Deep learning libraries have emerged as critical software systems for a diverse range of deep learning applications. However, the stability and reliability of these libraries are increasingly challenged by their rapidly expanding scale. In this article, we utilize the function call graph as a model to represent deep learning libraries and conduct an empirical study using an innovative approach based on complex network theory. This method facilitates a thorough exploration of the topological characteristics and functionalities of deep learning libraries, revealing their scale-free and small-world properties. Leveraging the characteristics, we utilizek-core decomposition to pinpoint critical functions within the libraries, and conduct a comprehensive analysis to discern the characteristics of their functionalities. Furthermore, we have compiled a comprehensive dataset comprising 12 774 defective functions within these libraries. This dataset enables us to analyze and compare the distribution and trend of defects across the investigated deep learning libraries, while examining the patterns of defect propagation. Our research presents 14 significant findings, offering insights for researchers in software reliability and testing.

Defect prediction is crucial for software quality assurance and has been extensively researched over recent decades. However, prior studies rarely focus on data complexity in defect prediction tasks, and even less on understanding the difficulties of these tasks from the perspective of data complexity. In this article, we conduct an empirical study to estimate the hardness of over 33,000 instances, employing a set of measures to characterize the inherent difficulty of instances and the characteristics of defect datasets. Our findings indicate that: (1) instance hardness in both classes displays a right-skewed distribution, with the defective class exhibiting a more scattered distribution; (2) class overlap is the primary factor influencing instance hardness and can be characterized through feature, structural, and instance-level overlap; (3) no universal preprocessing technique is applicable to all datasets, and it may not consistently reduce data complexity, fortunately, dataset complexity measures can help identify suitable techniques for specific datasets; (4) integrating data complexity information into the learning process can enhance an algorithm’s learning capacity. In summary, this empirical study highlights the crucial role of data complexity in defect prediction tasks, and provides a novel perspective for advancing research in defect prediction techniques.

Software defect prediction (SDP) techniques play a crucial role in identifying defective code regions and improving testing efficiency. Over recent decades, a plethora of SDP approaches has emerged, with machine learning (ML) models being the most widely employed. Despite their superior predictive performance, their black-box nature and uncertainties make it challenging for developers to trust their predictions. To address this issue, we propose a novel trustworthiness score, the adjusted trust score (ATS), which helps determine when to rely on classifier predictions. Furthermore, we employ ATS to develop a reject option for SDP models. Comprehensive experiments on 32 benchmark datasets and six prevalent ML classifiers reveal that high (low) ATS values successfully yield high precision in identifying correct (or incorrect) predictions. ATS also demonstrates superiority over its counterparts, as evidenced by the Wilcoxon signed-rank test. Furthermore, a comparative analysis of prediction performance, with and without a reject option, confirms the feasibility of designing a reject option for SDP models utilizing ATS. Our work highlights that ATS can assist developers in better comprehending the strengths and weaknesses of SDP models. Therefore, it is an essential component for guaranteeing trust from developers and deserves further investigation.

This article studies the min-consensus control of continuous-time real-valued multiagent systems, with sampled information, quantized communication, and switching topologies. Due to the limited bandwidth of the digital communication network, only finite-bit binary symbolic sequence can be exchanged among the agents. In order to realize the min-consensus control with quantized communication and limited bandwidth, a novel finite-level biased quantizer and a nonstrict decreasing scaling function are designed, and correspondingly a set of switching encoders and decoders are constructed. By means of the proposed encoders and decoders, the according sampled-data min-consensus control inputs are carefully constructed, and the memory variables are introduced into the control inputs and are monotonically decreasing no matter how the communication topology is switched. The proposed encoding-decoding-based control scheme can achieve accurate min-consensus with limited bandwidth, as long as the communication graphs are jointly strongly connected. The numerical simulations show the effectiveness of the proposed control scheme.

This article studies the appointed-time attitude tracking control of the spacecraft on the special orthogonal group, with the attitude forbidden zone, the parameter uncertainties, and the external disturbances. A novel projection function is proposed, such that the normalized boresight vector of the sensitive instrument is mapped to a reduced dimensional vector in the Euclidean space. If the reduced dimensional vector is uniformly bounded, the constraint on the attitude forbidden zone will be satisfied at all the time. By virtue of the designed reduced dimensional vector and the associated auxiliary vectors, a set of vector-based error functions, the appointed-time performance constraints, and the according switching law is carefully constructed. The proposed vector-based adaptive control scheme ensures that the spacecraft attitude can satisfy the attitude constraint and appointed-time control performance simultaneously, in the presence of parameter uncertainties and external disturbances. Simulation results show the effectiveness of the designed control scheme.

This article focuses on trajectory planning of the free-floating space manipulator (FFSM), so that the end-effector trajectory tracking and the spacecraft attitude stabilization are achieved simultaneously. A novel spacecraft attitude stabilization constraint with the time-decaying term and the time-varying gaining parameter is constructed, such that not only is the designed constraint satisfied at the initial instant but also the spacecraft attitude can converge into the small neighborhood of the desired attitude. Two constraints on joint accelerations are constructed, such that the constraints on joint angles/velocities/accelerations and the requirement on the end-effector trajectory tracking are both satisfied. Besides, for the cost function with the control efforts and the manipulability optimization, it can be equivalently converted as a strictly convex quadratic function. Correspondingly, the trajectory planning problem of the FFSM at the acceleration level can be formulated as a constrained convex quadratic programming problem. The proposed trajectory planning algorithm avoids the dynamic singularity of the FFSM. The effectiveness of the proposed algorithm is validated by the simulation results.