Metabolic network construction plays a pivotal role in unraveling the regulatory mechanism of biological activities,although it often proves to be challenging and labor-intensive,particularly with non-model organisms....Metabolic network construction plays a pivotal role in unraveling the regulatory mechanism of biological activities,although it often proves to be challenging and labor-intensive,particularly with non-model organisms.In this study,we develop a computational approach that employs reaction models based on the structure-guided chemical modification and related compounds to construct a metabolic network in wheat.This construction results in a comprehensive structure-guided network,including 625 identified metabolites and additional 333 putative reactions compared with the Kyoto Encyclopedia of Genes and Genomes database.Using a combination of gene annotation,reaction classification,structure similarity,and correlations from transcriptome and metabolome analysis,a total of 229 potential genes related to these reactions are identified within this network.To validate the network,the functionality of a hydroxycinnamoyltransferase(TraesCS3D01G314900)for the synthesis of polyphenols and a rhamnosyltransferase(TraesCS2D01G078700)for the modification of flavonoids are verified through in vitro enzymatic studies and wheat mutant tests,respectively.Our research thus supports the utility of structure-guided chemical modification as an effective tool in identifying causal candidate genes for constructing metabolic networks and further in metabolomic genetic studies.展开更多
The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate reg...The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.展开更多
This paper discusses closed-loop identification of unstable systems.In particular,wefirst apply the joint input–output identification method and then convert the identification problem of unstable systems into that of st...This paper discusses closed-loop identification of unstable systems.In particular,wefirst apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems,which can be tackled by using kernel-based regularization methods.We propose to identify two transfer functions by kernel regularization,the one from the reference signal to the input,and the one from the reference signal to the output.Since these transfer functions are stable,kernel regularization methods can construct their accurate models.Then the model of unstable system is constructed by ratio of these functions.The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.展开更多
Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is...Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.展开更多
The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modif...The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modified is introduced in this research,which is exampled by the Hotine kernel.In addition,the low-degree modified spheroidal kernel is proposed.Either cosine or linear modification factors can be utilized.The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel.Furthermore,the modified kernel augments the contribution rate of the measured data to height anomaly in the modified frequency domain.The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel.And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high-and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same.Since the computational efficiency of the low-degree modified kernel is much higher,the low-degree modified kernel behaves better in constructing the(quasi-)geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.展开更多
We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner...We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.展开更多
Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods ...Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods in neural networks,such as using complex network architectures and introducing sparse techniques,always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability.To address this issue,this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space(RKHS)as the first layer for standard neural networks,with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption.By investigating the influencing mechanism of parameters on the regularization procedure in RKHS,the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer.Besides,the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network.Moreover,exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem.Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments.展开更多
In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β...In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.展开更多
Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an a...Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.展开更多
Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected ...Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.展开更多
We propose an ？~1 regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly ...We propose an ？~1 regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly as the derivative of the underlying function. Moreover,our method could produce sparse representations with respect to empirical eigenfunctions.Numerical results show that our method is quite effective.展开更多
We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application...We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.展开更多
In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution...In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈（0,∞）, and give some conditions under which the optimal solution exists.展开更多
基金supported by the Young Top-notch Talent Cultivation Program of Hubei Province,the Natural Science Foundation for Distinguished Young Scientists of Hubei Province(2021CFA058)the First-Class Discipline Construction Funds of College of Plant Science and Technology,Huazhong Agricultural University(2023ZKPY005).
文摘Metabolic network construction plays a pivotal role in unraveling the regulatory mechanism of biological activities,although it often proves to be challenging and labor-intensive,particularly with non-model organisms.In this study,we develop a computational approach that employs reaction models based on the structure-guided chemical modification and related compounds to construct a metabolic network in wheat.This construction results in a comprehensive structure-guided network,including 625 identified metabolites and additional 333 putative reactions compared with the Kyoto Encyclopedia of Genes and Genomes database.Using a combination of gene annotation,reaction classification,structure similarity,and correlations from transcriptome and metabolome analysis,a total of 229 potential genes related to these reactions are identified within this network.To validate the network,the functionality of a hydroxycinnamoyltransferase(TraesCS3D01G314900)for the synthesis of polyphenols and a rhamnosyltransferase(TraesCS2D01G078700)for the modification of flavonoids are verified through in vitro enzymatic studies and wheat mutant tests,respectively.Our research thus supports the utility of structure-guided chemical modification as an effective tool in identifying causal candidate genes for constructing metabolic networks and further in metabolomic genetic studies.
文摘The regularized integrodifferential equation for the first kind of Fredholm, integral equation with a complex kernel is derived by generalizing the Tikhonov regularization method and the convergence of approximate regularized solutions is discussed. As an application of the method, an inverse problem in the two-dimensional wave-making problem of a flat plate is solved numerically, and a practical approach of choosing optimal regularization parameter is given.
文摘This paper discusses closed-loop identification of unstable systems.In particular,wefirst apply the joint input–output identification method and then convert the identification problem of unstable systems into that of stable systems,which can be tackled by using kernel-based regularization methods.We propose to identify two transfer functions by kernel regularization,the one from the reference signal to the input,and the one from the reference signal to the output.Since these transfer functions are stable,kernel regularization methods can construct their accurate models.Then the model of unstable system is constructed by ratio of these functions.The effectiveness of the proposed method is demonstrated by a numerical example and a practical experiment with a DC motor.
基金supported by the National Natural Science Fundation of China (60736021)the Joint Funds of NSFC-Guangdong Province(U0735003)
文摘Kernel-based methods work by embedding the data into a feature space and then searching linear hypothesis among the embedding data points. The performance is mostly affected by which kernel is used. A promising way is to learn the kernel from the data automatically. A general regularized risk functional （RRF） criterion for kernel matrix learning is proposed. Compared with the RRF criterion, general RRF criterion takes into account the geometric distributions of the embedding data points. It is proven that the distance between different geometric distdbutions can be estimated by their centroid distance in the reproducing kernel Hilbert space. Using this criterion for kernel matrix learning leads to a convex quadratically constrained quadratic programming （QCQP） problem. For several commonly used loss functions, their mathematical formulations are given. Experiment results on a collection of benchmark data sets demonstrate the effectiveness of the proposed method.
基金National Natural Science Foundation of China(Nos.41674025,41674082)Open Research Foundation of State Key Laboratory of Geo-information Engineering(Nos.SKLGIE2016-M-1-5,SKLGIE2018-ZZ-10)。
文摘The traditional spheroidal kernel results in the spectrum leakage,and the utilization rate of the removed degrees of the measured data is low.Hence,a kind of spheroidal kernel whose high-and low-degrees are both modified is introduced in this research,which is exampled by the Hotine kernel.In addition,the low-degree modified spheroidal kernel is proposed.Either cosine or linear modification factors can be utilized.The modified kernel functions can effectively control the spectrum leakage compared with the traditional spheroidal kernel.Furthermore,the modified kernel augments the contribution rate of the measured data to height anomaly in the modified frequency domain.The experimental results show that the accuracy of the quasi-geoid by the cosine or linear low-degree modified kernel is higher than that by the traditional spheroidal kernel.And the accuracy equals the accuracy of the quasi-geoid using the spheroidal kernel with high-and low-degrees modified approximately when the low-degree modification bandwidths of these two kinds of kernels are the same.Since the computational efficiency of the low-degree modified kernel is much higher,the low-degree modified kernel behaves better in constructing the(quasi-)geoid based on Stokes-Helmert or Hotine-Helmert boundary-value theory.
文摘We provide a kernel-regularized method to give theory solutions for Neumann boundary value problem on the unit ball. We define the reproducing kernel Hilbert space with the spherical harmonics associated with an inner product defined on both the unit ball and the unit sphere, construct the kernel-regularized learning algorithm from the view of semi-supervised learning and bound the upper bounds for the learning rates. The theory analysis shows that the learning algorithm has better uniform convergence according to the number of samples. The research can be regarded as an application of kernel-regularized semi-supervised learning.
基金Supported by National Natural Science Foundation of China(Grant Nos.12072188,11632011,11702171,11572189,51121063)Shanghai Municipal Natural Science Foundation of China(Grant No.20ZR1425200).
文摘Deep learning algorithms based on neural networks make remarkable achievements in machine fault diagnosis,while the noise mixed in measured signals harms the prediction accuracy of networks.Existing denoising methods in neural networks,such as using complex network architectures and introducing sparse techniques,always suffer from the difficulty of estimating hyperparameters and the lack of physical interpretability.To address this issue,this paper proposes a novel interpretable denoising layer based on reproducing kernel Hilbert space(RKHS)as the first layer for standard neural networks,with the aim to combine the advantages of both traditional signal processing technology with physical interpretation and network modeling strategy with parameter adaption.By investigating the influencing mechanism of parameters on the regularization procedure in RKHS,the key parameter that dynamically controls the signal smoothness with low computational cost is selected as the only trainable parameter of the proposed layer.Besides,the forward and backward propagation algorithms of the designed layer are formulated to ensure that the selected parameter can be automatically updated together with other parameters in the neural network.Moreover,exponential and piecewise functions are introduced in the weight updating process to keep the trainable weight within a reasonable range and avoid the ill-conditioned problem.Experiment studies verify the effectiveness and compatibility of the proposed layer design method in intelligent fault diagnosis of machinery in noisy environments.
基金Chen research is supported by NSF of China (10961015)Yang research is supported by NSF of China (10961016)the GAN PO555 Program of Jiangxi
文摘In this paper,we are concerned with the regularity and symmetry of positive solutions of the following nonlinear integral system u（x） = ∫R n G α（x-y）v（y） q/｜y｜β dy,v（x） = ∫R n G α（x-y）u（y） p/｜y｜β dy for x ∈ R n,where G α（x） is the kernel of Bessel potential of order α,0 ≤β 〈 α 〈 n,1 〈 p,q 〈 n-β/β and 1/p ＋ 1 ＋ 1/q ＋ 1 〉 n-α ＋ β/n.We show that positive solution pairs（u,v） ∈ L p ＋1（R n） × L q ＋1（R n） are Ho¨lder continuous,radially symmetric and strictly decreasing about the origin.
基金The project was supported by the Natural Science Foundation of Fujian Province of China (Z0511002)the National Science Foundation of China (10271097,10571144)+1 种基金Foundation of Tianyuan (10526033)Chen L P, the Corresponding author
文摘Using the method of localization, the authors obtain the permutation formula of singular integrals with Bochner-Martinelli kernel for a relative compact domain with C^（1） smooth boundary on a Stein manifold. As an application the authors discuss the regularization problem for linear singular integral equations with Bochner-Martinelli kernel and variable coefficients; using permutation formula, the singular integral equation can be reduced to a fredholm equation.
基金supported by Research Grant from the Kajima Foundation,JST CREST Grant No.JPMJCR1911,JapanJSPS KAKENHI(Nos.17K06633,21K04351).
文摘Data-driven computing in elasticity attempts to directly use experimental data on material,without constructing an empirical model of the constitutive relation,to predict an equilibrium state of a structure subjected to a specified external load.Provided that a data set comprising stress-strain pairs of material is available,a data-driven method using the kernel method and the regularized least-squares was developed to extract a manifold on which the points in the data set approximately lie(Kanno 2021,Jpn.J.Ind.Appl.Math.).From the perspective of physical experiments,stress field cannot be directly measured,while displacement and force fields are measurable.In this study,we extend the previous kernel method to the situation that pairs of displacement and force,instead of pairs of stress and strain,are available as an input data set.A new regularized least-squares problem is formulated in this problem setting,and an alternating minimization algorithm is proposed to solve the problem.
基金Supported by the National Nature Science Foundation of China(Grant Nos.11301052,11301045,11271060,11601064,11671068)the Fundamental Research Funds for the Central Universities(Grant No.DUT16LK33)the Fundamental Research of Civil Aircraft(Grant No.MJ-F-2012-04)
文摘We propose an ？~1 regularized method for numerical differentiation using empirical eigenfunctions. Compared with traditional methods for numerical differentiation, the output of our method can be considered directly as the derivative of the underlying function. Moreover,our method could produce sparse representations with respect to empirical eigenfunctions.Numerical results show that our method is quite effective.
基金Supported by the DGRST Research Project LR11ES11CMCU Program 10G/1503
文摘We study some class of Dunkl multiplier operators;and we establish for them the Heisenberg-Pauli-Weyl uncertainty principle and the Donoho-Stark＇s uncertainty principle.For these operators we give also an application of the theory of reproducing kernels to the Tikhonov regularization on the Sobolev-Dunkl spaces.
基金Supported by National Natural Science Foundation of China (Grant No.11071276)
文摘In regularized kernel methods, the solution of a learning problem is found by minimizing a functional consisting of a empirical risk and a regularization term. In this paper, we study the existence of optimal solution of multi-kernel regularization learning. First, we ameliorate a previous conclusion about this problem given by Micchelli and Pontil, and prove that the optimal solution exists whenever the kernel set is a compact set. Second, we consider this problem for Gaussian kernels with variance σ∈（0,∞）, and give some conditions under which the optimal solution exists.
