Related papers: Relative Squared Distances to a Conic Berserkless …
We extend our previous algorithm computing the minimum orbital intersection distance (MOID) to include hyperbolic orbits, and mixed combinations ellipse--hyperbola. The MOID is computed by finding all stationary points of the distance…
Invariant linearization criteria of square systems of second-order quadratically semi-linear ordinary differential equations (ODEs) that can be represented as geodesic equations are extended to square systems of ODEs cubically nonlinear in…
The increasing congestion in the near-Earth space environment has amplified the need for robust and efficient conjunction analysis techniques including the computation of the minimum distance between orbital paths in the presence of…
The distance transform algorithm is popular in computer vision and machine learning domains. It is used to minimize quadratic functions over a grid of points. Felzenszwalb and Huttenlocher (2004) describe an O(N) algorithm for computing the…
Recent research on computing the diameter of geometric intersection graphs has made significant strides, primarily focusing on the 2D case where truly subquadratic-time algorithms were given for simple objects such as unit-disks and…
We consider the problem of estimating the distance, or range, between two locations by measuring the phase of multiple sinusoidal signals transmitted between the locations. Traditional estimators developed for optical interferometry include…
Multidimensional scaling (MDS) is a popular technique for mapping a finite metric space into a low-dimensional Euclidean space in a way that best preserves pairwise distances. We study a notion of MDS on infinite metric measure spaces,…
We consider a linear ill-posed equation in the Hilbert space setting. Multiple independent unbiased measurements of the right hand side are available. A natural approach is to take the average of the measurements as an approximation of the…
The minimum orbital intersection distance is used as a measure to assess potential close approaches and collision risks between astronomical objects. Methods to calculate this quantity have been proposed in several previous publications.…
Among fundamental problems in the context of distributed computing by autonomous mobile entities, one of the most representative and well studied is {\sc Point Convergence}: given an arbitrary initial configuration of identical entities,…
Most existing out-of-distribution (OOD) detection benchmarks classify samples with novel labels as the OOD data. However, some marginal OOD samples actually have close semantic contents to the in-distribution (ID) sample, which makes…
Many Gibbs measures with mean field interactions are known to be chaotic, in the sense that any collection of $k$ particles in the $n$-particle system are asymptotically independent, as $n\to\infty$ with $k$ fixed or perhaps $k=o(n)$. This…
Inverse Optimal Control (IOC) aims to infer the underlying cost functional of an agent from observations of its expert behavior. This paper focuses on the IOC problem within the continuous-time linear quadratic regulator framework,…
Detecting out-of-distribution (OOD) instances is crucial for the reliable deployment of machine learning models in real-world scenarios. OOD inputs are commonly expected to cause a more uncertain prediction in the primary task; however,…
The ability of a deep learning network to distinguish between in-distribution (ID) and out-of-distribution (OOD) inputs is crucial for ensuring the reliability and trustworthiness of AI systems. Existing OOD detection methods often involve…
Recently, 4D millimetre-wave radar exhibits more stable perception ability than LiDAR and camera under adverse conditions (e.g. rain and fog). However, low-quality radar points hinder its application, especially the odometry task that…
Inclusion-based (i.e., Andersen-style) points-to analysis is a fundamental static analysis problem. The seminal work of Andersen gave a worst-case cubic $O(n^3)$ time points-to analysis algorithm for C, where $n$ is proportional to the…
Many statistical and machine learning approaches rely on pairwise distances between data points. The choice of distance metric has a fundamental impact on performance of these procedures, raising questions about how to appropriately…
We study the extreme and the periodic $L_p$ discrepancy of point sets in the $d$-dimensional unit cube. The extreme discrepancy uses arbitrary sub-intervals of the unit cube as test sets, whereas the periodic discrepancy is based on…
Out-of-distribution (OOD) detection seeks to identify samples from unknown classes, a critical capability for deploying machine learning models in open-world scenarios. Recent research has demonstrated that Vision-Language Models (VLMs) can…