The spread of online topics,which is a complex socio-psychological and information dissemination process,can significantly influence the online public opinion. The behavior of online topics spreading is explored and i...The spread of online topics,which is a complex socio-psychological and information dissemination process,can significantly influence the online public opinion. The behavior of online topics spreading is explored and its regularity is attempted to analyze. A general model for the spread of online topics is introduced,and the differential equation that describes the velocity of an online topic＇s spreading is derived. The velocity of an online topic＇s spread indicates the level of the topic＇s development and reflects its popularity over time. The proposed model has been theoretically analyzed and empirically studied,respectively. By analyzing the data set from a famous Internet forum,it is shown that the development of spread velocity of online topics has some certain features and our model matches the laws of reality. This method,which is suitable for forecasting the development trend of online topics’ spread velocity in short term,is also critical to the success of online topics’ regularity analysis.展开更多
In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubi...In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the sp展开更多
基金supported by the National Natural Science Foundation of China under Grant No. 60972012the Beijing Natural Science Foundation under Grant No. 4102047+2 种基金the Major Program for Research on Philosophy & Humanity Social Sciences of the Ministry of Education of China under Grant No. 08WL1101the Academic Discipline and Postgraduate Education Project of Beijing Municipal Commission of Educationthe Service Business of Scientists and Engineers Project under Grant No. 2009GJA00048
文摘The spread of online topics,which is a complex socio-psychological and information dissemination process,can significantly influence the online public opinion. The behavior of online topics spreading is explored and its regularity is attempted to analyze. A general model for the spread of online topics is introduced,and the differential equation that describes the velocity of an online topic＇s spreading is derived. The velocity of an online topic＇s spread indicates the level of the topic＇s development and reflects its popularity over time. The proposed model has been theoretically analyzed and empirically studied,respectively. By analyzing the data set from a famous Internet forum,it is shown that the development of spread velocity of online topics has some certain features and our model matches the laws of reality. This method,which is suitable for forecasting the development trend of online topics’ spread velocity in short term,is also critical to the success of online topics’ regularity analysis.
文摘In this paper,the forecasting equations of a 2nd-order space-time differential remainder are deduced from the Navier-Stokes primitive equations and Eulerian operator by Taylor-series expansion.Here we introduce a cubic spline numerical model(Spline Model for short),which is with a quasi-Lagrangian time-split integration scheme of fitting cubic spline/bicubic surface to all physical variable fields in the atmospheric equations on spherical discrete latitude-longitude mesh.A new algorithm of"fitting cubic spline—time step integration—fitting cubic spline—……"is developed to determine their first-and2nd-order derivatives and their upstream points for time discrete integral to the governing equations in Spline Model.And the cubic spline function and its mathematical polarities are also discussed to understand the Spline Model’s mathematical foundation of numerical analysis.It is pointed out that the Spline Model has mathematical laws of"convergence"of the cubic spline functions contracting to the original functions as well as its 1st-order and 2nd-order derivatives.The"optimality"of the 2nd-order derivative of the cubic spline functions is optimal approximation to that of the original functions.In addition,a Hermite bicubic patch is equivalent to operate on a grid for a 2nd-order derivative variable field.Besides,the slopes and curvatures of a central difference are identified respectively,with a smoothing coefficient of 1/3,three-point smoothing of that of a cubic spline.Then the slopes and curvatures of a central difference are calculated from the smoothing coefficient 1/3 and three-point smoothing of that of a cubic spline,respectively.Furthermore,a global simulation case of adiabatic,non-frictional and"incompressible"model atmosphere is shown with the quasi-Lagrangian time integration by using a global Spline Model,whose initial condition comes from the NCEP reanalysis data,along with quasi-uniform latitude-longitude grids and the so-called"shallow atmosphere"Navier-Stokes primitive equations in the sp
