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1. Alkynes to (Free) Carbenes to Polycyclic Cyclopropanes

   https://doi.org/10.1021/jacs.4c10897  

   Guzman, Alexander L; Mann, Alexis N; Hoye, Thomas R (October 2024, Journal of the American Chemical Society)

   ABSTRACT: Carbenes and carbenoids are commonly employed for the synthesis of cyclopropane-containing compounds. Here we report the metal-free, intramolecular cyclopropanation of tethered alkenes by free carbenes derived from alkynes to construct structurally unique, multicyclic cyclopropanes with perfect atom economy. The nature of the tether influences both the rate of carbene formation as well as subsequent competing reaction events. Some of the substrates lead to metastable cyclopropane intermediates that further fragment to furnish interesting isomeric products by mechanistically novel processes. A removable siloxane tether can be utilized to achieve formal intermolecular cyclopropanations and to access cyclopropanol derivatives. 

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2. From Binary Join to Free Join

   https://doi.org/10.1145/3665252.3665259  

   Remy_Wang, Yisu; Willsey, Max; Suciu, Dan (May 2024, ACM SIGMOD Record)

   Over the last decade, worst-case optimal join (WCOJ) algorithms have emerged as a new paradigm for one of the most fundamental challenges in query processing: computing joins efficiently. Such an algorithm can be asymptotically faster than traditional binary joins, all the while remaining simple to understand and implement. However, they have been found to be less efficient than the old paradigm, traditional binary join plans, on the typical acyclic queries found in practice. In an effort to unify and generalize the two paradigms, we proposed a new framework, called Free Join, in our SIGMOD 2023 paper. Not only does Free Join unite the worlds of traditional and worst-case optimal join algorithms, it uncovers optimizations and evaluation strategies that outperform both. In this article, we approach Free Join from the traditional perspective of binary joins, and re-derive the more general framework via a series of gradual transformations. We hope this perspective from the past can help practitioners better understand the Free Join framework, and find ways to incorporate some of the ideas into their own systems. 

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3. Structure-free Graph Condensation: From Large-scale Graphs to Condensed Graph-free Data

   Zheng, Xin; Zhang, Miao; Chen, Chunyang; Nguyen, Quoc_Viet_Hung; Zhu, Xingquan; Pan, Shirui (December 2023, Advances in Neural Information Processing Systems 36 (NeurIPS 2023))

   Oh, A; Naumann, T; Globerson, A; Saenko, K; Hardt, M; Levine, S (Ed.)
4. OBSTRUCTIONS TO FREE ACTIONS ON BAZAIKIN SPACES

   https://doi.org/10.1007/s00031-020-09625-w  

   SAMANI, E KHALILI (December 2022, Transformation Groups)
5. Graphical solutions to one-phase free boundary problems

   https://doi.org/10.1515/crelle-2023-0067  

   Engelstein, Max; Fernández-Real, Xavier; Yu, Hui (October 2023, Journal für die reine und angewandte Mathematik (Crelles Journal))

   Abstract We study viscosity solutions to the classical one-phase problem and its thin counterpart. In low dimensions, we show that when the free boundary is the graph of a continuous function, the solution is the half-plane solution. This answers, in the salient dimensions, a one-phase free boundary analogue of Bernstein’s problem for minimal surfaces.As an application, we also classify monotone solutions of semilinear equations with a bump-type nonlinearity. 

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