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This work presents gauge-equivariant architectures for flow-based sampling in fermionic lattice field theories using pseudofermions as stochastic estimators for the fermionic determinant. This is the default approach in state-of-the-art lattice field theory calculations, making this development critical to the practical application of flow models to theories such as QCD. Methods by which flow-based sampling approaches can be improved via standard techniques such as even/odd preconditioning and the Hasenbusch factorization are also outlined. Numerical demonstrations in two-dimensional U(1) and SU(3) gauge theories with $N_f=2$ flavors of fermions are provided., Comment: 15 pages, 7 figures. v3: accepted version for publication. New appendix C

We review problems raised by Fe II emission in AGNs and address the question of its relationship to other broad-line region (BLR) lines. The self-shielding, stratified, BLR model of Gaskell, Klimek & Nazarova (2007; GKN) predicts that Fe II emission comes from twice the radius of H$\beta$, in agreement with widths of lines of Fe II lines being only 70% of the widths of H$\beta$. This disagrees with some reverberation mapping results which have suggested that Fe II and H$\beta$ arise at similar radii. The highest quality reverberation mapping, however, supports the predictions that Fe II comes from twice the radius of H$\beta$. We suggest that lower quality reverberation mapping of Fe II is biased to give too small lags. We conclude that, in agreement with the GKN model, the region emitting Fe II is the outermost part of the BLR just inside the surrounding dust. The model naturally gives the Doppler broadening require by models of Fe II emission. Optical Fe II emission implies typical reddenings of E(B-V) ~ 0.20. This helps explain the ratio of UV to optical Fe II emission. Simulations show that the amplitude of Fe II variability is consistent with being the same as for H$\beta$ variability. The FeII/H$\beta$ ratio is a good proxy for the Eddington ratio. The ratio might be driven in part by the strong soft X-ray excess because the X-rays destroy grains and release iron into the gas phase. We propose that the correlation of Fe II strength with radio and host galaxy properties is a result of AGN downsizing., Comment: Accepted for publication in Astronomische Nachrichten. 21 pages. 13 figures