The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of co...The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.展开更多
Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized...Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.展开更多
To decompose an unbalanced multi-stage logistic system to multipleindependent single-stage logistic systems, a new notion of parameterized interface distribution ispresented. For encoding the logistic pattern on each ...To decompose an unbalanced multi-stage logistic system to multipleindependent single-stage logistic systems, a new notion of parameterized interface distribution ispresented. For encoding the logistic pattern on each stage, the Pruefer number is used. With theimproved decoding procedure, any Pruefer number produced stochastically can be decoded to a feasiblelogistic pattern, which can match with the capacities of the nodes of the logistic system. Withthese two innovations, a new modeling method based on parameterized interface distribution and thePriifer number coding is put forward. The corresponding genetic algorithm, named as PIP-GA, can findbetter solutions and require less computational time than st-GA. Although requiring a little moreconsumption of memory, PIP-GA is still an efficient and robust method in the modeling andoptimization of unbalanced multi-stage logistic systems.展开更多
This study focuses on the suburbanization and subcentering of population and examines the nature of spatial restructuring in terms of the population distribution in the Beijing metropolitan area.Instead of the classic...This study focuses on the suburbanization and subcentering of population and examines the nature of spatial restructuring in terms of the population distribution in the Beijing metropolitan area.Instead of the classic density function approach,we employ the nonparametric analysis to characterize the spatial pattern of population densities in the Beijing metropolitan area and identify the suburban subcenters.Our findings suggest that the population has spread with rapid urban growth in the Beijing metropolitan area,and the compact urban form has been replaced by a more dispersed polycentric spatial distribution.However,compared with the decentralization of western cities,the spatial extent of the decentralization of population in the Beijing metropolitan area is quite limited.The rapid growth of population in the near suburbs has expedited the sprawl of the central city,with a larger central agglomeration of population dominating the metropolitan area.In this sense,the spatial pattern of the Beijing metropolitan area is still characterized by the continuous compactness.However,our findings do provide the evidence that the city has been turning to a polycentric structure.We find significant population subcenters have emerged in the suburbs of Beijing since the 1980s.But the polycentricity emerged in the Beijing metropolitan area is very different by nature from that observed in Western cities.The subcenters emerged are adherent to the development scheme planned for the city,so it can be referred to as the so called 'planned polycentricity'.展开更多
基金Supported by the National Natural Science Foundation of China(12101004)the Natural Science Research Project of Anhui Educational Committee(2023AH030021)the Research Startup Foundation for Introducing Talent of Anhui Polytechnic University(2020YQQ064)。
文摘The present paper deals with the problem of nonparametric kernel density estimation of the trend function for stochastic processes driven by fractional Brownian motion of the second kind.The consistency,the rate of convergence,and the asymptotic normality of the kernel-type estimator are discussed.Besides,we prove that the rate of convergence of the kernel-type estimator depends on the smoothness of the trend of the nonperturbed system.
基金supported by the National High-Tech Research and Development Program of China(863 Program)(No.2008AA093001)
文摘Cauchy priori distribution-based Bayesian AVO reflectivity inversion may lead to sparse estimates that are sensitive to large reflectivities. For the inversion, the computation of the covariance matrix and regularized terms requires prior estimation of model parameters, which makes the iterative inversion weakly nonlinear. At the same time, the relations among the model parameters are assumed linear. Furthermore, the reflectivities, the results of the inversion, or the elastic parameters with cumulative error recovered by integrating reflectivities are not well suited for detecting hydrocarbons and fuids. In contrast, in Bayesian linear AVO inversion, the elastic parameters can be directly extracted from prestack seismic data without linear assumptions for the model parameters. Considering the advantages of the abovementioned methods, the Bayesian AVO reflectivity inversion process is modified and Cauchy distribution is explored as a prior probability distribution and the time-variant covariance is also considered. Finally, we propose a new method for the weakly nonlinear AVO waveform inversion. Furthermore, the linear assumptions are abandoned and elastic parameters, such as P-wave velocity, S-wave velocity, and density, can be directly recovered from seismic data especially for interfaces with large reflectivities. Numerical analysis demonstrates that all the elastic parameters can be estimated from prestack seismic data even when the signal-to-noise ratio of the seismic data is low.
文摘To decompose an unbalanced multi-stage logistic system to multipleindependent single-stage logistic systems, a new notion of parameterized interface distribution ispresented. For encoding the logistic pattern on each stage, the Pruefer number is used. With theimproved decoding procedure, any Pruefer number produced stochastically can be decoded to a feasiblelogistic pattern, which can match with the capacities of the nodes of the logistic system. Withthese two innovations, a new modeling method based on parameterized interface distribution and thePriifer number coding is put forward. The corresponding genetic algorithm, named as PIP-GA, can findbetter solutions and require less computational time than st-GA. Although requiring a little moreconsumption of memory, PIP-GA is still an efficient and robust method in the modeling andoptimization of unbalanced multi-stage logistic systems.
基金Under the auspices of National Key Basic Research Program of China (No. 2012CB955802)National Natural Science Foundation of China (No. 41001069)Grant Program of National Social Science Foundation of China (No.10zd&022)
文摘This study focuses on the suburbanization and subcentering of population and examines the nature of spatial restructuring in terms of the population distribution in the Beijing metropolitan area.Instead of the classic density function approach,we employ the nonparametric analysis to characterize the spatial pattern of population densities in the Beijing metropolitan area and identify the suburban subcenters.Our findings suggest that the population has spread with rapid urban growth in the Beijing metropolitan area,and the compact urban form has been replaced by a more dispersed polycentric spatial distribution.However,compared with the decentralization of western cities,the spatial extent of the decentralization of population in the Beijing metropolitan area is quite limited.The rapid growth of population in the near suburbs has expedited the sprawl of the central city,with a larger central agglomeration of population dominating the metropolitan area.In this sense,the spatial pattern of the Beijing metropolitan area is still characterized by the continuous compactness.However,our findings do provide the evidence that the city has been turning to a polycentric structure.We find significant population subcenters have emerged in the suburbs of Beijing since the 1980s.But the polycentricity emerged in the Beijing metropolitan area is very different by nature from that observed in Western cities.The subcenters emerged are adherent to the development scheme planned for the city,so it can be referred to as the so called 'planned polycentricity'.
