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Recovering the structure of debris disks non-parametrically from images

Debris disks common around Sun-like stars carry dynamical imprints in their structure that are key to understanding the formation and evolution history of planetary systems. In this paper, we extend an algorithm (rave) originally developed to model edge-on disks to be applicable to disks at all inclinations. The updated algorithm allows for non-parametric recovery of the underlying (i.e., deconvolved) radial profile and vertical height of optically thin, axisymmetric disks imaged in either thermal emission or scattered light. Application to simulated images demonstrates that the de-projection and deconvolution performance allows for accurate recovery of features comparable to or larger than the beam or PSF size, with realistic uncertainties that are independent of model assumptions. We apply our method to recover the radial profile and vertical height of a sample of 18 inclined debris disks observed with ALMA. Our recovered structures largely agree with those fitted with an alternative visibility-space de-projection and deconvolution method (frank). We find that for disks in the sample with a well-defined main belt, the belt radius, fractional width and fractional outer edge width all tend to increase with age, but do not correlate in a clear or monotonic way with dust mass or stellar temperature. In contrast, the scale height aspect ratio does not strongly correlate with age, but broadly increases with stellar temperature. These trends could reflect a combination of intrinsic collisional evolution in the disk and the interaction of perturbing planets with the disk's own gravity.

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Collaborative Filtering Meets Spectrum Shift: Connecting User-Item Interaction with Graph-Structured Side Information

Graph Neural Network (GNN) has demonstrated their superiority in collaborative filtering, where the user-item (U-I) interaction bipartite graph serves as the fundamental data format. However, when graph-structured side information (e.g., multimodal similarity graphs or social networks) is integrated into the U-I bipartite graph, existing graph collaborative filtering methods fall short of achieving satisfactory performance. We quantitatively analyze this problem from a spectral perspective. Recall that a bipartite graph possesses a full spectrum within the range of [-1, 1], with the highest frequency exactly achievable at -1 and the lowest frequency at 1; however, we observe as more side information is incorporated, the highest frequency of the augmented adjacency matrix progressively shifts rightward. This spectrum shift phenomenon has caused previous approaches built for the full spectrum [-1, 1] to assign mismatched importance to different frequencies. To this end, we propose Spectrum Shift Correction (dubbed SSC), incorporating shifting and scaling factors to enable spectral GNNs to adapt to the shifted spectrum. Unlike previous paradigms of leveraging side information, which necessitate tailored designs for diverse data types, SSC directly connects traditional graph collaborative filtering with any graph-structured side information. Experiments on social and multimodal recommendation demonstrate the effectiveness of SSC, achieving relative improvements of up to 23% without incurring any additional computational overhead.

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