Related papers: How to measure spatial distances?
Spatial statistics is an area of study devoted to the statistical analysis of data that have a spatial label associated with them. Geographers often refer to the "location information" associated with the "attribute information," whose…
The aim of this contribution is twofold. First, we show that when two (or more) different quantum groups share the same noncommutative spacetime, such an 'ambiguity' can be resolved by considering together their corresponding noncommutative…
It is known that for a variety of choices of metrics, including the standard bottleneck distance, the space of persistence diagrams admits geodesics. Typically these existence results produce geodesics that have the form of a convex…
With growing success in experimental implementations it is critical to identify a "gold standard" for quantum information processing, a single measure of distance that can be used to compare and contrast different experiments. We enumerate…
The dynamic time scan forecasting method relies on the premise that the most important pattern in a time series precedes the forecasting window, i.e., the last observed values. Thus, a scan procedure is applied to identify similar patterns,…
We find an upper bound for geodesic distances associated to monotone Riemannian metrics on positive definite matrices and density matrices.
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 overview the theory of classical MDS, along with its…
In algorithms for finite metric spaces, it is common to assume that the distance between two points can be computed in constant time, and complexity bounds are expressed only in terms of the number of points of the metric space. We…
This article concerns a class of metric spaces, which we call multigeodesic spaces, where between any two distinct points there exist multiple distinct minimising geodesics. We provide a simple characterisation of multigeodesic normed…
Friedrich's proofs for the global existence results of de Sitter-like space-times and of semi-global existence of Minkowski-like space-times [Comm. Math. Phys. \textbf{107}, 587 (1986)] are re-examined and discussed, making use of the…
Geometry and topology have generated impacts far beyond their pure mathematical primitive, providing a solid foundation for many applicable tools. Typically, real-world data are represented as vectors, forming a linear subspace for a given…
We give sufficient conditions for a finite metric space to be determined by the magnitude function. In particular, a generic finite metric space such that the distances between the points are rationally independent is determined by the…
A convenient approach to analyze spatial infinity is to use a cylinder representation $I$ and impose a gauge based on a congruence of conformal geodesics. This so-called conformal Gauss gauge comes along with the freedom to specify initial…
The purpose of this letter is to define a distance on the underlying phase space of a chaotic map, based on natural invariant density of the map. It is observed that for logistic map this distance is equivalent to Wootters' statistical…
The potential of gravitational lenses for providing direct, physical measurements of the Hubble constant, free from systematic errors associated with the traditional distance ladder, has long been recognized. However, it is only recently…
We define the notion of near geodesic between points of a metric space when no geodesic exists, and use this to extend Recio-Mitter's notion of geodesic complexity to non-geodesic spaces. This has potential application to topological…
Several physical problems such as the `twin paradox' in curved spacetimes have purely geometrical nature and may be reduced to studying properties of bundles of timelike geodesics. The paper is a general introduction to systematic…
We consider a Lorentzian metric in $\mathbb{R}\times\mathbb{R}^n$. We show that if we know the lengths of the space-time geodesics starting at $(0,y,\eta)$ when $t=0$, then we can recover the metric at $y$. We prove the rigidity of…
Rectangles are used to approximate objects, or sets of objects, in a plethora of applications, systems and index structures. Many tasks, such as nearest neighbor search and similarity ranking, require to decide if objects in one rectangle A…
Clock synchronization is the backbone of applications such as high-accuracy satellite navigation, geolocation, space-based interferometry, and cryptographic communication systems. The high accuracy of synchronization needed over…