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1. Biology Undergraduate Students’ Graphing Practice in Digital Versus Pen and Paper Graphing Environments

   https://doi.org/10.1007/s10956-020-09886-w  

   Gardner, Stephanie M.; Suazo-Flores, Elizabeth; Maruca, Susan; Abraham, Joel K.; Karippadath, Anupriya; Meir, Eli (June 2021, Journal of Science Education and Technology)

   null (Ed.)

   Abstract Graphing is an important practice for scientists and in K-16 science curricula. Graphs can be constructed using an array of software packages as well as by hand, with pen-and-paper. However, we have an incomplete understanding of how students’ graphing practice vary by graphing environment; differences could affect how best to teach and assess graphing. Here we explore the role of two graphing environments in students’ graphing practice. We studied 43 undergraduate biology students’ graphing practice using either pen-and-paper (PP) ( n  = 21 students) or a digital graphing tool GraphSmarts (GS) ( n  = 22 students). Participants’ graphs and verbal justifications were analyzed to identify features such as the variables plotted, number of graphs created, raw data versus summarized data plotted, and graph types (e.g., scatter plot, line graph, or bar graph) as well as participants’ reasoning for their graphing choices. Several aspects of participant graphs were similar regardless of graphing environment, including plotting raw vs. summarized data, graph type, and overall graph quality, while GS participants were more likely to plot the most relevant variables. In GS, participants could easily make more graphs than in PP and this may have helped some participants show latent features of their graphing practice. Those students using PP tended to focus more on ease of constructing the graph than GS. This study illuminates how the different characteristics of the graphing environment have implications for instruction and interpretation of assessments of student graphing practices. 

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2. Local Partition in Rich Graphs

   https://doi.org/10.1109/BigData.2018.8622227  

   Freitas, Scott; Cao, Nan; Xia, Yinglong; Chau, Duen Horng; Tong, Hanghang (December 2018, 2018 IEEE International Conference on Big Data (Big Data))

   Local graph partitioning is a key graph mining tool that allows researchers to identify small groups of interrelated nodes (e.g., people) and their connective edges (e.g., interactions). As local graph partitioning focuses primarily on the graph structure (vertices and edges), it often fails to consider the additional information contained in the attributes. We propose a scalable algorithm to improve local graph partitioning by taking into account both the graph structure and attributes. Experimental results show that our proposed AttriPart algorithm finds up to 1.6× denser local partitions, while running approximately 43× faster than traditional local partitioning techniques (PageRank-Nibble). 

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3. Graph Sparsification, Spectral Sketches, and Faster Resistance Computation, via Short Cycle Decompositions

   https://doi.org/10.1109/FOCS.2018.00042  

   Chu, Timothy; Gao, Yu; Peng, Richard; Sachdeva, Sushant; Sawlani, Saurabh; Wang, Junxing (October 2018, 2018 IEEE 59th Annual Symposium on Foundations of Computer Science)

   Abstract—We develop a framework for graph sparsification and sketching, based on a new tool, short cycle decomposition – a decomposition of an unweighted graph into an edge-disjoint collection of short cycles, plus a small number of extra edges. A simple observation gives that every graph G on n vertices with m edges can be decomposed in O(mn) time into cycles of length at most 2logn, and at most 2n extra edges. We give an m1+o(1) time algorithm for constructing a short cycle decomposition, with cycles of length no(1), and n1+o(1) extra edges. Both the existential and algorithmic variants of this decomposition enable us to make progress on several open problems in randomized graph algorithms. 

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4. Proposing and testing a model relating students’ graph selection and graph reasoning for dynamic situations

   https://doi.org/10.1007/s10649-024-10299-4  

   Johnson, Heather Lynn; Donovan, Courtney; Knurek, Robert; Whitmore, Kristin A.; Bechtold, Livvia (February 2024, Educational Studies in Mathematics)

   Abstract Using a mixed methods approach, we explore a relationship between students’ graph reasoning and graph selection via a fully online assessment. Our population includes 673 students enrolled in college algebra, an introductory undergraduate mathematics course, across four U.S. postsecondary institutions. The assessment is accessible on computers, tablets, and mobile phones. There are six items; for each, students are to view a video animation of a dynamic situation (e.g., a toy car moving along a square track), declare their understanding of the situation, select a Cartesian graph to represent a relationship between given attributes in the situation, and enter text to explain their graph choice. To theorize students’ graph reasoning, we draw on Thompson’s theory of quantitative reasoning, which explains students’ conceptions of attributes as being possible to measure. To code students’ written responses, we appeal to Johnson and colleagues’ graph reasoning framework, which distinguishes students’ quantitative reasoning about one or more attributes capable of varying (Covariation, Variation) from students’ reasoning about observable elements in a situation (Motion, Iconic). Quantitizing those qualitative codes, we examine connections between the latent variables of students’ graph reasoning and graph selection. Using structural equation modeling, we report a significant finding: Students’ graph reasoning explains 40% of the variance in their graph selection (standardized regression weight is 0.64,p < 0.001). Furthermore, our results demonstrate that students’ quantitative forms of graph reasoning (i.e., variational and covariational reasoning) influence the accuracy of their graph selection. 

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5. Graph Neural Networks for Charged Particle Tracking on FPGAs

   https://doi.org/10.3389/fdata.2022.828666  

   Elabd, Abdelrahman; Razavimaleki, Vesal; Huang, Shi-Yu; Duarte, Javier; Atkinson, Markus; DeZoort, Gage; Elmer, Peter; Hauck, Scott; Hu, Jin-Xuan; Hsu, Shih-Chieh; et al (March 2022, Frontiers in Big Data)

   The determination of charged particle trajectories in collisions at the CERN Large Hadron Collider (LHC) is an important but challenging problem, especially in the high interaction density conditions expected during the future high-luminosity phase of the LHC (HL-LHC). Graph neural networks (GNNs) are a type of geometric deep learning algorithm that has successfully been applied to this task by embedding tracker data as a graph—nodes represent hits, while edges represent possible track segments—and classifying the edges as true or fake track segments. However, their study in hardware- or software-based trigger applications has been limited due to their large computational cost. In this paper, we introduce an automated translation workflow, integrated into a broader tool called hls4ml , for converting GNNs into firmware for field-programmable gate arrays (FPGAs). We use this translation tool to implement GNNs for charged particle tracking, trained using the TrackML challenge dataset, on FPGAs with designs targeting different graph sizes, task complexites, and latency/throughput requirements. This work could enable the inclusion of charged particle tracking GNNs at the trigger level for HL-LHC experiments. 

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