Related papers: A research-informed graphical tool to visually app…
In this paper, we establish the existence of Stokes waves with piecewise smooth vorticity in a two-dimensional, infinitely deep fluid domain. These waves represent traveling water waves propagating over sheared currents in a semi-infinite…
3D Gaussian splatting, emerging as a groundbreaking approach, has drawn increasing attention for its capabilities of high-fidelity reconstruction and real-time rendering. However, it couples the appearance and geometry of the scene within…
The vast corpus of physics equations forms an implicit network of mathematical relationships that traditional analysis cannot fully explore. This work introduces a graph-based framework combining neural networks with symbolic analysis to…
Prior research suggest that introductory physics students have difficulty with graphing and interpreting graphs. Here, we discuss an investigation of student difficulties in translating between mathematical and graphical representations for…
We investigate introductory physics students' difficulties in translating between mathematical and graphical representations and the effect of scaffolding on students' performance. We gave a typical problem that can be solved using Gauss's…
The primary goal of Visual Analytics (VA) is to enable user-guided knowledge generation. Theoretical VA works to explain how the different aspects of a VA tool bring forth new insights through user interactivity, which itself can be…
This survey revisits classical results in vector calculus and analysis by exploring a generalised perspective on the exterior derivative, interpreting it as a measure of "infinitesimal flux". This viewpoint leads to a higher-dimensional…
Linear algebra's main concerns are sets of vectors, linear functions, subspaces, linear systems, matrices and concepts about those, such as whether the solution of linear system exists or is unique; a set of vectors is linearly independent…
We developed a new approach comprised of different visualizations for the comparative spatio-temporal analysis of displacement processes in porous media. We aim to analyze and compare ensemble datasets from experiments to gain insight into…
Distributions, i.e., subsets of tangent bundles formed by piecing together subspaces of tangent spaces, are commonly encountered in the theory and application of differential geometry. Indeed, the theory of distributions is a fundamental…
This text is a support for different courses of the master of Mechanics of the University Paris-Saclay. The content of this text is an introduction, for graduate students, to tensor algebra and analysis. Far from being exhaustive, the text…
In this paper we study the Gauss and Kummer hypergeometric equations in depth. In particular, we focus on the confluence of two regular singularities of the Gauss hypergeometric equation to produce the Kummer hypergeometric equation with an…
Diffusion models have demonstrated remarkable performance in generation tasks. Nevertheless, explaining the diffusion process remains challenging due to it being a sequence of denoising noisy images that are difficult for experts to…
We suggest a generalization of vector calculus for the case of non-integer dimensional space. The first and second orders operations such as gradient, divergence, the scalar and vector Laplace operators for non-integer dimensional space are…
In this paper the analogy between differential forms arising from integrals in additive calculus and forms arising from the integrals in product calculus is investigated. It is found that with an appropriate definition of scalar…
Graph theory provides fundamental concepts for many fields of science like statistical physics, network analysis and theoretical computer science. Here we give a pedagogical introduction to graph theory, divided into three sections. In the…
Visual illusions traditionally rely on spatial manipulations such as multi-view consistency. In this work, we introduce Progressive Semantic Illusions, a novel vector sketching task where a single sketch undergoes a dramatic semantic…
Teaching the general theory of relativity to high school or undergraduate students must be based on an approach that is conceptual rather than mathematical. In this paper we present such an approach that requires no more than elementary…
Taming diffusion models for generative segmentation has attracted increasing attention. While existing approaches primarily focus on architectural tweaks or training heuristics, there remains a limited understanding of the intrinsic…
Guiding Vector Fields (GVFs) are a powerful tool for robotic path following. However, classical methods assume smooth, ordered curves and fail when paths are unordered, multi-branch, or generated by probabilistic models. We propose a…