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New positive factorizations of the identity in the genus-two mapping class group emerge directly from algorithmic tracking of vanishing cycles across triangulated branched covers.
Minimax lower bounds for kernel discrepancy estimators hold firm at $n^{-1/2}$ even in unbounded spaces, reshaping our understanding of their optimality.
Kernel integrated $R^2$ offers a powerful new way to quantify statistical dependence for complex data types like images or text, where traditional correlation measures fall short.