The Social Internet of Things (SIoT) now penetrates our daily lives. As a strategy to alleviate the escalation of resource congestion, collaborative edge computing (CEC) has become a new paradigm for solving the needs of the Internet of Things (IoT). CEC can provide computing, storage, and network connection resources for remote devices. Because the edge network is closer to the connected devices, it involves a large amount of users' privacy. This also makes edge networks face more and more security issues, such as Denial-of-Service (DoS) attacks, unauthorized access, packet sniffing, and man-inthe-middle attacks. To combat these issues and enhance the security of edge networks, we propose a deep learning-based intrusion detection algorithm. Based on the generative adversarial network (GAN), we designed a powerful intrusion detection method. Our intrusion detection method includes three phases. First, we use the feature selection module to process the collaborative edge network traffic. Second, a deep learning architecture based on GAN is designed for intrusion detection aiming at a single attack. Finally, we propose a new intrusion detection model by combining several intrusion detection models that aim at a single attack. Intrusion detection aiming at multiple attacks is realized through the designed GAN-based deep learning architecture. Besides, we provide a comprehensive evaluation to verify the effectiveness of the proposed method. Index Terms-Collaborative edge computing (CEC), generative adversarial network (GAN), intrusion detection, social internet of things (SIoT).

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We propose a unified meshless method to solve classical and fractional PDE problems with (−∆) α 2 for α ∈ (0, 2]. The classical (α = 2) and fractional (α < 2) Laplacians, one local and the other nonlocal, have distinct properties. Therefore, their numerical methods and computer implementations are usually incompatible. We notice that for any α ≥ 0, the Laplacian (−∆) α 2 of generalized inverse multiquadric (GIMQ) functions can be analytically written by the Gauss hypergeometric function, and thus propose a GIMQ-based method. Our method unifies the discretization of classical and fractional Laplacians and also bypasses numerical approximation to the hypersingular integral of fractional Laplacian. These two merits distinguish our method from other existing methods for the fractional Laplacian. Extensive numerical experiments are carried out to test the performance of our method. Compared to other methods, our method can achieve high accuracy with fewer number of unknowns, which effectively reduces the storage and computational requirements in simulations of fractional PDEs. Moreover, the meshfree nature makes it free of geometric constraints and enables simple implementation for any dimension d ≥ 1. Additionally, two approaches of selecting shape parameters, including condition numberindicated method and random-perturbed method, are studied to avoid the ill-conditioning issues when large number of points.

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