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  1. This exploratory study delves into the complex challenge of analyzing and interpreting student responses to mathematical problems, typically conveyed through image formats within online learning platforms. The main goal of this research is to identify and differentiate various student strategies within a dataset comprising image-based mathematical work. A comprehensive approach is implemented, including various image representation, preprocessing, and clustering techniques, each evaluated to fulfill the study’s objectives. The exploration spans several methods for enhanced image representation, extending from conventional pixel-based approaches to the innovative deployment of CLIP embeddings. Given the prevalent noise and variability in our dataset, an ablation study is conducted to meticulously evaluate the impact of various preprocessing steps, assessing their potency in eradicating extraneous backgrounds and noise to more precisely isolate relevant mathematical content. Two clustering approaches—k-means and hierarchical clustering—are employed to categorize images based on student strategies that underlies their responses. Preliminary results underscore the hierarchical clustering method could distinguish between student strategies effectively. Our study lays down a robust framework for characterizing and understanding student strategies in online mathematics problem-solving, paving the way for future research into scalable and precise analytical methodologies while introducing a novel open-source image dataset for the learning analytics research community. 
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    Free, publicly-accessible full text available January 1, 2025
  2. Teachers today have increasing access to professional learning communities (PLCs) through a rapidly expanding menu of online professional development offerings. While a valued opportunity for growth, online PLCs can limit opportunities for co-teaching, pedagogical practice, and experiential learning. This paper examines a teacher professional development program implemented in 2022, where 14 middle school teachers joined either an online or an in-person version of a summer practicum in which PLCs were fostered. In both versions of the PD, teachers worked in small teams of co-teachers to learn and practice teaching middle school students about Artificial Intelligence (AI), a topic in which teachers were non-experts. Findings from qualitative analysis of teacher interviews suggest affordances and barriers to teacher learning online as compared to in-person PLCs. The paper offers recommendations for online PLC structure and co-teaching to enhance teacher learning. 
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    Free, publicly-accessible full text available June 14, 2024
  3. Teachers today have increasing access to professional learning communities (PLCs) through a rapidly expanding menu of online professional development offerings. While a valued opportunity for growth, online PLCs can limit opportunities for co-teaching, pedagogical practice, and experiential learning. This paper examines a teacher professional development program implemented in 2022, where 14 middle school teachers joined either an online or an in-person version of a summer practicum in which PLCs were fostered. In both versions of the PD, teachers worked in small teams of co-teachers to learn and practice teaching middle school students about Artificial Intelligence (AI), a topic in which teachers were non-experts. Findings from qualitative analysis of teacher interviews suggest affordances and barriers to teacher learning online as compared to in-person PLCs. The paper offers recommendations for online PLC structure and co-teaching to enhance teacher learning. 
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    Free, publicly-accessible full text available June 14, 2024
  4. Free, publicly-accessible full text available May 5, 2024
  5. Free, publicly-accessible full text available July 1, 2024
  6. Matni, N ; Morari, M ; Pappas, G.J. (Ed.)
    One of the long-term objectives of Machine Learning is to endow machines with the capacity of structuring and interpreting the world as we do. This is particularly challenging in scenes involving time series, such as video sequences, since seemingly different data can correspond to the same underlying dynamics. Recent approaches seek to decompose video sequences into their composing objects, attributes and dynamics in a self-supervised fashion, thus simplifying the task of learning suitable features that can be used to analyze each component. While existing methods can successfully disentangle dynamics from other components, there have been relatively few efforts in learning parsimonious representations of these underlying dynamics. In this paper, motivated by recent advances in non-linear identification, we propose a method to decompose a video into moving objects, their attributes and the dynamic modes of their trajectories. We model video dynamics as the output of a Koopman operator to be learned from the available data. In this context, the dynamic information contained in the scene is encapsulated in the eigenvalues and eigenvectors of the Koopman operator, providing an interpretable and parsimonious representation. We show that such decomposition can be used for instance to perform video analytics, predict future frames or generate synthetic video. We test our framework in a variety of datasets that encompass different dynamic scenarios, while illustrating the novel features that emerge from our dynamic modes decomposition: Video dynamics interpretation and user manipulation at test-time. We successfully forecast challenging object trajectories from pixels, achieving competitive performance while drawing useful insights. 
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  7. Despite the established convergence theory of Optimistic Gradient Descent Ascent (OGDA) and Extragradient (EG) methods for the convex-concave minimax problems, little is known about the theoretical guarantees of these methods in nonconvex settings. To bridge this gap, for the first time, this paper establishes the convergence of OGDA and EG methods under the nonconvex-strongly-concave (NC-SC) and nonconvex-concave (NC-C) settings by providing a unified analysis through the lens of single-call extra-gradient methods. We further establish lower bounds on the convergence of GDA/OGDA/EG, shedding light on the tightness of our analysis. We also conduct experiments supporting our theoretical results. We believe our results will advance the theoretical understanding of OGDA and EG methods for solving complicated nonconvex minimax real-world problems, e.g., Generative Adversarial Networks (GANs) or robust neural networks training. 
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  8. Brehm, Christoph ; Pandya, Shishir (Ed.)
    Computational fluid dynamics (CFD) and its uncertainty quantification are computationally expensive. We use Gaussian Process (GP) methods to demonstrate that machine learning can build efficient and accurate surrogate models to replace CFD simulations with significantly reduced computational cost without compromising the physical accuracy. We also demonstrate that both epistemic uncertainty (machine learning model uncertainty) and aleatory uncertainty (randomness in the inputs of CFD) can be accommodated when the machine learning model is used to reveal fluid dynamics. The demonstration is performed by applying simulation of Hagen-Poiseuille and Womersley flows that involve spatial and spatial-tempo responses, respectively. Training points are generated by using the analytical solutions with evenly discretized spatial or spatial-temporal variables. Then GP surrogate models are built using supervised machine learning regression. The error of the GP model is quantified by the estimated epistemic uncertainty. The results are compared with those from GPU-accelerated volumetric lattice Boltzmann simulations. The results indicate that surrogate models can produce accurate fluid dynamics (without CFD simulations) with quantified uncertainty when both epistemic and aleatory uncertainties exist. 
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