Search for: All records

Abstract Traditional weak-gravitational-lensing shear estimators are carefully calibrated but struggle to fully capture realistic galaxy morphologies, point-spread-function (PSF) effects, blending, and noise in deep surveys, while blindly trained machine learning (ML) models can introduce significant calibration biases. Here, we construct a fully D₄-equivariant deep neural network for galaxy shape measurement whose architecture enforces symmetry under 90° rotations and mirror transformations, and adopt the Analytical Calibration framework to calibrate the model using its backpropagated gradients. For isolated galaxies in LSST-like single-band simulations, we demonstrate that our approach achieves ∼10% lower shape noise than the traditional moment-based Fourier Power Function Shapelets estimator in the high-noise regime, equivalent to a 23% gain in effective galaxy number density, while simultaneously achieving multiplicative biases consistent with zero across a wide range of noise levels, PSF sizes and ellipticities, and magnitude selection cuts, with all measurements satisfying ∣m∣ < 10⁻³(i.e., within the 0.2% LSST requirement) and most at the ∼10⁻⁴level. We demonstrate this framework on isolated single-band galaxy images with Gaussian noise and known PSFs, establishing a rigorous, physics-informed foundation for future extensions of ML-based shear estimation to blended sources and multiband observations in Stage-IV surveys. All codes and data products will be made publicly available upon acceptance. 

Abstract The goal of this paper is to study the boundedness and compactness of the Bergman projection commutators in two weighted settings via the weighted BMO and VMO spaces, respectively. The novelty of our work lies in the distinct treatment of the symbolbin the commutator, depending on whether it is analytic or not, which turns out to be quite different. In particular, we show that an additional weight condition due to Aleman, Pott, and Reguera is necessary to study the commutators whenbis not analytic, while it can be relaxed whenbis analytic. In the analytic setting, we completely characterize boundedness and compactness, while in the non-analytic setting, we provide a sufficient condition which generalizes the Euclidean case and is also necessary in many cases of interest. Our work initiates a study of the commutators acting on complex function spaces with different symbols.