A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity numb...A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.展开更多
In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p <...In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.展开更多
Global population aging trends are intensifying,presenting multifaceted economic and social challenges for countries worldwide.As the world’s largest developing country,China has entered a phase of extreme demographi...Global population aging trends are intensifying,presenting multifaceted economic and social challenges for countries worldwide.As the world’s largest developing country,China has entered a phase of extreme demographic aging,posing significant questions about its impact on the ongoing upgrading of industrial structures.How does this demographic shift influence the upgrading of industrial structures,and does technological innovation mitigate or exacerbate this impact?The empirical results indicate that population aging impedes upgrading the industrial structure,while technological innovation positively affects the relationship between the two.Moreover,using technological innovation as a threshold variable,the impact of population aging on industrial structure upgrading evolves in a“gradient”manner from“impediment”to“insignificant”to“promotion”as the technological innovation levels increase.These findings offer practical guidance for tailoring industrial policies to different stages of technological advancement.展开更多
基金This research work is supported by the National Natural Science Foundation of China(Grant No.51975227).
文摘A parameter-free approach is proposed to determine the Lagrange multiplier for the constraint of material volume in the level set method.It is inspired by the procedure of determining the threshold of sensitivity number in the BESO method.It first computes the difference between the volume of current design and the upper bound of volume.Then,the Lagrange multiplier is regarded as the threshold of sensitivity number to remove the redundant material.Numerical examples proved that this approach is effective to constrain the volume.More importantly,there is no parameter in the proposed approach,which makes it convenient to use.In addition,the convergence is stable,and there is no big oscillation.
基金the National Natural Science Foundation of China(Nos.6136200161365013 and 51165033)+3 种基金the Natural Science Foundation of Jiangxi Province(Nos.20132BAB211030 and 20122BAB211015)the Technology Foundation of Department of Education in Jiangxi Province(Nos.GJJ 13061 and GJJ14196)the National Postdoctoral Research Funds(No.2014M551867)the Jiangxi Advanced Projects for Postdoctoral Research Funds(No.2014KY02)
文摘In recent years, it has shown that a generalized thresholding algorithm is useful for inverse problems with sparsity constraints. The generalized thresholding minimizes the non-convex p-norm based function with p < 1, and it penalizes small coefficients over a wider range meanwhile applies less bias to the larger coefficients.In this work, on the basis of two-level Bregman method with dictionary updating(TBMDU), we use the modified thresholding to minimize the non-convex function and propose the generalized TBMDU(GTBMDU) algorithm.The experimental results on magnetic resonance(MR) image simulations and real MR data, under a variety of sampling trajectories and acceleration factors, consistently demonstrate that the proposed algorithm can efficiently reconstruct the MR images and present advantages over the previous soft thresholding approaches.
基金supported by the Research Center for Aging Career and Industrial Development,Sichuan Key Research Base of Social Sciences[Grant No.XJLL2022009].
文摘Global population aging trends are intensifying,presenting multifaceted economic and social challenges for countries worldwide.As the world’s largest developing country,China has entered a phase of extreme demographic aging,posing significant questions about its impact on the ongoing upgrading of industrial structures.How does this demographic shift influence the upgrading of industrial structures,and does technological innovation mitigate or exacerbate this impact?The empirical results indicate that population aging impedes upgrading the industrial structure,while technological innovation positively affects the relationship between the two.Moreover,using technological innovation as a threshold variable,the impact of population aging on industrial structure upgrading evolves in a“gradient”manner from“impediment”to“insignificant”to“promotion”as the technological innovation levels increase.These findings offer practical guidance for tailoring industrial policies to different stages of technological advancement.
