The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(...The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.展开更多
A major difficulty in multivariable control design is the cross-coupling between inputs and outputs which obscures the effects of a specific controller on the overall behavior of the system. This paper considers the a...A major difficulty in multivariable control design is the cross-coupling between inputs and outputs which obscures the effects of a specific controller on the overall behavior of the system. This paper considers the application of kernel method in decoupling multivariable output feedback controllers. Simulation results are presented to show the feasibility of the proposed technique.展开更多
The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)...The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)Z^(1/3)formulae,and their improved versions by considering the isospin dependence are adopted as examples.The parameters in these six formulae are refitted using the Levenberg-Marquardt method,which give better results than the previous ones.The radius for each nucleus is predicted with the KRR network,which is trained with the deviations between experimental and calculated nuclear charge radii.For each formula,the resultant root-mean-square deviations of 884 nuclei with proton number Z≥8 Z≥8 and neutron number N≥8 N≥8 can be reduced to about 0.017fm after considering the modification of the KRR method.The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method.It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability.The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed.At last,the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.展开更多
We propose a novel indoor positioning algorithm based on the received signal strength(RSS) fingerprint. The proposed algorithm can be divided into three steps, an offline phase at which an advanced clustering(AC) stra...We propose a novel indoor positioning algorithm based on the received signal strength(RSS) fingerprint. The proposed algorithm can be divided into three steps, an offline phase at which an advanced clustering(AC) strategy is used, an online phase of approximate localization at which cluster matching is used, and an online phase of precise localization with kernel ridge regression. Specifically, after offline fingerprint collection and similarity measurement, we employ an AC strategy based on the K-medoids clustering algorithm using additional reference points that are geographically located at the outer cluster boundary to enrich the data of each cluster. During the approximate localization, RSS measurements are compared with the cluster radio maps to determine to which cluster the target most likely belongs. Both the Euclidean distance of the RSSs and the Hamming distance of the coverage vectors between the observations and training records are explored for cluster matching. Then, a kernel-based ridge regression method is used to obtain the ultimate positioning of the target. The performance of the proposed algorithm is evaluated in two typical indoor environments, and compared with those of state-of-the-art algorithms. The experimental results demonstrate the effectiveness and advantages of the proposed algorithm in terms of positioning accuracy and complexity.展开更多
This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression(KRR)approach.It is found that the KRR appr...This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression(KRR)approach.It is found that the KRR approach can reduce the root-mean-square(rms)deviation of the relative errors between the experimental data of the Maxwellian-averaged(n,γ)cross-sections and the corresponding theoretical predictions from 69.8%to 35.4%.By including the data with different temperatures in the training set,the rms deviation can be further significantly reduced to 2.0%.Moreover,the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.展开更多
The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the bindin...The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the binding energies of 9035 nuclei,the KRR method achieves a root-mean-square deviation of 0.96 MeV,and the KRRoe method remarkably reduces the deviation to 0.17 MeV.By investigating the shell effects,one-nucleon and twonucleon separation energies,odd-even mass differences,and empirical proton-neutron interactions extracted from the learned binding energies,the ability of the machine learning tool to grasp the known physics is discussed.It is found that the shell effects,evolutions of nucleon separation energies,and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods,although the odd-even mass differences can only be reproduced by the KRRoe method.展开更多
基金This work was supported by the National Natural Science Foundation of China(Nos.11875027,11975096).
文摘The extended kernel ridge regression(EKRR)method with odd-even effects was adopted to improve the description of the nuclear charge radius using five commonly used nuclear models.These are:(i)the isospin-dependent A^(1∕3) formula,(ii)relativistic continuum Hartree-Bogoliubov(RCHB)theory,(iii)Hartree-Fock-Bogoliubov(HFB)model HFB25,(iv)the Weizsacker-Skyrme(WS)model WS*,and(v)HFB25*model.In the last two models,the charge radii were calculated using a five-parameter formula with the nuclear shell corrections and deformations obtained from the WS and HFB25 models,respectively.For each model,the resultant root-mean-square deviation for the 1014 nuclei with proton number Z≥8 can be significantly reduced to 0.009-0.013 fm after considering the modification with the EKRR method.The best among them was the RCHB model,with a root-mean-square deviation of 0.0092 fm.The extrapolation abilities of the KRR and EKRR methods for the neutron-rich region were examined,and it was found that after considering the odd-even effects,the extrapolation power was improved compared with that of the original KRR method.The strong odd-even staggering of nuclear charge radii of Ca and Cu isotopes and the abrupt kinks across the neutron N=126 and 82 shell closures were also calculated and could be reproduced quite well by calculations using the EKRR method.
文摘A major difficulty in multivariable control design is the cross-coupling between inputs and outputs which obscures the effects of a specific controller on the overall behavior of the system. This paper considers the application of kernel method in decoupling multivariable output feedback controllers. Simulation results are presented to show the feasibility of the proposed technique.
基金Supported by National Natural Science Foundation of China(11875027,11775112.11775026.11775099,11975096)Fundamental Research Funds for the Central Universities(2021MS046)。
文摘The kernel ridge regression(KRR)method with Gaussian kernel is used to improve the description of the nuclear charge radius by several phenomenological formulae.The widely used A^(1/3)A^(1/3),N^(1/3)N^(1/3)and Z^(1/3)Z^(1/3)formulae,and their improved versions by considering the isospin dependence are adopted as examples.The parameters in these six formulae are refitted using the Levenberg-Marquardt method,which give better results than the previous ones.The radius for each nucleus is predicted with the KRR network,which is trained with the deviations between experimental and calculated nuclear charge radii.For each formula,the resultant root-mean-square deviations of 884 nuclei with proton number Z≥8 Z≥8 and neutron number N≥8 N≥8 can be reduced to about 0.017fm after considering the modification of the KRR method.The extrapolation ability of the KRR method for the neutron-rich region is examined carefully and compared with the radial basis function method.It is found that the improved nuclear charge radius formulae by KRR method can avoid the risk of overfitting and have a good extrapolation ability.The influence of the ridge penalty term on the extrapolation ability of the KRR method is also discussed.At last,the nuclear charge radii of several recently observed K and Ca isotopes have been analyzed.
基金Project supported by the National Natural Science Foundation of China (Nos. 51705324 and 61702332)。
文摘We propose a novel indoor positioning algorithm based on the received signal strength(RSS) fingerprint. The proposed algorithm can be divided into three steps, an offline phase at which an advanced clustering(AC) strategy is used, an online phase of approximate localization at which cluster matching is used, and an online phase of precise localization with kernel ridge regression. Specifically, after offline fingerprint collection and similarity measurement, we employ an AC strategy based on the K-medoids clustering algorithm using additional reference points that are geographically located at the outer cluster boundary to enrich the data of each cluster. During the approximate localization, RSS measurements are compared with the cluster radio maps to determine to which cluster the target most likely belongs. Both the Euclidean distance of the RSSs and the Hamming distance of the coverage vectors between the observations and training records are explored for cluster matching. Then, a kernel-based ridge regression method is used to obtain the ultimate positioning of the target. The performance of the proposed algorithm is evaluated in two typical indoor environments, and compared with those of state-of-the-art algorithms. The experimental results demonstrate the effectiveness and advantages of the proposed algorithm in terms of positioning accuracy and complexity.
基金partly supported by the National Key R&D Program of China(Contracts No.2018YFA0404400 and No.2017YFE0116700)the National Natural Science Foundation of China(Grants No.11875075,No.11935003,No.11975031,No.12141501 and No.12070131001)+1 种基金the China Postdoctoral Science Foundation under Grant No.2021M700256the High-performance Computing Platform of Peking University
文摘This article provides the first application of the machine-learning approach in the study of the cross-sections for neutron-capture reactions with the kernel ridge regression(KRR)approach.It is found that the KRR approach can reduce the root-mean-square(rms)deviation of the relative errors between the experimental data of the Maxwellian-averaged(n,γ)cross-sections and the corresponding theoretical predictions from 69.8%to 35.4%.By including the data with different temperatures in the training set,the rms deviation can be further significantly reduced to 2.0%.Moreover,the extrapolation performance of the KRR approach along different temperatures is found to be effective and reliable.
基金Supported by the National Natural Science Foundation of China(11875075,11935003,11975031,12141501,12070131001)the China Postdoctoral Science Foundation under(2021M700256)+1 种基金the State Key Laboratory of Nuclear Physics and Technology,Peking University(NPT2023ZX01,NPT2023KFY02)the President’s Undergraduate Research Fellowship(PURF)of Peking University
文摘The kernel ridge regression(KRR)method and its extension with odd-even effects(KRRoe)are used to learn the nuclear mass table obtained by the relativistic continuum Hartree-Bogoliubov theory.With respect to the binding energies of 9035 nuclei,the KRR method achieves a root-mean-square deviation of 0.96 MeV,and the KRRoe method remarkably reduces the deviation to 0.17 MeV.By investigating the shell effects,one-nucleon and twonucleon separation energies,odd-even mass differences,and empirical proton-neutron interactions extracted from the learned binding energies,the ability of the machine learning tool to grasp the known physics is discussed.It is found that the shell effects,evolutions of nucleon separation energies,and empirical proton-neutron interactions are well reproduced by both the KRR and KRRoe methods,although the odd-even mass differences can only be reproduced by the KRRoe method.
