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Evaluates DKT models’ ability to track individual knowledge components (KCs) in programming tasks. Proposes two enhancements—adding an explicit KC layer and code features—and shows that the KC layer yields modest improvements in KC-level interpretability, especially when tracking incorrect submissions. 

We present an algorithm that combines quantum scattering calculations with probabilistic machine-learning models to predict quantum dynamics rate coefficients for a large number of state-to-state transitions in molecule–molecule collisions much faster than with direct solutions of the Schrödinger equation. By utilizing the predictive power of Gaussian process regression with kernels, optimized to make accurate predictions outside of the input parameter space, the present strategy reduces the computational cost by about 75%, with an accuracy within 5%. Our method uses temperature dependences of rate coefficients for transitions from the isolated states of initial rotational angular momentum j, determined via explicit calculations, to predict the temperature dependences of rate coefficients for other values of j. The approach, demonstrated here for rovibrational transitions of SiO due to thermal collisions with H2, uses different prediction models and is thus adaptive to various time and accuracy requirements. The procedure outlined in this work can be used to extend multiple inelastic molecular collision databases without exponentially large computational resources required for conventional rigorous quantum dynamics calculations. 

Abstract Hydrogen chloride (HCl) is a key repository of chlorine in the interstellar medium. Accurate determinations of its abundance are critical to assessing the chlorine elemental abundance and constraining stellar nucleosynthesis models. To aid in modeling recent and future observations of HCl rovibrational spectra, we present cross sections and rate coefficients for collisions between HCl and molecular hydrogen. Transitions between rovibrational states of HCl are considered for temperatures ranging from 10 to 3000 K. Cross sections are computed using a full dimensional quantum close-coupling (CC) method and a reduced dimensionality coupled-states (CS) approach. The CS results, benchmarked against the CC results, are used with a recoupling approach to calculate hyperfine-resolved rate coefficients for rovibrational transitions of HCl induced by H₂. The rate coefficients will allow for a better determination of the HCl abundance in the interstellar medium and an improved understanding of interstellar chlorine chemistry. We demonstrate the utility of the new rate coefficients in a nonthermodynamic equilibrium radiative transfer model applied to observations of HCl rovibrational transitions in a circumstellar shell. 

Knowledge components (KCs) have many applications. In computing education, knowing the demonstration of specific KCs has been challenging. This paper introduces an entirely data-driven approach for (i) discovering KCs and (ii) demonstrating KCs, using students’ actual code submissions. Our system is based on two expected properties of KCs: (i) generate learning curves following the power law of practice, and (ii) are predictive of response correctness. We train a neural architecture (named KC-Finder) that classifies the correctness of student code submissions and captures problem-KC relationships. Our evaluation on data from 351 students in an introductory Java course shows that the learned KCs can generate reasonable learning curves and predict code submission correctness. At the same time, some KCs can be interpreted to identify programming skills. We compare the learning curves described by our model to four baselines, showing that (i) identifying KCs with naive methods is a difficult task and (ii) our learning curves exhibit a substantially better curve fit. Our work represents a first step in solving the data-driven KC discovery problem in computing education.