Zhimin Zhang

Beichuan Deng, Zhimin Zhang, Xuan Zhao

In this paper, superconvergence points are located for the approximation of the Riesz derivative of order $α$ using classical Lobatto-type polynomials when $α\in (0,1)$ and generalized Jacobi functions (GJF) for arbitrary $α> 0$, respectively. For the former, superconvergence points are zeros of the Riesz fractional derivative of the leading term in the truncated Legendre-Lobatto expansion. It is observed that the convergence rate for different $α$ at the superconvergence points is at least $O(N^{-2})$ better than the optimal global convergence rate. Furthermore, the interpolation is generalized to the Riesz derivative of order $α> 1$ with the help of GJF, which deal well with the singularities. The well-posedness, convergence and superconvergence properties are theoretically analyzed. The gain of the convergence rate at the superconvergence points is analyzed to be $O(N^{-(α+3)/2})$ for $α\in (0,1)$ and $O(N^{-2})$ for $α> 1$. Finally, we apply our findings in solving model FDEs and observe that the convergence rates are indeed much better at the predicted superconvergence points.

Fengji Zhang, Xiao Yu, Jacky Keung et al.

Context: Stack Overflow is very helpful for software developers who are seeking answers to programming problems. Previous studies have shown that a growing number of questions are of low quality and thus obtain less attention from potential answerers. Gao et al. proposed an LSTM-based model (i.e., BiLSTM-CC) to automatically generate question titles from the code snippets to improve the question quality. However, only using the code snippets in the question body cannot provide sufficient information for title generation, and LSTMs cannot capture the long-range dependencies between tokens. Objective: This paper proposes CCBERT, a deep learning based novel model to enhance the performance of question title generation by making full use of the bi-modal information of the entire question body. Method: CCBERT follows the encoder-decoder paradigm and uses CodeBERT to encode the question body into hidden representations, a stacked Transformer decoder to generate predicted tokens, and an additional copy attention layer to refine the output distribution. Both the encoder and decoder perform the multi-head self-attention operation to better capture the long-range dependencies. This paper builds a dataset containing around 200,000 high-quality questions filtered from the data officially published by Stack Overflow to verify the effectiveness of the CCBERT model. Results: CCBERT outperforms all the baseline models on the dataset. Experiments on both code-only and low-resource datasets show the superiority of CCBERT with less performance degradation. The human evaluation also shows the excellent performance of CCBERT concerning both readability and correlation criteria.

Wei Huang, Chen Liu, Yihua Zhao et al.

Hierarchical Text Classification (HTC), which aims to predict text labels organized in hierarchical space, is a significant task lacking in investigation in natural language processing. Existing methods usually encode the entire hierarchical structure and fail to construct a robust label-dependent model, making it hard to make accurate predictions on sparse lower-level labels and achieving low Macro-F1. In this paper, we propose a novel PAMM-HiA-T5 model for HTC: a hierarchy-aware T5 model with path-adaptive mask mechanism that not only builds the knowledge of upper-level labels into low-level ones but also introduces path dependency information in label prediction. Specifically, we generate a multi-level sequential label structure to exploit hierarchical dependency across different levels with Breadth-First Search (BFS) and T5 model. To further improve label dependency prediction within each path, we then propose an original path-adaptive mask mechanism (PAMM) to identify the label's path information, eliminating sources of noises from other paths. Comprehensive experiments on three benchmark datasets show that our novel PAMM-HiA-T5 model greatly outperforms all state-of-the-art HTC approaches especially in Macro-F1. The ablation studies show that the improvements mainly come from our innovative approach instead of T5.

Hehu Xie, Zhimin Zhang

A multilevel correction scheme is proposed to solve defective and nodefective of nonsymmetric partial differential operators by the finite element method. The method includes multi correction steps in a sequence of finite element spaces. In each correction step, we only need to solve two source problems on a finer finite element space and two eigenvalue problems on the coarsest finite element space. The accuracy of the eigenpair approximation is improved after each correction step. This correction scheme improves overall efficiency of the finite element method in solving nonsymmetric eigenvalue problems.