Related papers: Smoothing Algorithms and High-order Singularities …
Strong gravitational lensing provides valuable insights into the mass distribution of galaxies and the nature of dark matter. However, its modeling is computationally demanding due to the large volume of strong lensing observations. In this…
Training neural networks with high certified accuracy against adversarial examples remains an open challenge despite significant efforts. While certification methods can effectively leverage tight convex relaxations for bound computation,…
Strongly gravitational lensing systems (SGL) encodes cosmology information in source/lens distance ratios $\mathcal{D}_{\rm obs}=\mathcal{D}_{\rm ls}/\mathcal{D}_{\rm s}$, which can be used to precisely constrain cosmological parameters. In…
This paper formalizes and analyzes Gaussian smoothing applied to two prominent optimization methods: Stochastic Gradient Descent (GSmoothSGD) and Adam (GSmoothAdam) in deep learning. By attenuating small fluctuations, Gaussian smoothing…
Weak gravitational lensing surveys have the potential to directly probe mass density fluctuation in the universe. Recent studies have shown that it is possible to model the statistics of the convergence field at small angular scales by…
Traditional problems in computational geometry involve aspects that are both discrete and continuous. One such example is nearest-neighbor searching, where the input is discrete, but the result depends on distances, which vary continuously.…
If properly calibrated, the shapes of galaxy clusters can be used to investigate many physical processes: from feedback and quenching of star formation, to the nature of dark matter. Theorists frequently measure shapes using moments of…
The light we observe from distant astrophysical objects including supernovae and quasars allows us to determine large distances in terms of a cosmological model. Despite the success of the standard cosmological model in fitting the data,…
The growing prevalence of nonsmooth optimization problems in machine learning has spurred significant interest in generalized smoothness assumptions. Among these, the (L0, L1)-smoothness assumption has emerged as one of the most prominent.…
Graph spectral techniques for measuring graph similarity, or for learning the cluster number, require kernel smoothing. The choice of kernel function and bandwidth are typically chosen in an ad-hoc manner and heavily affect the resulting…
We report on an investigation of the environments of the SLACS sample of gravitational lenses. The local and global environments of the lenses are characterized using SDSS photometry and, when available, spectroscopy. We find that the lens…
In a strong gravitational lensing system, the distorted light from a source is analysed to infer the properties of the lens. However, light emitted by the lens itself can contaminate the image of the source, introducing systematic errors in…
We present a general probabilistic perspective on Gaussian filtering and smoothing. This allows us to show that common approaches to Gaussian filtering/smoothing can be distinguished solely by their methods of computing/approximating the…
Taking into account the noise from intrinsic ellipticities of source galaxies, we study the efficiency and completeness of halo detections from weak lensing convergence maps. Particularly, with numerical simulations, we compare the Gaussian…
In previous works, we proposed a method to characterize jointly self-similarity and anisotropy properties of a large class of self--similar Gaussian random fields. We provide here a mathematical analysis of our approach, proving that the…
Gravitational lensing allows us to probe the structure of matter on a broad range of astronomical scales, and as light from a distant source traverses an intervening galaxy, compact matter such as planets, stars, and black holes act as…
We propose a new technique to directly measure the shapes of dark matter halos of galaxies using weak gravitational lensing. Extending the standard galaxy-galaxy lensing method, we show that the shape parameters of the mass distribution of…
Many computational algorithms applied to geometry operate on discrete representations of shape. It is sometimes necessary to first simplify, or coarsen, representations found in modern datasets for practicable or expedited processing. The…
This article introduces a method for estimating the smoothness of a stationary, isotropic Gaussian random field from irregularly spaced data. This involves novel constructions of higher-order quadratic variations and the establishment of…
A comprehensive methodology is provided for smoothing noisy, irregularly sampled data with non-Gaussian noise using smoothing splines. We demonstrate how the spline order and tension parameter can be chosen a priori from physical reasoning.…