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The Course Difficulty Analysis Cookbook

arXiv.org Artificial Intelligence

Curriculum analytics (CA) studies curriculum structure and student data to ensure the quality of educational programs. An essential aspect is studying course properties, which involves assigning each course a representative difficulty value. This is critical for several aspects of CA, such as quality control (e.g., monitoring variations over time), course comparisons (e.g., articulation), and course recommendation (e.g., advising). Measuring course difficulty requires careful consideration of multiple factors: First, when difficulty measures are sensitive to the performance level of enrolled students, it can bias interpretations by overlooking student diversity. By assessing difficulty independently of enrolled students' performances, we can reduce the risk of bias and enable fair, representative assessments of difficulty. Second, from a measurement theoretic perspective, the measurement must be reliable and valid to provide a robust basis for subsequent analyses. Third, difficulty measures should account for covariates, such as the characteristics of individual students within a diverse populations (e.g., transfer status). In recent years, various notions of difficulty have been proposed. This paper provides the first comprehensive review and comparison of existing approaches for assessing course difficulty based on grade point averages and latent trait modeling. It further offers a hands-on tutorial on model selection, assumption checking, and practical CA applications. These applications include monitoring course difficulty over time and detecting courses with disparate outcomes between distinct groups of students (e.g., dropouts vs. graduates), ultimately aiming to promote high-quality, fair, and equitable learning experiences. To support further research and application, we provide an open-source software package and artificial datasets, facilitating reproducibility and adoption.



Deep Generative Model for Periodic Graphs

Neural Information Processing Systems

Their generative modeling has great potential in real-world applications such as material design and graphics synthesis. Classical models either rely on domain-specific predefined generation principles (e.g., in crystal net design),







Constrained Centroid Clustering: A Novel Approach for Compact and Structured Partitioning

arXiv.org Machine Learning

This paper presents Constrained Centroid Clustering (CCC), a method that extends classical centroid-based clustering by enforcing a constraint on the maximum distance between the cluster center and the farthest point in the cluster. Using a Lagrangian formulation, we derive a closed-form solution that maintains interpretability while controlling cluster spread. To evaluate CCC, we conduct experiments on synthetic circular data with radial symmetry and uniform angular distribution. Using ring-wise, sector-wise, and joint entropy as evaluation metrics, we show that CCC achieves more compact clusters by reducing radial spread while preserving angular structure, outperforming standard methods such as K-means and GMM. The proposed approach is suitable for applications requiring structured clustering with spread control, including sensor networks, collaborative robotics, and interpretable pattern analysis.


A Survey of Idiom Datasets for Psycholinguistic and Computational Research

arXiv.org Artificial Intelligence

Idioms are figurative expressions whose meanings often cannot be inferred from their individual words, making them difficult to process computationally and posing challenges for human experimental studies. This survey reviews datasets developed in psycholinguistics and computational linguistics for studying idioms, focusing on their content, form, and intended use. Psycholinguistic resources typically contain normed ratings along dimensions such as familiarity, transparency, and compositionality, while computational datasets support tasks like idiomaticity detection/classification, paraphrasing, and cross-lingual modeling. We present trends in annotation practices, coverage, and task framing across 53 datasets. Although recent efforts expanded language coverage and task diversity, there seems to be no relation yet between psycholinguistic and computational research on idioms.