Related papers: Planar additive bases for rectangles
It's well know that Radial Basis Function approximants suffers of bad conditioning if the simple basis of translates is used. A recent work of M.Pazouki and R.Schaback gives a quite general way to build stable, orthonormal bases for the…
We explore various techniques for counting the number of straight-edge crossing-free graphs that can be embedded on a planar point set. In particular, we derive a lower bound on the ratio of the number of such graphs with $m+1$ edges to the…
The main goal of this paper is to generalize several results concerning cardinal invariants to the statements about the associated families of sets. We also discuss the relationship between the additive properties of sets and their Borel…
We study the existence of scalar fields outside neutral reflecting shells. We consider static massive scalar fields non-minimally coupled to the Gauss-Bonnet invariant. We analytically investigated properties of scalar fields through the…
For a positive integer $t$ and a graph $G$, an additive $t$-spanner of $G$ is a spanning subgraph in which the distance between every pair of vertices is at most the original distance plus $t$. Minimum Additive $t$-Spanner Problem is to…
Metaplectic quantum basis is a universal multi-qutrit quantum basis, formed by the ternary Clifford group and the axial reflection gate $R=|0\rangle \langle 0| + |1\rangle \langle 1| - |2\rangle \langle 2|$. It is arguably, a ternary basis…
Given an arbitrary basis for a mathematical lattice, to find a ``good" basis for it is one of the classic and important algorithmic problems. In this note, we give a new and simpler proof of a theorem by Regavim (arXiv:2106.03183): we…
This paper introduces the first minimal solvers that jointly estimate lens distortion and affine rectification from the image of rigidly-transformed coplanar features. The solvers work on scenes without straight lines and, in general, relax…
Additive regression models are actively researched in the statistical field because of their usefulness in the analysis of responses determined by non-linear relationships with multivariate predictors. In this kind of statistical models,…
Many data-analysis problems involve large dense matrices that describe the covariance of stationary noise processes; the computational cost of inverting these matrices, or equivalently of solving linear systems that contain them, is often a…
We propose a new shape-based modeling technique for applications in imaging problems. Given a collection of shape priors (a shape dictionary), we define our problem as choosing the right dictionary elements and geometrically composing them…
A classical problem in the literature seeks the minimal number of proper subgroups whose union is a given finite group. A different question, with applications to error-correcting codes and graph colorings, involves covering vector spaces…
In 1989, Ne\v{s}et\v{r}il and Pudl\'ak posed the following challenging question: Do planar posets have bounded Boolean dimension? We show that every poset with a planar cover graph and a unique minimal element has Boolean dimension at most…
Multicriteria Decision Making problems are important both for individuals and groups. Pairwise comparisons have become popular in the theory and practice of preference modelling and quantification. We focus on decision problems where the…
Parity compilation is the challenge of laying out the required constraints for the parity mapping in a local way. We present the first constructive compilation algorithm for the parity architecture using plaquettes for arbitrary…
We study the two dimensional least gradient problem in a convex polygonal set in the plane. We show existence of solutions when the boundary data are attained in the trace sense. Due to the lack of strict convexity, the classical results…
In this paper we study the following problem: Given $k$ disjoint sets of points, $P_1, \ldots, P_k$ on the plane, find a minimum cardinality set $\mathcal{T}$ of arbitrary rectangles such that each rectangle contains points of just one set…
There exists a set $A$ of positive integers such that the number of representations of a large positive integer $m$ as a sum of two elements of $A$ grows with a lower bound of order $\log m$, but for which there is no subset $D$ of $A$…
As a typical application, the Lenstra-Lenstra-Lovasz lattice basis reduction algorithm (LLL) is used to compute a reduced basis of the orthogonal lattice for a given integer matrix, via reducing a special kind of lattice bases. With such…
In this paper we consider a family of algorithms for approximate implicitization of rational parametric curves and surfaces. The main approximation tool in all of the approaches is the singular value decomposition, and they are therefore…