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This study examined the relations among strategic planning, execution, and strategy efficiency during problem-solving in a digital algebra learning game with 7th-grade students. We used pre-solving pause time as a proxy indicator of strategic planning, and the productivity of the initial strategy as a measure of effective strategy execution. Additionally, we explored how these variables correlated with students’ posttest scores assessing algebraic knowledge. Mediation analyses at both the problem and student levels indicated that longer pre-solving pause times were associated with greater strategy efficiency. When considering both the direct and indirect effects of pre-solving pause time on strategy efficiency, the results revealed a partial positive mediation through the productivity of the initial strategy. Lastly, the results of a path analysis showed that strategy efficiency significantly predicted algebraic knowledge with a positive effect. These findings suggest that longer pause times are associated with more efficient problem solving as they increase the likelihood of a productive initial step, highlighting a positive mediating role of execution in the relation between planning and strategy efficiency in algebraic problem solving. 

In optimal experimental design, the objective is to select a limited set of experiments that maximizes information about unknown model parameters based on factor levels. This work addresses the generalized D-optimal design problem, allowing for nonlinear relationships in factor levels. We develop scalable algorithms suitable for cases where the number of candidate experiments grows exponentially with the factor dimension, focusing on both first- and second-order models under design constraints. Particularly, our approach integrates convex relaxation with pricing-based local search techniques, which can provide upper bounds and performance guarantees. Unlike traditional local search methods, such as the ``Fedorov exchange" and its variants, our method effectively accommodates arbitrary side constraints in the design space. Furthermore, it yields both a feasible solution and an upper bound on the optimal value derived from the convex relaxation. Numerical results highlight the efficiency and scalability of our algorithms, demonstrating superior performance compared to the state-of-the-art commercial software, \texttt{JMP}. 

Accurate identification of inundated areas is crucial for mitigating the impacts of flooding, which causes numerous casualties and significant economic losses. While polarimetric synthetic aperture radar (PolSAR) data have been utilized to detect inundated regions, the information contained within PolSAR features remains severely underutilized. We introduce a novel approach that involves extracting a large number of PolSAR features through various PolSAR decomposition techniques, selecting the most important ones using the decision tree–recursive feature elimination (DT-RFE) method, and ultimately detecting inundation using a convolutional neural network (CNN) model. The hybrid DT-RFE–CNN model was trained and tested over a region in southeastern North Carolina during Hurricane Florence on September 18, 2018, using PolSAR features derived from the Uninhabited Aerial Vehicle Synthetic Aperture Radar (UAVSAR). In terms of flood-mapping efficacy, the DT-RFE–CNN model outperformed a CNN model that used only PolSAR data across all metrics in both the training and testing stages. The performance of the trained DT-RFE–CNN model was evaluated by testing it over the same region for four more days (September 19, 20, 22, and 23, 2018); it achieved an average accuracy, precision, recall, F1 score, and intersection-over-union of 0.9304, 0.9089, 0.9584, 0.9324, and 0.8738, respectively, outperforming both the classical Otsu method and the FT-Transformer model using features selected by DT-RFE. Finally, we assessed the model’s generalizability by mapping another significant flood event, caused by Hurricane Harvey in Texas between August and September 2017. Based on the results, the hybrid model can accurately detect flooding, even in regions on which it has not been trained. Thus, the proposed method can facilitate flood monitoring and response efforts. 

Large language models (LLMs) are notoriously memory-intensive during training, particularly with the popular AdamW optimizer. This memory burden necessitates using more or higher-end GPUs or reducing batch sizes, limiting training scalability and throughput. To address this, various memory-efficient optimizers have been proposed to reduce optimizer memory usage. However, they face critical challenges: (i) reliance on costly SVD operations; (ii) significant performance trade-offs compared to AdamW; and (iii) still substantial optimizer memory overhead to maintain competitive performance. In this work, we identify that AdamW's learning rate adaptation rule can be effectively coarsened as a structured learning rate update. Based on this insight, we propose Approximated Gradient Scaling for Memory-Efficient LLM Optimization (APOLLO), which approximates learning rate scaling using an auxiliary low-rank optimizer state based on pure random projection. This structured learning rate update rule makes APOLLO highly tolerant to further memory reductions while delivering comparable pre-training performance. Even its rank-1 variant, APOLLO-Mini, achieves superior pre-training performance compared to AdamW with SGD-level memory costs. Extensive experiments demonstrate that the APOLLO series performs on-par with or better than AdamW, while achieving greater memory savings by nearly eliminating the optimization states of AdamW. These savings provide significant system-level benefits: (1) Enhanced Throughput: 3x throughput on an 8xA100-80GB setup compared to AdamW by supporting 4x larger batch sizes. (2) Improved Model Scalability: Pre-training LLaMA-13B with naive DDP on A100-80GB GPUs without system-level optimizations. (3) Low-End GPU Friendly Pre-training: Pre-training LLaMA-7B on a single GPU using less than 12 GB of memory with weight quantization. 

Recent work withJWSThas demonstrated its capability to identify and chemically characterize multiple populations in globular clusters down to the H-burning limit. In this study, we explore the kinematics of multiple populations in the globular cluster 47 Tucanae by combining data fromJWST, HST, Gaia, and ground-based telescopes. We analyzed velocity dispersion and anisotropy profiles from the cluster center out to ∼10R_h. Our findings indicate that while first population (1G) stars’ motions are isotropic, second population (2G) stars’ motions are significantly radially anisotropic. These results align with the predictions of simulations of the dynamical evolution of clusters where 2G stars are initially more centrally concentrated than 1G stars. Furthermore, we subdivided the 2G population into two subpopulations: 2G_Aand 2G_B, with the latter being more chemically extreme. We compared their dynamical profiles and found no significant differences. For the first time, we measured the degree of energy equipartition among the multiple populations of 47 Tucanae. Overall, within the analyzed radial range (∼2–4R_h), both populations exhibit a low degree of energy equipartition. The most significant differences between 1G and 2G stars are observed in the tangential velocity component, where 2G stars are characterized by a stronger degree of energy equipartition than 1G stars. In the radial component, the behavior of 1G and 2G stars is more variable, with differences largely dependent on radius. Moreover, our analysis reveals that the ratio of rotational velocity to velocity dispersion is larger for the 2G population. Finally, we found that 1G stars exhibit a higher skewness in their tangential proper motions than 2G stars, providing additional evidence of kinematic differences between the two stellar generations. 

This Letter presents a spatial filter based on saturated absorption in gas as an alternative to the solid pinhole in a lens–pinhole–lens filtering system. We develop an analytic model that describes this process and demonstrate spatial filtering with simulations and experiments. We show that an ultraviolet laser pulse focused through ozone will have its spatial profile cleaned if its peak fluence rises above the ozone saturation fluence. Specifically, we demonstrate that a 5 ns 266 nm beam with 4.2 mJ of the initial energy can be effectively cleaned by focusing through a 1.4% ozone–oxygen mixture, with about 76% of the main beam energy transmitted and 89% of the sidelobe energy absorbed. This process can be adapted to other gases and laser wavelengths, providing alignment-insensitive and damage-resistant pinholes for high-repetition-rate high-energy lasers.