Related papers: An open day in the metric space
In the present work we intend to introduce a system based on VR (Virtual Reality) for examining analytical-geometric structures that occur in the study of mathematics and physics concepts in the last high school classes. In our opinion, an…
For a bounded metric space X, we define a metric on the set of all finite subsets of X. This generalizes the sequence-subset distance introduced by Wentu Song, Kui Cai and Kees A. Schouhamer Immink to study error correcting codes for DNA…
Combining gravity with quantum theory is still work in progress. On the one hand, classical gravity, is the geometry of space-time determined by the energy-momentum tensor of matter and the resulting nonlinear equations; on the other hand,…
WWe define the notion of a random metric space and prove that with probability one such a space is isometricto the Urysohn universal metric space. The main technique is the study of universal and random distance matrices; we relate the…
This article provides an overview on the statistical modeling of complex data as increasingly encountered in modern data analysis. It is argued that such data can often be described as elements of a metric space that satisfies certain…
Given a metric pair $(X,A)$, i.e. a metric space $X$ and a distinguished closed set $A \subset X$, one may construct in a functorial way a pointed pseudometric space $\mathcal{D}_\infty(X,A)$ of persistence diagrams equipped with the…
Riemannian metric learning is an emerging field in machine learning, unlocking new ways to encode complex data structures beyond traditional distance metric learning. While classical approaches rely on global distances in Euclidean space,…
The definition of the augmented reality concept is based on the analysis of scientific publications. It is noted that online experiments with augmented reality provide students with the opportunity to observe and describe the operation with…
The reform of the upper secondary school in Italy has recently introduced physics in the curricula of professional schools, in realities where it was previously absent. Many teachers, often with a temporary position, are obliged to teaching…
We report results from a study designed to identify links between undergraduate students' views about experimental physics and their engagement in multiweek projects in lab courses. Using surveys and interviews, we explored whether students…
In models of emergent gravity the metric arises as the expectation value of some collective field. Usually, many different collective fields with appropriate tensor properties are candidates for a metric. Which collective field describes…
We designed a two-day laboratory exploration of fundamental concepts in digital images for an introductory engineering course at Maui Community College. Our objective was for the students to understand spatial vs. brightness resolution,…
A partially unusual behaviour was found among 14 sophomore students of civil engineering who took a pre test for a free fall laboratory session, in the context of a general mechanics course. An analysis contemplating mathematics models and…
Measuring online behavioural student engagement often relies on simple count indicators or retrospective, predictive methods, which present challenges for real-time application. To address these limitations, we reconceptualise an existing…
Framing affects how students interpret, approach, and accomplish tasks. Little is known, however, about how students frame tasks in physics labs. During the first lab of a sequence designed to teach students about modeling and critical…
In the present paper a distinguishability of bounded metric spaces by the set of the Gromov--Hausdorff distances to so-called simplexes (metric spaces with unique non-zero distance) is investigated. It is easy to construct an example of…
Sliding friction is usually introduced in high school, but rarely through activities in laboratory. A qualitative introduction to friction is presented by proposing exploration of different kind of materials in order to suggest which…
There is an increasing shift in technology towards biometric solutions, but one of the biggest barriers to widespread use is the acceptance by the users. In this paper we investigate the understanding, awareness and acceptance of biometrics…
In this paper we try to organize machine teaching as a coherent set of ideas. Each idea is presented as varying along a dimension. The collection of dimensions then form the problem space of machine teaching, such that existing teaching…
This note presents reflections drawn from my recent experiences in teaching a course on mathematics and sustainability, with a particular emphasis on raising awareness of the topic and its broader implications. The lectures were structured…