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1. Pairwise Rearrangement is Fixed-Parameter Tractable in the Single Cut-and-Join Model

   https://doi.org/10.4230/LIPIcs.SWAT.2024.3  

   Bailey, Lora; Blake, Heather Smith; Cochran, Garner; Fox, Nathan; Levet, Michael; Mahmoud, Reem; Singgih, Inne; Stadnyk, Grace; Wiedemann, Alexander (January 2024, Schloss Dagstuhl – Leibniz-Zentrum für Informatik)

   Bodlaender, Hans L (Ed.)

   Genome rearrangement is a common model for molecular evolution. In this paper, we consider the Pairwise Rearrangement problem, which takes as input two genomes and asks for the number of minimum-length sequences of permissible operations transforming the first genome into the second. In the Single Cut-and-Join model (Bergeron, Medvedev, & Stoye, J. Comput. Biol. 2010), Pairwise Rearrangement is #P-complete (Bailey, et. al., COCOON 2023), which implies that exact sampling is intractable. In order to cope with this intractability, we investigate the parameterized complexity of this problem. We exhibit a fixed-parameter tractable algorithm with respect to the number of components in the adjacency graph that are not cycles of length 2 or paths of length 1. As a consequence, we obtain that Pairwise Rearrangement in the Single Cut-and-Join model is fixed-parameter tractable by distance. Our results suggest that the number of nontrivial components in the adjacency graph serves as the key obstacle for efficient sampling. 

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2. Metallocarbenes as Substituents in 8‐Electron Electrocyclizations

   https://doi.org/10.1002/ejoc.202301183  

   Cao, Yumeng; Kong, Wang‐Yeuk; DeSnoo, William; Tantillo, Dean_J (January 2024, European Journal of Organic Chemistry)

   Abstract Density functional theory was used to elucidate the mechanism and the pericyclicity of chromium‐catalyzed bicyclization reactions that purportedly involve 8‐electron electrocyclization steps. Our computational results indicate that these reactions do indeed proceed via 8‐electron electrocyclization rather than an alternative pathway involving 4‐electron electrocyclization followed by Cope rearrangement. The role of C=[M] groups on the electrocyclization, specifically its pericyclicity, was examined in detail using modern theoretical tools. 

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3. Highly diastereo- and branched-selective rearrangement of substituted N -alloc- N -allyl ynamides

   https://doi.org/10.1039/d2cc03399b  

   Jackson, Oliver D.; Stankevich, Ksenia S.; Cook, Matthew J. (October 2022, Chemical Communications)

   An auto-tandem catalytic, branched-selective rearrangement of substituted N-alloc-N-allyl ynamides was developed. This reaction provides ready access to complex quaternary nitrile products with vinylogous stereocentres in excellent diastereoselectivity, including contiguous all-carbon quaternary centres. The stereochemical outcome is determined via a Pd(0) catalysed dipolar ketenimine aza-Claisen rearrangement and computational studies exemplify the key role ligand geometry plays. 

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4. N -Acyl pyrroles: chemoselective pyrrole dance vs. C–H functionalization/aroylation of toluenes

   https://doi.org/10.1039/D1QO00944C  

   Wang, Huan; Mao, Jianyou; Shuai, SuJuan; Chen, Shuguang; Zou, Dong; Walsh, Patrick J.; Li, Jie (October 2021, Organic Chemistry Frontiers)

   Chemoselectivity is one of the most challenging issues facing the chemical sciences. In this study, the first highly chemoselective reactions of N -acylpyrroles via either an anionic Fries rearrangement (pyrrole dance) or a C–H functionalization of toluene to provide aryl benzyl ketones are advanced. This efficient and operationally simple approach enables the synthesis of either 2-aroylpyrroles or aryl benzyl ketones in good to excellent yields under transition metal-free conditions. The choice of base plays a crucial role in controlling the chemoselectivity. The aroylation of toluene derivatives was observed with N -acylpyrroles when subjected to KN(SiMe 3 ) 2 , while anionic Fries rearrangement products were produced with LiN(SiMe 3 ) 2 . Surprisingly, cross-over experiments indicate that the anionic Fries rearrangement is an intermolecular process. The aroylation reaction has the advantage over Weinreb amide chemistry in that it does not require preformed organometallic reagents or cryogenic temperatures. 

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5. A rearrangement minimization problem corresponding to p -Laplacian equation

   https://doi.org/10.1051/cocv/2022004  

   Kao, Chiu-Yen; Mohammadi, Seyyed Abbas (January 2022, ESAIM: Control, Optimisation and Calculus of Variations)

   In this paper a rearrangement minimization problem corresponding to solutions of the p -Laplacian equation is considered. The solution of the minimization problem determines the optimal way of exerting external forces on a membrane in order to have a minimum displacement. Geometrical and topological properties of the optimizer is derived and the analytical solution of the problem is obtained for circular and annular membranes. Then, we find nearly optimal solutions which are shown to be good approximations to the minimizer for specific ranges of the parameter values in the optimization problem. A robust and efficient numerical algorithm is developed based upon rearrangement techniques to derive the solution of the minimization problem for domains with different geometries in ℝ 2 and ℝ 3 . 

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