Related papers: Fast error-safe MOID computation involving hyperbo…
This paper presents an a priori error analysis of the Deep Mixed Residual method (MIM) for solving high-order elliptic equations with non-homogeneous boundary conditions, including Dirichlet, Neumann, and Robin conditions. We examine MIM…
A fundamental problem in robotic perception is matching identical objects or data, with applications such as loop closure detection, place recognition, object tracking, and map fusion. While the problem becomes considerably more challenging…
We demonstrate the remarkable effectiveness of boundary value formulations coupled to numerical continuation for the computation of stable and unstable manifolds in systems of ordinary differential equations. Specifically, we consider the…
In this paper, a novel technique for tight outer-approximation of the intersection region of a finite number of ellipses in 2-dimensional (2D) space is proposed. First, the vertices of a tight polygon that contains the convex intersection…
We study orbits near collision in a non-autonomous restricted planar four-body problem. This restricted problem consists of a massless particle moving under the gravitational influence due to three bodies following the figure-eight…
We demonstrate a new approach to the computation of ratios of elliptic integrals. It turns out that almost closed polygons interscribed between two conics retain some of the properties of such closed polygons. We apply these retained…
Most existing distance metric learning methods assume perfect side information that is usually given in pairwise or triplet constraints. Instead, in many real-world applications, the constraints are derived from side information, such as…
Trajectory optimization of low-thrust perturbed orbit rendezvous is a crucial technology for space missions in low Earth orbits, which is difficult to solve due to its initial value sensitivity, especially when the transfer trajectory has…
Slow manifolds are important geometric structures in the state spaces of dynamical systems with multiple time scales. This paper introduces an algorithm for computing trajectories on slow manifolds that are normally hyperbolic with both…
We compute minimal bases of solutions for a general interpolation problem, which encompasses Hermite-Pad\'e approximation and constrained multivariate interpolation, and has applications in coding theory and security. This problem asks to…
We consider fast algorithms for monotone submodular maximization with a general matroid constraint. We present a randomized $(1 - 1/e - \epsilon)$-approximation algorithm that requires $\tilde{O}_{\epsilon}(\sqrt{r} n)$ independence oracle…
Initial orbit determination (IOD) is an important early step in the processing chain that makes sense of and reconciles the multiple optical observations of a resident space object. IOD methods generally operate on line-of-sight (LOS)…
In this work, we use algebraic methods for studying distance computation and subgraph detection tasks in the congested clique model. Specifically, we adapt parallel matrix multiplication implementations to the congested clique, obtaining an…
We study the complexity of approximating the multimarginal optimal transport (MOT) distance, a generalization of the classical optimal transport distance, considered here between $m$ discrete probability distributions supported each on $n$…
The Circular Restricted Three-Body Problem (CR3BP) models the motion of a massless body under the gravitational influence of two primaries. We present a method for approximating a given family of periodic orbits by low-degree implicit…
This paper gives simple distributed algorithms for the fundamental problem of computing graph distances in the Congested Clique model. One of the main components of our algorithms is fast matrix multiplication, for which we show an…
The problem of finding the distance from a given $n \times n$ matrix polynomial of degree $k$ to the set of matrix polynomials having the elementary divisor $(\lambda-\lambda_0)^j, \, j \geqslant r,$ for a fixed scalar $\lambda_0$ and $2…
In this work, we propose a method to efficiently compute smooth, time-optimal trajectories for micro aerial vehicles (MAVs) evading a moving obstacle. Our approach first computes an n-dimensional trajectory from the start- to an arbitrary…
The hyperbolic MBO is a threshold dynamic algorithm which approximates interfacial motion by hyperbolic mean curvature flow. We introduce a generalization of this algorithm for imparting damping terms onto the equation of motion. We also…
We present a novel algorithm for (i) detecting approximate symmetries inherently present among spatially localized molecular orbitals and (ii) enforcing these in numerically exact manners by means of unitary optimization techniques. The…