We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence...We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.展开更多
A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as...A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.展开更多
This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonl...This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.展开更多
C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolati...C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.展开更多
This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance betweenAHXXA an...This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance betweenAHXXA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.展开更多
This paper addresses the problem of Blind Source Separation (BSS) and presents a new BSS algorithm with a Signal-Adaptive Activation (SAA) function (SAA-BSS). By taking the sum of absolute values of the normalized kur...This paper addresses the problem of Blind Source Separation (BSS) and presents a new BSS algorithm with a Signal-Adaptive Activation (SAA) function (SAA-BSS). By taking the sum of absolute values of the normalized kurtoses as a contrast function, the obtained signal-adaptive activation function automatically satisfies the local stability and robustness conditions. The SAA-BSS exploits the natural gradient learning on the Stiefel manifold, and it is an equivariant algorithm with a moderate computational load. Computer simulations show that the SAA-BSS can perform blind separation of mixed sub-Gaussian and super-Gaussian signals and it works more efficiently than the existing algorithms in convergence speed and robustness against outliers.展开更多
Granier sap flow system is one of the most commonly used techniques for measurements of whole-tree water use in ecophysiological and forest hydrological studies.However,in the literature there is not one paper that ex...Granier sap flow system is one of the most commonly used techniques for measurements of whole-tree water use in ecophysiological and forest hydrological studies.However,in the literature there is not one paper that exclusively reviews the Granier method.In this paper,we recapitulate the theoretical basis of the Granier sap flow system and review recent developments in calibration and modification of the sensor probes.Practical issues,such as the determination of the non-flow signal values,natural thermal gradient,wounding effect,reversed sap flow pattern and extrapolation of individual measurement of sap flux density to whole-tree sap flow.are discussed in detail.In the perspectives,new approaches are put forward to use the strong coupling between photosynthesis and transpiration or canopy conductance,via the measurement of 13C discrimination,to estimate whole-canopy carbon assimilation.展开更多
Biodiversity underpins critical ecological processes,yet its relationship with phosphorus(P)remains poorly understood.Understanding the distinct responses of plant and soil microbial diversity to P availability change...Biodiversity underpins critical ecological processes,yet its relationship with phosphorus(P)remains poorly understood.Understanding the distinct responses of plant and soil microbial diversity to P availability changes is particularly crucial on a global scale.Integrating meta-analysis and natural gradient approaches,this study evaluates these responses globally.Specifically,we conducted a meta-analysis using 393 observations from 128 field P addition experiments and supplemented this with a natural gradient analysis of forest tree diversity and vascular plant diversity.Our meta-analysis results showed that P additions reduced plant species richness by 8.5%and Shannon index by 1.3%in global grasslands,while exerting minimal effects on soil bacterial and fungal diversity across major terrestrial ecosystems.Natural gradient analysis further demonstrated significant correlations between both forest tree richness and vascular plant richness with soil total P concentrations.Notably,partial correlation analyses showed negative correlations when controlling for gross primary productivity and edaphic variables,but positive correlations when controlling for climatic variables.These complementary approaches collectively suggest that plant diversity exhibits greater sensitivity to altered soil P availability than soil microbial diversity.Consequently,elucidating the differential responses of above-and below-ground biodiversity to nutrient supply changes provides a scientific foundation for sound management of terrestrial ecosystem functions and processes.展开更多
Variable selection identifies the best subset of covariates when building the prediction model,among all possible subsets.In this paper,we propose a novel reinforced variable selection method,called‘Actor-Critic-Pred...Variable selection identifies the best subset of covariates when building the prediction model,among all possible subsets.In this paper,we propose a novel reinforced variable selection method,called‘Actor-Critic-Predictor’.The actor takes an action to choose variables and the predictor evaluates the action based on a well-designed reward function,where the critic learns the reward baseline.We model the variable selection process as a multi-armed bandit and update the subset of selected variables using a natural policy gradient algorithm.We provide an analytical framework on how different errors impact the performance of our method theoretically.Large amounts of experiments on synthetic and real datasets show that the proposed framework is easily implemented and outperforms classical variable selection methods in a wide range of scenarios.展开更多
The contrast function remains to be an open problem in blind source separation （BSS） when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual...The contrast function remains to be an open problem in blind source separation （BSS） when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.展开更多
The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult t...The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.展开更多
Photoenergy harvesting is promising to power Internet-of-Things(IoT)sensors,freeing the limitations of wired power sources or batteries,enabling bio-integrated devices.However,existing photoenergy harvesting systems a...Photoenergy harvesting is promising to power Internet-of-Things(IoT)sensors,freeing the limitations of wired power sources or batteries,enabling bio-integrated devices.However,existing photoenergy harvesting systems are restricted to solid or liquid configurations—limiting biocompatibility and space utilization—which makes obtaining flexible,biocompatible,light-harvesting devices a significant challenge.In this paper,inspired by natural ion gradient diffusion in organisms,offering an ion-hydrogel drops-based photoenergy harvesting base on ammonium molybdate.Through the photochemical process of ammonium molybdate,the electric potential of the device is regulated by the altered ion gradient and the redox pairs([Mo_(7)O_(24)]^(6-)/[Mo_(1)O_(46)]^(10-)),to generate energy.When exposed to excitation light,a photo driven ammonium molybdate-hydrogel photoenergy harvester(PAPH)can generate an open-circuit potential of~250 mV,and it can still obtain a considerable output power for milliseconds to thousands of seconds after the termination of the initial illumination.The reversible hydrogel droplets network allows for the recovery and fabrication of arbitrary structures of the PAPH.We further demonstrate the scalable PAPH networks can on-demand regulation of cell epithelial growth factor secretion and receptor expression,stimulate the cell proliferation,thereby facilitating biological tissue wound repair.This ionic hydrogel opens a new avenue for flexible,photoenergy harvesting,biocompatible devices.展开更多
基金co-supported by the National Natural Science Foundation of China(Nos.61790552 and 61976080)the Innovation Foundation for Doctor Dissertation of Northwestern Polytechnical University,China(No.CX201915)。
文摘We propose a technique based on the natural gradient method for variational lower bound maximization for a variational Bayesian Kalman filter.The natural gradient approach is applied to the Kullback-Leibler divergence between the parameterized variational distribution and the posterior density of interest.Using a Gaussian assumption for the parametrized variational distribution,we obtain a closed-form iterative procedure for the Kullback-Leibler divergence minimization,producing estimates of the variational hyper-parameters of state estimation and the associated error covariance.Simulation results in both a Doppler radar tracking scenario and a bearing-only tracking scenario are presented,showing that the proposed natural gradient method outperforms existing methods which are based on other linearization techniques in terms of tracking accuracy.
文摘A new framework based on the curved Riemannian manifold is proposed to calculate the numerical solution of the Lyapunov matrix equation by using a natural gradient descent algorithm and taking the geodesic distance as the objective function. Moreover, a gradient descent algorithm based on the classical Euclidean distance is provided to compare with this natural gradient descent algorithm. Furthermore, the behaviors of two proposed algorithms and the conventional modified conjugate gradient algorithm are compared and demonstrated by two simulation examples. By comparison, it is shown that the convergence speed of the natural gradient descent algorithm is faster than both of the gradient descent algorithm and the conventional modified conjugate gradient algorithm in solving the Lyapunov equation.
文摘This paper focuses on the problem of adaptive blind source separation (BSS). First, a recursive least-squares (RLS) whitening algorithm is proposed. By combining it with a natural gradient-based RLS algorithm for nonlinear principle component analysis (PCA), and using reasonable approximations, a novel RLS algorithm which can achieve BSS without additional pre-whitening of the observed mixtures is obtained. Analyses of the equilibrium points show that both of the RLS whitening algorithm and the natural gradient-based RLS algorithm for BSS have the desired convergence properties. It is also proved that the combined new RLS algorithm for BSS is equivariant and has the property of keeping the separating matrix from becoming singular. Finally, the effectiveness of the proposed algorithm is verified by extensive simulation results.
基金supported by the SDUST Spring Bud (2009AZZ021)Taian Science and Technology Development (20112001)
文摘C^1 natural element method （C^1 NEM） is applied to strain gradient linear elasticity, and size effects on mi crostructures are analyzed. The shape functions in C^1 NEM are built upon the natural neighbor interpolation （NNI）, with interpolation realized to nodal function and nodal gradient values, so that the essential boundary conditions （EBCs） can be imposed directly in a Galerkin scheme for partial differential equations （PDEs）. In the present paper, C^1 NEM for strain gradient linear elasticity is constructed, and sev- eral typical examples which have analytical solutions are presented to illustrate the effectiveness of the constructed method. In its application to microstructures, the size effects of bending stiffness and stress concentration factor （SCF） are studied for microspeciem and microgripper, respectively. It is observed that the size effects become rather strong when the width of spring for microgripper, the radius of circular perforation and the long axis of elliptical perforation for microspeciem come close to the material characteristic length scales. For the U-shaped notch, the size effects decline obviously with increasing notch radius, and decline mildly with increasing length of notch.
文摘This communique is opted to study the approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices.We choose the geodesic distance betweenAHXXA and P as the cost function,and put forward the Extended Hamiltonian algorithm(EHA)and Natural gradient algorithm(NGA)for the solution.Finally,several numerical experiments give you an idea about the effectiveness of the proposed algorithms.We also show the comparison between these two algorithms EHA and NGA.Obtained results are provided and analyzed graphically.We also conclude that the extended Hamiltonian algorithm has better convergence speed than the natural gradient algorithm,whereas the trajectory of the solution matrix is optimal in case of Natural gradient algorithm(NGA)as compared to Extended Hamiltonian Algorithm(EHA).The aim of this paper is to show that the Extended Hamiltonian algorithm(EHA)has superior convergence properties as compared to Natural gradient algorithm(NGA).Upto the best of author’s knowledge,no approximate solution of the Algebraic Lyapunov equation on the manifold of positive-definite Hermitian matrices is found so far in the literature.
基金Supported by the major program of the National Natural Science Foundation of China (No.60496311)the Chinese Postdoctoral Science Foundation (No.2004035061)the Foundation of Intel China Research Center.
文摘This paper addresses the problem of Blind Source Separation (BSS) and presents a new BSS algorithm with a Signal-Adaptive Activation (SAA) function (SAA-BSS). By taking the sum of absolute values of the normalized kurtoses as a contrast function, the obtained signal-adaptive activation function automatically satisfies the local stability and robustness conditions. The SAA-BSS exploits the natural gradient learning on the Stiefel manifold, and it is an equivariant algorithm with a moderate computational load. Computer simulations show that the SAA-BSS can perform blind separation of mixed sub-Gaussian and super-Gaussian signals and it works more efficiently than the existing algorithms in convergence speed and robustness against outliers.
文摘Granier sap flow system is one of the most commonly used techniques for measurements of whole-tree water use in ecophysiological and forest hydrological studies.However,in the literature there is not one paper that exclusively reviews the Granier method.In this paper,we recapitulate the theoretical basis of the Granier sap flow system and review recent developments in calibration and modification of the sensor probes.Practical issues,such as the determination of the non-flow signal values,natural thermal gradient,wounding effect,reversed sap flow pattern and extrapolation of individual measurement of sap flux density to whole-tree sap flow.are discussed in detail.In the perspectives,new approaches are put forward to use the strong coupling between photosynthesis and transpiration or canopy conductance,via the measurement of 13C discrimination,to estimate whole-canopy carbon assimilation.
基金National Natural Science Foundation of China(32322054,32271644)Guangdong Basic and Applied Basic Research Foundation(2022B1515020014,2023A1515010957,2022A1515110926).
文摘Biodiversity underpins critical ecological processes,yet its relationship with phosphorus(P)remains poorly understood.Understanding the distinct responses of plant and soil microbial diversity to P availability changes is particularly crucial on a global scale.Integrating meta-analysis and natural gradient approaches,this study evaluates these responses globally.Specifically,we conducted a meta-analysis using 393 observations from 128 field P addition experiments and supplemented this with a natural gradient analysis of forest tree diversity and vascular plant diversity.Our meta-analysis results showed that P additions reduced plant species richness by 8.5%and Shannon index by 1.3%in global grasslands,while exerting minimal effects on soil bacterial and fungal diversity across major terrestrial ecosystems.Natural gradient analysis further demonstrated significant correlations between both forest tree richness and vascular plant richness with soil total P concentrations.Notably,partial correlation analyses showed negative correlations when controlling for gross primary productivity and edaphic variables,but positive correlations when controlling for climatic variables.These complementary approaches collectively suggest that plant diversity exhibits greater sensitivity to altered soil P availability than soil microbial diversity.Consequently,elucidating the differential responses of above-and below-ground biodiversity to nutrient supply changes provides a scientific foundation for sound management of terrestrial ecosystem functions and processes.
基金supported by the National Natural Science Foundation of China[grant numbers 12401387,11771268,12001356]the Fujian Alliance of Mathematics[grand number 2024SXLMQN01]the Talent Fund Project of Fuzhou University[grand number XRC-24048].
文摘Variable selection identifies the best subset of covariates when building the prediction model,among all possible subsets.In this paper,we propose a novel reinforced variable selection method,called‘Actor-Critic-Predictor’.The actor takes an action to choose variables and the predictor evaluates the action based on a well-designed reward function,where the critic learns the reward baseline.We model the variable selection process as a multi-armed bandit and update the subset of selected variables using a natural policy gradient algorithm.We provide an analytical framework on how different errors impact the performance of our method theoretically.Large amounts of experiments on synthetic and real datasets show that the proposed framework is easily implemented and outperforms classical variable selection methods in a wide range of scenarios.
基金supported by the National Natural Science Foundation of China(Grant No.60496311).
文摘The contrast function remains to be an open problem in blind source separation （BSS） when the number of source signals is unknown and/or dynamically changed. The paper studies this problem and proves that the mutual information is still the contrast function for BSS if the mixing matrix is of full column rank. The mutual information reaches its minimum at the separation points, where the random outputs of the BSS system are the scaled and permuted source signals, while the others are zero outputs. Using the property that the transpose of the mixing matrix and a matrix composed by m observed signals have the indentical null space with probability one, a practical method, which can detect the unknown number of source signals n, ulteriorly traces the dynamical change of the sources number with a few of data, is proposed. The effectiveness of the proposed theorey and the developed novel algorithm is verified by adaptive BSS simulations with unknown and dynamically changing number of source signals.
基金the National Natural Science Foundation of China (Grant Nos. 60505005, 60674033, 60774094 and U0635001)Natural Science Fund of Guangdong Province, China (Grant Nos. 05103553 and 05006508)+1 种基金Postdoctoral Science Foundation for Innovation from South China University of TechnologyChina Postdoctoral Science Foundation (Grant No. 20070410237)
文摘The independence priori is very often used in the conventional blind source separation （BSS）. Naturally, independent component analysis （ICA） is also employed to perform BSS very often. However, ICA is difficult to use in some challenging cases, such as underdetermined BSS or blind separation of dependent sources. Recently, sparse component analysis （SCA） has attained much attention because it is theoretically available for underdetermined BSS and even for blind dependent source separation sometimes. However, SCA has not been developed very sufficiently. Up to now, there are only few existing algorithms and they are also not perfect as well in practice. For example, although Lewicki-Sejnowski＇s natural gradient for SCA is superior to K-mean clustering, it is just an approximation without rigorously theoretical basis. To overcome these problems, a new natural gradient formula is proposed in this paper. This formula is derived directly from the cost function of SCA through matrix theory. Mathematically, it is more rigorous. In addition, a new and robust adaptive BSS algorithm is developed based on the new natural gradient. Simulations illustrate that this natural gradient formula is more robust and reliable than Lewicki-Sejnowski＇s gradient.
基金financial support from the National Natural Science Foundation of China(U23A20481,62275010,62075004 and 62471021)the Beijing Natural Science Foundation(1232027)the Analysis&Testing Center in Beihang University,the Fundamental Research Funds for the Central Universities.
文摘Photoenergy harvesting is promising to power Internet-of-Things(IoT)sensors,freeing the limitations of wired power sources or batteries,enabling bio-integrated devices.However,existing photoenergy harvesting systems are restricted to solid or liquid configurations—limiting biocompatibility and space utilization—which makes obtaining flexible,biocompatible,light-harvesting devices a significant challenge.In this paper,inspired by natural ion gradient diffusion in organisms,offering an ion-hydrogel drops-based photoenergy harvesting base on ammonium molybdate.Through the photochemical process of ammonium molybdate,the electric potential of the device is regulated by the altered ion gradient and the redox pairs([Mo_(7)O_(24)]^(6-)/[Mo_(1)O_(46)]^(10-)),to generate energy.When exposed to excitation light,a photo driven ammonium molybdate-hydrogel photoenergy harvester(PAPH)can generate an open-circuit potential of~250 mV,and it can still obtain a considerable output power for milliseconds to thousands of seconds after the termination of the initial illumination.The reversible hydrogel droplets network allows for the recovery and fabrication of arbitrary structures of the PAPH.We further demonstrate the scalable PAPH networks can on-demand regulation of cell epithelial growth factor secretion and receptor expression,stimulate the cell proliferation,thereby facilitating biological tissue wound repair.This ionic hydrogel opens a new avenue for flexible,photoenergy harvesting,biocompatible devices.
