AbstractWe will review some recent progress on the general geometric behavior of homologically area-minimizing subvarieties, namely, objects that minimize area with respect to homologous competitors. They are prevalent in geometry, for instance, as holomorphic subvarieties of a Kahler manifold, or as special Lagrangians on a Calabi-Yau, etc. A fine understanding of the geometric structure of ho...
In statistical learning, various mathematical optimalities are used to characterize performances of different learning methods. They include minimax optimality from a worst-case standpoint and asymptotic efficiency from a rosy view that the regression function to be learned sits there to be discovered. When multiple models, e.g., trees, neural networks and support vector machines, are considere...
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