Related papers: Approximation of Set-Valued Functions with images …
Approximation of entire functions by their pad\'e approximants has been examined in the past. It is true that generically such an approximation holds. However, examining this problem from another viewpoint, we obtain stronger generic…
Many combinatorial optimization problems can be formulated as the search for a subgraph that satisfies certain properties and minimizes the total weight. We assume here that the vertices correspond to points in a metric space and can take…
A common problem encountered in many real-world applications is level set estimation where the goal is to determine the region in the function domain where the function is above or below a given threshold. When the function is black-box and…
We study the approximate fixed point property (AFPP) for continuous single-valued functions and for continuous multivalued functions in digital topology. We extend what is known about these notions and discuss errors that have appeared in…
In this paper we consider the coupled task scheduling problem with exact delay times on a single machine with the objective of minimizing the total completion time of the jobs. We provide constant-factor approximation algorithms for several…
Scene graphs are a powerful structured representation of the underlying content of images, and embeddings derived from them have been shown to be useful in multiple downstream tasks. In this work, we employ a graph convolutional network to…
We show that in finite-dimensional nonlinear approximations, the best $r$-term approximant of a function $f$ almost always exists over $\mathbb{C}$ but that the same is not true over $\mathbb{R}$, i.e., the infimum $\inf_{f_1,\dots,f_r \in…
Many computer vision and human-computer interaction applications developed in recent years need evaluating complex and continuous mathematical functions as an essential step toward proper operation. However, rigorous evaluation of this kind…
In this article we treat a notion of continuity for a multi-valued function $F$ and we compute the descriptive set-theoretic complexity of the set of all $x$ for which $F$ is continuous at $x$. We give conditions under which the latter set…
Algorithms for listing the subgraphs satisfying a given property (e.g.,being a clique, a cut, a cycle, etc.) fall within the general framework of set systems. A set system (U, F) uses a ground set U (e.g., the network nodes) and an…
Let $U\subseteq\mathbb{R}^d$ be open and convex. We prove that every (not necessarily Lipschitz or strongly) convex function $f:U\to\mathbb{R}$ can be approximated by real analytic convex functions, uniformly on all of $U$. We also show…
Randomized methods of neural network learning suffer from a problem with the generation of random parameters as they are difficult to set optimally to obtain a good projection space. The standard method draws the parameters from a fixed…
We consider functions $f$ of two real variables, given as trigonometric functions over a finite set $F$ of frequencies. This set is assumed to be closed under rotations in the frequency plane of angle $\frac{2k\pi}{M}$ for some integer $M$.…
The zero locus of a function f on a graph G is defined as the graph with vertex set consisting of all complete subgraphs of G, on which f changes sign and where x,y are connected if one is contained in the other. For d-graphs, finite simple…
We consider the problem of exact reconstruction of univariate functions with jump discontinuities at unknown positions from their moments. These functions are assumed to satisfy an a priori unknown linear homogeneous differential equation…
We consider a recently introduced fair repetitive scheduling problem involving a set of clients, each asking for their associated job to be daily scheduled on a single machine across a finite planning horizon. The goal is to determine a job…
Ordered matchings, defined as graphs with linearly ordered vertices, where each vertex is connected to exactly one edge, play a crucial role in the area of ordered graphs and their homomorphisms. Therefore, we consider related problems from…
We consider the problem of approximating a given matrix by a low-rank matrix so as to minimize the entrywise $\ell_p$-approximation error, for any $p \geq 1$; the case $p = 2$ is the classical SVD problem. We obtain the first provably good…
We consider the problem of approximating a given element $f$ from a Hilbert space $\mathcal{H}$ by means of greedy algorithms and the application of such procedures to the regression problem in statistical learning theory. We improve on the…
The motivation of this paper is the development of an optimisation method for solving optimisation problems appearing in Chebyshev rational and generalised rational approximation problems, where the approximations are constructed as ratios…