The optimal development of third-party payment platforms presents some very complex problems. One of the key issues is to identify the most promising potential customers. Hence, customer mining has come to prominence in financial research. This paper describes a way of modeling a third-party payment system in the context of a rough complex network, underpinned by rough set theory. The study of knowledge discovery on rough complex networks provides a quantitative and actionable method, which can be used to mine potential customers in rough complex networks. In addition to developing a way of analyzing data on a third-party payment platform, the paper uncovers a new application area for rough set theory, pointing the way to further utilization of this technology.

Blind image inpainting is a challenging task in image processing. Motivated by the excellent performance of low dimensional manifold model (LDMM) in image inpainting for large-scale pixels missing, we introduce a novel blind inpainting model to repair images with missing pixels or damaged with impulse noise, in spite of the unknown locations of the corrupted pixels. We applied logarithmic transformation to separate the image and binary mask. LDMM regularization and l0 norm regularization were applied respectively to simultaneously estimate the image and the mask. The resulted minimization problem was then solved by the split Bregman algorithm. The simulation results showed that the proposed model, compared with the existing ones, can effectively restore the image with large uniform and non-uniform missing rate.

Due to the unpredictability of Covid-19 and the complexity of community transmission, the existing theories and methods of system resilience assessment can not meet the needs of city epidemic prevention complex network resilience assessment. Therefore, this paper constructs a epidemic transmission complex network and studies the epidemic transmission model on the network---the Improved SEIR. And the paper predicts the development of the epidemic, point out the vulnerability of the network and the vulnerability of epidemic prevention. Then, according to the network structure of epidemic prevention and the results of SEIR model, the new theory and method of epidemic prevention resilience assessment in City A were constructed, and the resilience assessment of complex epidemic prevention network was divided into two dimensions: network structure resilience and urban function resilience. The new methods for the city epidemic prevention complex network resilience assessment are simulationed through measured data. The results show that when the epidemic comes, improving the resilience of urban epidemic prevention functions has a better effect on epidemic prevention and control. The paper integrates improved SEIR models with urban anti-epidemic measures, providing a new approach to resilience assessment of complex systems.