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   https://doi.org/10.1109/TNET.2023.3265127  

   Wang, Chen; Hu, Qin; Yu, Dongxiao; Cheng, Xiuzhen (April 2023, IEEE/ACM Transactions on Networking)
2. Virtual Markov Chains

   https://doi.org/10.53733/147  

   Evans, Steven; Jaffe, Adam (September 2021, New Zealand Journal of Mathematics)

   We introduce the space of virtual Markov chains (VMCs) as a projective limit of the spaces of all finite state space Markov chains (MCs), in the same way that the space of virtual permutations is the projective limit of the spaces of all permutations of finite sets.We introduce the notions of virtual initial distribution (VID) and a virtual transition matrix (VTM), and we show that the law of any VMC is uniquely characterized by a pair of a VID and VTM which have to satisfy a certain compatibility condition.Lastly, we study various properties of compact convex sets associated to the theory of VMCs, including that the Birkhoff-von Neumann theorem fails in the virtual setting. 

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3. Minimum variance constrained estimator

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   Mishra, Prabhat K.; Chowdhary, Girish; Mehta, Prashant G. (March 2022, Automatica)
4. Spherical Minimum Description Length

   https://doi.org/10.3390/e20080575  

   Herntier, Trevor; Ihou, Koffi; Smith, Anthony; Rangarajan, Anand; Peter, Adrian (August 2018, Entropy)

   We consider the problem of model selection using the Minimum Description Length (MDL) criterion for distributions with parameters on the hypersphere. Model selection algorithms aim to find a compromise between goodness of fit and model complexity. Variables often considered for complexity penalties involve number of parameters, sample size and shape of the parameter space, with the penalty term often referred to as stochastic complexity. Current model selection criteria either ignore the shape of the parameter space or incorrectly penalize the complexity of the model, largely because typical Laplace approximation techniques yield inaccurate results for curved spaces. We demonstrate how the use of a constrained Laplace approximation on the hypersphere yields a novel complexity measure that more accurately reflects the geometry of these spherical parameters spaces. We refer to this modified model selection criterion as spherical MDL. As proof of concept, spherical MDL is used for bin selection in histogram density estimation, performing favorably against other model selection criteria. 

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5. Minimum Cut and Minimum k -Cut in Hypergraphs via Branching Contractions

   https://doi.org/10.1145/3570162  

   Fox, Kyle; Panigrahi, Debmalya; Zhang, Fred (April 2023, ACM Transactions on Algorithms)

   On hypergraphs withmhyperedges andnvertices, wherepdenotes the total size of the hyperedges, we provide the following results:We give an algorithm that runs in\(\widetilde{O}(mn^{2k-2})\)time for finding a minimumk-cut in hypergraphs of arbitrary rank. This algorithm betters the previous best running time for the minimumk-cut problem, fork> 2.We give an algorithm that runs in\(\widetilde{O}(n^{\max \lbrace r,2k-2\rbrace })\)time for finding a minimumk-cut in hypergraphs of constant rankr. This algorithm betters the previous best running times for both the minimum cut and minimumk-cut problems for dense hypergraphs.Both of our algorithms are Monte Carlo, i.e., they return a minimumk-cut (or minimum cut) with high probability. These algorithms are obtained as instantiations of a genericbranching randomized contractiontechnique on hypergraphs, which extends the celebrated work of Karger and Stein on recursive contractions in graphs. Our techniques and results also extend to the problems of minimum hedge-cut and minimum hedge-k-cut on hedgegraphs, which generalize hypergraphs. 

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