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Elementary construction of some Jenkins-Strebel differentials

We give an explicit multi-parametric construction for Jenkins-Strebel differentials on real algebraic curves. Roughly speaking, the square of any real holomorphic abelian differential subjected to certain linear restrictions will be a JS quadratic differential.
arxiv.org

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Estimation for High-Dimensional Linear Mixed-Effects Models Using $\ell_1$-Penalization

We propose an $\ell_1$-penalized estimation procedure for high-dimensional linear mixed-effects models. The models are useful whenever there is a grouping structure among high-dimensional observations, i.e. for clustered data. We prove a consistency and an oracle optimality result and we develop an algorithm with provable numerical convergence. Furthermore, we demonstrate the performance of the method on simulated and a real high-dimensional data set.
arxiv.org

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