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The rapid spread of COVID-19 disease has had a significant impact on the world. In this paper, we study COVID-19 data interpretation and visualization using open-data sources for 351 cities and towns in Massachusetts from December 6, 2020 to September 25, 2021. Because cities are embedded in rather complex transportation networks, we construct the spatio-temporal dynamic graph model, in which the graph attention neural network is utilized as a deep learning method to learn the pandemic transition probability among major cities in Massachusetts. Using the spectral graph wavelet transform (SGWT), we process the COVID-19 data on the dynamic graph, which enables us to design effective tools to analyze and detect spatio-temporal patterns in the pandemic spreading. We design a new node classification method, which effectively identifies the anomaly cities based on spectral graph wavelet coefficients. It can assist administrations or public health organizations in monitoring the spread of the pandemic and developing preventive measures. Unlike most work focusing on the evolution of confirmed cases over time, we focus on the spatio-temporal patterns of pandemic evolution among cities. Through the data analysis and visualization, a better understanding of the epidemiological development at the city level is obtained and can be helpful with city-specific surveillance.

In this paper, we focus on high‐order approximate solutions of (N + 1)‐level systems with near‐resonance control over a long period of time. A high‐order renormalization group (RG) method with rigorous proof is developed to deal with such open quantum systems. By constructing high‐order RG equations, we obtained the high‐order long‐time RG approximate solutions of (N + 1)‐level systems in several kinds of near‐resonance cases. The numerical simulation results show that our high‐order RG method has the same accuracy as the fourth‐order Runge–Kutta method in O(1) time scale but more reliable in O()1ε time scale.