Related papers: An open day in the metric space
In this paper, a new structure is defined on a topological space that equips the space with a concept of distance in order to do that firstly, a generalization of quasi-pseudo-metric space named R.O-metric space is introduced, and some of…
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…
In the literature, there have been several methods and definitions for working out if two theories are "equivalent" (essentially the same) or not. In this article, we do something subtler. We provide means to measure distances (and explore…
We developed a two-day physics class that uses a nearby forest as a teaching location. Using low-cost material, students design and carry out physics projects outside of the usual controlled environment that is a classroom. In this way they…
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…
In this paper, we propose a generalized notion of a distance function, called a $g$-metric. The $g$-metric with degree $n$ is a distance of $n+1$ points, generalizing the ordinary distance between two points and $G$-metric between three…
Size and distance perception in Virtual Reality (VR) have been widely studied, albeit in a controlled laboratory setting with a small number of participants. We describe a fully remote perceptual study with a gamified protocol to encourage…
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…
We set up a model for reasoning about metric spaces with belief theoretic measures. The uncertainty in these spaces stems from both probability and metric. To represent both aspect of uncertainty, we choose an expected distance function as…
We propose a novel measure of statistical depth, the metric spatial depth, for data residing in an arbitrary metric space. The measure assigns high (low) values for points located near (far away from) the bulk of the data distribution,…
The cognitive framework of conceptual spaces [3] provides geometric means for representing knowledge. A conceptual space is a high-dimensional space whose dimensions are partitioned into so-called domains. Within each domain, the Euclidean…
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…
Finite metric spaces arise in many different contexts. Enormous bodies of data, scientific, commercial and others can often be viewed as large metric spaces. It turns out that the metric of graphs reveals a lot of interesting information.…
From antiquity the conceptual perception of space changed painfully and at a relatively slow pace. It went through mythological descriptions, religious beliefs, metaphysical worldviews and cosmological models with a mechanistic structure,…
For non-empty sets X we define notions of distance and pseudo metric with values in a partially ordered set that has a smallest element $\theta $. If $h_X$ is a distance in $X$ (respectively, a pseudo metric in $X$), then the pair $(X,h_X)$…
A new method of metric space investigation, based on classification of its finite subspaces, is suggested. It admits to derive information on metric space properties which is encoded in metric. The method describes geometry in terms of only…
We study the metric structure of walks on graphs, understood as Lipschitz sequences. To this end, a weighted metric is introduced to handle sequences, enabling the definition of distances between walks based on stepwise vertex distances and…
Due to its amazing three-dimensional effects, holography is a very motivating, yet very demanding subject for physics classes at the upper level in school. For this reason an instruction unit on holography that supplement holographic…
In the last years it is becoming more and more evident the importance in providing to the students, and people in general, a more realistic view on the scientific research world. In this framework many initiatives are beeing carried out to…
Human-centered environments are rich with a wide variety of spatial relations between everyday objects. For autonomous robots to operate effectively in such environments, they should be able to reason about these relations and generalize…