Related papers: Mathematical Foundations in Visualization
Software security visualization is an interdisciplinary field that combines the technical complexity of cybersecurity, including threat intelligence and compliance monitoring, with visual analytics, transforming complex security data into…
This paper revisits the role of quantitative and qualitative methods in visualization research in the context of advancements in artificial intelligence (AI). The focus is on how we can bridge between the different methods in an integrated…
Visualization has matured into an established research field, producing widely adopted tools, design frameworks, and empirical foundations. As the field has grown, ideas from outside computer science have increasingly entered visualization…
Appropriate evaluation is a key component in visualization research. It is typically based on empirical studies that assess visualization components or complete systems. While such studies often include the user of the visualization,…
Both metamathematics and physics are posited to emerge from samplings by observers of the unique ruliad structure that corresponds to the entangled limit of all possible computations. The possibility of higher-level mathematics accessible…
The foundations of mathematics have long been considered settled by the Zermelo-Fraenkel-Choice axioms. But set theory abounds in models with different truths and even classical questions such as the measurability of projective sets can…
Data visualization is powerful in persuading an audience. However, when it is done poorly or maliciously, a visualization may become misleading or even deceiving. Visualizations give further strength to the dissemination of misinformation…
This paper explores the use of scenario-based visualisation examples as a pedagogical strategy for teaching students the complexities of data insight, representation, and interpretation. Teaching data visualisation often involves explaining…
Researchers got success in mining the Web usage data effectively and efficiently. But representation of the mined patterns is often not in a form suitable for direct human consumption. Hence mechanisms and tools that can represent mined…
We provide a formal introduction into the classic theorems of general topology and its axiomatic foundations in set theory. In this second part we introduce the fundamental concepts of topological spaces, convergence, and continuity, as…
This book provides an introduction to the mathematical analysis of deep learning. It covers fundamental results in approximation theory, optimization theory, and statistical learning theory, which are the three main pillars of deep neural…
A pedagogical but concise overview of Riemannian geometry is provided, in the context of usage in physics. The emphasis is on defining and visualizing concepts and relationships between them, as well as listing common confusions,…
Politics is the set of activities related to strategic decision-making in groups. Political scientists study the strategic interactions between states, institutions, politicians, and citizens; they seek to understand the causes and…
A visual type theory is a cognitive tool that has much in common with language, and may be regarded as an exceptional form of spatial text adjunct. A mathematical visual type theory, called NPM, has been under development that can be viewed…
Many have wondered how mathematics, which appears to be the result of both human creativity and human discovery, can possibly exhibit the degree of success and seemingly-universal applicability to quantifying the physical world as…
The amount of visual communication we are facing is rapidly increasing, and skills to process, understand, and generate visual representations are in high demand. Especially students focusing on computer graphics and visualization can…
This article serves as an introduction to the study of networks of social systems. First, we introduce the reader to key mathematical tools to study social networks, including mathematical representations of networks and essential…
In this paper I propose the idea to establish a clear distinction between the foundations of truth and the foundations of meaning in Mathematics. I explore on the most basic example, the mathematical line, the possibility that the…
Group Theory has become an invaluable tool in the physics community. Despite numerous introductory books, the subject remains challenging for beginners. Mathematica has emerged as a popular tool for research and education, offering various…
In visualization, the process of transforming raw data into visually comprehensible representations is pivotal. While existing models like the Information Visualization Reference Model describe the data-to-visual mapping process, they often…