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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.