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Theoretical and computational properties of a vector equation $Ax-\|x\|_1x=b$ are investigated, where $A$ is an invertible $M$-matrix and $b$ is a nonnegative vector. Existence and uniqueness of a nonnegative solution is proved. Fixed-point…
Researchers have now achieved great success on dealing with 2D images using deep learning. In recent years, 3D computer vision and Geometry Deep Learning gain more and more attention. Many advanced techniques for 3D shapes have been…
We introduce a representation of a 2D steady vector field ${{\mathbf v}}$ by two scalar fields $a$, $b$, such that the isolines of $a$ correspond to stream lines of ${{\mathbf v}}$, and $b$ increases with constant speed under integration of…
Visual Question Answering (VQA) is a challenging task that has received increasing attention from both the computer vision and the natural language processing communities. Given an image and a question in natural language, it requires…
We report our experience in two installations of a course on data visualization that featured project-based learning. Given the rationale of this approach, we show which input was provided when necessary for the students to achieve their…
Geometric algebra is the natural outgrowth of the concept of a vector and the addition of vectors. After reviewing the properties of the addition of vectors, a multiplication of vectors is introduced in such a way that it encodes the famous…
The ability to flexibly transform between different representations (e.g., from mathematical to graphical representations) of the same concept is a hallmark of expertise. Prior research suggests that many introductory physics students show…
Learning representations of multimodal data that are both informative and robust to missing modalities at test time remains a challenging problem due to the inherent heterogeneity of data obtained from different channels. To address it, we…
Students' answers to tasks provide a valuable source of information in teaching as they result from applying cognitive processes to a learning content addressed in the task. Due to steadily increasing course sizes, analyzing student answers…
We examine visual representations of data that make use of combinations of both 2D and 3D data mappings. Combining 2D and 3D representations is a common technique that allows viewers to understand multiple facets of the data with which they…
Vector data is prevalent across business and scientific applications, and its popularity is growing with the proliferation of learned embeddings. Vector data collections often reach billions of vectors with thousands of dimensions, thus,…
Students in introductory physics struggle with vector algebra and these challenges are often associated with contextual and representational features of the problems. Performance on problems about cross product direction is particularly…
Visual question answering requires a deep understanding of both images and natural language. However, most methods mainly focus on visual concept; such as the relationships between various objects. The limited use of object categories…
Visual question answering (VQA) demands simultaneous comprehension of both the image visual content and natural language questions. In some cases, the reasoning needs the help of common sense or general knowledge which usually appear in the…
Data are often represented as graphs. Many common tasks in data science are based on distances between entities. While some data science methodologies natively take graphs as their input, there are many more that take their input in…
When we view visualizations, we not only have a visual representation of the data, but also a verbal one. Recent work has shown that these visual representations of data can be biased, such that the position of a line in a chart will be…
Geometric modeling by constraints, whose applications are of interest to communities from various fields such as mechanical engineering, computer aided design, symbolic computation or molecular chemistry, is now integrated into standard…
Generative AI systems have rapidly advanced, with multimodal input capabilities enabling reasoning beyond text-based tasks. In education, these advancements could influence assessment design and question answering, presenting both…
Visual Question Answering(VQA) is a highly complex problem set, relying on many sub-problems to produce reasonable answers. In this paper, we present the hypothesis that Visual Question Answering should be viewed as a multi-task problem,…
Answering semantically-complicated questions according to an image is challenging in Visual Question Answering (VQA) task. Although the image can be well represented by deep learning, the question is always simply embedded and cannot well…