The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the int...The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.展开更多
Due to the nature of ultra-short-acting opioid remifentanil of high time-varying,complex compartment model and low-accuracy of plasma concentration prediction,the traditional estimation method of population pharmacoki...Due to the nature of ultra-short-acting opioid remifentanil of high time-varying,complex compartment model and low-accuracy of plasma concentration prediction,the traditional estimation method of population pharmacokinetics parameters,nonlinear mixed effects model(NONMEM),has the abuses of tedious work and plenty of man-made jamming factors.The Elman feedback neural network was built.The relationships between the patients’plasma concentration of remifentanil and time,patient’age,gender,lean body mass,height,body surface area,sampling time,total dose,and injection rate through network training were obtained to predict the plasma concentration of remifentanil,and after that,it was compared with the results of NONMEM algorithm.In conclusion,the average error of Elman network is 6.34%,while that of NONMEM is 18.99%.The absolute average error of Elman network is 27.07%,while that of NONMEM is 38.09%.The experimental results indicate that Elman neural network could predict the plasma concentration of remifentanil rapidly and stably,with high accuracy and low error.For the characteristics of simple principle and fast computing speed,this method is suitable to data analysis of short-acting anesthesia drug population pharmacokinetic and pharmacodynamics.展开更多
The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build ...The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build early exercise European option and early termination American option pricing models. Firstly, the authors reviewed the characteristics of American option and European option, then there was compares between them. Base on continuous-time American option pricing model, this research analyzed the value of these options.展开更多
基金supported by the National Natural Science Foundation of China[grant numbers 41375110,11471244]
文摘The computational uncertainty principle states that the numerical computation of nonlinear ordinary differential equations（ODEs） should use appropriately sized time steps to obtain reliable solutions.However,the interval of effective step size（IES） has not been thoroughly explored theoretically.In this paper,by using a general estimation for the total error of the numerical solutions of ODEs,a method is proposed for determining an approximate IES by translating the functions for truncation and rounding errors.It also illustrates this process with an example.Moreover,the relationship between the IES and its approximation is found,and the relative error of the approximation with respect to the IES is given.In addition,variation in the IES with increasing integration time is studied,which can provide an explanation for the observed numerical results.The findings contribute to computational step-size choice for reliable numerical solutions.
基金Project(31200748)supported by the National Natural Science Foundation of China
文摘Due to the nature of ultra-short-acting opioid remifentanil of high time-varying,complex compartment model and low-accuracy of plasma concentration prediction,the traditional estimation method of population pharmacokinetics parameters,nonlinear mixed effects model(NONMEM),has the abuses of tedious work and plenty of man-made jamming factors.The Elman feedback neural network was built.The relationships between the patients’plasma concentration of remifentanil and time,patient’age,gender,lean body mass,height,body surface area,sampling time,total dose,and injection rate through network training were obtained to predict the plasma concentration of remifentanil,and after that,it was compared with the results of NONMEM algorithm.In conclusion,the average error of Elman network is 6.34%,while that of NONMEM is 18.99%.The absolute average error of Elman network is 27.07%,while that of NONMEM is 38.09%.The experimental results indicate that Elman neural network could predict the plasma concentration of remifentanil rapidly and stably,with high accuracy and low error.For the characteristics of simple principle and fast computing speed,this method is suitable to data analysis of short-acting anesthesia drug population pharmacokinetic and pharmacodynamics.
文摘The maximum relative error between continuous-time American option pricing model and binomial tree model is very small. In order to improve the European and American options in trade course, the thesis tried to build early exercise European option and early termination American option pricing models. Firstly, the authors reviewed the characteristics of American option and European option, then there was compares between them. Base on continuous-time American option pricing model, this research analyzed the value of these options.
