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By carrying out refined curvature estimates, we prove better rigidity theorems of complete noncompact ancient solutions to the mean curvature flow in higher codimension under various Gauss image restriction.

Due to the highly dynamic changes in wireless network topologies, efficiently obtaining network status information and flexibly forwarding data to improve communication quality of service are important challenges. This article introduces an intelligent routing algorithm (DRL-PPONSA) based on proximal policy optimization deep reinforcement learning with network situational awareness under a software-defined wireless networking architecture. First, a specific data plane is designed for network topology construction and data forwarding. The control plane collects network traffic information, sends flow tables, and uses a GCN-GRU prediction mechanism to perceive future traffic change trends to achieve network situational awareness. Second, a DRL-based data forwarding mechanism is designed in the knowledge plane. The predicted network traffic matrix and topology information matrix are treated as the environment for DRL agents, while next-hop adjacent nodes are treated as executable actions. Accordingly, action selection strategies are designed for different network conditions to achieve more intelligent, flexible, and efficient routing control. The reward function is designed using network link information and various reward and penalty mechanisms. Additionally, importance sampling and gradient clipping techniques are employed during gradient updating to enhance convergence speed and stability. Experimental results show that DRL-PPONSA outperforms traditional routing methods in network throughput, delay, packet loss rate, and wireless node distance. Compared to value-function-based Dueling DQN routing, the convergence speed is significantly improved, and the convergence effect is more stable. Simultaneously, its consumption of hardware storage space is reduced, and efficient routing decisions can be made in real-time using the current network state information.

Multicast communication technology is widely applied in wireless environments with a high device density. Traditional wireless network architectures have difficulty flexibly obtaining and maintaining global network state information and cannot quickly respond to network state changes, thus affecting the throughput, delay, and other QoS requirements of existing multicasting solutions. Therefore, this paper proposes a new multicast routing method based on multiagent deep reinforcement learning (MADRL-MR) in a software-defined wireless networking (SDWN) environment. First, SDWN technology is adopted to flexibly configure the network and obtain network state information in the form of traffic matrices representing global network links information, such as link bandwidth, delay, and packet loss rate. Second, the multicast routing problem is divided into multiple subproblems, which are solved through multiagent cooperation. To enable each agent to accurately understand the current network state and the status of multicast tree construction, the state space of each agent is designed based on the traffic and multicast tree status matrices, and the set of AP nodes in the network is used as the action space. A novel single-hop action strategy is designed, along with a reward function based on the four states that may occur during tree construction: progress, invalid, loop, and termination. Finally, a decentralized training approach is combined with transfer learning to enable each agent to quickly adapt to dynamic network changes and accelerate convergence. Simulation experiments show that MADRL-MR outperforms existing algorithms in terms of throughput, delay, packet loss rate, etc., and can establish more intelligent multicast routes.

Message transmission and message synchronization for multicontroller interdomain routing in software-defined networking (SDN) have long adaptation times and slow convergence speeds, coupled with the shortcomings of traditional interdomain routing methods, such as cumbersome configuration and inflexible acquisition of network state information. These drawbacks make it difficult to obtain a global state information of the network, and the optimal routing decision cannot be made in real time, affecting network performance. This paper proposes a cross-domain intelligent SDN routing method based on a proposed multiagent deep reinforcement learning. First, the network is divided into multiple subdomains managed by multiple local controllers, and the state information of each subdomain is flexibly obtained by the designed SDN multithreaded network measurement mechanism. Then, a cooperative communication module is designed to realize message transmission and message synchronization between root and local controllers, and socket technology is used to ensure the reliability and stability of message transmission between multiple controllers to realize the real-time acquisition of global network state information. Finally, after the optimal intradomain and interdomain routing paths are adaptively generated by the agents in the root and local controllers, a prediction mechanism for the network traffic state is designed to improve the awareness of the cross-domain intelligent routing method and enable the generation of the optimal routing paths in the global network in real time. Experimental results show that the proposed cross-domain intelligent routing method can significantly improve the network throughput, reduce the network delay and the packet loss rate compared to the Dijkstra and OSPF routing methods., Comment: 19 pages, 21 figures

Due to the issue that existing wireless sensor network (WSN)-based anomaly detection methods only consider and analyze temporal features, in this paper, a self-supervised learning-based anomaly node detection method based on an autoencoder is designed. This method integrates temporal WSN data flow feature extraction, spatial position feature extraction and intermodal WSN correlation feature extraction into the design of the autoencoder to make full use of the spatial and temporal information of the WSN for anomaly detection. First, a fully connected network is used to extract the temporal features of nodes by considering a single mode from a local spatial perspective. Second, a graph neural network (GNN) is used to introduce the WSN topology from a global spatial perspective for anomaly detection and extract the spatial and temporal features of the data flows of nodes and their neighbors by considering a single mode. Then, the adaptive fusion method involving weighted summation is used to extract the relevant features between different models. In addition, this paper introduces a gated recurrent unit (GRU) to solve the long-term dependence problem of the time dimension. Eventually, the reconstructed output of the decoder and the hidden layer representation of the autoencoder are fed into a fully connected network to calculate the anomaly probability of the current system. Since the spatial feature extraction operation is advanced, the designed method can be applied to the task of large-scale network anomaly detection by adding a clustering operation. Experiments show that the designed method outperforms the baselines, and the F1 score reaches 90.6%, which is 5.2% higher than those of the existing anomaly detection methods based on unsupervised reconstruction and prediction. Code and model are available at https://github.com/GuetYe/anomaly_detection/GLSL

We obtain a rigidity result of symplectic translating solitons via the complex phase map. It indicates that we can remove the bounded second fundamental form assumption for symplectic translating solitons in [13].

By using a new test function and the gradient estimate technique, we obtain a better Bernstein type result of translating solitons.

Anomaly detection is widely used to distinguish system anomalies by analyzing the temporal and spatial features of wireless sensor network (WSN) data streams; it is one of critical technique that ensures the reliability of WSNs. Currently, graph neural networks (GNNs) have become popular state-of-the-art methods for conducting anomaly detection on WSN data streams. However, the existing anomaly detection methods based on GNNs do not consider the temporal and spatial features of WSN data streams simultaneously, such as multi-node, multi-modal and multi-time features, seriously impacting their effectiveness. In this paper, a novel anomaly detection model is proposed for multimodal WSN data flows, where three GNNs are used to separately extract the temporal features of WSN data flows, the correlation features between different modes and the spatial features between sensor node positions. Specifically, first, the temporal features and modal correlation features extracted from each sensor node are fused into one vector representation, which is further aggregated with the spatial features, i.e., the spatial position relationships of the nodes; finally, the current time-series data of WSN nodes are predicted, and abnormal states are identified according to the fusion features. The simulation results obtained on a public dataset show that the proposed approach is able to significantly improve upon the existing methods in terms of its robustness, and its F1 score reaches 0.90, which is 14.2% higher than that of the graph convolution network (GCN) with long short-term memory (LSTM).

We proved that any complete hypersurface in the Euclidean space $\mathbb{R}^{n+1}$ whose Gauss image is contained in an open hemisphere has to be proper. As applications, we derive a counterpart of Hoffman-Osserman-Schoen's result for $\lambda$-hypersurfaces, which gives an affirmative answer to the Bernstein type problem proposed by Cheng-Wei \cite{CW14b}., Comment: There is an error in the proof of the main theorem

In this paper, we firstly establish a new volume growth estimate for spacelike entire graphs in the pseudo-Euclidean space $\mathbb{R}^{m+n}_n$. Then by using this volume growth estimate and the Co-Area formula, we prove various rigidity results for spacelike entire self-shrinking graphs.

In this paper, we prove the extensions of Bonnet--Myers' type theorems obtained by Calabi and Cheeger--Gromov--Taylor via Bakry--Emery Ricci curvature, which generalize the results of \cite{FG, Lim1, Wan, Wang, WW, Wu}.

In this paper, we firstly prove that every hyper-Lagrangian submanifold $L^{2n} (n > 1)$ in a hyperk\"ahler $4n$-manifold is a complex Lagrangian submanifold. Secondly, we demonstrate an optimal rigidity theorem with the condition on the complex phase map of self-shrinking surfaces in $\mathbb{R}^4$. Last but not least, by using the previous rigidity result, we show that the mean curvature flow from a closed surface with the image of the complex phase map contained in $\mathbb{S}^2\setminus\overline{\mathbb{S}}^{1}_{+}$ in a hyperk\"ahler $4$-manifold does not develop any Type \Rmn{1} singularity.