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Juncheol, Pyo; Nguyen, Dung; Tran, Hung(
, Proceedings of the American Mathematical Society)
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
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 »models while achieving considerably stronger privacy protections and without significantly raising computational costs. This work is the first to apply modern and general federated learning methods that explicitly incorporate differential privacy to clinical and epidemiological research—across a spectrum of units of federation, model architectures, complexity of learning tasks and diseases. As a result, it enables health research participants to remain in control of their data and still contribute to advancing science—aspects that used to be at odds with each other.« less
Free, publicly-accessible full text available December 1, 2022
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