Liang Bai

Maintaining end-to-end connectivity under disruption is a central problem in systems resilience. This study examines how limited protection resources can increase the minimum node-removal cost required to disconnect a specified service. Mission-Path Cut Fortification (MPCF) models a directed service as a functional graph and treats protection as a finite increase in node-removal cost. Node splitting yields a compact mixed-integer linear program, and an independent cut-generation formulation verifies its optimal value. On 45 synthetic graphs, mean minimum-cut values are 33.62 for MPCF-Exact and MPCF-CG, 32.30 for MPCF-Greedy, 30.41 for PathFrequency, and 27.38 without fortification. Graph-level analyses treat budgets as repeated measurements, and a 90-graph extension reproduces the paired effects for the nine designated methods. Further experiments assess heterogeneous fortification costs and effectiveness. Scaling to 1000 nodes identifies the computational limits of both exact formulations through stopping times and optimality bounds. Ten source–sink cases from public transport and telecommunications networks demonstrate applicability to empirical path topologies. Partial-capacity analysis shows that complete-disconnection and residual-capacity criteria can favor different fortification sets. The findings support joint node-set selection for resistance to complete disconnection and show that the service criterion should be specified before resources are allocated.

Kill-web absorption resilience depends on whether directed mission paths remain available after disruption. This study addresses how to allocate a limited fortification budget to mission-function nodes so that an adaptive interdictor must incur the greatest possible cost to disconnect all valid mission paths. We formulate Mission-Path Cut Fortification ( MPCF), which maximizes the post-fortification minimum node-cut cost. Node-capacity splitting converts the interdiction response for a fixed fortification set into an equivalent maximum-flow minimum-cut problem. A compact mixed-integer linear program provides the primary exact solution, and an independent cut-generation formulation cross-checks the optimum in cut space. Across 135 graph-budget pairs from 45 prespecified synthetic networks, the mean optimality gaps of MPCF-Greedy and PathFrequency are 2.76% and 9.50%, respectively. Across 810 combinations under six role-composition profiles, the two exact formulations obtain identical objective values; MPCF-Greedy has a mean gap of 1.98%, whereas the best non-MPCF method under each profile has a mean gap of 8.11%–10.12%. Exact optimization also agrees with exhaustive enumeration on 72 small fortification instances and 72 capacity-interdiction instances, and cut-space verification agrees on 30 public-network instances. These results show that mission-path fortification benefits from joint optimization of the protected node set and the adaptive minimum-cut response.

In complex networks, the identification of critical nodes is vital for optimizing information dissemination. Given the significant role of these nodes in network structures, researchers have proposed various identification methods. In recent years, deep learning has emerged as a promising approach for identifying key nodes in networks. However, existing algorithms fail to effectively integrate local and global structural information, leading to incomplete and limited network understanding. To overcome this limitation, we introduce a transformer framework with multi-scale feature fusion (MSF-Former). In this framework, we construct local and global feature maps for nodes and use them as input. Through the transformer module, node information is effectively aggregated, thereby improving the model’s ability to recognize key nodes. We perform evaluations using six real-world and three synthetic network datasets, comparing our method against multiple baselines using the SIR model to validate its effectiveness. Experimental analysis confirms that MSF-Former achieves consistently high accuracy in the identification of influential nodes across real-world and synthetic networks.

The continuous operation of modern society is dominated by interdependent networks, such as energy networks, communication networks, and traffic networks. As a result, the robustness of interdependent networks has become increasingly important in recent years. On the basis of past research, a no-feedback interdependent networks model is introduced. Compared with previous work, this model is more consistent with the characteristics of real interdependent systems. In addition, two types of failure modes, unilateral failure and bilateral failure, are defined. For each failure mode, the influence of coupling strength and dependency strength on the robustness of no-feedback interdependent networks was analyzed and discussed in relation to various giant component sizes. The simulation results indicated that the robustness of the no-feedback interdependent networks was inversely proportional to coupling strength and dependency strength, and the effect of coupling strength and dependency strength on the robustness was equivalent. These conclusions are beneficial for helping researchers and engineers to build more robust interdependent systems.

Critical infrastructures (CI) are the cornerstone of modern society, and they are connected with each other through material, energy, or information. The robustness of interdependent CI systems under attack has been a hot topic in recent years, but previous studies mainly focused on malicious attacks or random failure. To analyze the impact of some natural disasters whose destructive force is mainly related to distance with respect to interdependent CI systems, we present a new localized attack mode considering destructive force decays with distance, and carry out simulations on several interdependent networks constructed by artificial and real world networks. Furthermore, this article analyzes the influence of coupling strength and coupling pattern on the robustness of interdependent system. The results show that dependency links between networks decrease the robustness of interdependence networks, but the robustness under failure probability degradation is not vulnerable like that under malicious attack or random failure. In addition, the coupling preference has little effect on the robustness of interdependent networks under the new localized attack strategy; when the average degree of subnetworks is large, the same conclusion can be obtained for the coupling strength.

Unmanned Aerial Vehicles (UAVs) have recently received notable attention because of their wide range of applications in urban civilian use and in warfare. With air traffic densities increasing, it is more and more important for UAVs to be able to predict and avoid collisions. The main goal of this research effort is to adjust real-time trajectories for cooperative UAVs to avoid collisions in three-dimensional airspace. To explore potential collisions, predictive state space is utilized to present the waypoints of UAVs in the upcoming situations, which makes the proposed method generate the initial collision-free trajectories satisfying the necessary constraints in a short time. Further, a rolling optimization algorithm (ROA) can improve the initial waypoints, minimizing its total distance. Several scenarios are illustrated to verify the proposed algorithm, and the results show that our algorithm can generate initial collision-free trajectories more efficiently than other methods in the common airspace.