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1. The set of bounded continuous nowhere locally uniformly continuous functions is not Borel

   Alexander J. Izzo (January 2022, Houston journal of mathematics)

   It is known that for $$X$$ a nowhere locally compact metric space, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $$X$$ contains a dense $$G_\delta$$ set in the space $$C_b(X)$$ of all bounded continuous real-valued functions on $$X$$ in the supremum norm. Furthermore, when $$X$$ is separable, the set of bounded continuous, nowhere locally uniformly continuous real-valued functions on $$X$$ is itself a $$G_\delta$$ set. We show that in contrast, when $$X$$ is nonseparable, this set of functions is not even a Borel set. 

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2. One size does not fit all: an empirical study of containerized continuous deployment workflows

   https://doi.org/10.1145/3236024.3236033  

   Zhang, Yang; Vasilescu, Bogdan; Wang, Huaimin; Filkov, Vladimir (January 2018, Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering)
3. 1129-P: Continuous Glucose Monitoring (CGM) Initiation Shortly after Diagnosis Does Not Worsen Psychosocial States

   https://doi.org/10.2337/db23-1129-P  

   ADDALA, ANANTA; RITTER, VICTOR; SHAW, BLAKE; PANG, ERICA; CORTES-NAVARRO, ANA L.; BALISTRERI, ILENIA; LOYOLA, ALONDRA; ALAMARIE, SELMA A.; SCHNEIDER-UTAKA, AIKA; BISHOP, FRANZISKA K.; et al (June 2023, Diabetes)

   Psychosocial impacts of early CGM initiation in youth soon after T1D diagnosis are underexplored. We report parent/guardian (PG) and youth trends in Patient Reported Outcomes (PROs) for families in the 4T Study 1. Of the 133 participants in the 4T Study 1, 125 PG and 60 youth (≥11 years) were eligible for PROs. PROs included Diabetes Distress Scale - Parent (mean DDS-P) for PG and for youth, Diabetes Distress Scale (DDS sum), PROMIS Pediatric Global Health (PGH sum), Diabetes Technology Attitudes (DTA sum), and CGM Benefits/Burden (BenCGM and BurCGM sum). Kruskal Wallis rank sum test evaluated temporal trends and sociodemographics were evaluated (Numerical: Wilcoxon rank; Categorical: Fisher's if n<5, Chi-squared if n≥5). PROs completion rates were higher for PG than youth at baseline (74% v 59%), 3 months (70% v 53%), and 6 months (66% v 50%). PG DDS-P remained low throughout the study (Table). Youth had favorable psychosocial trends (low DDS and high PGH), and perceived technology positively (high DTA and BenCGM with low BurCGM). Age, DKA at diagnosis, gender, ethnicity, insurance status, and language spoken were not associated with PROs scores in PG or youth. CGM initiation shortly after T1D diagnosis is not associated with poor or worsening PROs for PG and youth. These data suggest that early CGM initiation does not adversely impact psychosocial states for families and youth with T1D. Disclosure A.Addala: None. F.K.Bishop: None. D.P.Zaharieva: Advisory Panel; Dexcom, Inc., Research Support; Hemsley Charitable Trust, International Society for Pediatric and Adolescent Diabetes, Insulet Corporation, Speaker's Bureau; American Diabetes Association, Ascensia Diabetes Care, Medtronic. P.Prahalad: None. M.Desai: None. D.M.Maahs: Advisory Panel; Medtronic, LifeScan Diabetes Institute, MannKind Corporation, Consultant; Abbott, Research Support; Dexcom, Inc. K.K.Hood: Consultant; Cecelia Health. V.Ritter: None. B.Shaw: None. E.Pang: None. A.L.Cortes-navarro: None. I.Balistreri: None. A.Loyola: None. S.A.Alamarie: None. A.Schneider-utaka: None. Funding National Institutes of Health (K23DK13134201, R18DK122422) 

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4. Learning continuous models for continuous physics

   https://doi.org/10.1038/s42005-023-01433-4  

   Krishnapriyan, Aditi S; Queiruga, Alejandro F; Erichson, N Benjamin; Mahoney, Michael W (December 2023, Communications Physics)

   Dynamical systems that evolve continuously over time are ubiquitous throughout science and engineering. Machine learning (ML) provides data-driven approaches to model and predict the dynamics of such systems. A core issue with this approach is that ML models are typically trained on discrete data, using ML methodologies that are not aware of underlying continuity properties. This results in models that often do not capture any underlying continuous dynamics—either of the system of interest, or indeed of any related system. To address this challenge, we develop a convergence test based on numerical analysis theory. Our test verifies whether a model has learned a function that accurately approximates an underlying continuous dynamics. Models that fail this test fail to capture relevant dynamics, rendering them of limited utility for many scientific prediction tasks; while models that pass this test enable both better interpolation and better extrapolation in multiple ways. Our results illustrate how principled numerical analysis methods can be coupled with existing ML training/testing methodologies to validate models for science and engineering applications. 

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5. Continuous LWE

   Bruna, J; Regev, O; Song, M; Tang, Y (June 2021, Proceedings of the Annual ACM Symposium on Theory of Computing)

   null (Ed.)

   We introduce a continuous analogue of the Learning with Errors (LWE) problem, which we name CLWE. We give a polynomial-time quantum reduction from worst-case lattice problems to CLWE, showing that CLWE enjoys similar hardness guarantees to those of LWE. Alternatively, our result can also be seen as opening new avenues of (quantum) attacks on lattice problems. Our work resolves an open problem regarding the computational complexity of learning mixtures of Gaussians without separability assumptions (Diakonikolas 2016, Moitra 2018). As an additional motivation, (a slight variant of) CLWE was considered in the context of robust machine learning (Diakonikolas et al. FOCS 2017), where hardness in the statistical query (SQ) model was shown; our work addresses the open question regarding its computational hardness (Bubeck et al. ICML 2019). 

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