相关论文: Robust formula for $N$-point Pad\'e approximant ca…

In the maximum coverage problem, we are given subsets $T_1, \ldots, T_m$ of a universe $[n]$ along with an integer $k$ and the objective is to find a subset $S \subseteq [m]$ of size $k$ that maximizes $C(S) := \Big|\bigcup_{i \in S}…

We design new approximation algorithms for the Multiway Cut problem, improving the previously known factor of 1.32388 [Buchbinder et al., 2013]. We proceed in three steps. First, we analyze the rounding scheme of Buchbinder et al., 2013 and…

In this study, novel physics-informed neural network (PINN) methods for coupling neighboring support points and their derivative terms which are obtained by automatic differentiation (AD), are proposed to allow efficient training with…

A method for detecting and approximating fault lines or surfaces, respectively, or decision curves in two and three dimensions with guaranteed accuracy is presented. Reformulated as a classification problem, our method starts from a set of…

We propose a method for finding approximate solutions to multiple-choice knapsack problems. To this aim we transform the multiple-choice knapsack problem into a bi-objective optimization problem whose solution set contains solutions of the…

We present a new method for approximating real-valued functions on ${\mathbb R}^+$ by linear combinations of exponential functions with complex coefficients. The approach is based on a multi-point Pad\'e approximation of the Laplace…

We discuss some topics concerning rational approximations in Quantum Chromodynamics, especially those related with the mathematical theory of Pad\'e Approximants. We focus on two kind of problems: the first one related with meromorphic…

This work discusses the main analogies and differences between the deterministic approach underlying most cosmological N-body simulations and the probabilistic interpretation of the problem that is often considered in mathematics and…

The inspiral of two compact objects in gravitational wave astronomy is described by a post-Newtonian expansion in powers of $(v/c)$. In most cases, it is believed that the post-Newtonian expansion is asymptotically divergent. A standard…

Interior-point methods offer a highly versatile framework for convex optimization that is effective in theory and practice. A key notion in their theory is that of a self-concordant barrier. We give a suitable generalization of…

The expression for the Debye shielding in plasma physics is usually derived under the assumptions that the plasma particles are weakly coupled, so their kinetic energy is much larger than the potential energy between them, and that the…

Well--defined criteria are proposed for assessing the accuracy of quantum master equations whose memory functions are approximated by Pad\'e resummation of the first two moments in the electronic coupling. These criteria partition the…

We consider the problem of identifying n points in the plane using disks, i.e., minimizing the number of disks so that each point is contained in a disk and no two points are in exactly the same set of disks. This problem can be seen as an…

Each non-zero point in $\mathbb{R}^d$ identifies a closest point $x$ on the unit sphere $\mathbb{S}^{d-1}$. We are interested in computing an $\epsilon$-approximation $y \in \mathbb{Q}^d$ for $x$, that is exactly on $\mathbb{S}^{d-1}$ and…

Recently, it has been great interest in the development of methods for solving nonlinear differential equations directly. Here, it is shown an algorithm based on Pad\'e approximants for solving nonlinear partial differential equations…

Building on previous Bayesian approaches, we introduce a novel formulation of probabilistic cross-identification, where detections are directly associated to (hypothesized) astronomical objects in a globally optimal way. We show that this…

The problem of principle component analysis (PCA) is traditionally solved by spectral or algebraic methods. We show how computing the leading principal component could be reduced to solving a \textit{small} number of well-conditioned {\it…

Given n elements with nonnegative integer weights w1,..., wn and an integer capacity C, we consider the counting version of the classic knapsack problem: find the number of distinct subsets whose weights add up to at most the given…

The focus in this paper is interior-point methods for bound-constrained nonlinear optimization, where the system of nonlinear equations that arise are solved with Newton's method. There is a trade-off between solving Newton systems…

We study the approximability of two related problems on graphs with $n$ nodes and $m$ edges: $n$-Pairs Shortest Paths ($n$-PSP), where the goal is to find a shortest path between $O(n)$ prespecified pairs, and All Node Shortest Cycles…