If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continu...If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.展开更多
In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear supe...In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition（POD）. Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.展开更多
Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach ofte...Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.展开更多
A new algorithm of measurement slub yarn parameter was put forward to improve precision and efficient. The basic principal of measurement slub yarn by parallel-plate capacitor was introduced,and slub yarns were tested...A new algorithm of measurement slub yarn parameter was put forward to improve precision and efficient. The basic principal of measurement slub yarn by parallel-plate capacitor was introduced,and slub yarns were tested with a measurement system developed by ourselves. Time sequence for slub length and slub space can be got. And distributions of slub length,slub space and slub scaling factor can also be obtained. The agreement can be attained compared with those original settings. Some error was analyzed also. Consequently this system is effective,and can be adopted in practice.展开更多
High-dimensional,higher-order tensor data are gaining prominence in a variety of fields,including but not limited to computer vision and network analysis.Tensor factor models,induced from noisy versions of tensor deco...High-dimensional,higher-order tensor data are gaining prominence in a variety of fields,including but not limited to computer vision and network analysis.Tensor factor models,induced from noisy versions of tensor decompositions or factorizations,are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent.However,it is still in the early stage of developing statistical inferential theories for the estimation of various low-rank structures,which are customary to play the role of signals of tensor factor models.In this paper,we attempt to“decode”the estimation of a higher-order tensor factor model by leveraging tensor matricization.Specifically,we recast it into mode-wise traditional highdimensional vector/fiber factor models,enabling the deployment of conventional principal components analysis(PCA)for estimation.Demonstrated by the Tucker tensor factor model(TuTFaM),which is induced from the noisy version of the widely-used Tucker decomposition,we summarize that estimations on signal components are essentially mode-wise PCA techniques,and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extents.We establish the inferential theory of the proposed estimators,conduct rich simulation experiments and illustrate how the proposed estimations can work in tensor reconstruction and clustering for independent video and dependent economic datasets,respectively.展开更多
A direct as well as iterative method(called the orthogonally accumulated projection method, or the OAP for short) for solving linear system of equations with symmetric coefficient matrix is introduced in this paper. W...A direct as well as iterative method(called the orthogonally accumulated projection method, or the OAP for short) for solving linear system of equations with symmetric coefficient matrix is introduced in this paper. With the Lanczos process the OAP creates a sequence of mutually orthogonal vectors, on the basis of which the projections of the unknown vectors are easily obtained, and thus the approximations to the unknown vectors can be simply constructed by a combination of these projections. This method is an application of the accumulated projection technique proposed recently by the authors of this paper, and can be regarded as a match of conjugate gradient method(CG) in its nature since both the CG and the OAP can be regarded as iterative methods, too. Unlike the CG method which can be only used to solve linear systems with symmetric positive definite coefficient matrices, the OAP can be used to handle systems with indefinite symmetric matrices. Unlike classical Krylov subspace methods which usually ignore the issue of loss of orthogonality, OAP uses an effective approach to detect the loss of orthogonality and a restart strategy is used to handle the loss of orthogonality.Numerical experiments are presented to demonstrate the efficiency of the OAP.展开更多
Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically reso...Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically resolved imaging capability.Here,we demonstrate a single-frame multiwavelength CDI approach that can provide complex transmittance images of a sample at multiple wavelengths.The superior performance of our method in terms of rapid convergence and improved image quality over current methods has been validated through high-harmonic extreme ultraviolet experiments.The feasibility of our method for single-frame chemical imaging is also demonstrated by the simulation.This work can pave the way for implementing in situ chemical imaging with tabletop high-harmonic generation extreme ultraviolet sources.展开更多
In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to...In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number±ℓ.We show,that each of those pair/quadruple of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions,which are satisfied for our examples and the common InAs/GaAs heterojunction.Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40%of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.展开更多
基金This research is partially supported by NIH,No.R15EB024283.
文摘If a spatial-domain function has a finite support,its Fourier transform is an entire function.The Taylor series expansion of an entire function converges at every finite point in the complex plane.The analytic continuation theory suggests that a finite-sized object can be uniquely determined by its frequency components in a very small neighborhood.Trying to obtain such an exact Taylor expansion is difficult.This paper proposes an iterative algorithm to extend the measured frequency components to unmeasured regions.Computer simulations show that the proposed algorithm converges very slowly,indicating that the problem is too ill-posed to be practically solvable using available methods.
基金supported by the National Basic Research Program of China(No.2014CB744804)
文摘In this paper a new flow field prediction method which is independent of the governing equations, is developed to predict stationary flow fields of variable physical domain. Predicted flow fields come from linear superposition of selected basis modes generated by proper orthogonal decomposition（POD）. Instead of traditional projection methods, kriging surrogate model is used to calculate the superposition coefficients through building approximate function relationships between profile geometry parameters of physical domain and these coefficients. In this context,the problem which troubles the traditional POD-projection method due to viscosity and compressibility has been avoided in the whole process. Moreover, there are no constraints for the inner product form, so two forms of simple ones are applied to improving computational efficiency and cope with variable physical domain problem. An iterative algorithm is developed to determine how many basis modes ranking front should be used in the prediction. Testing results prove the feasibility of this new method for subsonic flow field, but also prove that it is not proper for transonic flow field because of the poor predicted shock waves.
基金supported by the National Science Foundation for Distinguished Young Scholars(Grant No.62125104)the National Natural Science Foundation of China(Grant No.52071111).
文摘Traditional direction of arrival(DOA)estimation methods based on sparse reconstruction commonly use convex or smooth functions to approximate non-convex and non-smooth sparse representation problems.This approach often introduces errors into the sparse representation model,necessitating the development of improved DOA estimation algorithms.Moreover,conventional DOA estimation methods typically assume that the signal coincides with a predetermined grid.However,in reality,this assumption often does not hold true.The likelihood of a signal not aligning precisely with the predefined grid is high,resulting in potential grid mismatch issues for the algorithm.To address the challenges associated with grid mismatch and errors in sparse representation models,this article proposes a novel high-performance off-grid DOA estimation approach based on iterative proximal projection(IPP).In the proposed method,we employ an alternating optimization strategy to jointly estimate sparse signals and grid offset parameters.A proximal function optimization model is utilized to address non-convex and non-smooth sparse representation problems in DOA estimation.Subsequently,we leverage the smoothly clipped absolute deviation penalty(SCAD)function to compute the proximal operator for solving the model.Simulation and sea trial experiments have validated the superiority of the proposed method in terms of higher resolution and more accurate DOA estimation performance when compared to both traditional sparse reconstruction methods and advanced off-grid techniques.
基金Pre-research Foundation of Jiangnan University,China(No.206000-52210761)
文摘A new algorithm of measurement slub yarn parameter was put forward to improve precision and efficient. The basic principal of measurement slub yarn by parallel-plate capacitor was introduced,and slub yarns were tested with a measurement system developed by ourselves. Time sequence for slub length and slub space can be got. And distributions of slub length,slub space and slub scaling factor can also be obtained. The agreement can be attained compared with those original settings. Some error was analyzed also. Consequently this system is effective,and can be adopted in practice.
基金supported by the Young Scientists Fund of the National Natural Science Foundation of China(Grant No.12301338)the Postdoc Fellowship of Chinese Academy of Sciences Academy of Mathematics and Systems Science and the Hong Kong Polytechnic University Joint Laboratory of Applied Mathematics+6 种基金supported by General Research Fund(Grant No.17306121)supported by General Research Fund(Grant No.15301519)Research Grants Council,Hong Kong Special Administrative Region,the Key Program of National Natural Science Foundation of China(Grant No.72033002)Research Grants Council,Hong Kong Special Administrative Region,Hong Kong Polytechnic University Research Grant(Grant No.P0045497)the General Program of National Natural Science Foundation of China(Grant No.12271060)supported by the National Key Research and Development Program of China(Grant No.2020YFA0714100)the Key Program of National Natural Science Foundation of China(Grant No.12431009)。
文摘High-dimensional,higher-order tensor data are gaining prominence in a variety of fields,including but not limited to computer vision and network analysis.Tensor factor models,induced from noisy versions of tensor decompositions or factorizations,are natural potent instruments to study a collection of tensor-variate objects that may be dependent or independent.However,it is still in the early stage of developing statistical inferential theories for the estimation of various low-rank structures,which are customary to play the role of signals of tensor factor models.In this paper,we attempt to“decode”the estimation of a higher-order tensor factor model by leveraging tensor matricization.Specifically,we recast it into mode-wise traditional highdimensional vector/fiber factor models,enabling the deployment of conventional principal components analysis(PCA)for estimation.Demonstrated by the Tucker tensor factor model(TuTFaM),which is induced from the noisy version of the widely-used Tucker decomposition,we summarize that estimations on signal components are essentially mode-wise PCA techniques,and the involvement of projection and iteration will enhance the signal-to-noise ratio to various extents.We establish the inferential theory of the proposed estimators,conduct rich simulation experiments and illustrate how the proposed estimations can work in tensor reconstruction and clustering for independent video and dependent economic datasets,respectively.
基金supported by National Natural Science Foundation of China (Grant Nos. 91430108 and 11171251)the Major Program of Tianjin University of Finance and Economics (Grant No. ZD1302)
文摘A direct as well as iterative method(called the orthogonally accumulated projection method, or the OAP for short) for solving linear system of equations with symmetric coefficient matrix is introduced in this paper. With the Lanczos process the OAP creates a sequence of mutually orthogonal vectors, on the basis of which the projections of the unknown vectors are easily obtained, and thus the approximations to the unknown vectors can be simply constructed by a combination of these projections. This method is an application of the accumulated projection technique proposed recently by the authors of this paper, and can be regarded as a match of conjugate gradient method(CG) in its nature since both the CG and the OAP can be regarded as iterative methods, too. Unlike the CG method which can be only used to solve linear systems with symmetric positive definite coefficient matrices, the OAP can be used to handle systems with indefinite symmetric matrices. Unlike classical Krylov subspace methods which usually ignore the issue of loss of orthogonality, OAP uses an effective approach to detect the loss of orthogonality and a restart strategy is used to handle the loss of orthogonality.Numerical experiments are presented to demonstrate the efficiency of the OAP.
基金supported by the National Natural Science Foundation of China(No.12074167)the Shenzhen ScienceandTechnologyInnovationProgram(No.JCYJ20241202125334045)。
文摘Coherent diffraction imaging(CDI)enables diffraction-limited high-resolution imaging without using high-quality lenses.It will be desirable to combine it with multiple spectral light sources to achieve chemically resolved imaging capability.Here,we demonstrate a single-frame multiwavelength CDI approach that can provide complex transmittance images of a sample at multiple wavelengths.The superior performance of our method in terms of rapid convergence and improved image quality over current methods has been validated through high-harmonic extreme ultraviolet experiments.The feasibility of our method for single-frame chemical imaging is also demonstrated by the simulation.This work can pave the way for implementing in situ chemical imaging with tabletop high-harmonic generation extreme ultraviolet sources.
基金We would like to thank Oleksandr Voskoboynikov for his comments on the physical relevance of the model under consideration.We also thank the anonymous referees for their comments helping us to improve this manuscript.
文摘In this work the one-band effective Hamiltonian governing the electronic states of a quantum dot/ring in a homogenous magnetic field is used to derive a pair/quadruple of nonlinear eigenvalue problems corresponding to different spin orientations and in case of rotational symmetry additionally to quantum number±ℓ.We show,that each of those pair/quadruple of nonlinear problems allows for the minmax characterization of its eigenvalues under certain conditions,which are satisfied for our examples and the common InAs/GaAs heterojunction.Exploiting the minmax property we devise efficient iterative projection methods simultaneously handling the pair/quadruple of nonlinear problems and thereby saving up to 40%of the computational time as compared to the nonlinear Arnoldi method applied to each of the problems separately.
