To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solut...To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.展开更多
Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of th...Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.展开更多
Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational...Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.展开更多
目的探讨两种干预方法缓解早产儿眼底筛查所致疼痛的效果。方法纳入2017年7月~2019年6月某三级甲等专科医院早产儿病房进行眼底筛查的168例早产儿进行研究,依据随机对照原则分为三组,各56例,对照组早产儿采取常规眼底筛查,非营养性吸吮(...目的探讨两种干预方法缓解早产儿眼底筛查所致疼痛的效果。方法纳入2017年7月~2019年6月某三级甲等专科医院早产儿病房进行眼底筛查的168例早产儿进行研究,依据随机对照原则分为三组,各56例,对照组早产儿采取常规眼底筛查,非营养性吸吮(NNS)组早产儿接受NNS护理,25%葡萄糖(GS)+NNS组早产儿接受25%GS安慰奶嘴护理。比较三组早产儿不同时间点疼痛、心率(HR)、血氧饱和度(SpO2)变化情况。结果 NNS组与25%GS+NNS组早产儿筛查过程中、筛查后1 min PIPP评分、HR均低于对照组,SpO2均高于对照组,差异显著(P<0.05);GS+NNS组早产儿筛查过程中、筛查后1 min PIPP评分、HR均低于NNS组,SpO2高于NNS组,差异显著(P<0.05)。结论采取25%GS+NNS的干预方式能够有效减轻早产儿眼底筛查所致疼痛,值得临床推荐。展开更多
基金V. ACKN0WLEDGMENT This work was supported by the National Natural Sci- ence Foundation of China （No.10375024） and the Science Foundation of Hunan Educational Committee.
文摘To expose the statistical properties of the degenerated spectrum, with the aid of the random matrix theory, a possible form of the NNS distribution function of the degenerate spectrum was proposed by providing a solution in terms of the same-degeneracy case. The results indicate that the target spectrum is transformed into two sub-spectra： a random one and a regular one, and that the repulsion level of the regular spectrum is also decreased.
文摘Based on the concept of the energy level repulsion, a potential function followed by the energy level particles is suggested. By regarding the energy level fluctuation spectrum as a dynamic system which consists of the pairs of energy level particles behaving as the generalized harmonic oscillator, a generalized Schrdinger equation valid for the nearest neighbor space (NNS) distribution of the levels is established. It turns out that the different kinds of NNS distributions found so far are the solutions of this equation: Both the Poisson type and Wigner type are its eigen solutions whereas the Gaussian unitary ensemble (GUE) type and the Brody type of NNS distribution are its composite solutions. Furthermore, the influences of the small perturbation on the NNS distribution are analyzed.
基金supported by the National Key R&D Program of China under Grant No.2021ZD0110400.
文摘Many important problems in science and engineering require solving the so-called parametric partial differential equations(PDEs),i.e.,PDEs with different physical parameters,boundary conditions,shapes of computational domains,etc.Typical reduced order modeling techniques accelerate the solution of the parametric PDEs by projecting them onto a linear trial manifold constructed in the ofline stage.These methods often need a predefined mesh as well as a series of precomputed solution snapshots,and may struggle to balance between the efficiency and accuracy due to the limitation of the linear ansatz.Utilizing the nonlinear representation of neural networks(NNs),we propose the Meta-Auto-Decoder(MAD)to construct a nonlinear trial manifold,whose best possible performance is measured theoretically by the decoder width.Based on the meta-learning concept,the trial manifold can be learned in a mesh-free and unsupervised way during the pre-training stage.Fast adaptation to new(possibly heterogeneous)PDE parameters is enabled by searching on this trial manifold,and optionally fine-tuning the trial manifold at the same time.Extensive numerical experiments show that the MAD method exhibits a faster convergence speed without losing the accuracy than other deep learning-based methods.
文摘目的探讨两种干预方法缓解早产儿眼底筛查所致疼痛的效果。方法纳入2017年7月~2019年6月某三级甲等专科医院早产儿病房进行眼底筛查的168例早产儿进行研究,依据随机对照原则分为三组,各56例,对照组早产儿采取常规眼底筛查,非营养性吸吮(NNS)组早产儿接受NNS护理,25%葡萄糖(GS)+NNS组早产儿接受25%GS安慰奶嘴护理。比较三组早产儿不同时间点疼痛、心率(HR)、血氧饱和度(SpO2)变化情况。结果 NNS组与25%GS+NNS组早产儿筛查过程中、筛查后1 min PIPP评分、HR均低于对照组,SpO2均高于对照组,差异显著(P<0.05);GS+NNS组早产儿筛查过程中、筛查后1 min PIPP评分、HR均低于NNS组,SpO2高于NNS组,差异显著(P<0.05)。结论采取25%GS+NNS的干预方式能够有效减轻早产儿眼底筛查所致疼痛,值得临床推荐。
