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Abstract Students lose interest in science as they progress from elementary to high school. There is a need for authentic, place‐based science learning experiences that can increase students' interest in science. Scientists have unique skillsets that can complement the work of educators to create exciting experiences that are grounded in pedagogy and science practices. As scientists and educators, we co‐developed a lesson plan for high school students on the Eastern Shore of Virginia, a historically underserved coastal area, that demonstrated realistic scientific practices in students' local estuaries. After implementation of the lesson plan, we observed that students had a deeper understanding of ecosystem processes compared to their peers who had not been involved, were enthusiastic about sharing their experiences, and had a more well‐rounded ability to think like a scientist than before the lesson plan. We share our experiences and five best practices that can serve as a framework for scientists and educators who are motivated to do similar work. Through collaboration, scientists and educators have the potential to bolster student science identities and increase student participation in future scientific endeavors. 

Heart rate variability (HRV) features support several clinical applications, including sleep staging, and ballistocardiograms (BCGs) can be used to unobtrusively estimate these features. Electrocardiography is the traditional clinical standard for HRV estimation, but BCGs and electrocardiograms (ECGs) yield different estimates for heartbeat intervals (HBIs), leading to differences in calculated HRV parameters. This study examines the viability of using BCG-based HRV features for sleep staging by quantifying the impact of these timing differences on the resulting parameters of interest. We introduced a range of synthetic time offsets to simulate the differences between BCG- and ECG-based heartbeat intervals, and the resulting HRV features are used to perform sleep staging. Subsequently, we draw a relationship between the mean absolute error in HBIs and the resulting sleep-staging performances. We also extend our previous work in heartbeat interval identification algorithms to demonstrate that our simulated timing jitters are close representatives of errors between heartbeat interval measurements. This work indicates that BCG-based sleep staging can produce accuracies comparable to ECG-based techniques such that at an HBI error range of up to 60 ms, the sleep-scoring error could increase from 17% to 25% based on one of the scenarios we examined. 

Finding locally optimal solutions for MAX-CUT and MAX- k -CUT are well-known PLS-complete problems. An instinctive approach to finding such a locally optimum solution is the FLIP method. Even though FLIP requires exponential time in worst-case instances, it tends to terminate quickly in practical instances. To explain this discrepancy, the run-time of FLIP has been studied in the smoothed complexity framework. Etscheid and Röglin (ACM Transactions on Algorithms, 2017) showed that the smoothed complexity of FLIP for max-cut in arbitrary graphs is quasi-polynomial. Angel, Bubeck, Peres, and Wei (STOC, 2017) showed that the smoothed complexity of FLIP for max-cut in complete graphs is ( O Φ 5 n 15.1 ), where Φ is an upper bound on the random edge-weight density and Φ is the number of vertices in the input graph. While Angel, Bubeck, Peres, and Wei’s result showed the first polynomial smoothed complexity, they also conjectured that their run-time bound is far from optimal. In this work, we make substantial progress toward improving the run-time bound. We prove that the smoothed complexity of FLIP for max-cut in complete graphs is O (Φ n 7.83 ). Our results are based on a carefully chosen matrix whose rank captures the run-time of the method along with improved rank bounds for this matrix and an improved union bound based on this matrix. In addition, our techniques provide a general framework for analyzing FLIP in the smoothed framework. We illustrate this general framework by showing that the smoothed complexity of FLIP for MAX-3-CUT in complete graphs is polynomial and for MAX - k - CUT in arbitrary graphs is quasi-polynomial. We believe that our techniques should also be of interest toward showing smoothed polynomial complexity of FLIP for MAX - k - CUT in complete graphs for larger constants k .