Zhihao Ge, Xiaogang Zhu
In the paper, we propose three new hp discontinuous Galerkin methods for the elasticity problem and make a comparison of the three numerical methods. And we prove the optimal order of convergence in energy norm and $L^2$-norm by the superpenalization technique. Finally, we give a numerical example to verify our theoretical results.
Xiangju Li, Dong Yang, Xiaogang Zhu et al.
Span-level emotion-cause-category triplet extraction represents a novel and complex challenge within emotion cause analysis. This task involves identifying emotion spans, cause spans, and their associated emotion categories within the text to form structured triplets. While prior research has predominantly concentrated on clause-level emotion-cause pair extraction and span-level emotion-cause detection, these methods often confront challenges originating from redundant information retrieval and difficulty in accurately determining emotion categories, particularly when emotions are expressed implicitly or ambiguously. To overcome these challenges, this study explores a fine-grained approach to span-level emotion-cause-category triplet extraction and introduces an innovative framework that leverages instruction tuning and data augmentation techniques based on large language models. The proposed method employs task-specific triplet extraction instructions and utilizes low-rank adaptation to fine-tune large language models, eliminating the necessity for intricate task-specific architectures. Furthermore, a prompt-based data augmentation strategy is developed to address data scarcity by guiding large language models in generating high-quality synthetic training data. Extensive experimental evaluations demonstrate that the proposed approach significantly outperforms existing baseline methods, achieving at least a 12.8% improvement in span-level emotion-cause-category triplet extraction metrics. The results demonstrate the method's effectiveness and robustness, offering a promising avenue for advancing research in emotion cause analysis. The source code is available at https://github.com/zxgnlp/InstruDa-LLM.
Kunpeng Zhang, Xi Xiao, Xiaogang Zhu et al.
Coverage-guided Greybox Fuzzing (CGF) is one of the most successful and widely-used techniques for bug hunting. Two major approaches are adopted to optimize CGF: (i) to reduce search space of inputs by inferring relationships between input bytes and path constraints; (ii) to formulate fuzzing processes (e.g., path transitions) and build up probability distributions to optimize power schedules, i.e., the number of inputs generated per seed. However, the former is subjective to the inference results which may include extra bytes for a path constraint, thereby limiting the efficiency of path constraints resolution, code coverage discovery, and bugs exposure; the latter formalization, concentrating on power schedules for seeds alone, is inattentive to the schedule for bytes in a seed. In this paper, we propose a lightweight fuzzing approach, Truzz, to optimize existing Coverage-guided Greybox Fuzzers (CGFs). To address two aforementioned challenges, Truzz identifies the bytes related to the validation checks (i.e., the checks guarding error-handling code), and protects those bytes from being frequently mutated, making most generated inputs examine the functionalities of programs, in lieu of being rejected by validation checks. The byte-wise relationship determination mitigates the problem of loading extra bytes when fuzzers infer the byte-constraint relation. Furthermore, the proposed path transition within Truzz can efficiently prioritize the seed as the new path, harvesting many new edges, and the new path likely belongs to a code region with many undiscovered code lines. The experimental results show that on average, Truzz can generate 16.14% more inputs flowing into functional code, in addition to 24.75% more new edges than the vanilla fuzzers. Finally, our approach exposes 13 bugs in 8 target programs, and 6 of them have not been identified by the vanilla fuzzers.
Xiaogang Zhu, Yufeng Nie
In this work, a new collocation approach using a combination of a wavelet operational matrix method and the exponential spline interpolation is proposed to solve the time-fractional convection-diffusion equation with variable coefficients. The operational matrix of fractional order integration is first derived based on sine-cosine wavelet functions, which helps to convert the underlying equation into a linear algebraic system. Then, an exponential B-spline method is introduced in spatial direction. On selecting a set of proper collocation points, the method in presence is evaluated on several test problems and the numerical results finally illustrate its validity and applicability.