Related papers: How to measure spatial distances?
Ideal rods and clocks are defined as an infinitesimal symmetry of the spacetime. Since no a priori geometric structure is considered, all the possible models of spacetime are obtained.
A spherically symmetric and static metric that describes physical coordinates is introduced. It is defined to be a metric that gives coordinate independent results for physically observable quantities without a further coordinate…
Spatial approximations have been traditionally used in spatial databases to accelerate the processing of complex geometric operations. However, approximations are typically only used in a first filtering step to determine a set of candidate…
Many classical geometric inequalities on functionals of convex bodies depend on the dimension of the ambient space. We show that this dimension dependence may often be replaced (totally or partially) by different symmetry measures of the…
The most useful data mining primitives are distance measures. With an effective distance measure, it is possible to perform classification, clustering, anomaly detection, segmentation, etc. For single-event time series Euclidean Distance…
Time serie classification is used in a diverse range of domain such as meteorology, medicine and physics. It aims to classify chronological data. Many accurate approaches have been built during the last decade and shapelet transformation is…
This paper presents a general approach for measuring distances between board games within the Ludii general game system. These distances are calculated using a previously published set of general board game concepts, each of which…
Temporal information conveyed by language describes how the world around us changes through time. Events, durations and times are all temporal elements that can be viewed as intervals. These intervals are sometimes temporally related in…
The concepts of similarity and distance are crucial in data mining. We consider the problem of defining the distance between two data sets by comparing summary statistics computed from the data sets. The initial definition of our distance…
The physics associated with spherically symmetric charged black holes is analyzed from the point of view of using weak gravitational lensing as a means for determining the dimensionality of spacetime. In particular, for exact solutions of…
Using only the principle of relativity and Euclidean geometry we show in this pedagogical article that the square of proper time or length in a two-dimensional spacetime diagram is proportional to the Euclidean area of the corresponding…
When are two collider events similar? Despite the simplicity and generality of this question, there is no established notion of the distance between two events. To address this question, we develop a metric for the space of collider events…
A labeled metric space is intuitively speaking a metric space together with a special set of points to be understood as the geometric boundary of the space. We study basic properties of a recently introduced labeled Gromov-Hausdorff…
Consider a stationary agent A at an unknown location and a mobile agent B that must move to the vicinity of and then circumnavigate A at a prescribed distance from A. In doing so, B can only measure its distance from A, and knows its own…
Recognizing spatial relations and reasoning about them is essential in multiple applications including navigation, direction giving and human-computer interaction in general. Spatial relations between objects can either be explicit --…
A coordinate system is proposed that replaces the usual three-dimensional Cartesian x,y,z position coordinates, for use in robotic localization applications. Range, azimuth, and elevation measurement models become greatly simplified, and,…
We propose a definition of magnitude for a length space with a Borel measure, which involves integrals over the set of geodesics. This quantity agrees with the magnitude of finite metric spaces, up to re-scaling the metric to ensure the…
Operational definition of space-time in light of quantum mechanics and general relativity inevitably indicates an intrinsic imprecision in space-time structure which has to do with space-time dimension as well. The operational dimension of…
Timelike geodesics on a hyperplane orthogonal to the symmetry axis of the G\"odel spacetime appear to be elliptic-like if standard coordinates naturally adapted to the cylindrical symmetry are used. The orbit can then be suitably described…
The definition of weighted distance measure involves weights. The paper proposes a weighted distance measure without the help of weights. Here, weights are intrinsically added to the measure, and for this, the concept of metric space is…