相关论文: A note on linear approximately orthogonality prese…

Given a point $s$ and a set of $h$ pairwise disjoint polygonal obstacles of totally $n$ vertices in the plane, we present a new algorithm for building an $L_1$ shortest path map of size O(n) in $O(T)$ time and O(n) space such that for any…

We introduce an algorithm of joint approximation of a function and its first derivative by alternative orthogonal polynomials on the interval [0,1].The algorithm exhibits properties of shape preserving approximation for the function. A weak…

Eigenmaps are important in analysis, geometry, and machine learning, especially in nonlinear dimension reduction. Approximation of the eigenmaps of a Laplace operator depends crucially on the scaling parameter $\epsilon$. If $\epsilon$ is…

Orthogonal graph drawings are used in applications such as UML diagrams, VLSI layout, cable plans, and metro maps. We focus on drawing planar graphs and assume that we are given an \emph{orthogonal representation} that describes the desired…

It is known, by Gelfand theory, that every commutative JB$^*$-triple admits a representation as a space of continuous functions of the form $$C_0^{\mathbb{T}}(L) = \{ a\in C_0(L) : a(\lambda t ) = \lambda a(t), \ \forall \lambda\in…

We study $\varepsilon$-stability in continuous logic. We first consider stability in a model, where we obtain a definability of types result with a better approximation than that in the literature. We also prove forking symmetry for…

Orthogonal drawings, i.e., embeddings of graphs into grids, are a classic topic in Graph Drawing. Often the goal is to find a drawing that minimizes the number of bends on the edges. A key ingredient for bend minimization algorithms is the…

The epsilon alternating least squares ($\epsilon$-ALS) is developed and analyzed for canonical polyadic decomposition (approximation) of a higher-order tensor where one or more of the factor matrices are assumed to be columnwisely…

In this paper we introduce the notion of orthogonally constant mapping in an isosceles orthogonal space and establish stability of orthogonally constant mappings. As an application, we discuss the orthogonal stability of the Pexiderized…

In the whole space $R^d$, $d\ge 2$, we study homogenization of a divergence form elliptic fourth-order operator $A_\varepsilon$ with measurable $\varepsilon$-periodic coefficients, where $\varepsilon$ is a small parameter. For the resolvent…

We study zero-temperature stability of topological phases of matter under weak time-independent perturbations. Our results apply to quantum spin Hamiltonians that can be written as a sum of geometrically local commuting projectors on a…

We study two popular ways to sketch the shortest path distances of an input graph. The first is distance preservers, which are sparse subgraphs that agree with the distances of the original graph on a given set of demand pairs. Prior work…

Recently, the stability of certain topological phases of matter under weak perturbations was proven. Here, we present a short, alternate proof of the same result. We consider models of topological quantum order for which the unperturbed…

In this paper, we establish an $\varepsilon$-regularity theorem for minimizers of an Alt-Phillips type functional subject to constraint maps. We prove that under sufficiently small energy, the minimizers exhibit regularity, and hence…

The goal of this work is to fill a gap in [Yang, SIAM J. Matrix Anal. Appl, 41 (2020), 1797--1825]. In that work, an approximation procedure was proposed for orthogonal low-rank tensor approximation; however, the approximation lower bound…

This work studies the symmetries, the associated momentum map, and relative equilibria of a mechanical system consisting of a small axisymmetric magnetic body-dipole in an also axisymmetric external magnetic field that additionally exhibits…

Let $E$ be a real Banach space. For $x,y \in E,$ we follow R.James in saying that $x$ is orthogonal to $y$ if $\|x+\alpha y\|\geq \|x\|$ for every $\alpha \in R$. We prove that every operator from $E$ into itself preserving orthogonality is…

Given an orthogonal polygon $ P $ with $ n $ vertices, the goal of the watchman route problem is finding a path $ S $ of the minimum length in $ P $ such that every point of the polygon $ P $ is visible from at least one of the point of $ S…

The problem of computing the smallest fixed point of an order-preserving map arises in the study of zero-sum positive stochastic games. It also arises in static analysis of programs by abstract interpretation. In this context, the discount…

Given an initial placement of a set of rectangles in the plane, we consider the problem of finding a disjoint placement of the rectangles that minimizes the area of the bounding box and preserves the orthogonal order i.e.\ maintains the…