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In this paper, we study the first eigenvalue of the Jacobi operator on an integral n-varifold with constant mean curvature in the unit sphere Sn+1. We found the optimal upper bound and prove a rigidity result characterizing the case when it is attained. This gives a new characterization for certain singular Clifford tori.Free, publicly-accessible full text available January 1, 2023
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Abstract Privacy protection is paramount in conducting health research. However, studies often rely on data stored in a centralized repository, where analysis is done with full access to the sensitive underlying content. Recent advances in federated learning enable building complex machine-learned models that are trained in a distributed fashion. These techniques facilitate the calculation of research study endpoints such that private data never leaves a given device or healthcare system. We show—on a diverse set of single and multi-site health studies—that federated models can achieve similar accuracy, precision, and generalizability, and lead to the same interpretation as standard centralized statisticalmore »Free, publicly-accessible full text available December 1, 2022