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Abstract Conventional planet formation theories predict a paucity of massive planets around small stars, especially very low-mass (0.1−0.3M_⊙) mid-to-late M dwarfs. Such tiny stars are expected to form planets of terrestrial sizes but not much bigger. However, this expectation is challenged by the recent discovery of LHS 3154 b, a planet with period of 3.7 days and minimum mass of 13.2M_⊕orbiting a 0.11M_⊙star. Here, we propose that close-in Neptune-mass planets like LHS 3154 b formed through an anomalous series of mergers from a primordial compact system of super-Earths. We perform simulations within the context of the “breaking the chains” scenario, in which super-Earths initially form in tightly spaced chains of mean-motion resonances before experiencing dynamical instabilities and collisions. Planets as massive and close-in as LHS 3154 b (M_p∼ 12−20M_⊕,P< 7 days) are produced in ∼1% of simulated systems, in broad agreement with their low observed occurrence. These results suggest that such planets do not require particularly unusual formation conditions but rather are an occasional by-product of a process that is already theorized to explain compact multiplanet systems. Interestingly, our simulated systems with LHS 3154 b-like planets also contain smaller planets at around ∼30 days, offering a possible test of this hypothesis. 

The underlying physics of imaging processes and associated instrumentation limitations mean that blurring artifacts are unavoidable in many applications such as astronomy, microscopy, radar and medical imaging. In several such imaging modalities, convolutional models are used to describe the blurring process; the observed image or function is a convolution of the true underlying image and a point spread function (PSF) which characterizes the blurring artifact. In this work, we propose and analyze a technique - based on convolutional edge detectors and Gaussian curve fitting - to approximate unknown Gaussian PSFs when the underlying true function is piecewise-smooth. For certain simple families of such functions, we show that this approximation is exponentially accurate. We also provide preliminary two dimensional extensions of this technique. These findings - confirmed by numerical simulations - demonstrate the feasibility of recovering accurate approximations to the blurring function, which serves as an important prerequisite to solving deblurring problems.