Related papers: Mathematical Foundations in Visualization
Critical Visualization is gaining popularity and academic focus, yet relatively few academic courses have been offered to support students in this complex area. This experience report describes a recent experimental course on the topic,…
Empirical studies form an integral part of visualization research. Not only can they facilitate the evaluation of various designs, techniques, systems, and practices in visualization, but they can also enable the discovery of the…
Classification is an important goal in many branches of mathematics. The idea is to describe the members of some class of mathematical objects, up to isomorphism or other important equivalence in terms of relatively simple invariants. Where…
This article is an updated version of an entry of the Encyclopedia of Mathematics Education (2018). In the same time, it is the seed of the HAL collection DAD-MULTILINGUAL, constituted by the translation of this entry in various…
We draw a connection between data modeling and visualization, namely that a visualization specification defines a mapping from database constraints to visual representations of those constraints. Using this formalism, we show how many…
Matrix syntax is a formal model of syntactic relations in language. The purpose of this paper is to explain its mathematical foundations, for an audience with some formal background. We make an axiomatic presentation, motivating each axiom…
Introduction. Development of methodical system for training course "Foundations of mathematical informatics" plays a key role in forming the students' of technical universities competencies in mathematical informatics. So it is very…
Robust preparation of future secondary mathematics teachers requires attention to the acquisition of mathematical knowledge for teaching. Many future teachers learn mathematics content primarily through mathematics major courses that are…
Conceptual Scaling is a useful standard tool in Formal Concept Analysis and beyond. Its mathematical theory, as elaborated in the last chapter of the FCA monograph, still has room for improvement. As it stands, even some of the basic…
The paper discusses fundamental problems in mathematical description of social systems based on physical concepts, with so-called statistical social systems being the main subject of consideration. Basic properties of human beings and human…
We introduce a conceptual model for scalability designed for visualization research. With this model, we systematically analyze over 120 visualization publications from 1990-2020 to characterize the different notions of scalability in these…
Few concepts are as ubiquitous in computational fields as trust. However, in the case of information visualization, there are several unique and complex challenges, chief among them: defining and measuring trust. In this paper, we…
Composite visualization is a popular design strategy that represents complex datasets by integrating multiple visualizations in a meaningful and aesthetic layout, such as juxtaposition, overlay, and nesting. With this strategy, numerous…
Developments in data visualization research have enabled visualization systems to achieve great general usability and application across a variety of domains. These advancements have improved not only people's understanding of data, but…
Usually the first course in mathematics is calculus. Its a core course in the curriculum of the Business, Engineering and the Sciences. However many students face difficulties to learn calculus. These difficulties are often caused by the…
In recent years, narrative visualization has gained much attention. Researchers have proposed different design spaces for various narrative visualization genres and scenarios to facilitate the creation process. As users' needs grow and…
In this review the foundations of Geometric Quantization are explained and discussed. In particular, we want to clarify the mathematical aspects related to the geometrical structures involved in this theory: complex line bundles, hermitian…
In applied mathematics and related disciplines, the modeling-simulation-optimization workflow is a prominent scheme, with mathematical models and numerical algorithms playing a crucial role. For these types of mathematical research data,…
The role of mathematical models in physics has for longer been well established. The issue of their proper building and use appears to be less clear. Examples in this regard from relativity and quantum mechanics are mentioned. Comments…
This essay considers the special character of mathematical reasoning, and draws on observations from interactive theorem proving and the history of mathematics to clarify the nature of formal and informal mathematical language. It proposes…