The Complex Nonlinear Causal Coupling Patterns between PM2.5 and Meteorological Factors in Tibetan Plateau: A Case Study in Xining

PM2.5 pollution influences the population health and people’s daily life. Because meteorological factors are main factor affecting the formation of PM2.5, the interaction between PM2.5 and meteorological factors needs to be better understood, both for air quality management and for PM2.5 projection. Here, we use a nonlinear state space method called the convergent cross mapping method to identify the complex coupling patterns between PM2.5 and meteorological factors in a plateau city: Xining. The results prove that PM2.5-meteorological coupling patterns change with seasons and PM2.5-meteorological coupling patterns are fixed in spring, autumn and winter. In spring, there is a negative unidirectional effect from precipitation to PM2.5 and a negative bidirectional effect between relative humidity and PM2.5. In autumn, there are some negative bidirectional effects between PM2.5 and relative humidity, precipitation, and air pressure, while solar radiation has a positive bidirectional effect on PM2.5. In winter, there are negative bidirectional couplings between PM2.5 and wind speed and temperature and a positive bidirectional coupling between relative humidity and PM2.5. Furthermore, relative humidity is a consistent driving factor affecting PM2.5. Air quality managers may alleviate PM2.5 by increasing relative humidity. Thus, the results provide a meteorological means for improving air quality in plateau cities.

Determination of the exact mode frequencies of multi-storey structures by state-space method and a comparison with mode superposition method

A comparative research has been carried out for obtaining the time-consuming exact solution (state-space) and approximate solution (mode superposition) of transient and steady-state vibrations of linearly damped linear frame buildings. In the mode superposition method, the proportional damping matrix has been constructed by different approaches such as modal combination of mass and stiffness matrixes (Rayleigh) and disregarding the off-diagonal elements of the non-classical damping matrix, while in the state-space method the non-proportional damping matrix is constructed in exact situation. These observations are individually investigated, which the most suitable parameter to render the approximate results as close as possible to the exact results. Harmonic forces are applied on the different storeys of three and five storey frame buildings, and the responses are displayed in comparative tables and figures. The maximum responses are calculated by square root of sum of the squares (SRSS) method. A MATLAB code is generated and the equations of exact and approximate methods are solved.

Estimating the time-varying reproduction number of COVID-19 with a state-space method

After slowing down the spread of the novel coronavirus COVID-19, many countries have started to relax their confinement measures in the face of critical damage to socioeconomic structures. At this stage, it is desirable to monitor the degree to which political measures or social affairs have exerted influence on the spread of disease. Though it is difficult to trace back individual transmission of infections whose incubation periods are long and highly variable, estimating the average spreading rate is possible if a proper mathematical model can be devised to analyze daily event-occurrences. To render an accurate assessment, we have devised a state-space method for fitting a discrete-time variant of the Hawkes process to a given dataset of daily confirmed cases. The proposed method detects changes occurring in each country and assesses the impact of social events in terms of the temporally varying reproduction number, which corresponds to the average number of cases directly caused by a single infected case. Moreover, the proposed method can be used to predict the possible consequences of alternative political measures. This information can serve as a reference for behavioral guidelines that should be adopted according to the varying risk of infection.