To underscore the significance of the interactive frequency among diverse vertices in each snapshot, prior research has extended the$k$-core of general graphs to the$(k,h)$-core of temporal graphs, in which each vertex has at least$k$neighbors and is connected by at least$h$edges to each of these neighbors. Due to the numerous combinations of$k$and$h$, the quantity of$(k,h)$-cores is substantial, which necessitates considerable time and space for querying and decomposition. As a temporal graph evolves, for instance, with edges being inserted or removed from the previous snapshot, the affected$(k,h)$-cores must also be updated to reflect the latest structure. To address these challenges, we initially develop a novel$(k,h)$-core storage index that exhibits excellent query performance while consuming linear space regarding the graph size. Subsequently, we design an efficient decomposition algorithm to extract$(k,h)$-cores from a snapshot. Following this, we offer two maintenance algorithms to manage temporal graph evolution. Finally, we validate the effectiveness of our proposed methods on actual temporal graphs. Experimental results indicate that our methods surpass existing techniques by two orders of magnitude.

Maximum Satisfiability (MaxSAT) is a prototypical constrained optimization problem that can be extended to Partial MaxSAT (PMS) and Weighted Partial MaxSAT (WPMS).In these variations, clauses are categorized into hard and soft clauses, which enables more flexible optimization.Local search algorithms are a key approach for solving (W)PMS.However, there are two key problems with the existing clause weighting scheme: first, starting to adjust the weights of soft clauses before any feasible solution has been found may cause the search process to move away from the feasible region; second, the uniform initialization of soft clause weights imposes a significant influence on the algorithm's performance.These problems limit the stability and effectiveness of local search algorithms in complex instances.To this end, this paper proposes to introduce a Feasible Solution Constraint (FSC) scheme, which is used to strengthen the priority guarantee of the feasible solutions of hard clauses in the local search process, and to ensure that the search advances efficiently in the feasible region.Meanwhile, we also design an adaptive softclause weight initialization strategy as an effective complement to FSC to enhance the robustness of the algorithm under different problem structures.We integrate the proposed scheme into a state-of-the-art MaxSAT local search solver and evaluate it on standard benchmarks.Experimental results demonstrate that FSC significantly enhances solver performance, achieving a better trade-off between generality and efficiency.

In this research, the adaptive neural network consensus control problem is addressed for a class of non-affine multiagent systems (MASs) with actuator faults and stochastic disturbances. To overcome difficulties associated with actuator faults and uncertain functions of the designed MAS, a neural network fault-tolerant control scheme is developed. Moreover, an adaptive backstepping controller is developed to solve the non-affine appearance in multiagent stochastic non-affine systems using the mean value theorem. Being different from the existing control methods, the developed adaptive fixed-time control approach can ensure that the outputs of all followers track the reference signal synchronously in the fixed time, and all signals of the controlled system are semi-globally uniformly fixed-time stable. The simulation results confirm that the presented control strategy is effective in achieving control goals.

A$k$-core is the special cohesive subgraph where each vertex has at least$k$degree. It is widely used in graph mining applications such as community detection, visualization, and clique discovery. Because dynamic graphs frequently evolve, obtaining their$k$-cores via decomposition is inefficient. Instead, previous studies proposed various methods for updating$k$-cores based on inserted (removed) edges. Unfortunately, the parallelism of existing approaches is limited due to their theoretical constraints. To further improve the parallelism of maintenance algorithms, we refine the$k$-core maintenance theorem and propose two effective parallel methods to update$k$-cores for insertion and removal cases. Experimental results show that our methods outperform the state-of-the-art algorithms on real-world graphs by one order of magnitude.

In this article, finite-time-prescribed performance-based adaptive fuzzy control is considered for a class of strict-feedback systems in the presence of actuator faults and dynamic disturbances. To deal with the difficulties associated with the actuator faults and external disturbance, an adaptive fuzzy fault-tolerant control strategy is introduced. Different from the existing controller design methods, a modified performance function, which is called the finite-time performance function (FTPF), is presented. It is proved that the presented controller can ensure all the signals of the closed-loop system are bounded and the tracking error converges to a predetermined region in finite time. The effectiveness of the presented control scheme is verified through the simulation results.