Source localization has attracted increasing attention in recent years due to its vital role in governing the harmful propagation. However, existing localization methods do not fully consider the temporal characteristics in propagation and struggle to leverage the continuous-time information of real-world propagation scenarios. Moreover, the aggregation ability of GNN based localization models is limited by the structural noise commonly present in complicated real-world topologies. To address these challenges, a Spectral Neural Ordinary Differential Equation (SNODE) is proposed to infer the source in real-world continuous-time scenarios. First, the forward propagation is formulated as a flow based ODE system, and the source localization problem is transformed into an inverse ODE modeling task. Second, a neural process based on a graph variational autoencoder is introduced to encode global latent propagation patterns as a conditioning variable for the ODE system. Third, a spectral graph optimization is performed to suppress topological noise by filtering out high-frequency components that degrade the quality of graph aggregation in the neural process. Comprehensive experiments demonstrate that SNODE not only outperforms the optimal baseline in real-world continuous-time propagation scenarios with an average performance improvement of 43.8%, but also achieves consistently superior performance in synthetic discrete-time datasets with an improvement of 4.5%, highlighting its strong generalization ability in different propagation settings. Our code is available at https://github.com/cgao-comp/SNODE.

The eXplicit Control Protocol (XCP) was developed to overcome the limitations of TCP, such as unstable throughput, low utilization, limited fairness, and large persistent queue length. However, Low proves that the XCP equilibrium solves a constrained max-min fairness problem, in a multi-bottleneck environment, XCP may cause some bottleneck links to be underutilized, and a flow may only receive a small fraction of its maxmin fair bandwidth allocation. To address this problem, Zan proposes an improved version of XCP (iXCP), which shuffles bandwidth only among flows that are bottlenecked at current routers. In this paper, according to the robust control theory, with the help of a recently developed Lyapunov-Krasovskii functional, we propose an XCP bandwidth compensation algorithm based on state feedback (S-XCP). The synthesis problem is reduced to a convex optimization scheme expressed in terms of linear matrix inequalities (LMI). Extensive simulations have shown that S-XCP achieves efficient and fair bandwidth allocation in a multi-bottleneck environment. Compared with iXCP, (1)S-XCP have the same packet header overhead of XCP; (2)computing complexity significantly declines; (3)and more effective control in highly dynamic situations.

In the resource-rich grid computing environment, there are plenty of idle resources that compete for similar tasks. In order to make resources gained the maximum benefit, a guarantee of victorious probability algorithm (GVP) based on game theory is presented in this paper. This algorithm predicts the action of adversaries based on historical information, and determines its own action based on the forecast. We use GridSim toolkit to implement a resource-rich environment and verify our algorithm through experiments. The experimental results show that the resources using GVP algorithm can be close to their expectation of victorious probability comparing with the other resources using the random algorithms. The two-player game and multi-player game are discussed and a more in-depth analysis is made. Finally the Nash equilibrium of game among resources is also discussed.