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1. From graphs as task to graphs as tool

   https://doi.org/10.1002/tea.21930  

   Stephens, A Lynn (May 2024, Journal of Research in Science Teaching)

   Abstract It is widely recognized that we need to prepare students to think with data. This study investigates student interactions with digital data graphs and seeks to identify what might prompt them to shift toward using their graphs as thinking tools in the authentic activity of doing science. Drawing from video screencast data of three small groups engaged in sensor‐based and computer simulation‐based experiments in high school physics classes, exploratory qualitative methods are used to identify the student interactions with their graphs and what appeared to prompt shifts in those interactions. Analysis of the groups, one from a 9th grade class and two from 11th/12th grade combined classes, revealed that unexpected data patterns and graphical anomalies sometimes, but not always, preceded deeper engagement with the graphs. When shifts toward deeper engagement did occur, transcripts revealed that the students perceived the graphical patterns to be misaligned with the actions they had taken to produce those data. Misalignments between the physical, digital, and conceptual worlds of the investigations played an important role in these episodes, appearing to motivate students to revise either their experimental procedures or their conceptions of the phenomena being explored. If real‐time graphs can help foster a sense in students that there should be alignments between their data production and data representations, it is suggested that pedagogy leverage this as a way to support deeper student engagement with graphs. 

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2. Dependent type systems as macros

   https://doi.org/10.1145/3371071  

   Chang, Stephen; Ballantyne, Michael; Turner, Milo; Bowman, William_J (December 2019, Proceedings of the ACM on Programming Languages)

   We present Turnstile+, a high-level, macros-based metaDSL for building dependently typed languages. With it, programmers may rapidly prototype and iterate on the design of new dependently typed features and extensions. Or they may create entirely new DSLs whose dependent type ``power'' is tailored to a specific domain. Our framework's support of language-oriented programming also makes it suitable for experimenting with systems of interacting components, e.g., a proof assistant and its companion DSLs. This paper explains the implementation details of Turnstile+, as well as how it may be used to create a wide-variety of dependently typed languages, from a lightweight one with indexed types, to a full spectrum proof assistant, complete with a tactic system and extensions for features like sized types and SMT interaction. 

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3. Soybean growth and production as affected by struvite as a phosphorus source in eastern Arkansas

   https://doi.org/10.1002/csc2.20852  

   Omidire, Niyi S.; Brye, Kristofor R.; English, Leah; Kekedy‐Nagy, Laszlo; Greenlee, Lauren; Popp, Jennie; Roberts, Trenton L. (January 2023, Crop Science)

   Abstract Struvite (MgNH₄PO₄·6H₂O) has been precipitated from liquid waste streams to recover valuable nutrients, such as phosphorus (P) and nitrogen (N), that can be used as an alternative fertilizer‐P source. Because prior research has focused on greenhouse studies, it is necessary to expand struvite evaluations to the field‐scale to include row‐crop responses. The objective of this field study was to evaluate the effects of two struvite materials (electrochemically precipitated struvite, ECST; and chemically precipitated struvite, CPST) relative to other common fertilizer‐P sources (diammonium phosphate, DAP; triple superphosphate, TSP; rock phosphate, RP; and monoammonium phosphate, MAP) on soybean [Glycine max(L.) Merr.] response and economics in two consecutive growing seasons in a P‐deficient, silt‐loam soil (Aquic Fraglossudalfs) in eastern Arkansas. Averaged across years, soybean aboveground tissue P uptake was largest (P < .05) from ECST (28.4 kg ha⁻¹), which was similar to CPST (26.7 kg ha⁻¹) and TSP (25.9 kg ha⁻¹) and was smallest from RP (21.4 kg ha⁻¹). In 2019, seed yield was largest (P < .05) from ECST (4.1 Mg ha⁻¹), which was similar to DAP, CPST, RP, TSP, and MAP, and was smallest from the unamended control (3.6 Mg ha⁻¹). In 2020, seed yield was numerically greatest from CPST (2.8 Mg ha⁻¹) and was numerically smallest from ECST (2.2 Mg ha⁻¹). Results showed that wastewater‐recovered struvite materials have the potential to be a viable, alternative fertilizer‐P source for soybean production in a P‐deficient, silt‐loam soil, but further work is needed to confirm struvite's cost effectiveness. 

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4. Associahedra as moment polytopes

   https://doi.org/10.1112/blms.13212  

   Gekhtman, Michael; Thomas, Hugh (December 2024, Bulletin of the London Mathematical Society)

   Abstract Generalized associahedra are a well‐studied family of polytopes associated with a finite‐type cluster algebra and a choice of starting cluster. We show that the generalized associahedra constructed by Padrol, Palu, Pilaud, and Plamondon, building on ideas from Arkani‐Hamed, Bai, He, and Yan, can be naturally viewed as moment polytopes for an open patch of the quotient of the cluster ‐variety with universal coefficients by its maximal natural torus action. We prove our result by showing that the construction of Padrol, Palu, Pilaud, and Plamondon can be understood on the basis of the way that moment polytopes behave under symplectic reduction. 

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5. Realizing finite groups as automizers

   https://doi.org/10.1515/jgth-2022-0145  

   Bayard, Sylvia; Lynd, Justin (February 2024, Journal of Group Theory)

   Abstract It is shown that any finite group 𝐴 is realizable as the automizer in a finite perfect group 𝐺 of an abelian subgroup whose conjugates generate 𝐺.The construction uses techniques from fusion systems on arbitrary finite groups, most notably certain realization results for fusion systems of the type studied originally by Park. 

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