The dependence of the structure of planet-opened gaps in protoplanetary disks on radiative cooling

Planets can excite density waves and open annular gas gaps in protoplanetary disks. The depth of gaps is influenced by the evolving angular momentum carried by density waves. While the impact of radiative cooling on the evolution of density waves has been studied, a quantitative correlation to connect gap depth with the cooling timescale is lacking. To address this gap in knowledge, we employ the grid-based code Athena++ to simulate disk-planet interactions, treating cooling as a thermal relaxation process. We establish quantitative dependences of steady-state gap depth (Eq. 36) and width (Eq. 41) on planetary mass, Shakura-Sunyaev viscosity, disk scale height, and thermal relaxation timescale $(\beta)$. We confirm previous results that gap opening is the weakest when thermal relaxation timescale is comparable to local dynamical timescale. Significant variations in gap depth, up to an order of magnitude, are found with different $\beta$. In terms of width, a gap is at its narrowest around $\beta=1$, approximately $10\%$ to $20\%$ narrower compared to the isothermal case. When $\beta\sim100$, it can be $\sim20\%$ wider, and higher viscosity enhances this effect. We derive possible masses of the gas gap-opening planets in AS 209, HD 163296, MWC 480, and HL Tau, accounting for the uncertainties in local thermal relaxation timescale.Comment: 19 pages, 16 figures, 4 tables, accepted for publication in Ap

Multi-granularity Item-based Contrastive Recommendation

Contrastive learning (CL) has shown its power in recommendation. However, most CL-based recommendation models build their CL tasks merely focusing on the user's aspects, ignoring the rich diverse information in items. In this work, we propose a novel Multi-granularity item-based contrastive learning (MicRec) framework for the matching stage (i.e., candidate generation) in recommendation, which systematically introduces multi-aspect item-related information to representation learning with CL. Specifically, we build three item-based CL tasks as a set of plug-and-play auxiliary objectives to capture item correlations in feature, semantic and session levels. The feature-level item CL aims to learn the fine-grained feature-level item correlations via items and their augmentations. The semantic-level item CL focuses on the coarse-grained semantic correlations between semantically related items. The session-level item CL highlights the global behavioral correlations of items from users' sequential behaviors in all sessions. In experiments, we conduct both offline and online evaluations on real-world datasets, verifying the effectiveness and universality of three proposed CL tasks. Currently, MicRec has been deployed on a real-world recommender system, affecting millions of users. The source code will be released in the future.Comment: 17 pages, under revie

Improve Transformer Pre-Training with Decoupled Directional Relative Position Encoding and Representation Differentiations

In this work, we revisit the Transformer-based pre-trained language models and identify two problems that may limit the expressiveness of the model. Firstly, existing relative position encoding models (e.g., T5 and DEBERTA) confuse two heterogeneous information: relative distance and direction. It may make the model unable to capture the associative semantics of the same direction or the same distance, which in turn affects the performance of downstream tasks. Secondly, we notice the pre-trained BERT with Mask Language Modeling (MLM) pre-training objective outputs similar token representations and attention weights of different heads, which may impose difficulties in capturing discriminative semantic representations. Motivated by the above investigation, we propose two novel techniques to improve pre-trained language models: Decoupled Directional Relative Position (DDRP) encoding and MTH pre-training objective. DDRP decouples the relative distance features and the directional features in classical relative position encoding for better position information understanding. MTH designs two novel auxiliary losses besides MLM to enlarge the dissimilarities between (a) last hidden states of different tokens, and (b) attention weights of different heads, alleviating homogenization and anisotropic problem in representation learning for better optimization. Extensive experiments and ablation studies on GLUE benchmark demonstrate the effectiveness of our proposed methods