Related papers: Approximately angle preserving mappings

We propose a method for efficiently computing orientation-preserving and approximately continuous correspondences between non-rigid shapes, using the functional maps framework. We first show how orientation preservation can be formulated…

In this paper we determine all the bijective linear maps on the space of bounded observables which preserve a fixed moment or the variance. Nonlinear versions of the corresponding results are also presented.

Random projections are random linear maps, sampled from appropriate distributions, that approx- imately preserve certain geometrical invariants so that the approximation improves as the dimension of the space grows. The well-known…

We construct a matrix $M\in R^{m\otimes d^c}$ with just $m=O(c\,\lambda\,\varepsilon^{-2}\text{poly}\log1/\varepsilon\delta)$ rows, which preserves the norm $\|Mx\|_2=(1\pm\varepsilon)\|x\|_2$ of all $x$ in any given $\lambda$ dimensional…

The $c$-packedness property, proposed in 2010, is a geometric property that captures the spatial distribution of a set of edges. Despite the recent interest in $c$-packedness, its utility has so far been limited to Fr\'echet distance…

We study directions along which the norms of vectors are preserved under a linear map. In particular, we find families of matrices for which these directions are determined by integer vectors. We consider the two-dimensional case in detail,…

Convex hulls are fundamental objects in computational geometry. In moderate dimensions or for large numbers of vertices, computing the convex hull can be impractical due to the computational complexity of convex hull algorithms. In this…

This paper introduce a new class of operators and contraction mapping for a cyclical map T on G-metric spaces and the approximately fixed point properties. Also,we prove two general lemmas regarding approximate fixed Point of cyclical…

We introduce the following notion: a digraph $D=(V,A)$ with arc weights $c: A\rightarrow \R$ is called nearly conservative if every negative cycle consists of two arcs. Computing shortest paths in nearly conservative digraphs is NP-hard,…

We present new methods for uniformly sampling the solid angle subtended by a disk. To achieve this, we devise two novel area-preserving mappings from the unit square $[0,1]^2$ to a spherical ellipse (i.e. the projection of the disk onto the…

This article addresses structure-preserving smooth approximation of semiconcave functions. semiconcave functions are of particular interest because they naturally arise in a variety of variational problems, including {optimal feedback…

Let $n\geq 2$. In this paper, we obtain approximation properties of various families of normalized univalent mappings $f$ on the Euclidean unit ball $\mathbb{B}^n$ in $\mathbb{C}^n$ by automorphisms of $\mathbb{C}^n$ whose restrictions to…

Auto-encoder models that preserve similarities in the data are a popular tool in representation learning. In this paper we introduce several auto-encoder models that preserve local distances when mapping from the data space to the latent…

We display four approximation theorems for manifold-valued mappings. The first one approximates holomorphic embeddings on pseudoconvex domains in $\Bbb C^n$ with holomorphic embeddings with dense images. The second theorem approximates…

Let X be a data matrix of rank \rho, whose rows represent n points in d-dimensional space. The linear support vector machine constructs a hyperplane separator that maximizes the 1-norm soft margin. We develop a new oblivious dimension…

We determine the structure of linear maps on the tensor product of matrices which preserve the numerical range or numerical radius.

Consider discrete conformal maps defined on the basis of two conformally equivalent triangle meshes, that is edge lengths are related by scale factors associated to the vertices. Given a smooth conformal map $f$, we show that it can be…

We study Lipschitz, positively homogeneous and finite suprema preserving mappings defined on a max-cone of positive elements in a normed vector lattice. We prove that the lower spectral radius of such a mapping is always a minimum value of…

Metric embeddings traditionally study how to map $n$ items to a target metric space such that distance lengths are not heavily distorted; but what if we only care to preserve the relative order of the distances (and not their length)? In…

Finite elements of higher continuity, say conforming in $H^2$ instead of $H^1$, require a mapping from reference cells to mesh cells which is continuously differentiable across cell interfaces. In this article, we propose an algorithm to…