PRIMARY SUBHYPERGRAPH ANALYSIS METHOD FOR HYPERNETWORKS

The concepts of hypernetwork, composite hypergraph and its primary subhyper-graph are introduced, and the principle and algorithm of a new topological method-pri-mary subhypergraph method is presented for linear active hypernetwork analysis. The ex-pressions of the symbolic network functions generated by this method are very compactand contain no cancellation terms. Its computing time complexity is O（m3c2nh+m1uG∑nl）;its order of magnitude is less than that in Refs. [1,2] by 2-3 orders.

A local-world evolving hypernetwork model

Complex hypernetworks are ubiquitous in the real system. It is very important to investigate the evolution mecha- nisms. In this paper, we present a local-world evolving hypernetwork model by taking into account the hyperedge growth and local-world hyperedge preferential attachment mechanisms. At each time step, a newly added hyperedge encircles a new coming node and a number of nodes from a randomly selected local world. The number of the selected nodes from the local world obeys the uniform distribution and its mean value is m. The analytical and simulation results show that the hyperdegree approximately obeys the power-law form and the exponent of hyperdegree distribution is 7 = 2 ＋ 1/m. Furthermore, we numerically investigate the node degree, hyperedge degree, clustering coefficient, as well as the average distance, and find that the hypemetwork model shares the scale-flee and small-world properties, which shed some light for deeply understanding the evolution mechanism of the real systems.

Dynamic Hypergraph Modeling and Robustness Analysis for SIoT

The Social Internet of Things(SIoT)integrates the Internet of Things(IoT)and social networks,taking into account the social attributes of objects and diversifying the relationship between humans and objects,which overcomes the limitations of the IoT’s focus on associations between objects.Artificial Intelligence(AI)technology is rapidly evolving.It is critical to build trustworthy and transparent systems,especially with system security issues coming to the surface.This paper emphasizes the social attributes of objects and uses hypergraphs to model the diverse entities and relationships in SIoT,aiming to build an SIoT hypergraph generation model to explore the complex interactions between entities in the context of intelligent SIoT.Current hypergraph generation models impose too many constraints and fail to capture more details of real hypernetworks.In contrast,this paper proposes a hypergraph generation model that evolves dynamically over time,where only the number of nodes is fixed.It combines node wandering with a forest fire model and uses two different methods to control the size of the hyperedges.As new nodes are added,the model can promptly reflect changes in entities and relationships within SIoT.Experimental results exhibit that our model can effectively replicate the topological structure of real-world hypernetworks.We also evaluate the vulnerability of the hypergraph under different attack strategies,which provides theoretical support for building a more robust intelligent SIoT hypergraph model and lays the foundation for building safer and more reliable systems in the future.

Resource Allocation for URLLC with Parameter Generation Network

Deep learning enables real-time resource allocation for ultra-reliable and low-latency communications(URLLC),one of the major use cases in the next-generation cellular networks.Yet the high training complexity and weak generalization ability of neural networks impede the practical use of the learning-based methods in dynamic wireless environments.To overcome these obstacles,we propose a parameter generation network(PGN)to efficiently learn bandwidth and power allocation policies in URLLC.The PGN consists of two types of fully-connected neural networks(FNNs).One is a policy network,which is used to learn a resource allocation policy or a Lagrangian multiplier function.The other type of FNNs are hypernetworks,which are designed to learn the weight matrices and bias vectors of the policy network.Only the hypernetworks require training.Using the well-trained hypernetworks,the policy network is generated through forward propagation in the test phase.By introducing a simple data processing,the hypernetworks can well learn the weight matrices and bias vectors by inputting their indices,resulting in low training cost.Simulation results demonstrate that the learned bandwidth and power allocation policies by the PGNs perform very close to a numerical algorithm.Moreover,the PGNs can be well generalized to the number of users and wireless channels,and are with significantly lower memory costs,fewer training samples,and shorter training time than the traditional learning-based methods.

The Analysis of Phase Synchronisation in the Uniform Scale-Free Hypernetwork

Many phenomena in realistic complex systems can be explained by the synchronisation behavior of complex systems,such as cricket chirping in uni-son.The synchronisation behavior occurring on a hypernetwork can be used to explain the swarming behavior occurring on a multivariate interacting system,such as the synchronised forwarding of group messages.There is a lack of results related to phase synchronization of hypernetwork in the existing studies on the synchronization behavior of hypernetworks.To address this problem,this paper investigates the node-based and hyperedge-based phase synchronisation of a scale-free hypernetwork using the Kuramoto model with the order parameter r as the synchronisation degree indicator.The comparative analysis reveals that the phase synchronisation of the scale-free hypernetwork is related to the uniformity k of the hypernetwork but not to the number of nodes and hyperedges,and the phase synchronisation based on hyperedges is more likely to occur than that based on nodes as the coupling strength increases.In addition,the degree of phase syn-chronisation of scale-free hypernetworks is related to the number of new_nodes of newly added nodes when the hyperedge grows during the construction of the hypernetwork,which shows that the smaller the new_nodes is,the better the degree of synchronisation of the hypernetwork is.