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We prove that energy conservation holds for weak solutions to classical Vlasov-Poisson systems with proper regularity. In particular, there exists a solution that conserves energy with |v|mf0∈Lx,v1for m> 9/4.

Due to advances in automated image acquisition and analysis, whole-brain connectomes with 100,000 or more neurons are on the horizon. Proofreading of whole-brain automated reconstructions will require many person-years of effort, due to the huge volumes of data involved. Here we present FlyWire, an online community for proofreading neural circuits in a Drosophila melanogasterbrain and explain how its computational and social structures are organized to scale up to whole-brain connectomics. Browser-based three-dimensional interactive segmentation by collaborative editing of a spatially chunked supervoxel graph makes it possible to distribute proofreading to individuals located virtually anywhere in the world. Information in the edit history is programmatically accessible for a variety of uses such as estimating proofreading accuracy or building incentive systems. An open community accelerates proofreading by recruiting more participants and accelerates scientific discovery by requiring information sharing. We demonstrate how FlyWire enables circuit analysis by reconstructing and analyzing the connectome of mechanosensory neurons.