Related papers: Flat Maps that improve on the Winkel Tripel
We present GEO-FPT (Geometric Fitted Perturbation Theory), a new model for the galaxy bispectrum anisotropic signal in redshift space, with functional form rooted in perturbation theory. It also models the dependence of the bispectrum with…
Precision weak gravitational lensing experiments require measurements of galaxy shapes accurate to <1 part in 1000. We investigate measurement biases, noted by Voigt and Bridle (2009) and Melchior et al. (2009), that are common to shape…
In a recent paper, a new conformally flat metric was introduced, describing an expanding scalar field in a spherically symmetric geometry. The spacetime can be interpreted as a Schwarzschild-like model with an apparent horizon surrounding…
Monocular depth estimation is an ambiguous problem, thus global structural cues play an important role in current data-driven single-view depth estimation methods. Panorama images capture the complete spatial information of their…
Wigner's theorem characterizes isometries of the set of all rank one projections on a Hilbert space. In metric geometry nonexpansive maps and noncontractive maps are well studied generalizations of isometries. We show that under certain…
Accurate maps of Greenland's subglacial bed are essential for sea-level projections, but radar observations are sparse and uneven. We introduce GraphTopoNet, a graph-learning framework that fuses heterogeneous supervision and explicitly…
Let (M,g) a compact Riemannian n-dimensional manifold with umbilic boundary. It is well know that, under certain hypothesis, in the conformal class of g there are scalar-flat metrics that have the boundary of M as a constant mean curvature…
This report starts by describing the continuum model used by Lingle & Clark (1985) to approximate the deformation of the earth under changing ice sheet and ocean loads. That source considers a single ice stream, but we apply their…
We classify all smooth flat Riemannian metrics on the two-dimensional plane. In the complete case, it is well-known that these metrics are isometric to the Euclidean metric. In the incomplete case, there is an abundance of…
A piecewise flat Finsler metric on a triangulated surface $M$ is a metric whose restriction to any triangle is a flat triangle in some Minkowski space with straight edges. One of the main purposes of this work is to study the properties of…
We develop an inversion technique of annual scattered light curves to sketch a two-dimensional albedo map of exoplanets in face-on orbits. As a test-bed for future observations of extrasolar terrestrial planets, we apply this mapping…
We explore the following problem: given a collection of creases on a piece of paper, each assigned a folding direction of mountain or valley, is there a flat folding by a sequence of simple folds? There are several models of simple folds;…
Evaluating massive-scale point cloud maps in Simultaneous Localization and Mapping (SLAM) remains challenging, primarily due to the absence of unified, robust and efficient evaluation frameworks. We present MapEval, an open-source framework…
Let $\mathcal{C}$ be the space of smooth metrics $g$ on a given compact manifold $M^{n}$ ($n\geq3$) with constant scalar curvature and unitary volume. The goal of this paper is to study the critical point of the total scalar curvature…
Due to the emergence of new high resolution numerical weather prediction (NWP) models and the availability of new or more reliable remote sensing data, the importance of efficient spatial verification techniques is growing. Wavelet…
We prove that each complete flat cone metric on a surface, perhaps with boundary and punctures, can be triangulated with finitely many types of triangles. We derive Gauss-Bonnet formula for this kind of cone metrics. In addition, we prove…
In this paper, close surfaces are considered in 3-dimensional harmonic conformally flat space in point of the variation. It is shown that if the conformal vector field be tangent to surface and the sign of the mean curvature does not change…
Differential flatness enables efficient planning and control for underactuated robotic systems, but we lack a systematic and practical means of identifying a flat output (or determining whether one exists) for an arbitrary robotic system.…
Given a sequence of Marcinkiewicz-Zygmund inequalities in $L_2$ on a usual compact space $\mathcal M$, Gr\"ochenig introduced the weighted least squares polynomials and the least squares quadrature from pointwise samples of a function, and…
[Abridged] We apply the multipole vector framework to full-sky maps derived from the first year WMAP data. We significantly extend our earlier work showing that the two lowest cosmologically interesting multipoles, l=2 and 3, are not…