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Following Bauschke and Combettes (Convex analysis and monotone operator theory in Hilbert spaces, Springer, Cham, 2017), we introduce ProxNet, a collection of deep neural networks with ReLU activation which emulate numerical solution operators of variational inequalities (VIs). We analyze the...
Dyson’s rank function and the Andrews–Garvan crank function famously give combinatorial witnesses for Ramanujan’s partition function congruences modulo 5, 7, and 11. While these functions can be used to show that the corresponding sets of partitions split into 5, 7, or 11 equally sized sets, one...
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