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This paper is one of a series in which elementary-education practice is analyzed by comparison with the history of mathematics, mathematical structure, modern practice, and (occasionally) cognitive neuroscience. The primary concerns are:…
In modern computer vision, the optimal representation of 3D shape continues to be task-dependent. One fundamental operation applied to such representations is differentiable rendering, as it enables inverse graphics approaches in learning…
The study of multiple extrasolar planetary systems has the opportunity to obtain constraints for the planetary masses and orbital inclinations via the detection of mutual perturbations. The analysis of precise radial velocity measurements…
Bias formation in deep neural networks (DNNs) remains a critical yet poorly understood challenge, influencing both fairness and reliability in artificial intelligence systems. Inspired by the human visual system, which decouples object…
In recent years, machine learning methods have been widely used to study physical systems that are challenging to solve with governing equations. Physicists and engineers are framing the data-driven paradigm as an alternative approach to…
We investigate the problem of determining if a given graph corresponds to the dual of a triangulation of a simple polygon. This is a graph recognition problem, where in our particular case we wish to recognize a graph which corresponds to…
Stereo vision generally involves the computation of pixel correspondences and estimation of disparities between rectified image pairs. In many applications, including simultaneous localization and mapping (SLAM) and 3D object detection, the…
Symmetry detection and discrimination are of fundamental meaning in science, technology, and engineering. This paper introduces reflection invariants and defines the directional moment to detect symmetry for shape analysis and object…
Six specific modes of reasoning about ratio and proportion have been delineated as a means of operationalizing expert practice. These modes stem from consideration of how physicists reason in context, are informed by prior work in physics…
Identifying the relevant physics principles is a central component of problem solving. A major goal of most introductory physics courses is to help students discern the deep similarities between problems based upon the physics principles so…
While multimodal LLMs (MLLMs) demonstrate remarkable reasoning progress, their application in specialized scientific domains like physics reveals significant gaps in current evaluation benchmarks. Specifically, existing benchmarks often…
Boundary conditions (BCs) are considered as an important topic that advanced physics under- graduates are expected to understand and apply. We report findings from an investigation of student difficulties using boundary conditions (BCs) in…
Modeling complex physical dynamics is a fundamental task in science and engineering. Traditional physics-based models are sample efficient, and interpretable but often rely on rigid assumptions. Furthermore, direct numerical approximation…
Data visualizations are ubiquitous in all disciplines and have become the primary means of analysing data and communicating insights. However, the predominant reliance on visual encoding of data continues to create accessibility barriers…
Geometry problem solving, a crucial aspect of mathematical reasoning, is vital across various domains, including education, the assessment of AI's mathematical abilities, and multimodal capability evaluation. The recent surge in deep…
In physics, two systems that radically differ at short scales can exhibit strikingly similar macroscopic behaviour: they are part of the same long-distance universality class. Here we apply this viewpoint to geometry and initiate a program…
Many students in upper-division physics courses struggle with the mathematically sophisticated tools and techniques that are required for advanced physics content. We have developed an analytical framework to assist instructors and…
Proficiency with calculating, reporting, and understanding measurement uncertainty is a nationally recognized learning outcome for undergraduate physics lab courses. The Physics Measurement Questionnaire (PMQ) is a research-based assessment…
We initiate the study of active learning polynomial threshold functions (PTFs). While traditional lower bounds imply that even univariate quadratics cannot be non-trivially actively learned, we show that allowing the learner basic access to…
Diabetic retinopathy (DR) is a prevalent complication of diabetes associated with a significant risk of vision loss. Timely identification is critical to curb vision impairment. Algorithms for DR staging from digital fundus images (DFIs)…