Linking engagement and performance: The social network analysis perspective

Theories developed by Tinto and Nora identify academic performance, learning gains, and involvement in learning communities as significant facets of student engagement that, in turn, support student persistence. Collaborative learning environments, such as those employed in the Modeling Instruction introductory physics course, provide structure for student engagement by encouraging peer-to-peer interactions. Because of the inherently social nature of collaborative learning, we examine student interactions in the classroom using network analysis. We use centrality---a family of measures that quantify how connected or "central" a particular student is within the classroom network---to study student engagement longitudinally. Bootstrapped linear regression modeling shows that students' centrality predicts future academic performance over and above prior GPA for three out of four centrality measures tested. In particular, we find that closeness centrality explains 28 % more of the variance than prior GPA alone. These results confirm that student engagement in the classroom is critical to supporting academic performance. Furthermore, we find that this relationship for social interactions does not emerge until the second half of the semester, suggesting that classroom community develops over time in a meaningful way

On the Number of Balanced Words of Given Length and Height over a Two-Letter Alphabet

We exhibit a recurrence on the number of discrete line segments joining two integer points in the plane using an encoding of such segments as balanced words of given length and height over the two-letter alphabet $\{0,1\}$. We give generating functions and study the asymptotic behaviour. As a particular case, we focus on the symmetrical discrete segments which are encoded by balanced palindromes.Comment: 24 page

Neural Posterior Estimation with Differentiable Simulators

Simulation-Based Inference (SBI) is a promising Bayesian inference framework that alleviates the need for analytic likelihoods to estimate posterior distributions. Recent advances using neural density estimators in SBI algorithms have demonstrated the ability to achieve high-fidelity posteriors, at the expense of a large number of simulations ; which makes their application potentially very time-consuming when using complex physical simulations. In this work we focus on boosting the sample-efficiency of posterior density estimation using the gradients of the simulator. We present a new method to perform Neural Posterior Estimation (NPE) with a differentiable simulator. We demonstrate how gradient information helps constrain the shape of the posterior and improves sample-efficiency.Comment: Accepted at the ICML 2022 Workshop on Machine Learning for Astrophysic

The Relationship Between Molecular Gas, HI, and Star Formation in the Low-Mass, Low-Metallicity Magellanic Clouds

The Magellanic Clouds provide the only laboratory to study the effect of metallicity and galaxy mass on molecular gas and star formation at high (~20 pc) resolution. We use the dust emission from HERITAGE Herschel data to map the molecular gas in the Magellanic Clouds, avoiding the known biases of CO emission as a tracer of H$_{2}$. Using our dust-based molecular gas estimates, we find molecular gas depletion times of ~0.4 Gyr in the LMC and ~0.6 SMC at 1 kpc scales. These depletion times fall within the range found for normal disk galaxies, but are shorter than the average value, which could be due to recent bursts in star formation. We find no evidence for a strong intrinsic dependence of the molecular gas depletion time on metallicity. We study the relationship between gas and star formation rate across a range in size scales from 20 pc to ~1 kpc, including how the scatter in molecular gas depletion time changes with size scale, and discuss the physical mechanisms driving the relationships. We compare the metallicity-dependent star formation models of Ostriker, McKee, and Leroy (2010) and Krumholz (2013) to our observations and find that they both predict the trend in the data, suggesting that the inclusion of a diffuse neutral medium is important at lower metallicity.Comment: 24 pages, 14 figures, accepted for publication in ApJ. FITS files of the dust-based estimates of the H2 column densities for the LMC and SMC (shown in Figures 2 and 3) will be available online through Ap

Haplotype Network Branch Diversity, a New Metric Combining Genetic and Topological Diversity to Compare the Complexity of Haplotype Networks

A common way of illustrating phylogeographic results is through the use of haplotype networks. While these networks help to visualize relationships between individuals, populations, and species, evolutionary studies often only quantitatively analyze genetic diversity among haplotypes and ignore other network properties. Here, we present a new metric, haplotype network branch diversity (HBd), as an easy way to quantifiably compare haplotype network complexity. Our metric builds off the logic of combining genetic and topological diversity to estimate complexity previously used by the published metric haplotype network diversity (HNd). However, unlike HNd which uses a combination of network features to produce complexity values that cannot be defined in probabilistic terms, thereby obscuring the values’ implication for a sampled population, HBd uses frequencies of haplotype classes to incorporate topological information of networks, keeping the focus on the population and providing easy-to-interpret probabilistic values for randomly sampled individuals. The goal of this study is to introduce this more intuitive metric and provide an R script that allows researchers to calculate diversity and complexity indices from haplotype networks. A group of datasets, generated manually (model dataset) and based on published data (empirical dataset), were used to illustrate the behavior of HBd and both of its terms, haplotype diversity, and a new index called branch diversity. Results followed a predicted trend in both model and empirical datasets, from low metric values in simple networks to high values in complex networks. In short, the new combined metric joins genetic and topological diversity of haplotype networks, into a single complexity value. Based on our analysis, we recommend the use of HBd, as it makes direct comparisons of network complexity straightforward and provides probabilistic values that can readily discriminate situations that are difficult to resolve with available metrics