Andrew Gould

J. Skowron, A. Gould

We present a new algorithm to solve polynomial equations, and publish its code, which is 1.6-3 times faster than the ZROOTS subroutine that is commercially available from Numerical Recipes, depending on application. The largest improvement, when compared to naive solvers, comes from a fail-safe procedure that permits us to skip the majority of the calculations in the great majority of cases, without risking catastrophic failure in the few cases that these are actually required. Second, we identify a discriminant that enables a rational choice between Laguerre's Method and Newton's Method (or a new intermediate method) on a case-by-case basis. We briefly review the history of root solving and demonstrate that "Newton's Method" was discovered neither by Newton (1671) nor by Raphson (1690), but only by Simpson (1740). Some of the arguments leading to this conclusion were first given by the British historian of science Nick Kollerstrom in 1992, but these do not appear to have penetrated the astronomical community. Finally, we argue that Numerical Recipes should voluntarily surrender its copyright protection for non-profit applications, despite the fact that, in this particular case, such protection was the major stimulant for developing our improved algorithm.

Javier Viaña, Kyu-Ha Hwang, Zoë de Beurs et al.

Traditional microlensing event vetting methods require highly trained human experts, and the process is both complex and time-consuming. This reliance on manual inspection often leads to inefficiencies and constrains the ability to scale for widespread exoplanet detection, ultimately hindering discovery rates. To address the limits of traditional microlensing event vetting, we have developed LensNet, a machine learning pipeline specifically designed to distinguish legitimate microlensing events from false positives caused by instrumental artifacts, such as pixel bleed trails and diffraction spikes. Our system operates in conjunction with a preliminary algorithm that detects increasing trends in flux. These flagged instances are then passed to LensNet for further classification, allowing for timely alerts and follow-up observations. Tailored for the multi-observatory setup of the Korea Microlensing Telescope Network (KMTNet) and trained on a rich dataset of manually classified events, LensNet is optimized for early detection and warning of microlensing occurrences, enabling astronomers to organize follow-up observations promptly. The internal model of the pipeline employs a multi-branch Recurrent Neural Network (RNN) architecture that evaluates time-series flux data with contextual information, including sky background, the full width at half maximum of the target star, flux errors, PSF quality flags, and air mass for each observation. We demonstrate a classification accuracy above 87.5%, and anticipate further improvements as we expand our training set and continue to refine the algorithm.