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1. Unimodular graded Poisson Hopf algebras: GRADED POISSON HOPF ALGEBRAS

   https://doi.org/10.1112/blms.12194  

   Brown, Kenneth A.; Zhang, James J. (October 2018, Bulletin of the London Mathematical Society)
2. Poisson Trace Orders

   https://doi.org/10.1093/imrn/rnad086  

   Brown, Ken; Yakimov, Milen (May 2023, International Mathematics Research Notices)

   Abstract The two main approaches to the study of irreducible representations of orders (via traces and Poisson orders) have so far been applied in a completely independent fashion. We define and study a natural compatibility relation between the two approaches leading to the notion of Poisson trace orders. It is proved that all regular and reduced traces are always compatible with any Poisson order structure. The modified discriminant ideals of all Poisson trace orders are proved to be Poisson ideals and the zero loci of discriminant ideals are shown to be unions of symplectic cores, under natural assumptions (maximal orders and Cayley–Hamilton algebras). A base change theorem for Poisson trace orders is proved. A broad range of Poisson trace orders are constructed based on the proved theorems: quantized universal enveloping algebras, quantum Schubert cell algebras and quantum function algebras at roots of unity, symplectic reflection algebras, 3D and 4D Sklyanin algebras, Drinfeld doubles of pre-Nichols algebras of diagonal type, and root of unity quantum cluster algebras. 

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3. Poisson Count Time Series

   Kong Jiajie; Lund, Robert (February 2024, Journal of Time Series Analysis)

   Robert Taylor (Ed.)
4. Poisson Vector Graphics (PVG)

   https://doi.org/10.1109/TVCG.2018.2867478  

   Hou, Fei; Sun, Qian; Fang, Zheng; Liu, Yong-Jin; Hu, Shi-Min; Qin, Hong; Hao, Aimin; He, Ying (February 2020, IEEE Transactions on Visualization and Computer Graphics)

   null (Ed.)
5. Generalized fiducial inference on the mean of zero-inflated Poisson and Poisson hurdle models

   https://doi.org/10.1186/s40488-021-00117-0  

   Zou, Yixuan; Hannig, Jan; Young, Derek S. (December 2021, Journal of Statistical Distributions and Applications)

   null (Ed.)

   Abstract Zero-inflated and hurdle models are widely applied to count data possessing excess zeros, where they can simultaneously model the process from how the zeros were generated and potentially help mitigate the effects of overdispersion relative to the assumed count distribution. Which model to use depends on how the zeros are generated: zero-inflated models add an additional probability mass on zero, while hurdle models are two-part models comprised of a degenerate distribution for the zeros and a zero-truncated distribution. Developing confidence intervals for such models is challenging since no closed-form function is available to calculate the mean. In this study, generalized fiducial inference is used to construct confidence intervals for the means of zero-inflated Poisson and Poisson hurdle models. The proposed methods are assessed by an intensive simulation study. An illustrative example demonstrates the inference methods. 

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