Related papers: Uniqueness in Discrete Tomography of Delone Sets w…
We present a novel deep learning approach to approximate the solution of large, sparse, symmetric, positive-definite linear systems of equations. These systems arise from many problems in applied science, e.g., in numerical methods for…
The present paper develops two concepts of pointwise differentiability of higher order for arbitrary subsets of Euclidean space defined by comparing their distance functions to those of smooth submanifolds. Results include that…
We construct examples of Delone sets of the plane (that is, discrete subsets that are uniformly separated and coarsely dense) that are repetitive (each patch of the set appears in every large-enough ball) though non-rectifiable (i.e. non…
The densest subgraph problem, introduced in the 80s by Picard and Queyranne as well as Goldberg, is a classic problem in combinatorial optimization with a wide range of applications. The lowest outdegree orientation problem is known to be…
Machine learning methods are commonly used to solve inverse problems, wherein an unknown signal must be estimated from few indirect measurements generated via a known acquisition procedure. In particular, neural networks perform well…
Given an iterated function system of affine dilations with fixed points the vertices of a regular polygon, we characterize which points in the limit set lie on the boundary of its convex hull.
We study the structure of infinite discrete sets D definable in expansions of ordered Abelian groups whose theories are strong and definably complete, with particular emphasis on the set D' comprised of differences between successive…
Object counting and localization problems are commonly addressed with point supervised learning, which allows the use of less labor-intensive point annotations. However, learning based on point annotations poses challenges due to the high…
This paper presents high-order numerical methods for solving boundary value problems associated with the Lane-Emden equation, which frequently arises in astrophysics and various nonlinear models. A major challenge in studying this equation…
We consider the method of alternating projections for finding a point in the intersection of two closed sets, possibly nonconvex. Assuming only the standard transversality condition (or a weaker version thereof), we prove local linear…
We consider the problem of multi-class classification, where a stream of adversarially chosen queries arrive and must be assigned a label online. Unlike traditional bounds which seek to minimize the misclassification rate, we minimize the…
We study affine invariant 2D triangulation methods. That is, methods that produce the same triangulation for a point set $S$ for any (unknown) affine transformation of $S$. Our work is based on a method by Nielson [A characterization of an…
Motivated by a M\"obius invariant subdivision scheme for polygons, we study a curvature notion for discrete curves where the cross-ratio plays an important role in all our key definitions. Using a particular M\"obius invariant…
The idea of replacing hardware by software to compensate for scattered radiation in flat-panel X-ray imaging is well established in the literature. Recently, deep-learningbased image translation approaches, most notably the U-Net, have…
Segmentation of distinct bones plays a crucial role in diagnosis, planning, navigation, and the assessment of bone metastasis. It supplies semantic knowledge to visualisation tools for the planning of surgical interventions and the…
Interior point methods for solving linearly constrained convex programming involve a variable projection matrix at each iteration to deal with the linear constraints. This matrix often becomes ill-conditioned near the boundary of the…
This paper analyzes the structure of the set of positive solutions of a class of one-dimensional superlinear indefinite bvp's. It is a paradigm of how mathematical analysis aids the numerical study of a problem, whereas simultaneously its…
We show that for any tolerance $R$ on $U$, the ordered sets of lower and upper rough approximations determined by $R$ form ortholattices. These ortholattices are completely distributive, thus forming atomistic Boolean lattices, if and only…
Let $\mathrm{R}$ be a real closed field, and $\mathrm{D} \subset \mathrm{R}$ an ordered domain. We describe an algorithm that given as input a polynomial $P \in \mathrm{D} [ X_{1},\ldots,X_{k} ]$, and a finite set, $\mathcal{A}= \{ p_{1},…
A symmetric subset of the reals is one that remains invariant under some reflection z --> c-z. We consider, for any 0 < x <= 1, the largest real number D(x) such that every subset of $[0,1]$ with measure greater than x contains a symmetric…