This project aims to propose a novel approach for visualizing 4D geometry through the utilization of augmented reality (AR). While previous work has explored virtual reality (VR) as a means to bring 4D objects into a 3D environment, as well as 2D projections to display 4D geometry on screens, this project seeks to extend the possibilities by leveraging the immersive nature of AR technology. By overlaying virtual 4D objects onto the real world, users can experience a more tangible representation and gain a deeper understanding of the complex structures present in higher dimensions.

Specification of PM_2.5 transmission characteristics is important for pollution control and policymaking. We apply higher-order organization of complex networks to identify major potential PM_2.5 contributors and PM_2.5 transport pathways of a network of 189 cities in China. The network we create in this paper consists of major cities in China and contains information on meteorological conditions of wind speed and wind direction, data on geographic distance, mountains, and PM_2.5 concentrations. We aim to reveal PM_2.5 mobility between cities in China. Two major conclusions are revealed through motif analysis of complex networks. First, major potential PM_2.5 pollution contributors are identified for each cluster by one motif, which reflects movements from source to target. Second, transport pathways of PM_2.5 are revealed by another motif, which reflects transmission routes. To our knowledge, this is the first work to apply higher-order network analysis to study PM_2.5 transport.

Brucellosis is a bacterial disease caused by brucella; mainly spread by direct contact transmission through the brucella carriers, or indirect contact transmission by the environment containing large quantities of bacteria discharged by the infected individuals. At the beginning of 21st century, the epidemic among dairy cows in Zhejiang province, began to come back and has become a localized prevalent epidemic. Combining the pathology of brucellosis, the reported positive data characteristics, and the feeding method in Zhejiang province, this paper establishes an SEIV dynamic model to excavate the internal transmission dynamics, fit the real disease situation, predict brucellosis tendency and assess control measures in dairy cows. By careful analysis, we give some quantitative results as follows. (1) The external input of dairy cows from northern areas may lead to high fluctuation of the number of the infectious cows in Zhejiang province that can reach several hundreds. In this case, the disease cannot be controlled and the infection situation cannot easily be predicted. Thus, this paper encourages cows farms to insist on self-supplying production of the dairy cows. (2) The effect of transmission rate of brucella in environment to dairy cattle on brucellosis spreading is greater than transmission rate of the infectious dairy cattle to susceptible cattle. The prevalence of the epidemic is mainly aroused by environment transmission. (3) Under certain circumstances, the epidemic will become a periodic phenomenon. (4) For Zhejiang province, besides measures that have already been adopted, sterilization times of the infected regions is suggested as twice a week, and should be combined with management of the birth rate of dairy cows to control brucellosis spread.