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The optimal transport problem has many applications in machine learning, physics, biology, economics, etc. Although its goal is very clear and mathematically well-defined, finding its optimal solution can be challenging for large datasets…
Let $\mathscr O$ be a set of $n$ disjoint obstacles in $\mathbb{R}^2$, $\mathscr M$ be a moving object. Let $s$ and $l$ denote the starting point and maximum path length of the moving object $\mathscr M$, respectively. Given a point $p$ in…
Black holes represent extreme conditions of physical laws. Being predicted about a century ago, they are now accepted as astrophysical reality by most of the scientific community. Only recently more direct evidence of their existence has…
We propose a new search strategy for high-multiplicity hadronic final states. When new particles are produced at threshold, the distribution of their decay products is approximately isotropic. If there are many partons in the final state,…
Close planetary flybys are frequently employed as a technique to place spacecraft on extreme solar system trajectories that would otherwise require much larger booster vehicles or may not even be feasible when relying solely on chemical…
We study a fundamental cooperative message-delivery problem on the plane. Assume $n$ robots which can move in any direction, are placed arbitrarily on the plane. Robots each have their own maximum speed and can communicate with each other…
One of the most challenging tasks for a flying robot is to autonomously navigate between target locations quickly and reliably while avoiding obstacles in its path, and with little to no a-priori knowledge of the operating environment. This…
We address the 'plane of satellites problem' by studying planar configurations around two disc galaxies with no late major mergers, formed in zoom-in hydro-simulations. Due to the current lack of good quality kinematic data for M31…
The observed population of the Milky Way satellite galaxies offer a unique testing ground for galaxy formation theory on small-scales. Our novel approach was to investigate the clustering of the known Milky Way satellite galaxies and to…
Search-based motion planning algorithms have been widely utilized for unmanned aerial vehicles (UAVs). However, deploying these algorithms on real UAVs faces challenges due to limited onboard computational resources. The algorithms struggle…
As air traffic volume is continuously increasing, it has become a priority to improve traffic control algorithms to handle future air travel demand and improve airspace capacity. We address the conflict resolution problem in air traffic…
Most of the routing algorithms for unmanned vehicles, that arise in data gathering and monitoring applications in the literature, rely on the Global Positioning System (GPS) information for localization. However, disruption of GPS signals…
How well do multisymplectic discretisations preserve travelling wave solutions? To answer this question, the 5-point central difference scheme is applied to the semi-linear wave equation. A travelling wave ansatz leads to an ordinary…
A decade ago cosmological simulations of increasingly higher resolution were used to demonstrate that virialized regions of Cold Dark Matter (CDM) halos are filled with a multitude of dense, gravitationally-bound clumps. These dark matter…
Satellite conjunction analysis is the assessment of collision risk during a close encounter between a satellite and another object in orbit. A counterintuitive phenomenon has emerged in the conjunction analysis literature, namely,…
We present a novel predict-then-optimize framework for maritime search operations that integrates trajectory forecasting with UAV deployment optimization-an end-to-end approach not addressed in prior work. A large language model predicts…
In this paper, we study the trajectory optimization of a cellular-connected unmanned aerial vehicle (UAV) which aims to sense the location of a target while maintaining satisfactory communication quality with the ground base stations…
This letter presents a new spectral-clustering-based approach to the subspace clustering problem. Underpinning the proposed method is a convex program for optimal direction search, which for each data point d finds an optimal direction in…
The research project has been made for mathematical modeling of aerospace system Space-to-Surface for avoid intercepting process by flight objects Surface-to-Air. The research has been completed and created mathematical models which used…
This paper presents a new connectivity condition on the information flow between UAVs to achieve coordinated path following. The information flow is directional, so that the underlying communication network topology is represented by a…