Modeling Spreading Dynamics And Reconstruction On Higher-order Networks

Network science has demonstrated its scientific importance and practical value as a powerful tool for studying various complex systems,enhancing our understanding of disease,society,life,and emergent phenomena in complex systems.Previously,complex systems were usually modeled as pairwise relationship networks,but as our exploration of real-world systems deepens,it has been realized that such pairwise relationships are often not enough to describe the multiple interactions that exist in real systems,and the higher-order networks have been proven an effective way to study such complex systems.In view of this,this study will investigate the spreading dynamics and network reconstruction under the theme of higher-order networks.The main research of this dissertation is as follows:(1)In the aspect of spreading dynamics based on higher-order networks,we propose a novel coupled awareness-disease model to explore the interplay of simplicial awareness contagion and epidemic spreading.Specifically,the higher-order network with 2-simplicial complexes structure is considered as the virtual information layer,and the time-varying network with memory mechanism is constructed as the physical contact layer.The theoretical analysis based on the microscopic Markov chain approach is developed and the critical threshold for the model is also analytically derived.The experimental results show that our theoretical method is in good agreement with the Monte Carlo simulations.Specifically,we find that the synergistic reinforcement mechanism coming from the group interactions promotes the diffusion of awareness and effectively suppresses the spread of epidemics.Furthermore,our results illustrate that the contact capacity of individuals,activity heterogeneity,and memory strength also have a significant impact on the coupling dynamics,and yields a cross-over phenomenon.When the higher-order network structure is known,modeling of the spreading dynamics becomes an important research direction.However,in cases where the structure of the higher-order network is unknown but the time-series date is available,we are faced with the challenge of reconstructing this higher-order network structure.Therefore,in order to address the problem of higher-order network reconstruction,this study primarily focuses on binary time-series data and investigates the following three different scenarios.(2)As a preliminary attempt to reconstruct higher-order networks,we first study on how to reconstruct the 2-simplicial complexes based on the data arising from social contagion dynamics,then the problem includes how to determine the neighbors and the2-simplex structures of each node.To this end,we combine the statistical inference framework and the expectation-maximization algorithm to calculate the probability of all possible two-and three-body connections.We further articulate a two-step scheme to improve the reconstruction accuracy while significantly reducing the computational load.Through experiments on synthetic and real-world 2-simplicial complexes,the results show that pairwise connections and 2-simplex structures in the network can be well reconstructed under reasonable time-series length.In addition,the experimental impact parameters and the robustness of the method are analyzed.(3)We further reconstruct the 2-simplicial complexes using the simplicial Ising dynamics data,which is a model in which the bi-directional transfer probabilities are both affected by the neighboring states.In contrast,social contagion models are characterized by unidirectional transfer probabilities influenced by the state of neighbors.Therefore,simplicial Ising dynamics data contains richer information compared to social contagion models.By directly adopting the two-step reconstruction strategy and probability statistics method,we can infer the 1-simplex and 2-simplex structures of each node.Furthermore,the accuracy of the experimental results is verified on synthetic and real data sets,respectively.(4)Due to the requirement of closure property in simplicial complexes,while general hypergraphs do not possess this property,this study further investigates a specific type of hypergraph-the uniform hypergraph-and its reconstruction problem.To address this issue,a two-stage scheme is proposed based on the social contagion dynamics and the general theoretical framework of statistical inference.The scheme involves inferring the complete underlying network structure first and then reconstructing the uniform hypergraph.By reconstructing the synthetic and real-word 3-uniform hypergraphs and4-uniform hypergraphs respectively,the results show that the method can well solve the uniform hypergraph reconstruction.More importantly,the method is not only applicable to arbitrary 6)-uniform hypergraphs,but also does not need to know the specific parameters of the propagation model and only depends on the states of the nodes at different times.