Related papers: Minimum Orbital Intersection Distance: Asymptotic …
We develop a formalism for calculating probabilities for the outcomes of stellar dynamical interactions, based on results from $N$-body scattering experiments. We focus here on encounters involving up to six particles and calculate…
Fast computational method for Hertzian contact theory is proposed. An incremental formula is introduced to calculate the ellipticity of the contact disk when two elastic bodies are in contact. This method can determine the ellipticity with…
Weighting methods are widely used to adjust for covariates in observational studies, sample surveys, and regression settings. In this paper, we study a class of recently proposed weighting methods which find the weights of minimum…
We initiate the study of diameter computation in geometric intersection graphs from the fine-grained complexity perspective. A geometric intersection graph is a graph whose vertices correspond to some shapes in $d$-dimensional Euclidean…
For given system dynamics, observer structure, and observer-based fault/attack detection procedure, we provide mathematical tools -- in terms of Linear Matrix Inequalities (LMIs) -- for computing outer ellipsoidal bounds on the set of…
In real-world applications of mobile robots, collision avoidance is of critical importance. Typically, global motion planning in constrained environments is addressed through high-level control schemes. However, additionally integrating…
In the first paper of this series we examined existing methods of optical meteor trajectory estimation and developed a novel method which simultaneously uses both the geometry and the dynamics of meteors to constrain their trajectories. We…
Radiative transfer (RT) simulations are a powerful tool that enables the calculation of synthetic images of a wide range of astrophysical objects. These simulations are often based on the Monte Carlo (MC) method, as it provides the needed…
A minimum Manhattan distance (MMD) approach to multiple criteria decision making in multiobjective optimization problems (MOPs) is proposed. The approach selects the final solution corresponding with a vector that has the MMD from a…
We provide a spectrum of new theoretical insights and practical results for finding a Minimum Dilation Triangulation (MDT), a natural geometric optimization problem of considerable previous attention: Given a set $P$ of $n$ points in the…
Current state-of-the-art multi-objective optimization solvers, by computing gradients of all $m$ objective functions per iteration, produce after $k$ iterations a measure of proximity to critical conditions that is upper-bounded by…
Typically we can deliver astrometric positions of natural satellites with errors in the 50-150 mas range. Apparent distances from mutual phenomena, have much smaller errors, less than 10 mas. However, this method can only be applied during…
This paper considers estimation and inference in semiparametric econometric models. Standard procedures estimate the model based on an independence restriction that induces a minimum distance between a joint cumulative distribution function…
The minimum-time path for intercepting a moving target with a prescribed impact angle is studied in the paper. The candidate paths from Pontryagin's maximum principle are analyzed, so that each candidate is related to a zero of a…
We present an efficient algorithm to compute tight upper bounds of collision probability between two objects with positional uncertainties, whose error distributions are represented with non-Gaussian forms. Our approach can handle noisy…
When dealing with an orbit determination problem, uncertainties naturally arise from intrinsic errors related to observation devices and approximation models. Following the least squares method and applying approximation schemes such as the…
By employing the closest point method, we extend the applicability of minimizing movements to the surface PDE setting. The corresponding approximation methods are created, and their convergence is observed. The numerical methods are then…
A method to compute optimal collision avoidance maneuvers for short-term encounters is presented. The maneuvers are modeled as multiple-impulses to handle impulsive cases and to approximate finite burn arcs associated either with short…
A numerical integration method for guiding-center orbits of charged particles in toroidal fusion devices with three-dimensional field geometry is described. Here, high order interpolation of electromagnetic fields in space is replaced by a…
Efficient comparison of spherical probability distributions becomes important in fields such as computer vision, geosciences, and medicine. Sliced optimal transport distances, such as spherical and stereographic spherical sliced Wasserstein…