Graph contrastive learning (GCL) has gained considerable attention as a self-supervised learning technique that has been successfully employed in various applications, such as node classification, node clustering, and link prediction. Despite its achievements, GCL has limited exploration of the community structure of graphs. This paper presents a novel online framework called Community Contrastive Learning (Community-CL) for simultaneously learning node representations and detecting communities in a network. The proposed method employs contrastive learning to minimize the difference in the latent representations of nodes and communities in different graph views. To achieve this, learnable graph augmentation views using a graph auto-encoder (GAE) are proposed, followed by a shared encoder that learns the feature matrix of the original graph and augmentation views. This joint contrastive framework enables more accurate representation learning of the network and results in more expressive embeddings than traditional community detection algorithms that solely optimize for community structure. Experimental results demonstrate that Community-CL achieves superior performance compared to state-of-the-art baselines in community detection. Specifically, the NMI of Community-CL is reported to be 0.714 (0.551) on the Amazon-Photo (Amazon-Computers) dataset, which represents a performance improvement of up to 16% compared with the best baseline.

In this paper, a Caputo fractional-order HCV Periodic immune response model with saturation incidence, cell-to-cell and drug control was proposed. We derive two different basic reproductive numbers and their relation with infection-free equilibrium and the immune-exhausted equilibrium. Moreover, there exists some symmetry in the relationship between the two equilibria and the basic reproduction numbers. We obtain the global stability of the infection-free equilibrium by using Lyapunov function and the local stability of the immune-exhausted equilibrium. The optimal control problem is also considered and two control strategies are given; one is for ITX5061 monotherapy, the other is for ITX5061 and DAAs combination therapy. Matlab numerical simulation shows that combination therapy has lower objective function value; therefore, it is worth trying to use combination therapy to treat HCV infection.

The network coding always brings additional resource consumption while it can make the network to achieve the required rate. It is necessary to minimize the resource consumption in the network while achieving the desired throughput. Most of the other papers consider the minimum number of encoding nodes or the minimum number of encoding links separately. Of course some papers consider trade-offs between coding and link cost, but the optimal choice for different trade-offs is not clear. This paper provides a heuristic judgment method to derive the optimal result on the selection. In this paper, the total value of the link cost and coding cost is treated as the only objective function, and the objective function is minimized based on the improved ant colony algorithm. The consideration of multi-source situation and the different value of different links is a new attempt.

In this paper, a general degenerate multiscale HCV diffusive model with spatial heterogeneity was established and analyzed. We derived the variational formula of the basic reproduction number $ {{\Re }_{0}} $. The existence of positive nonhomogeneous equilibrium was demonstrated through proving the uniform persistence of the model when $ {{\Re }_{0}}>1 $. Through constructing the Lyapunov function, the global asymptotic stability of the disease-free nonhomogeneous equilibrium was demonstrated if $ {{\Re }_{0}}1 $. Numerical simulations were consistent with theoretical analysis. The simulations also show that infection risk may increase with increasing spatial heterogeneity intensity.