相关论文: A Cayley-Menger formula for the earth mover's simp…

The so-called drag-based model (DBM) simulates analytically the propagation of coronal mass ejections (CMEs) in interplanetary space and allows the prediction of their arrival times and impact speeds at any point in the heliosphere…

Kantorovich distance (or 1-Wasserstein distance) on the probability simplex of a finite metric space is the value of a Linear Programming problem for which a closed-form expression is known in some cases. When the ground distance is defined…

We discuss a scenario of ``the path to physics at the Planck scale'' where todays theory of the interactions of elementary particles, the so called Standard Model (SM), emerges as a low energy effective theory describing the long distance…

In a recent issue of this journal, Mordukhovich et al.\ pose and solve an interesting non-differentiable generalization of the Heron problem in the framework of modern convex analysis. In the generalized Heron problem one is given $k+1$…

Magnitude homology is an $\mathbf{R}^+$-graded homology theory of metric spaces that captures information on the complexity of geodesics. Here we address the question: when are two metric spaces magnitude homology equivalent, in the sense…

We study Geometric Graph Edit Distance (GGED), a graph-editing model to compute the minimum edit distance of intersection graphs that uses moving objects as an edit operation. We first show an $O(n\log n)$-time algorithm that minimises the…

By "geodesic" we mean any sequence of vertices $(v_1,v_2,...,v_k)$ of a graph $G$ that constitute a shortest path from $v_1$ to $v_k$. We propose a novel, natural algorithm to enumerate all geodesics of $G$, and pit it (using Mathematica)…

Multiview varieties are mathematical models for the set of image feature correspondences that can be produced by a given camera arrangement. They possess an invariant known as their Euclidean distance (ED) degree, which measures the…

The inner product provides a conceptually and algorithmically simple method for calculating the comoving distance between two cosmological objects given their redshifts, right ascension and declination, and arbitrary constant curvature. The…

Sequence comparison is a basic task to capture similarities and differences between two or more sequences of symbols, with countless applications such as in computational biology. An alignment is a way to compare sequences, where a giving…

This paper presents a distance function between sets based on an average of distances between their elements. The distance function is a metric if the sets are non-empty finite subsets of a metric space. It can be applied to produce various…

We address the estimation problem for general finite mixture models, with a particular focus on the elliptical mixture models (EMMs). Compared to the widely adopted Kullback-Leibler divergence, we show that the Wasserstein distance provides…

Geometric characteristics of metric spaces that appear in formulas of the Gromov--Hausdorff distances from these spaces to so-called simplexes, i.e., to the metric spaces, all whose non-zero distances are the same are studied. The…

We establish that many fundamental concepts and techniques in quantum field theory and collider physics can be naturally understood and unified through a simple new geometric language. The idea is to equip the space of collider events with…

Most Machine Learning (ML) methods, from clustering to classification, rely on a distance function to describe relationships between datapoints. For complex datasets it is hard to avoid making some arbitrary choices when defining a distance…

Empirical Mode Decomposition(EMD) is an adaptive data analysis technique for analyzing nonlinear and nonstationary data[1]. EMD decomposes the original data into a number of Intrinsic Mode Functions(IMFs)[1] for giving better physical…

Vector similarity measures play a fundamental role in various fields, including machine learning, natural language processing, information retrieval, and data mining. These measures quantify the closeness between two vectors in a…

Starting with a similarity function between objects, it is possible to define a distance metric on pairs of objects, and more generally on probability distributions over them. These distance metrics have a deep basis in functional analysis,…

In curved spacetime, Maxwell's equations can be expressed in forms valid in Minkowski background, with the effect of the metric (gravity) appearing as effective polarizations and magnetizations. The electric and magnetic (EM) fields depend…

We present \texttt{ethraid}, an open source Python package designed to measure the mass ($m_c$) and separation ($a$) of a bound companion from measurements covering a fraction of the orbital period. \texttt{ethraid} constrains $m_c$ and $a$…