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Aliasing refers to the phenomenon that high frequency signals degenerate into com- pletely different ones after sampling. It arises as a problem in the context of deep learning as downsampling layers are widely adopted in deep architectures to reduce parameters and computation. The standard solution is to apply a low-pass filter (e.g., Gaussian blur) before downsampling [37]. However, it can be suboptimal to apply the same filter across the entire content, as the frequency of feature maps can vary across both spatial locations and feature channels. To tackle this, we propose an adaptive content-aware low-pass filtering layer, which predicts separate filter weights for each spatial location and chan- nel group of the input feature maps. We investigate the effectiveness and generalization of the proposed method across multiple tasks including ImageNet classification, COCO instance segmentation, and Cityscapes semantic segmentation. Qualitative and quanti- tative results demonstrate that our approach effectively adapts to the different feature frequencies to avoid aliasing while preserving useful information for recognition. Code is available at https://maureenzou.github.io/ddac/. 

Although low-dimensionalS = 1 antiferromagnets remain of great interest, difficulty in obtaining high-quality single crystals of the newest materials hinders experimental research in this area. Polycrystalline samples are more readily produced, but there are inherent problems in extracting the magnetic properties of anisotropic systems from powder data. Following a discussion of the effect of powder-averaging on various measurement techniques, we present a methodology to overcome this issue using thermodynamic measurements. In particular we focus on whether it is possible to characterise the magnetic properties of polycrystalline, anisotropic samples using readily available laboratory equipment. We test the efficacy of our method using the magnets [Ni(H₂O)₂(3,5-lutidine)₄](BF₄)₂and Ni(H₂O)₂(acetate)₂(4-picoline)₂, which have negligible exchange interactions, as well as the antiferromagnet [Ni(H₂O)₂(pyrazine)₂](BF₄)₂, and show that we are able to extract the anisotropy parameters in each case. The results obtained from the thermodynamic measurements are checked against electron-spin resonance and neutron diffraction. We also present a density functional method, which incorporates spin–orbit coupling to estimate the size of the anisotropy in [Ni(H₂O)₂(pyrazine)₂](BF₄)₂.