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1. Estranged facets and k-facets of Gaussian random point sets

   https://doi.org/10.1017/jpr.2024.114  

   Leroux, Brett; Rademacher, Luis (April 2025, Journal of Applied Probability)

   Abstract Gaussian random polytopes have received a lot of attention, especially in the case where the dimension is fixed and the number of points goes to infinity. Our focus is on the less-studied case where the dimension goes to infinity and the number of points is proportional to the dimensiond. We study several natural quantities associated with Gaussian random polytopes in this setting. First, we show that the expected number of facets is equal to$$C(\alpha)^{d+o(d)}$$, where$$C(\alpha)$$is some constant which depends on the constant of proportionality$$\alpha$$. We also extend this result to the expected number ofk-facets. We then consider the more difficult problem of the asymptotics of the expected number of pairs ofestranged facetsof a Gaussian random polytope. When the number of points is 2d, we determine the constantCsuch that the expected number of pairs of estranged facets is equal to$$C^{d+o(d)}$$. 

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2. Facets of Neutrino--Nucleus Interactions

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   Balantekin, A.B. (January 2018, Acta Physica Polonica B)
3. The many facets of shape

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   Todd, James T.; Petrov, Alexander A. (January 2022, Journal of Vision)
4. A Free Boundary Problem with Facets

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   Feldman, William M.; Smart, Charles K. (April 2019, Archive for Rational Mechanics and Analysis)
5. The Many Facets of Data Equity

   Jagadish, H.V.; Stoyanovich, Julia; Howe, Bill (January 2021, theWorkshop Proceedings of the EDBT/ICDT 2021 Joint Conference)

   Costa, Constantinos; Pitoura, Evaggelia (Ed.)

   Data-driven systems can be unfair, in many different ways. All too often, as data scientists, we focus narrowly on one technical aspect of fairness. In this paper, we attempt to address equity broadly, and identify the many different ways in which it is manifest in data-driven systems. 

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