[This corrects the article DOI: 10.1371/journal.pcbi.1011530.].

We introduce Catalyst.jl, a flexible and feature-filled Julia library for modeling and high-performance simulation of chemical reaction networks (CRNs). Catalyst supports simulating stochastic chemical kinetics (jump process), chemical Langevin equation (stochastic differential equation), and reaction rate equation (ordinary differential equation) representations for CRNs. Through comprehensive benchmarks, we demonstrate that Catalyst simulation runtimes are often one to two orders of magnitude faster than other popular tools. More broadly, Catalyst acts as both a domain-specific language and an intermediate representation for symbolically encoding CRN models as Julia-native objects. This enables a pipeline of symbolically specifying, analyzing, and modifying CRNs; converting Catalyst models to symbolic representations of concrete mathematical models; and generating compiled code for numerical solvers. Leveraging ModelingToolkit.jl and Symbolics.jl, Catalyst models can be analyzed, simplified, and compiled into optimized representations for use in numerical solvers. Finally, we demonstrate Catalyst's broad extensibility and composability by highlighting how it can compose with a variety of Julia libraries, and how existing open-source biological modeling projects have extended its intermediate representation.

Intelligent virtual agents have tremendous potential for facilitating collaborative learning by modeling and reinforcing desirable collaborative practices. Despite recent work in this area, the extent to which intelligent virtual agents can facilitate improvements in the collaborative behavior of children is largely unknown. This study employed a wizard-of-oz study design and investigated elementary children's collaborative behavior after interacting with virtual agents. These agents model exploratory talk for upper elementary school dyads, such as asking higher-order questions and listening to their partners. The findings uncover associations between elementary learner dyads' positive changes in collaboration after agent interventions, the dyads' affective reactions to interventions, and their attentiveness to the agents. Our results also reveal associations between positive changes in collaboration and the timing of interventions: for example, earlier interventions had a higher occurrence of positive changes, and positive changes in collaboration typically happened within five seconds of interventions. The results suggest ways in which intelligent virtual agents may be used to promote effective collaborative learning practices for children.

Collaborative problem solving has numerous benefits for learners, such as improving higher-level reasoning and developing critical thinking. While learners engage in collaborative activities, they often experience impasse, a potentially brief encounter with differing opinions or insufficient ideas to progress. Impasses provide valuable opportunities for learners to critically discuss the problem and re-evaluate their existing knowledge. Yet, despite the increasing research efforts on developing multimodal modeling techniques to analyze collaborative problem solving, there is limited research on detecting impasse in collaboration. This paper investigates multimodal detection of impasse by analyzing 46 middle school learners’ collaborative dialogue—including speech and facial behaviors—during a coding task. We found that the semantics and speaker information in the linguistic modality, the pitch variation in the audio modality, and the facial muscle movements in the video modality are the most significant unimodal indicators of impasse. We also trained several multimodal models and found that combining indicators from these three modalities provided the best impasse detection performance. To the best of our knowledge, this work is the first to explore multimodal modeling of impasse during the collaborative problem solving process. This line of research contributes to the development of real-time adaptive support for collaboration.

The COVID-19 pandemic shifted many U.S. schools from in-person to remote instruction. While collaborative CS activities had become increasingly common in classrooms prior to the pandemic, the sudden shift to remote learning presented challenges for both teachers and students in implementing and supporting collaborative learning. Though some research on remote collaborative CS learning has been conducted with adult learners, less has been done with younger learners such as elementary school students. This experience report describes lessons learned from a remote after-school camp with 24 elementary school students who participated in a series of individual and paired learning activities over three weeks. We describe the design of the learning activities, participant recruitment, group formation, and data collection process. We also provide practical implications for implementation such as how to guide facilitators, pair students, and calibrate task difficulty to foster collaboration. This experience report contributes to the understanding of remote CS learning practices, particularly for elementary school students, and we hope it will provoke methodological advancement in this important area.

Democratization of machine learning requires architectures that automatically adapt to new problems. Neural Differential Equations (NDEs) have emerged as a popular modeling framework by removing the need for ML practitioners to choose the number of layers in a recurrent model. While we can control the computational cost by choosing the number of layers in standard architectures, in NDEs the number of neural network evaluations for a forward pass can depend on the number of steps of the adaptive ODE solver. But, can we force the NDE to learn the version with the least steps while not increasing the training cost? Current strategies to overcome slow prediction require high order automatic differentiation, leading to significantly higher training time. We describe a novel regularization method that uses the internal cost heuristics of adaptive differential equation solvers combined with discrete adjoint sensitivities to guide the training process towards learning NDEs that are easier to solve. This approach opens up the blackbox numerical analysis behind the differential equation solver’s algorithm and directly uses its local error estimates and stiffness heuristics as cheap and accurate cost estimates. We incorporate our method without any change in the underlying NDE framework and show that our method extends beyond Ordinary Differential Equations to accommodate Neural Stochastic Differential Equations. We demonstrate how our approach can halve the prediction time and, unlike other methods which can increase the training time by an order of magnitude, we demonstrate similar reduction in training times. Together this showcases how the knowledge embedded within state-of-the-art equation solvers can be used to enhance machine learning.