Related papers: Gale transform of a starshaped sphere
Gravitational lensing has now become a popular tool to measure the mass distribution of structures in the Universe on various scales. Here we focus on the study of galaxy's scale dark matter halos with galaxy-galaxy lensing techniques:…
Consider a random set of points on the unit sphere in $\mathbb{R}^d$, which can be either uniformly sampled or a Poisson point process. Its convex hull is a random inscribed polytope, whose boundary approximates the sphere. We focus on the…
We present in this paper new multiscale transforms on the sphere, namely the isotropic undecimated wavelet transform, the pyramidal wavelet transform, the ridgelet transform and the curvelet transform. All of these transforms can be…
The conditions for a cuspidal edge, swallowtail and other fundamental singularities are given in the context of Lie sphere geometry. We then use these conditions to study the Lie sphere transformations of a surface.
We discuss the notion of the orbifold transform, and illustrate it on simple examples. The basic properties of the transform are presented, including transitivity and the exponential formula for symmetric products. The connection with the…
In this paper, we present a method to efficiently generate large, free, and guaranteed convex space among arbitrarily cluttered obstacles. Our method operates directly on point clouds, avoids expensive calculations, and processes thousands…
The multiple images of lensed quasars provide evidence on the mass distribution of the lensing galaxy. The lensing invariants are constructed from the positions of the images, their parities and their fluxes. They depend only on the…
The mathematical software system polymake provides a wide range of functions for convex polytopes, simplicial complexes, and other objects. A large part of this paper is dedicated to a tutorial which exemplifies the usage. Later sections…
Scattering transforms are a new type of summary statistics recently developed for the study of highly non-Gaussian processes, which have been shown to be very promising for astrophysical studies. In particular, they allow one to build…
The advent of transformation optics has lead to the initiation of designing devices and applications associated to electromagnetic wave propagation in anisotropic media. Here, a method is suggested using a coordinate transformation with…
A one parameter set of noncommutative complex algebras is given. These may be considered deformation quantisation algebras. The commutative limit of these algebras correspond to the algebra of polynomial functions over a manifold or…
We describe how a certain simple modification of general relativity, in which the local cosmological constant is allowed to depend on the space-time curvature, predicts the existence of halos of modified gravity surrounding…
Metamorphism is a recently introduced integral transform, which is useful in solving partial differential equations. Basic properties of metamorphism can be verified by direct calculations. In this paper we present metamorphism as a sort of…
A biconvex polytope is a classical and tropical convex hull of finitely many points. Given a biconvex polytope, for each vertex of it we construct a directed bigraph and a gammoid so that the collection of base polytopes of those gammoids…
Factorization into spheres is achieved for skeleta of the simplex, cube, and cross-polytope, both explicitly and using Keevash's proof of existence of designs.
Thermal convection is one of the main mechanisms of heat transport and mixing in stars in general and also in the photospheric layers which emit the radiation that we observe with astronomical instruments. The present lecture notes first…
In this article we define an algebraic vertex of a generalized polyhedron and show that it is the smallest set of points needed to define the polyhedron. We prove that the indicator function of a generalized polytope $P$ is a linear…
We describe a simple geometric transformation of triangles which leads to an efficient and effective algorithm to smooth triangle and tetrahedral meshes. Our focus lies on the convergence properties of this algorithm: we prove the…
The scattering transform is a multilayered, wavelet-based transform initially introduced as a model of convolutional neural networks (CNNs) that has played a foundational role in our understanding of these networks' stability and invariance…
In [7], a notion of constant scalar curvature metrics on piecewise flat manifolds is defined. Such metrics are candidates for canonical metrics on discrete manifolds. In this paper, we define a class of vertex transitive metrics on certain…