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1. Snowflake: Supporting Programming and Proofs

   Alabi, Oluwatobi; Vu, Anh; Osera, Peter-Michael (March 2023, SIGCSE 2023: Proceedings of the 54th ACM Technical Symposium on Computer Science Education)

   Rigorous, mathematical reasoning, i.e., proof, is the foundation of any undergraduate computer science education. However, students find mathematical proof exceedingly challenging, but also at the same time do not see its relevance to programming. We address these concerns with Snowflake, an educational proof assistant designed to help undergraduates overcome these difficulties when authoring mathematical proof. Snowflake does this by operating in a context where mathematical proof is introduced alongside programming in either a CS1 or CS2 context. The lens that we use to unite the two concepts is program correctness, a topic that immediately makes relevant the concept of formal reasoning as students are perpetually faced with the issue of whether their code is correct. Snowflake is a proof assistant designed for the needs of undergraduates in courses that closely time programming and proof. It is a web-based application that helps students author proofs not only in the context of program correctness in-the-small, but also other topics found in discrete mathematics courses. We report on the design of Snowflake, the kinds of reasoning it enables, and our plans to deploy Snowflake in the classroom. 

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2. Interlace polynomials of 4n-snowflake graphs

   https://doi.org/10.5614/ejgta.2023.11.1.14  

   Champanerkar, Jyoti; Li, Aihua (April 2023, Electronic Journal of Graph Theory and Applications)
3. Snowflake Measurement and Analysis System (SMAS)

   https://doi.org/10.1109/AP-S/USNC-URSI47032.2022.9886325  

   Thant, H; Huang, G.-J.; Bringi, V.N.; Notaros, B. M (January 2022, Proceedings of the 2022 IEEE International Symposium on Antennas and Propagation, July 10–15, 2022, Denver, Colorado)
4. A universal scaling law for Lagrangian snowflake accelerations in atmospheric turbulence

   https://doi.org/10.1063/5.0173359  

   Singh, Dhiraj K; Pardyjak, Eric R; Garrett, Timothy J (December 2023, Physics of Fluids)

   We use a novel experimental setup to obtain the vertical velocity and acceleration statistics of snowflakes settling in atmospheric surface-layer turbulence, for Taylor microscale Reynolds numbers (Reλ) between 400 and 67 000, Stokes numbers (St) between 0.12 and 3.50, and a broad range of snowflake habits. Despite the complexity of snowflake structures and the non-uniform nature of the turbulence, we find that mean snowflake acceleration distributions can be uniquely determined from the value of St. Ensemble-averaged snowflake root mean square (rms) accelerations scale nearly linearly with St. Normalized by the rms value, the acceleration distribution is nearly exponential, with a scaling factor for the (exponent) of −3/2 that is independent of Reλ and St; kurtosis scales with Reλ, albeit weakly compared to fluid tracers in turbulence; gravitational drift with sweeping is observed for St < 1. Surprisingly, the same exponential distribution describes a pseudo-acceleration calculated from fluctuations of snowflake terminal fall speed in still air. This equivalence suggests an underlying connection between how turbulence determines the trajectories of particles and the microphysics determining the evolution of their shapes and sizes. 

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5. Advanced Deep Learning-Based Supervised Classification of Multi-Angle Snowflake Camera Images

   https://doi.org/10.1175/JTECH-D-20-0189.1  

   Key, C.; Hicks, A.; Notaroš, B. M. (June 2021, Journal of Atmospheric and Oceanic Technology)

   null (Ed.)

   Abstract We present improvements over our previous approach to automatic winter hydrometeor classification by means of convolutional neural networks (CNNs), using more data and improved training techniques to achieve higher accuracy on a more complicated dataset than we had previously demonstrated. As an advancement of our previous proof-of-concept study, this work demonstrates broader usefulness of deep CNNs by using a substantially larger and more diverse dataset, which we make publicly available, from many more snow events. We describe the collection, processing, and sorting of this dataset of over 25,000 high-quality multiple-angle snowflake camera (MASC) image chips split nearly evenly between five geometric classes: aggregate, columnar crystal, planar crystal, graupel, and small particle. Raw images were collected over 32 snowfall events between November 2014 and May 2016 near Greeley, Colorado and were processed with an automated cropping and normalization algorithm to yield 224x224 pixel images containing possible hydrometeors. From the bulk set of over 8,400,000 extracted images, a smaller dataset of 14,793 images was sorted by image quality and recognizability (Q&R) using manual inspection. A presorting network trained on the Q&R dataset was applied to all 8,400,000+ images to automatically collect a subset of 283,351 good snowflake images. Roughly 5,000 representative examples were then collected from this subset manually for each of the five geometric classes. With a higher emphasis on in-class variety than our previous work, the final dataset yields trained networks that better capture the imperfect cases and diverse forms that occur within the broad categories studied to achieve an accuracy of 96.2% on a vastly more challenging dataset. 

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