Spatial Agglomeration and Diffusion of Population Based on a Regional Density Function Approach:A Case Study of Shandong Province in China

Population density functions have long been used to describe the spatial structure of regional population distributions.Several studies have been conducted to examine the population distribution in Shandong Province,China,but few have applied regional density functions to the analysis.Therefore,based on the 2000,2010,and 2020 population censuses,this study used monocentric and polycentric regional density functions to study the characteristics of population agglomeration and diffusion in Shandong.This is followed by an in-depth discussion based on population growth rate data and hot-and cold-spot analyses.The results showed that the Shandong Province population was spatially unevenly distributed.Population growth rates were higher in urban centers and counties,with more significant changes in population size in the eastern coastal areas than in the inland areas.As verified in this study,the logarithmic form of the single-center regional density function R2 was greater than 0.8,which was in line with the population spatial structure of Shandong Province.During the study period,the estimated population density of the regional center and the absolute value of the regional population density gradient both increased,indicating a clear and increasing trend of centripetal agglomeration of regional centers over the study period.Overall,the R2 value of the multicenter region density function was higher than that of the single-center region density function.The polycentric regional density function showed that the population density gradient of some centers had a downward trend,which reflected the spatial development trend of outward diffusion in these centers.Meanwhile,the variation in the estimated population density and the population density gradient exhibited differences in the central population distribution patterns at different levels.

Thailand-Japan＇s Volume of Trade Influencing on Socio-economic and Well-Being Development Using Maximum Entropy Bootstrap

This paper is preliminary information on some empirical findings based on an analysis of Thailand＇s macroeconomic data. The purpose of the study is to quantify social-economic well-being development with special emphasis on poverty. The maximum entropy bootstrap was presented that did not require the property of stationarity. Moreover, the methodology was stratified both the ergodic theorem and the central limit theorem. Thailand＇s GINI index and Thailand-Japan＇s volume of trade data cover the 14-year period from 1998 to 2011. There is a statistically significant negative non-linear relationship between endogenous Thailand＇s GINI index and exogenous Thailand-Japan＇s volume of trade. The results confirmed that every lagged one percent increase in Thailand-Japan＇s volume of trade influenced by a decrease of Thailand＇s GINI index coefficient 0.039 percent with the asymmetric around 0-almost closed to range condition -0.034824348 at 2.5%.

Regional moment-independent sensitivity analysis with its applications in engineering

Traditional Global Sensitivity Analysis（GSA） focuses on ranking inputs according to their contributions to the output uncertainty.However,information about how the specific regions inside an input affect the output is beyond the traditional GSA techniques.To fully address this issue,in this work,two regional moment-independent importance measures,Regional Importance Measure based on Probability Density Function（RIMPDF） and Regional Importance Measure based on Cumulative Distribution Function（RIMCDF）,are introduced to find out the contributions of specific regions of an input to the whole output distribution.The two regional importance measures prove to be reasonable supplements of the traditional GSA techniques.The ideas of RIMPDF and RIMCDF are applied in two engineering examples to demonstrate that the regional moment-independent importance analysis can add more information concerning the contributions of model inputs.

Core-softened potentials, multiple liquid-liquid critical points, and density anomaly regions： An exact solution

The pressure versus temperature phase diagram of a shoulder-like potential is exactly computed in one system of particles interacting through a multiscale dimension. The N-shoulder potential exhibits N density anomaly regions in the phase diagram if the length scales can be connected by a convex curve The result is analyzed in terms of the convexity of the Gibbs free energy.

Asymptotic properties of plug-in level set estimators for right censored data

We assume T1,..., Tn are i.i.d. data sampled from distribution function F with density function f and C1,...,Cn are i.i.d. data sampled from distribution function G. Observed data consists of pairs （Xi, δi）, em= 1,..., n, where Xi = min{Ti,Ci}, δi = I（Ti 6 Ci）, I（A） denotes the indicator function of the set A. Based on the right censored data {Xi, δi}, em=1,..., n, we consider the problem of estimating the level set {f 〉 c} of an unknown one-dimensional density function f and study the asymptotic behavior of the plug-in level set estimators. Under some regularity conditions, we establish the asymptotic normality and the exact convergence rate of the λg-measure of the symmetric difference between the level set {f ≥ c} and its plug-in estimator {fn ≥ c}, where f is the density function of F, and fn is a kernel-type density estimator of f. Simulation studies demonstrate that the proposed method is feasible. Illustration with a real data example is also provided.