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1. DESCRIPTIVE COMPLEXITY IN CANTOR SERIES

   https://doi.org/10.1017/jsl.2021.77  

   AIREY, DYLAN; JACKSON, STEVE; MANCE, BILL (September 2022, The Journal of Symbolic Logic)

   Abstract A Cantor series expansion for a real number x with respect to a basic sequence $$Q=(q_1,q_2,\dots )$$ , where $$q_i \geq 2$$ , is a generalization of the base b expansion to an infinite sequence of bases. Ki and Linton in 1994 showed that for ordinary base b expansions the set of normal numbers is a $$\boldsymbol {\Pi }^0_3$$ -complete set, establishing the exact complexity of this set. In the case of Cantor series there are three natural notions of normality: normality, ratio normality, and distribution normality. These notions are equivalent for base b expansions, but not for more general Cantor series expansions. We show that for any basic sequence the set of distribution normal numbers is $$\boldsymbol {\Pi }^0_3$$ -complete, and if Q is $$1$$ -divergent then the sets of normal and ratio normal numbers are $$\boldsymbol {\Pi }^0_3$$ -complete. We further show that all five non-trivial differences of these sets are $$D_2(\boldsymbol {\Pi }^0_3)$$ -complete if $$\lim _i q_i=\infty $$ and Q is $$1$$ -divergent. This shows that except for the trivial containment that every normal number is ratio normal, these three notions are as independent as possible. 

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2. Race detection and reachability in nearly series-parallel DAGs

   https://doi.org/10.1137/1.9781611975031.11  

   Agrawal, Kunal; Devietti, Joseph; Fineman, Jeremy T.; Lee, I-Ting Angelina; Utterback, Robert; Xu, Changming (January 2018, Twenty-Ninth Annual ACM-SIAM Symposium on Discrete Algorithms)
3. Teaching Series and Parallel Connections

   https://doi.org/10.1109/TE.2021.3129505  

   Skromme, B. J.; Wong, M. L.; Redshaw, C. J.; O'Donnell, M. A. (December 2021, IEEE Transactions on Education)

   Contribution: A new operational definition of series connections is given based on elements belonging to the same two meshes, which is properly dual to the usual definition of parallel elements being connected to the same two nodes. Furthermore, computer-based exercises have been developed and tested to teach students about such connections in gateway linear circuits courses, using color coding of nodes and meshes as a pedagogical device. Background: Series and parallel connections are a crucial but difficult concept. Existing textbooks give them limited attention, resulting in later difficulties learning circuit analysis. Research Questions: RQ1: Can an improved definition of series elements aid student understanding and student satisfaction? RQ2: Can a computer-based ``game'' lead to effective mastery and student satisfaction at a wide range of institutions, including minority-serving ones? Methodology: Standard and new definitions were elaborated in a multiple-choice tutorial. A game was developed focusing on identifying series and parallel connections, with color coding of both nodes and meshes. Student learning was assessed over eight years using pretest and posttest in 14 varied institutions. Student opinions were assessed using several types of surveys. Findings: Strong learning gains were observed every semester from built-in pretest and posttest, with average scores of 28% and 87%, respectively. Large improvements were observed at every institution including five minority-serving ones. The posttest score is increased by a statistically significant amount after introducing the new definition of series elements. Students preferred the new definition of series and recommended its use, and very strongly endorsed color coding. 

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4. Removing aliases in time-series photometry

   https://doi.org/10.1016/j.ascom.2023.100711  

   Kramer, D.; Gowanlock, M.; Trilling, D.; McNeill, A.; Erasmus, N. (July 2023, Astronomy and Computing)
5. Generating series for networks of Chen–Fliess series

   https://doi.org/10.1016/j.sysconle.2020.104827  

   Gray, W. Steven; Ebrahimi-Fard, Kurusch (January 2021, Systems & Control Letters)

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