Related papers: Analysis on Metric Spaces
Similarity search in math is to find mathematical expressions that are similar to a user's query. We conceptualized the similarity factors between mathematical expressions, and proposed an approach to math similarity search (MSS) by…
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…
This is an updated version of the lectures notes for a course on condensed mathematics taught in the summer term 2019 at the University of Bonn. The material presented is joint work with Dustin Clausen. This is intended as a stable citable…
This work presents a large-scale analysis of artificial intelligence (AI) and machine learning (ML) references within news articles and scientific publications between 2011 and 2019. We implement word association measurements that…
Learning Spaces are certain set systems that are applied in the mathematical modeling of education. We propose a suitable compression (without loss of information) of such set systems to facilitate their logical and statistical analysis.…
This is a lecture notes for a mini-course in Department of Mathematics, Ghent University, 14 Mar.-25 Mar. 2023.
We survey selected developments in the metric geometry of the space of K\"ahler metrics, emphasizing results from the past decade, highlighting open problems along the way.
These lecture notes contain an introduction to some of the fundamental ideas and results in analysis and probability on infinite-dimensional spaces, mainly Gaussian measures on Banach spaces. They originated as the notes for a topics course…
A new sequential approach to investigations of structure of metric spaces at infinity is proposed. Criteria for finiteness and boundedness of metric spaces at infinity are found.
In this paper, we propose a metric on the space of finite sets of trajectories for assessing multi-target tracking algorithms in a mathematically sound way. The main use of the metric is to compare estimates of trajectories from different…
A compilation of descriptive statistics of responses to the X-PIPS-M suite of surveys for students, student instructors, and faculty instructors of introductory mathematics courses. Data were obtained from Precalculus, Calculus 1, and…
Some concepts, such as non-compactness measure and condensing operators, defined on metric spaces are extended to uniform spaces. Such extensions allow us to locate, in the context of uniform spaces, some classical results existing in…
This white paper presents the current status of the R&D for Analysis Facilities (AFs) and attempts to summarize the views on the future direction of these facilities. These views have been collected through the High Energy Physics (HEP)…
This volume contains the proceedings of the Ninth Workshop on Mathematically Structured Functional Programming (MSFP 2022). The meeting took place on the 2nd of April as a satellite of European Joint Conferences on Theory & Practice of…
This note is a survey of $J$-spaces.
Notes on algebraic stacks, prepared for an 11-lecture course at the NCTS, Taipei, during the fall of 2022.
MEMICS provides a forum for doctoral students interested in applications of mathematical and engineering methods in computer science. Besides a rich technical programme (including invited talks, regular papers, and presentations), MEMICS…
Author developed a uniform model for different spaces where distance and angle measure kinds are parameters. This model is calculus centric, but can also be used in theoretical research. It is useful in the following domains: deduction of…
Similarity search finds objects that are similar to a given query object based on a similarity metric. As the amount and variety of data continue to grow, similarity search in metric spaces has gained significant attention. Metric spaces…
We carry out a thorough bibliometric analysis of recent publications in mathematics based on the database Web of Science. The individual relations between various features and the citations are provided, and the importance of the features…