Related papers: Effective equidistribution of shears and applicati…

Forthcoming Stage-IV dark energy optical surveys, such as LSST, have the ambitious goal of measuring cosmological parameters at sub-percent precision. Realizing their full scientific potential requires very precise measurement of the cosmic…

Since the Universe is inhomogeneous on scales well below the Hubble radius, light bundles from distant galaxies are deflected and distorted by the tidal gravitational field of the large-scale matter distribution as they propagate through…

The distributional properties of the translation flow on the unit square have been considered in different fields of mathematics, including algebraic geometry and discrepancy theory. One method to quantify equidistribution is to compare the…

We introduce a new approach to spectral sparsification that approximates the quadratic form of the pseudoinverse of a graph Laplacian restricted to a subspace. We show that sparsifiers with a near-linear number of edges in the dimension of…

Covariance representations are developed for the uniform distributions on the Euclidean spheres in terms of spherical gradients and Hessians. They are applied to derive a number of Sobolev type inequalities and to recover and refine the…

We introduce bendlets, a shearlet-like system that is based on anisotropic scaling, translation, shearing, and bending of a compactly supported generator. With shearing being linear and bending quadratic in spatial coordinates, bendlets…

It was recently shown by Aka, Einsiedler and Shapira that if d>2, the set of primitive vectors on large spheres when projected to the d-1-dimensional sphere coupled with the shape of the lattice in their orthogonal complement equidistribute…

It is shown that gravitational lensing by point masses arranged in an infinitely extended regular lattice can be studied analytically using the Weierstrass functions. In particular, we draw the critical curves and the caustic networks for…

We present the theoretical and analytical bases of optimal techniques to measure weak gravitational shear from images of galaxies. We first characterize the geometric space of shears and ellipticity, then use this geometric interpretation…

The set of primitive vectors on large spheres in the euclidean space of dimension d>2 equidistribute when projected on the unit sphere. We consider here a refinement of this problem concerning the direction of the vector together with the…

In this paper we extend the recent theory of shear-localization in 2-dimensional amorphous solids to 3-D. In 2-D the fundamental instability of shear-localization is related to the appearance of a line of displacement quadrupoles, that…

We present new results on the gravitational lensing shear and magnification power spectra obtained from numerical simulations of a flat cosmology with a cosmological constant. These results are of considerable interest since both the shear…

This paper explores the characterization of equivariant linear layers for representations of permutations and related groups. Unlike traditional approaches, which address these problems using parameter-sharing, we consider an alternative…

We construct differential algebras in which spaces of (one-dimensional) periodic ultradistributions are embedded. By proving a Schwartz impossibility type result, we show that our embeddings are optimal in the sense of being consistent with…

We study equidistribution of certain subsets of periodic orbits for subshifts of finite type. Our results solely rely on the growth of these subsets. As a consequence, effective equidistribution results are obtained for both hyperbolic…

Weight-equitable partitions of graphs, which are a natural extension of the well-known equitable partitions, have been shown to be a powerful tool to weaken the regularity assumption in several well-known eigenvalue bounds. In this work we…

We prove an effective equidistribution theorem for orbits of certain unipotent subgroups in arithmetic quotients of perfect Lie groups with a polynomial error term. Even for semisimple quotients, our result provides the first infinite…

The shearlets are a special case of the wavelets with composite dilation that, among other things, have a basis-like structure and multi resolution analysis properties. These relatively new representation systems have encountered wide range…

We consider the impact of second order corrections to the geodesic equation governing gravitational lensing. We start from the full second order metric, including scalar, vector and tensor perturbations, and retain all relevant…

We investigate the extent to which cosmic size magnification may be used to com- plement cosmic shear in weak gravitational lensing surveys, with a view to obtaining high-precision estimates of cosmological parameters. Using simulated…