Related papers: Analysis on Metric Spaces
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…
These are lecture notes for five sessions in the AMSI Winter School on 'Computational Modelling of Heterogeneous Media' held at QUT in July 2019 [https://ws.amsi.org.au/]. Aim: Discuss a mix of new mathematical approaches for multiscale…
We use the notion of topological data analysis to compare metrics on data sets. We provide two different motivating examples for this. The first of these is a point cloud data set that has $\mathbb{R}^2$ as its ambient space, and is…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM} and developed the idea further in \cite{AS}. In this paper we study locally $M$-metrizable spaces and the products of $M$-metrizable spaces. Finally we…
Detecting and analyzing dense groups or communities from social and information networks has attracted immense attention over last one decade due to its enormous applicability in different domains. Community detection is an ill-defined…
In the recent work [Metrically round and sleek metric spaces, \emph{The Journal of Analysis} (2022), pp 1--17], the authors proved some results on metrically round and sleek linear metric spaces and metric spaces. In continuation, the…
We aim to conduct a systematic mapping in the area of testing ML programs. We identify, analyze and classify the existing literature to provide an overview of the area. We followed well-established guidelines of systematic mapping to…
These informal notes deal with some basic properties of metric spaces, especially concerning lengths of curves.
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…
This paper, written in relation to the Current Developments in Mathematics 2012 Conference, discusses the recent papers on perfectoid spaces. Apart from giving an introduction to their content, it includes some open questions, as well as…
In this paper we aim at providing a general reflection around the present and future of social media metrics (or altmetrics) and how they could evolve into a new discipline focused on the study of the relationships and interactions between…
We introduced the concept of a metric value set (MVS) in an earlier paper \cite{GM}. In this paper we study the algebraic structure of MVSs. For an MVS $M$ we define the concept of $M$-metrizability of a topological space and prove some…
Pairs of metrics in a two-dimensional linear vector space are considered, one of which is a Minkowski type metric. Their simultaneous diagonalizability is studied and canonical presentations for them are suggested.
This volume contains the proceedings of MARS 2020, the fourth workshop on Models for Formal Analysis of Real Systems held as part of ETAPS 2020, the European Joint Conferences on Theory and Practice of Software. The MARS workshop brings…
A strong sense of classroom community is associated with many positive learning outcomes and is a critical contributor to undergraduate students' persistence in STEM, particularly for women and students of color. This chapter describes a…
This is a slightly updated version of lectures notes for a course on analytic geometry taught in the winter term 2019/20 at the University of Bonn. The material presented is part of joint work with Dustin Clausen. This is intended as a…
The present informal set of notes covers the material that has been presented by the author in a series of lectures for the Doctoral School in Mathematics of the Southern Federal State University of Rostov-on-Don in the Fall of 2020 and…
The question in the title is discussed briefly, with emphasis on a few basic examples and their properties.
We present a complete study of measure-theoretic area formulas in metric spaces, providing different measurability conditions.
This article is based upon lectures given at the 2013 IAS/Park City Mathematics Institute summer program in geometric analysis.