Related papers: Bounds for discrete tomography solutions
A variety of boundary value problems in linear transport theory are expressed as a diffusion equation of the two-way, or forward-backward, type. In such problems boundary data are specified only on part of the boundary, which introduces…
We apply duality theory to discretized convex minimization problems to obtain computable guaranteed upper bounds for the distance of given discrete functions and the exact discrete minimizer. Furthermore, we show that the discrete duality…
A solution manifold is the collection of points in a $d$-dimensional space satisfying a system of $s$ equations with $s<d$. Solution manifolds occur in several statistical problems including hypothesis testing, curved-exponential families,…
Multidimensional continuous-domain inverse problems are often solved by the minimization of a loss functional, formed as the sum of a data fidelity and a regularization. In this work, we present a new construction where the regularization…
An approach is proposed for bounding the number of zeros that solutions of linear differential systems with polynomial coefficients may have. A bound is obtained in a special case which improves upon currently existing.
This work proposes a nonlinear finite element method whose nodal values preserve bounds known for the exact solution. The discrete problem involves a nonlinear projection operator mapping arbitrary nodal values into bound-preserving ones…
Line spectral estimation is a classical signal processing problem that aims to estimate the line spectra from their signal which is contaminated by deterministic or random noise. Despite a large body of research on this subject, the…
We consider the problem of approximating a two-dimensional shape contour (or curve segment) using discrete assembly systems, which allow to build geometric structures based on limited sets of node and edge types subject to edge length and…
The reach of a submanifold of $\mathbb{R}^N$ is defined as the largest radius of a tubular neighbourhood around the submanifold that avoids self-intersections. While essential in geometric and topological applications, computing the reach…
We derive a mixed integer nonlinear programming formulation for the problem of finding a convex polygon with a given number of vertices that is small (diameter at most one) and has maximum perimeter. The formulation is based on a geometric…
We address the restriction problem for viscosity subsolutions of a fully nonlinear PDE on a manifold Z. The constraints on the restrictions of smooth subsolutions to a submanifold X in Z determine a restricted subequation on X. The problem…
This paper aims to develop and analyze a numerical scheme for solving the backward problem of semilinear subdiffusion equations. We establish the existence, uniqueness, and conditional stability of the solution to the inverse problem by…
In distance query reconstruction, we wish to reconstruct the edge set of a hidden graph by asking as few distance queries as possible to an oracle. Given two vertices $u$ and $v$, the oracle returns the shortest path distance between $u$…
We give a sharp lower bound to the largest possible Euclidean norm of signed sums of $n$ vectors in the plane. This is achieved by connecting the signed vector sum problem to the isoperimetric problem for the circumradius of polygons. In…
We introduce a novel type of approximation spaces for functions with values in a nonlinear manifold. The discrete functions are constructed by piecewise polynomial interpolation in a Euclidean embedding space, and then projecting pointwise…
Delsarte's method and its extensions allow to consider the upper bound problem for codes in 2-point-homogeneous spaces as a linear programming problem with perhaps infinitely many variables, which are the distance distribution. We show that…
Estimating the number of vertices of a two dimensional projection, called a shadow, of a polytope is a fundamental tool for understanding the performance of the shadow simplex method for linear programming among other applications. We prove…
A joint of a set of lines $\mathcal{L}$ in $\mathbb{F}^d$ is a point that is contained in $d$ lines with linearly independent directions. The joints problem asks for the maximum number of joints that are formed by $L$ lines. Guth and Katz…
This article firstly develops a proximal explicit approach for the generalized method of lines. In such a method, the domain of the PDE in question is discretized in lines and the equation solution is written on these lines as functions of…
The curvature regularities are well-known for providing strong priors in the continuity of edges, which have been applied to a wide range of applications in image processing and computer vision. However, these models are usually non-convex,…