相关论文: Flexion and Skewness in Map Projections of the Ear…
Goldberg & Gott (2008) developed six error measures to rate flat map projections on their verisimilitude to the sphere: Isotropy, Area, Flexion, Skewness, Distances, and Boundary Cuts. The first two depend on the metric of the projection,…
In weak gravitational lensing, the image distortion caused by shear measures the projected tidal gravitational field of the deflecting mass distribution. To lowest order, the shear is proportional to the mean image ellipticity. If the image…
Weak gravitational lensing has proven to be a powerful tool to map directly the distribution of dark matter in the Universe. The technique, currently used, relies on the accurate measurement of the gravitational shear that corresponds to…
We account for all the image distortions relevant to weak gravitational lensing to second order. Besides the familiar shear, convergence, rotation and flexions, we find a new image distortion with two distinct descriptions, the twist and…
This research work aims to explore the distortions in distance in equidistant cylindrical projection. The horizontal bending that occurs in the projection process can be assessed by performing a geometric analysis using Tissot's…
In this paper, we investigate the impact of higher-order distortions on the precise measurement of weak gravitational lensing shear and flexion. We begin by defining generalized higher-order distortions and outlining methods for measuring…
Gravitational flexion, caused by derivatives of the gravitational tidal field, is potentially important for the analysis of the dark-matter distribution in gravitational lenses, such as galaxy clusters or the dark-matter haloes of galaxies.…
We consider here a new statistical measure for cosmic shear, the aperture mass Map, which is defined as a spatially filtered projected density field and which can be measured directly from the image distortions of high-redshift galaxies. By…
Quasiconformal maps in the plane are orientation preserving homeomorphisms that satisfy certain distortion inequalities; infinitesimally, they map circles to ellipses of bounded eccentricity. Such maps have many useful geometric distortion…
To perform visual data exploration, many dimensionality reduction methods have been developed. These tools allow data analysts to represent multidimensional data in a 2D or 3D space, while preserving as much relevant information as…
In order to best improve constraints on cosmological parameters and on models of modified gravity using current and future galaxy surveys it is necessary maximally exploit the available data. As redshift-space distortions mean statistical…
As the fields of optical microscopy, semiconductor technology and fundamental science increasingly aim for precision at or below the nanoscale, there is a burgeoning demand for sub-nanometric displacement and position sensing. We show that…
A large driver of the complexity of graph learning is the interplay between structure and features. When analyzing the expressivity of graph neural networks, however, existing approaches ignore features in favor of structure, making it…
Given a galaxy image, one cannot simply measure its flexion. An image's spin one and three shape properties, typically associated with F- and G-flexion, are actually complicated functions of the galaxy's intrinsic shape and the telescope's…
Weak gravitational lensing is normally assumed to have only two principle effects: a magnification of a source and a distortion of the sources shape in the form of a shear. However, further distortions are actually present owing to changes…
Flexion is the significant third-order weak gravitational lensing effect responsible for the weakly skewed and arc-like appearance of lensed galaxies. Here we demonstrate how flexion measurements can be used to measure galaxy halo density…
Image representations (artificial or biological) are often compared in terms of their global geometric structure; however, representations with similar global structure can have strikingly different local geometries. Here, we propose a…
In this investigation we focus on the problem of mapping the ground reflectivity with multiple laser scanners mounted on mobile robots/vehicles. The problem originates because regions of the ground become populated with a varying number of…
Using orthogonal projections, we investigate distance of a given elasticity tensor to classes of elasticity tensors exhibiting particular material symmetries. These projections depend on the orientation of the elasticity tensor, hence the…
In this paper, we introduce some known map projections from a model of the Earth to a flat sheet of paper or map and derive the plotting equations for these projections. The first fundamental form and the Gaussian fundamental quantities are…