Related papers: Analysis on Metric Spaces
We present a new domain-agnostic synthesis technique for generating programs from input-output examples. Our method, called metric program synthesis, relaxes the well-known observational equivalence idea (used widely in bottom-up…
These are the notes from my courses on the arithmetic of quadratic forms.
We offer an insight into our mathematical endeavors, which aim to advance the foundational understanding of energy systems in a broad context, encompassing facets such as charge transport, energy storage, markets, and collective behavior.…
The lectures were prepared for the \'{E}cole Th\'{e}matique sur les Incertitudes en Calcul Scientifique (ETICS) in September 2021.
These Notes deal with various areas of mathematics, and seek reciprocal combinations, explore mutual relations, ranging from abstract objects to problems in physics.
These notes, connected to a "potpourri" topics class currently underway, discuss some basic topics in analysis and connections with other areas of mathematics.
The evolution of mobile mapping systems (MMSs) has gained more attention in the past few decades. MMSs have been widely used to provide valuable assets in different applications. This has been facilitated by the wide availability of…
These notes grew out of a mini-course given by the second-named author at Casa Matem\'atica Oaxaca in the Fall of 2022. Their purpose is to provide an exposition, directed at graduate students, of the basic properties of complex analytic…
Context: A number of Systematic Mapping Studies (SMSs) that cover Software Engineering (SE) are reported in literature. Tertiary studies synthesize the secondary studies to provide a holistic view of an area. Objectives: We synthesize SMSs…
In this article, the notion of a mathematical model in science is attempted to be enlightened from several points of view. In particular, it is shown that mathematical models are introduced differently and used differently in different…
This volume contains the proceedings of PLACES 2025, the 16th edition of the Workshop on Programming Language Approaches to Concurrency and Communication-cEntric Software. The workshop is scheduled to take place in Hamilton, Canada, on May…
This volume contains the proceedings of PLACES 2026, the 17th edition of the Workshop on Programming Language Approaches to Concurrency and Communication-cEntric Software. The workshop is scheduled to take place in Turin, Italy, on April…
Rational design of compounds with specific properties requires conceptual understanding and fast evaluation of molecular properties throughout chemical compound space (CCS) -- the huge set of all potentially stable molecules. Recent…
In recent years, there has been remarkable progress in leveraging Language Models (LMs), encompassing Pre-trained Language Models (PLMs) and Large-scale Language Models (LLMs), within the domain of mathematics. This paper conducts a…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
We present a new algorithm for community detection. The algorithm uses random walks to embed the graph in a space of measures, after which a modification of $k$-means in that space is applied. The algorithm is therefore fast and easily…
The article contains a methodology for social statistics assessing. The significance of minorities (groups that differ in their attributes from the majority) has grown substantially in the modern postindustrial economy and society. In the…
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
We give an informal survey, emphasizing examples and open problems, of two interconnected research programs in moduli of curves: the systematic classification of modular compactifications of $M_{g,n}$, and the study of Mori chamber…
This is an expository paper (in Spanish) about the metric approximation of groups.