Related papers: An open day in the metric space
The metric dimension of a graph is the smallest number of nodes required to identify all other nodes based on shortest path distances uniquely. Applications of metric dimension include discovering the source of a spread in a network,…
In this paper, our aim is to discuss the outcome of a ten-year experimental workshop activity carried out by the Center `matematita' (http://www.matematita.it/) with classes of pre-university students of any age. We analyse the potential…
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…
Physics in schools is distinctly different from, and struggles to capture the excitement of, university research-level work. Initiatives where students engage in independent research linked to cutting-edge physics within their school over…
The increasing number of robots in home environments leads to an emerging coexistence between humans and robots. Robots undertake common tasks and support the residents in their everyday life. People appreciate the presence of robots in…
This document reviews the definition of the kernel distance, providing a gentle introduction tailored to a reader with background in theoretical computer science, but limited exposure to technology more common to machine learning,…
A particular science is not only defined by its object of study, but also by the point of view and method under which it considers that same object. Taking space and time as an illustrative example, our main aim here is to bring out an…
Historically, non-disabled individuals have viewed disability as a personal deficit requiring change to the disabled individual. However, models have emerged from disability activists and disabled intellectuals that emphasize the role of…
We report on the development of students' ideas of probability and probability density in a University of Maine laboratory-based general education physics course called Intuitive Quantum Physics. Students in the course are generally math…
The concept of depth has proved very important for multivariate and functional data analysis, as it essentially acts as a surrogate for the notion a ranking of observations which is absent in more than one dimension. Motivated by the rapid…
Distance metric learning is a branch of machine learning that aims to learn distances from the data, which enhances the performance of similarity-based algorithms. This tutorial provides a theoretical background and foundations on this…
It has been reported that students often leave the introductory physics classroom believing that physics is less connected to the real world than when they entered. In this paper we aim to complicate that narrative by considering students'…
Gromov introduced two distance functions, the box distance and the observable distance, on the space of isomorphism classes of metric measure spaces and developed the convergence theory of metric measure spaces. We investigate several…
Computational physics is a key part of what it means to do physics in the twenty-first century. However, upper division computational physics remains a largely understudied area. We set out to understand the experiences of students in an…
We introduce strings in metric spaces and define string complexes of metric spaces. We describe the class of 2-dimensional topological spaces which arise in this way from finite metric spaces.
It is well-understood that different algorithms, training processes, and corpora produce different word embeddings. However, less is known about the relation between different embedding spaces, i.e. how far different sets of embeddings…
The suggested approach makes it possible to produce a consistent description of motions of a physical system. It is shown that the concept of force fields defining the systems dynamics is equivalent to the choice of the corresponding metric…
A distance measure is presented between two unitary propagators of quantum systems of differing dimensions along with a corresponding method of computation. A typical application is to compare the propagator of the actual (real) process…
Iteratively building and testing machine learning models can help children develop creativity, flexibility, and comfort with machine learning and artificial intelligence. We explore how children use machine teaching interfaces with a team…
The human visual system is able to recognize objects despite transformations that can drastically alter their appearance. To this end, much effort has been devoted to the invariance properties of recognition systems. Invariance can be…