Related papers: Smooth maps from clumpy data: generalizations
We describe a accurate and fast pixel-based statistical method to interpolate fields of arbitrary spin on the sphere. We call this method Fast and Lean Interpolation on the Sphere (FLINTS). The method predicts the optimal interpolated…
The matter density is an important knowledge for today cosmology as many phenomena are linked to matter fluctuations. However, this density is not directly available, but estimated through lensing maps or galaxy surveys. In this article, we…
We present sufficient conditions on a smooth uniformly flat hypersurface W in the unit ball to be an interpolation hypersurface or a sampling hypersurface for generalized Bergman spaces associated to the unit ball with its Bergman metric.…
Fold maps are higher dimensional versions of Morse functions, which play important roles in the studies of smooth manifolds, and such general maps also have been fundamental tools in the studies of smooth manifolds by using generic maps. In…
The estimation of potential fields such as the gravitational or magnetic potential at the surface of a spherical planet from noisy observations taken at an altitude over an incomplete portion of the globe is a classic example of an…
Diffraction-based methods have become an invaluable tool for the detailed assessment of residual strain and stress within experimental mechanics. These methods typically measure a component of the average strain within a gauge volume. It is…
We consider the Reeb graph of a thickening of points sampled from an unknown space. Our main contribution is a framework to transfer reconstruction results similar to the well-known work of Niyogi, Smale, and Weinberger to the setting of…
Long-baseline interferometry at optical and near-infrared wavelengths is an emerging technology which is quickly becoming a useful tool to investigate stellar atmospheres and to compare observations with models. Stellar atmosphere models…
Most cosmic shear analyses to date have relied on summary statistics (e.g. $\xi_+$ and $\xi_-$). These types of analyses are necessarily sub-optimal, as the use of summary statistics is lossy. In this paper, we forward-model the convergence…
In the era of big data, we first need to manage the data, which requires us to find missing data or predict the trend, so we need operations including interpolation and data fitting. Interpolation is a process to discover deducing new data…
The main goal of galaxy surveys is to map the distribution of the galaxies, for the purpose of understanding the properties of this distribution and its implications for the content and the evolution of the universe. However, in order to…
Large patterns could exist on the microwave sky as a result of various non-standard possibilities for the large-scale Universe -- rotation or shear, non-trivial topology, and single topological defects are specific examples. All-sky (or…
In many astrophysical systems, smoothly-varying large-scale variations coexist with small-scale fluctuations. For example, a large-scale velocity or density gradient can exist in molecular clouds that exhibit small-scale turbulence. In…
The universe is not isotropic or spatially homogeneous on local scales. The averaging of local inhomogeneities in general relativity can lead to significant dynamical effects on the evolution of the universe and on the interpretation of…
After generalizing the concept of clusters to incorporate clusters that are linked to other clusters through some relatively narrow bridges, an approach for detecting patches of separation between these clusters is developed based on an…
Analytic continuation of imaginary time or frequency data to the real axis is a crucial step in extracting dynamical properties from quantum Monte Carlo simulations. The average spectrum method provides an elegant solution by integrating…
Many recent studies have demonstrated that scaling arguments, such as the so-called hierarchical {\em ansatz}, are extremely useful in understanding the statistical properties of weak gravitational lensing. This is especially true on small…
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.…
The problem of extrapolation and interpolation of asymptotic series is considered. Several new variants of improving the accuracy of the self-similar approximants are suggested. The methods are illustrated by examples typical of chemical…
We present precise anisotropic interpolation error estimates for smooth functions using a new geometric parameter and derive inverse inequalities on anisotropic meshes. In our theory, the interpolation error is bounded in terms of the…