactic and semantic mistakes by combining multi-modal prompts, iterative querying, test-case-based selection of few-shots, and program chunking. We evaluate PyDex on 286 real student programs and compare to three baselines, including one that combines a state-of-the-art Python syntax repair engine, BIFI, and a state-of-the-art Python semantic repair engine for student assignments, Refactory. We find that PyDex can fix more programs and produce smaller patches on average. 

Abstract The origin of short gamma-ray bursts is associated with outflows powered by the remnant of a binary neutron star merger. This remnant can be either a black hole or a highly magnetized, fast-spinning neutron star, also known as a magnetar. Here we present the results of two relativistic magnetohydrodynamical simulations aimed at investigating the large-scale dynamics and propagation of magnetar collimated outflows through the medium surrounding the remnant. The first simulation evolves a realistic jet by injecting external simulation data, while the second evolves an analytical model jet with similar properties for comparison. We find that both outflows remain collimated and successfully emerge through the static medium surrounding the remnant. However, they fail to attain relativistic velocities and only reach a mean maximum speed of ∼0.7cfor the realistic jet and ∼0.6cfor the analytical jet. We also find that the realistic jet has a much more complex structure. The lack of highly relativistic speeds, which makes these jets unsuitable as short gamma-ray burst sources, is due to numerical limitations and is not general to all possible magnetar outflows. A jet like the one we study, however, could give rise to or augment a blue kilonova component. In addition, it would make the propagation of a relativistic jet easier, should one be launched after the neutron star collapses into a black hole. 

Abstract Long and shortγ-ray bursts (GRBs) are traditionally associated with galactic environments, where circumburst densities are small or moderate (few to hundreds of protons per cubic centimeter). However, both are also expected to occur in the disks of active galactic nuclei, where the ambient medium density can be much larger. In this work we study, via semianalytical methods, the propagation of the GRB outflow, its interaction with the external material, and the ensuing prompt radiation. In particular, we focus on the case in which the external shock develops early in the evolution at a radius that is smaller than the internal shock one. We find that bursts in such high-density environments are likely characterized by a single, long emission episode that is due to the superposition of individual pulses, with a characteristic hard-to-soft evolution irrespective of the light-curve luminosity. While multipulse light curves are not impossible, they would require the central engine to go dormant for a long time before reigniting. In addition, short GRB engines would produce bursts with prompt duration that would exceed the canonical 2 s separation threshold and likely be incorrectly classified as long events, even though they would not be accompanied by a simultaneous supernova. Finally, these events have a large dynamical efficiency, which would produce a bright prompt emission followed by a somewhat dim afterglow.