Some new coupled map lattice (CML) models are developed for simulating both convection, diffusion terms and weakly or strongly coupled terms. The structure and features of model are analysed. Numerical results show th...Some new coupled map lattice (CML) models are developed for simulating both convection, diffusion terms and weakly or strongly coupled terms. The structure and features of model are analysed. Numerical results show that the new models are effective for studying spatiotemporal chaos. Finally, the mechanism of turbulence is analysed via the numerical results.展开更多
A new coupled map lattic (CML) model is given by using some stability analysis for the related difference equations. Numerical results show that the new model is an effective one of studying spatiotemporal chaos, espe...A new coupled map lattic (CML) model is given by using some stability analysis for the related difference equations. Numerical results show that the new model is an effective one of studying spatiotemporal chaos, especially for strongly coupled systems.展开更多
A family of coupled map lattice （CML） models has been developed to simulate the interaction of convection, diffusion and dispersion in both weakly and strongly coupled cases. With variation of parameters, the models...A family of coupled map lattice （CML） models has been developed to simulate the interaction of convection, diffusion and dispersion in both weakly and strongly coupled cases. With variation of parameters, the models can simulate those systems of convection dominating, diffusion dominating, and dispersion dominating states. Not only coherent and turbulent properties as well as their interrelations, but also the transitional state between any modes with local coupling and global coupling are analysed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and thus can be conveniently used to analyse an initiative and driven coupled system. Results of numerical simulation also lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. Finally, the duality of wave and particle characters of turbulence is illustrated in the numerical simulation.展开更多
A family of coupled map lattice （CML） models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only cohe...A family of coupled map lattice （CML） models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.展开更多
In the analysis of censored survival data,it is crucial to consider the heterogeneity of treatment effects in order to avoid biased inferences.The deep neural network-based heterogeneous partially linear Cox model off...In the analysis of censored survival data,it is crucial to consider the heterogeneity of treatment effects in order to avoid biased inferences.The deep neural network-based heterogeneous partially linear Cox model offers a flexible and robust solution by incorporating both heterogeneous linear and homogeneous nonlinear components.The authors propose a novel approach to subgroup detection for this model under right-censoring,using deep neural networks to approximate nonlinear effects.To simultaneously estimate parameters and identify subgroups,the authors employ a concave pairwise penalty and the alternating direction method of multipliers(ADMM)algorithm.Furthermore,the authors demonstrate that the proposed estimator possesses oracle properties and achieves model selection consistency.Through simulation studies and empirical data analysis on breast cancer,the authors illustrate the effectiveness of the proposed method.展开更多
文摘Some new coupled map lattice (CML) models are developed for simulating both convection, diffusion terms and weakly or strongly coupled terms. The structure and features of model are analysed. Numerical results show that the new models are effective for studying spatiotemporal chaos. Finally, the mechanism of turbulence is analysed via the numerical results.
文摘A new coupled map lattic (CML) model is given by using some stability analysis for the related difference equations. Numerical results show that the new model is an effective one of studying spatiotemporal chaos, especially for strongly coupled systems.
文摘A family of coupled map lattice （CML） models has been developed to simulate the interaction of convection, diffusion and dispersion in both weakly and strongly coupled cases. With variation of parameters, the models can simulate those systems of convection dominating, diffusion dominating, and dispersion dominating states. Not only coherent and turbulent properties as well as their interrelations, but also the transitional state between any modes with local coupling and global coupling are analysed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and thus can be conveniently used to analyse an initiative and driven coupled system. Results of numerical simulation also lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. Finally, the duality of wave and particle characters of turbulence is illustrated in the numerical simulation.
基金supported by National Natural Science Foundation of China under Grant No.40535025
文摘A family of coupled map lattice （CML） models has been developed to simulate the evolutional mechanism of interactions of convection, diffusion, and dispersion in both weakly and strongly coupled cases. Not only coherent and turbulent properties as well as their relations, but also the transitional states between convection dominating, diffusion dominating and dispersion dominating are analyzed to demonstrate the essential characteristics of any state. Numerical results show that the models are capable of simulating both layered coupling and stochastic mechanism, and lead us to understand whether or not turbulence coherent structure is formed by modulation of wave packet. The duality of wave and particle characters of turbulence is illustrated in the numerical simulation; a sketch picture is given to explain the questions associated with the turbulent inverse cascade, which is the result of the mutual interactions among the physical factors of nonlinearity, dissipation and dispersion.
基金partially supported by the National Nature Science Foundation of China under Grant Nos.12171328,12326613,and 12031016Beijing Natural Science Foundation under Grant No.Z210003Beijing Outstanding Young Scientist Program under Grant No.JWZQ20240101027。
文摘In the analysis of censored survival data,it is crucial to consider the heterogeneity of treatment effects in order to avoid biased inferences.The deep neural network-based heterogeneous partially linear Cox model offers a flexible and robust solution by incorporating both heterogeneous linear and homogeneous nonlinear components.The authors propose a novel approach to subgroup detection for this model under right-censoring,using deep neural networks to approximate nonlinear effects.To simultaneously estimate parameters and identify subgroups,the authors employ a concave pairwise penalty and the alternating direction method of multipliers(ADMM)algorithm.Furthermore,the authors demonstrate that the proposed estimator possesses oracle properties and achieves model selection consistency.Through simulation studies and empirical data analysis on breast cancer,the authors illustrate the effectiveness of the proposed method.
