Related papers: A computational and pedagogical framework for proj…
Mathematical concepts and tools have shaped the field of visualization in fundamental ways and played a key role in the development of a large variety of visualization techniques. In this chapter, we sample the visualization literature to…
We present a method for incorporating a stochastic point of view into physics exercises of mathematics education. The core of our method is the randomization of some inputs, the system model used does not differ from what we would use in…
A tutorial introduction to projective geometric algebra (PGA), a modern, coordinate-free framework for doing euclidean geometry. PGA features: uniform representation of points, lines, and planes; robust, parallel-safe join and meet…
Background: As traditional coding tasks in education become increasingly vulnerable to the use of Generative AI, there is a critical need for authentic, project-based assessments that evaluate students' scientific inquiry. To address this…
Communication of dense information between humans and machines is relatively low bandwidth. Many modern search and recommender systems operate as machine learning black boxes, giving little insight as to how they represent information or…
A powerful data transformation method named guided projections is proposed creating new possibilities to reveal the group structure of high-dimensional data in the presence of noise variables. Utilising projections onto a space spanned by a…
A classic problem of the motion of a point mass (projectile) thrown at an angle to the horizon is reviewed. The air drag force is taken into account with the drag factor assumed to be constant. An analytic approach is mainly used for the…
Despite advancements in generating visually stunning content, video diffusion models (VDMs) often yield physically inconsistent results due to pixel-only reconstruction. To address this, we propose MMPhysVideo, the first framework to scale…
Discrete mathematics is the foundation of computer science. It focuses on concepts and reasoning methods that are studied using math notations. It has long been argued that discrete math is better taught with programming, which takes…
Answering visual queries is a complex task that requires both visual processing and reasoning. End-to-end models, the dominant approach for this task, do not explicitly differentiate between the two, limiting interpretability and…
The Euclidean projection onto a convex set is an important problem that arises in numerous constrained optimization tasks. Unfortunately, in many cases, computing projections is computationally demanding. In this work, we focus on…
A classic problem of the motion of a projectile thrown at an angle to the horizon in a medium with a quadratic resistance law is studied. An approximate analytical solution of the equations of projectile motion is presented, which has a…
Data-driven machine learning models often require extensive datasets, which can be costly or inaccessible, and their predictions may fail to comply with established physical laws. Current approaches for incorporating physical priors…
In this paper, we detail the integration of Python data analysis into a first-year physics laboratory course, a task accomplished without significant alterations to the existing course structure. We introduced tailored laboratory…
Images often communicate more than they literally depict: a set of tools can suggest an occupation and a cultural artifact can suggest a tradition. This kind of indirect visual reference, known as visual metonymy, invites viewers to recover…
This chapter provides three tutorial exercises on physics-constrained regression. These are implemented as toy problems that seek to mimic grand challenges in (1) the super-resolution and data assimilation of the velocity field in image…
We introduce visual deprojection: the task of recovering an image or video that has been collapsed along a dimension. Projections arise in various contexts, such as long-exposure photography, where a dynamic scene is collapsed in time to…
Current evaluation protocols predominantly assess physical reasoning in stationary scenes, creating a gap in evaluating agents' abilities to interact with dynamic events. While contemporary methods allow agents to modify initial scene…
Modeling should play a central role in K-12 STEM education, where it could make classes much more engaging. A model underlies every scientific theory, and models are central to all the STEM disciplines (Science, Technology, Engineering,…
During the last decade we have witnessed an impressive development in so-called interpreted languages and computational environments such as Maple, Mathematica, IDL, Matlab etc. Problems which until recently were typically solved on…