For this study, we investigated efficient strategies for the recovery of individual links in power grids governed by the direct current (DC) power flow model, under random link failures. Our primary objective was to explore the efficacy of recovering failed links based solely on topological network metrics. In total, we considered 13 recovery strategies, which encompassed 2 strategies based on link centrality values (link betweenness and link flow betweenness), 8 strategies based on the products of node centrality values at link endpoints (degree, eigenvector, weighted eigenvector, closeness, electrical closeness, weighted electrical closeness, zeta vector, and weighted zeta vector), and 2 heuristic strategies (greedy recovery and two-step greedy recovery), in addition to the random recovery strategy. To evaluate the performance of these proposed strategies, we conducted simulations on three distinct power systems: the IEEE 30, IEEE 39, and IEEE 118 systems. Our findings revealed several key insights: Firstly, there were notable variations in the performance of the recovery strategies based on topological network metrics across different power systems. Secondly, all such strategies exhibited inferior performance when compared to the heuristic recovery strategies. Thirdly, the two-step greedy recovery strategy consistently outperformed the others, with the greedy recovery strategy ranking second. Based on our results, we conclude that relying solely on a single metric for the development of a recovery strategy is insufficient when restoring power grids following link failures. By comparison, recovery strategies employing greedy algorithms prove to be more effective choices.

Epidemic prediction is of practical significance in public health, enabling early intervention, resource allocation, and strategic planning. However, privacy concerns often hinder the sharing of health data among institutions, limiting the development of accurate prediction models. In this paper, we develop a general privacy-preserving framework for node-level epidemic prediction on networks based on federated learning (FL). We frame the spatio-temporal spread of epidemics across multiple data-isolated subnetworks, where each node state represents the aggregate epidemic severity within a community. Then, both the pure temporal LSTM model and the spatio-temporal model i.e., Spatio-Temporal Graph Attention Network (STGAT) are proposed to address the federated epidemic prediction. Extensive experiments are conducted on various epidemic processes using a practical airline network, offering a comprehensive assessment of FL efficacy under diverse scenarios. By introducing the efficacy energy metric to measure system robustness under various client configurations, we systematically explore key factors influencing FL performance, including client numbers, aggregation strategies, graph partitioning, missing infectious reports. Numerical results manifest that STGAT excels in capturing spatio-temporal dependencies in dynamic processes whereas LSTM performs well in simpler pattern. Moreover, our findings highlight the importance of balancing feature consistency and volume uniformity among clients, as well as the prediction dilemma between information richness and intrinsic stochasticity of dynamic processes. This study offers practical insights into the efficacy of FL scenario in epidemic management, demonstrates the potential of FL to address broader collective dynamics.

The emergence of congestion is a critical phenomenon in transport systems. Transport is organized along pathways abstracted by links, which connect different nodes as regions to form the network. The modeling of traffic has so far mainly been based on one-dimensional lattices or networked queuing systems, which restricts mechanistic insights and analytical tractability for traffic dynamics on general networks. An interpretable kinetics model is necessary for understanding the impact of the network structure on traffic congestion in large-scale networks. Considering a generalized flow-density relation within each node, we propose and investigate a general traffic model on networks with external injections and exits. We observe various phases in terms of node density that exhibit distinct behaviors under different injection rates. The onset of congestion along with the coexistence of free nodes and congested nodes, manifested by the spatial localization of traffic congestion, is induced by the asymmetry of the flow transitions between neighbors in the network. The proposed congestion centrality allows us to determine the congestion threshold, identify congested nodes and predict congestion propagation. Our model and results are shown to cover a broad spectrum of implications for transport dynamics on networks as well as offer a practical prospect for traffic optimizations such as congestion alleviation and targeted diffusion.