Investigating the spatial and temporal variance in productivity along natural precipitation gradients is one of the most efficient approaches to improve understanding of how ecosystems respond to climate change. In th...Investigating the spatial and temporal variance in productivity along natural precipitation gradients is one of the most efficient approaches to improve understanding of how ecosystems respond to climate change. In this paper, by using the natural precipitation gradient of the Inner Mongolian Plateau from east to west determined by relatively long-term observations, we analyzed the temporal and spatial dynamics of aboveground net primary productivity (ANPP) of the temperate grasslands covering this region. Across this grassland transect, ANPP increased exponentially with the increase of mean annual precipitation (MAP) (ANPP=24.47e0.005MAP, R2=0.48). Values for the three vegetation types desert steppe, typical steppe, and meadow steppe were: 60.86 gm-2a-1, 167.14 gm-2a-1 and 288.73 gm-2a-1 respectively. By contrast, temperature had negative effects on ANPP. The moisture index (K ), which takes into ac- count both precipitation and temperature could explain the spatial variance of ANPP better than MAP alone (ANPP=2020.34K1.24, R2=0.57). Temporally, we found that the inter-annual variation in ANPP (cal- culated as the coefficient of variation, CV) got greater with the increase of aridity. However, this trend was not correlated with the inter-annual variation of precipitation. For all of the three vegetation types, ANPP had greater inter-annual variation than annual precipitation (PPT). Their difference (ANPP CV/PPT CV) was greatest in desert steppe and least in meadow steppe. Our results suggest that in more arid regions, grasslands not only have lower productivity, but also higher inter-annual variation of production. Climate change may have significant effects on the productivity through changes in precipitation pattern, vegetation growth potential, and species diversity.展开更多
In this paper,we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected)gradient(SG)methods,including two popular types...In this paper,we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected)gradient(SG)methods,including two popular types of SG:stepsize diminished SG and batch size increased SG.We also show that the standard variance uniformly bounded assumption,which is frequently used in the literature to investigate the convergence of SG,is actually not required when the gradient of the objective function is Lipschitz continuous.Finally,we show that our framework can also be used for analyzing the convergence of a mini-batch stochastic extragradient method for stochastic variational inequality.展开更多
In view of the obvious changes in color between the upper and lower leaf scar in sugarcane nodes,a method of simultaneous multi-nodes identification on a single sugarcane stem was proposed based on the analysis of gra...In view of the obvious changes in color between the upper and lower leaf scar in sugarcane nodes,a method of simultaneous multi-nodes identification on a single sugarcane stem was proposed based on the analysis of gradient characteristics of sugarcane images.In combination with image processing and machine vision recognition technology,two cameras were used to acquire different parts of sugarcane images,and the two images were integrated into a complete image of sugarcane by image mosaicking.The Sobel operator is used to calculate the gradient of the sugarcane image in a horizontal direction,and the gradient image is obtained.The sugarcane gradient image was scanned by a rectangular template with a width of 14 pixels and a step length of 12 pixels.The features of average gradient and variance gradient were used to identify sugarcane nodes for the first time.The experimental results showed that the recognition accuracy was 96.8952%,and there were fewer false detected sugarcane segments.The detection efficiency could be improved by detecting multi-nodes on a single sugarcane stem at the same time.展开更多
策略梯度算法是深度强化学习领域中广泛使用的一类无模型强化学习方法,在实际应用中取得了突破性进展。策略梯度算法一直受到梯度估计方差大的困扰,基于参数探索的策略梯度算法(policy gradients with parameterbased exploration,PGPE...策略梯度算法是深度强化学习领域中广泛使用的一类无模型强化学习方法,在实际应用中取得了突破性进展。策略梯度算法一直受到梯度估计方差大的困扰,基于参数探索的策略梯度算法(policy gradients with parameterbased exploration,PGPE)从根本上缓解了该问题。通过最优基线技术的引入,策略梯度估计的方差进一步减小。然而,现有最优基线技术只使用标量值作为基线,忽略了策略梯度各维度之间的差异。针对此问题,本文提出一种向量基线概念并推导PGPE算法的最优向量基线表示,在理论上证明了引入最优向量基线的PGPE算法可以得到更小的梯度估计方差,并且实验验证了此算法的有效性。展开更多
Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this pap...Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this paper, the performance of 7 protocols corresponding to 6, 9, 12, 15, 20, 25, and 30 noncollinear number of diffusion gradi-ent directions (NDGD) were discussed by com-paring signal-noise ratio (SNR) of tensor- de-rived measurement maps and fractional ani-sotropy (FA) values. All DTI data (eight healthy volunteers) were downloaded from the website of Johns Hopkins Medical Institute Laboratory of Brain Anatomi-cal MRI with permission. FA, apparent diffusion constant mean (ADC-mean), the largest eigen-value (LEV), and eigenvector orientation (EVO) maps associated with LEV of all subjects were calculated derived from tensor in the 7 proto-cols via DTI Studio. A method to estimate the variance was presented to calculate SNR of these tensor-derived maps. Mean ±standard deviation of the SNR and FA values within re-gion of interest (ROI) selected in the white mat-ter were compared among the 7 protocols. The SNR were improved significantly with NDGD increasing from 6 to 20 (P<0.05). From 20 to 30, SNR were improved significantly for LEV and EVO maps (P<0.05), but no significant dif-ferences for FA and ADC-mean maps (P>0.05). There were no significant variances in FA val-ues within ROI between any two protocols (P>0.05). The SNR could be improved with NDGD in-creasing, but an optimum protocol is needed because of clinical limitations.展开更多
Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of ...Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.展开更多
When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem...When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.展开更多
基金Supported by the National Key Research and Development Program (Grant No. 2002CB412501)the National Natural Science Foundation of China (Grant No. 30590381)
文摘Investigating the spatial and temporal variance in productivity along natural precipitation gradients is one of the most efficient approaches to improve understanding of how ecosystems respond to climate change. In this paper, by using the natural precipitation gradient of the Inner Mongolian Plateau from east to west determined by relatively long-term observations, we analyzed the temporal and spatial dynamics of aboveground net primary productivity (ANPP) of the temperate grasslands covering this region. Across this grassland transect, ANPP increased exponentially with the increase of mean annual precipitation (MAP) (ANPP=24.47e0.005MAP, R2=0.48). Values for the three vegetation types desert steppe, typical steppe, and meadow steppe were: 60.86 gm-2a-1, 167.14 gm-2a-1 and 288.73 gm-2a-1 respectively. By contrast, temperature had negative effects on ANPP. The moisture index (K ), which takes into ac- count both precipitation and temperature could explain the spatial variance of ANPP better than MAP alone (ANPP=2020.34K1.24, R2=0.57). Temporally, we found that the inter-annual variation in ANPP (cal- culated as the coefficient of variation, CV) got greater with the increase of aridity. However, this trend was not correlated with the inter-annual variation of precipitation. For all of the three vegetation types, ANPP had greater inter-annual variation than annual precipitation (PPT). Their difference (ANPP CV/PPT CV) was greatest in desert steppe and least in meadow steppe. Our results suggest that in more arid regions, grasslands not only have lower productivity, but also higher inter-annual variation of production. Climate change may have significant effects on the productivity through changes in precipitation pattern, vegetation growth potential, and species diversity.
基金the National Natural Science Foundation of China(Nos.11871135 and 11801054)the Fundamental Research Funds for the Central Universities(No.DUT19K46)。
文摘In this paper,we establish a unified framework to study the almost sure global convergence and the expected convergencerates of a class ofmini-batch stochastic(projected)gradient(SG)methods,including two popular types of SG:stepsize diminished SG and batch size increased SG.We also show that the standard variance uniformly bounded assumption,which is frequently used in the literature to investigate the convergence of SG,is actually not required when the gradient of the objective function is Lipschitz continuous.Finally,we show that our framework can also be used for analyzing the convergence of a mini-batch stochastic extragradient method for stochastic variational inequality.
文摘In view of the obvious changes in color between the upper and lower leaf scar in sugarcane nodes,a method of simultaneous multi-nodes identification on a single sugarcane stem was proposed based on the analysis of gradient characteristics of sugarcane images.In combination with image processing and machine vision recognition technology,two cameras were used to acquire different parts of sugarcane images,and the two images were integrated into a complete image of sugarcane by image mosaicking.The Sobel operator is used to calculate the gradient of the sugarcane image in a horizontal direction,and the gradient image is obtained.The sugarcane gradient image was scanned by a rectangular template with a width of 14 pixels and a step length of 12 pixels.The features of average gradient and variance gradient were used to identify sugarcane nodes for the first time.The experimental results showed that the recognition accuracy was 96.8952%,and there were fewer false detected sugarcane segments.The detection efficiency could be improved by detecting multi-nodes on a single sugarcane stem at the same time.
文摘策略梯度算法是深度强化学习领域中广泛使用的一类无模型强化学习方法,在实际应用中取得了突破性进展。策略梯度算法一直受到梯度估计方差大的困扰,基于参数探索的策略梯度算法(policy gradients with parameterbased exploration,PGPE)从根本上缓解了该问题。通过最优基线技术的引入,策略梯度估计的方差进一步减小。然而,现有最优基线技术只使用标量值作为基线,忽略了策略梯度各维度之间的差异。针对此问题,本文提出一种向量基线概念并推导PGPE算法的最优向量基线表示,在理论上证明了引入最优向量基线的PGPE算法可以得到更小的梯度估计方差,并且实验验证了此算法的有效性。
文摘Diffusion tensor imaging (DTI) is mainly applied to white matter fiber tracking in human brain, but there is still a debate on how many diffusion gradient directions should be used to get the best results. In this paper, the performance of 7 protocols corresponding to 6, 9, 12, 15, 20, 25, and 30 noncollinear number of diffusion gradi-ent directions (NDGD) were discussed by com-paring signal-noise ratio (SNR) of tensor- de-rived measurement maps and fractional ani-sotropy (FA) values. All DTI data (eight healthy volunteers) were downloaded from the website of Johns Hopkins Medical Institute Laboratory of Brain Anatomi-cal MRI with permission. FA, apparent diffusion constant mean (ADC-mean), the largest eigen-value (LEV), and eigenvector orientation (EVO) maps associated with LEV of all subjects were calculated derived from tensor in the 7 proto-cols via DTI Studio. A method to estimate the variance was presented to calculate SNR of these tensor-derived maps. Mean ±standard deviation of the SNR and FA values within re-gion of interest (ROI) selected in the white mat-ter were compared among the 7 protocols. The SNR were improved significantly with NDGD increasing from 6 to 20 (P<0.05). From 20 to 30, SNR were improved significantly for LEV and EVO maps (P<0.05), but no significant dif-ferences for FA and ADC-mean maps (P>0.05). There were no significant variances in FA val-ues within ROI between any two protocols (P>0.05). The SNR could be improved with NDGD in-creasing, but an optimum protocol is needed because of clinical limitations.
文摘Generalized Least Squares (least squares with prior information) requires the correct assignment of two prior covariance matrices: one associated with the uncertainty of measurements;the other with the uncertainty of prior information. These assignments often are very subjective, especially when correlations among data or among prior information are believed to occur. However, in cases in which the general form of these matrices can be anticipated up to a set of poorly-known parameters, the data and prior information may be used to better-determine (or “tune”) the parameters in a manner that is faithful to the underlying Bayesian foundation of GLS. We identify an objective function, the minimization of which leads to the best-estimate of the parameters and provide explicit and computationally-efficient formula for calculating the derivatives needed to implement the minimization with a gradient descent method. Furthermore, the problem is organized so that the minimization need be performed only over the space of covariance parameters, and not over the combined space of model and covariance parameters. We show that the use of trade-off curves to select the relative weight given to observations and prior information is not a form of tuning, because it does not, in general maximize the posterior probability of the model parameters, and can lead to a different weighting than the procedure described here. We also provide several examples that demonstrate the viability, and discuss both the advantages and limitations of the method.
基金supported by the National 973 Foundation of China(61322201)the National Natural Science Foundation of China(41304022,41174026,41104047)Key Laboratory Foundation of Geo-space Environment and Geodesy,Ministry of Education(11-01-03)
文摘When the computational point is approaching the poles, the variance and covariance formulae of the disturbing gravity gradient tensors tend to be infinite, and this is a singular problem. In order to solve the problem, the authors deduced the practical non-singular computational formulae of the first- and second-order derivatives of the Legendre functions and two kinds of spherical harmonic functions, and then constructed the nonsingular formulae of variance and eovarianee function of disturbing gravity gradient tensors.
