This article describes how to assess an approximation in a wavelet collocation method which minimizes the sum of squares of residuals. In a research project several different types of differential equations were appro...This article describes how to assess an approximation in a wavelet collocation method which minimizes the sum of squares of residuals. In a research project several different types of differential equations were approximated with this method. A lot of parameters must be adjusted in the discussed method here. For example one parameter is the number of collocation points. In this article we show how we can detect whether this parameter is too small and how we can assess the error sum of squares of an approximation. In an example we see a correlation between the error sum of squares and a criterion to assess the approximation.展开更多
Designing optimal time and spatial difference step size is the key technology for quantum-random filtering(QSF)to realize time-varying frequency periodic signal filtering.In this paper,it was proposed to use the short...Designing optimal time and spatial difference step size is the key technology for quantum-random filtering(QSF)to realize time-varying frequency periodic signal filtering.In this paper,it was proposed to use the short-time Fourier transform(STFT)to dynamically estimate the signal to noise ratio(SNR)and relative frequency of the input time-varying frequency periodic signal.Then the model of time and space difference step size and signal to noise ratio(SNR)and relative frequency of quantum random filter is established by least square method.Finally,the parameters of the quantum filter can be determined step by step by analyzing the characteristics of the actual signal.The simulation results of single-frequency signal and frequency time-varying signal show that the proposed method can quickly and accurately design the optimal filter parameters based on the characteristics of the input signal,and achieve significant filtering effects.展开更多
This work started out with the in-depth feasibil-ity study and limitation analysis on the current disease spread estimating and countermea-sures evaluating models, then we identify that the population variability is a...This work started out with the in-depth feasibil-ity study and limitation analysis on the current disease spread estimating and countermea-sures evaluating models, then we identify that the population variability is a crucial impact which has been always ignored or less empha-sized. Taking HIV/AIDS as the application and validation background, we propose a novel al-gorithm model system, EEA model system, a new way to estimate the spread situation, evaluate different countermeasures and analyze the development of ARV-resistant disease strains. The model is a series of solvable ordi-nary differential equation (ODE) models to es-timate the spread of HIV/AIDS infections, which not only require only one year’s data to deduce the situation in any year, but also apply the piecewise constant method to employ multi- year information at the same time. We simulate the effects of therapy and vaccine, then evaluate the difference between them, and offer the smallest proportion of the vaccination in the population to defeat HIV/AIDS, especially the advantage of using the vaccination while the deficiency of using therapy separately. Then we analyze the development of ARV-resistant dis-ease strains by the piecewise constant method. Last but not least, high performance computing (HPC) platform is applied to simulate the situa-tion with variable large scale areas divided by grids, and especially the acceleration rate will come to around 4 to 5.5.展开更多
文摘This article describes how to assess an approximation in a wavelet collocation method which minimizes the sum of squares of residuals. In a research project several different types of differential equations were approximated with this method. A lot of parameters must be adjusted in the discussed method here. For example one parameter is the number of collocation points. In this article we show how we can detect whether this parameter is too small and how we can assess the error sum of squares of an approximation. In an example we see a correlation between the error sum of squares and a criterion to assess the approximation.
基金Projects(2017H0022,2016H6015)supported by Fujian Science and Technology Key Project,China
文摘Designing optimal time and spatial difference step size is the key technology for quantum-random filtering(QSF)to realize time-varying frequency periodic signal filtering.In this paper,it was proposed to use the short-time Fourier transform(STFT)to dynamically estimate the signal to noise ratio(SNR)and relative frequency of the input time-varying frequency periodic signal.Then the model of time and space difference step size and signal to noise ratio(SNR)and relative frequency of quantum random filter is established by least square method.Finally,the parameters of the quantum filter can be determined step by step by analyzing the characteristics of the actual signal.The simulation results of single-frequency signal and frequency time-varying signal show that the proposed method can quickly and accurately design the optimal filter parameters based on the characteristics of the input signal,and achieve significant filtering effects.
文摘This work started out with the in-depth feasibil-ity study and limitation analysis on the current disease spread estimating and countermea-sures evaluating models, then we identify that the population variability is a crucial impact which has been always ignored or less empha-sized. Taking HIV/AIDS as the application and validation background, we propose a novel al-gorithm model system, EEA model system, a new way to estimate the spread situation, evaluate different countermeasures and analyze the development of ARV-resistant disease strains. The model is a series of solvable ordi-nary differential equation (ODE) models to es-timate the spread of HIV/AIDS infections, which not only require only one year’s data to deduce the situation in any year, but also apply the piecewise constant method to employ multi- year information at the same time. We simulate the effects of therapy and vaccine, then evaluate the difference between them, and offer the smallest proportion of the vaccination in the population to defeat HIV/AIDS, especially the advantage of using the vaccination while the deficiency of using therapy separately. Then we analyze the development of ARV-resistant dis-ease strains by the piecewise constant method. Last but not least, high performance computing (HPC) platform is applied to simulate the situa-tion with variable large scale areas divided by grids, and especially the acceleration rate will come to around 4 to 5.5.
