In this paper,a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory(HWENO)scheme is designed for hyperbolic conservation laws.The main idea of this scheme is derived from our previous...In this paper,a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory(HWENO)scheme is designed for hyperbolic conservation laws.The main idea of this scheme is derived from our previous work[J.Comput.Phys.,446(2021)110653],in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the boundaries.However,in this paper,only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order moments.In addition,an extra modification procedure is used to modify those first order moments in the troubledcells,which leads to an improvement of stability and an enhancement of resolution near discontinuities.To obtain the same order of accuracy,the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the generalWENO scheme.Moreover,the linear weights are not unique and are independent of the node position,and the CFL number can still be 0.6whether for the one or two dimensional case,which has to be 0.2 in the two dimensional case for other HWENO schemes.Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.展开更多
Given image sequences of closely packed particles, the underlying aim is to estimate diameters without explicit segmentation. In a way, this is similar to the task of counting objects without directly counting them. S...Given image sequences of closely packed particles, the underlying aim is to estimate diameters without explicit segmentation. In a way, this is similar to the task of counting objects without directly counting them. Such calculations may, for example, be useful）Cast estimation of particle size in different application areas. The topic is that of estimating average size （=average diameter） of packed particles, from formulas involving edge density, and the edges from moment-based thresholding are used. An average shape factor is involved in the calculations, obtained for some frames from crude partial segmentation. Measurement results from about 80frames have been analyzed.展开更多
This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future un...This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.展开更多
In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms und...In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.展开更多
The Nakagami-Gamma(NG) shadow fading model based on the moment-based method(MoM) generates lower tail approximation, which is inaccuracy when the gamma random variables are replaced by the lognormal random variables. ...The Nakagami-Gamma(NG) shadow fading model based on the moment-based method(MoM) generates lower tail approximation, which is inaccuracy when the gamma random variables are replaced by the lognormal random variables. The channel parameters of composite NG shadow fading based on the method of minimizing the Kullback-Leibler(KL) divergence were estimated and a closed-form expression for the system bit error rate(BER) was derived in this paper. The simulation results show that the KL estimated parameters solve the lower tail approximation problem, and the replacement effect of the lognormal function by the gamma function is better than the MoM when the shading parameters are around the typical value of 4 dB-9 dB. Moreover, the KL method has a lower mean square error(MSE) value for the channel analysis.展开更多
基金partly supported by AFOSR grant FA9550-20-1-0055 and NSF grant DMS-2010107partly supported by NSFC grant 12071392.
文摘In this paper,a high-order moment-based multi-resolution Hermite weighted essentially non-oscillatory(HWENO)scheme is designed for hyperbolic conservation laws.The main idea of this scheme is derived from our previous work[J.Comput.Phys.,446(2021)110653],in which the integral averages of the function and its first order derivative are used to reconstruct both the function and its first order derivative values at the boundaries.However,in this paper,only the function values at the Gauss-Lobatto points in the one or two dimensional case need to be reconstructed by using the information of the zeroth and first order moments.In addition,an extra modification procedure is used to modify those first order moments in the troubledcells,which leads to an improvement of stability and an enhancement of resolution near discontinuities.To obtain the same order of accuracy,the size of the stencil required by this moment-based multi-resolution HWENO scheme is still the same as the general HWENO scheme and is more compact than the generalWENO scheme.Moreover,the linear weights are not unique and are independent of the node position,and the CFL number can still be 0.6whether for the one or two dimensional case,which has to be 0.2 in the two dimensional case for other HWENO schemes.Extensive numerical examples are given to demonstrate the stability and resolution of such moment-based multi-resolution HWENO scheme.
文摘Given image sequences of closely packed particles, the underlying aim is to estimate diameters without explicit segmentation. In a way, this is similar to the task of counting objects without directly counting them. Such calculations may, for example, be useful）Cast estimation of particle size in different application areas. The topic is that of estimating average size （=average diameter） of packed particles, from formulas involving edge density, and the edges from moment-based thresholding are used. An average shape factor is involved in the calculations, obtained for some frames from crude partial segmentation. Measurement results from about 80frames have been analyzed.
基金This study was funded by the MITACS Accelerate Grant-Award Number IT12339the Foreign Young Talents Program of the Ministry of Science and Technology of China(QN20200017001)the China Postdoctoral Science Foundation(2020M672913).
文摘This study considers the risk management of insurance policies in line with the implementation of the new International Financial Reporting Standards 17.It applies the paid-incurred chain method to model the future unpaid losses by combining the information channels of both the incurred claims and paid losses.We propose the recovery of the empirical distribution of the outstanding claims liabilities associated with a group of contracts via moment-based density approximation.We determine the risk measures and adjustments that are compliant with the new standard using the Monte–Carlo simulation method and approximated distributions.The historical data on the aggregate Ontario automobile insurance claims over a 15-year period are analyzed to examine the appropriateness and accuracy of our approach.
基金supported by National Natural Science Foundation of China(Grant Nos.11991023 and 12371324)National Key R&D Program of China(Grant No.2022YFA1004000)。
文摘In this paper,we study the distributionally robust joint chance-constrained Markov decision process.Utilizing the logarithmic transformation technique,we derive its deterministic reformulation with bi-convex terms under the moment-based uncertainty set.To cope with the non-convexity and improve the robustness of the solution,we propose a dynamical neural network approach to solve the reformulated optimization problem.Numerical results on a machine replacement problem demonstrate the efficiency of the proposed dynamical neural network approach when compared with the sequential convex approximation approach.
基金supported by the Hunan Provincial Natural Science Foundation (2023JJ50045)the Project of Education Bureau of Hunan Province (22B0676,23C0217)。
文摘The Nakagami-Gamma(NG) shadow fading model based on the moment-based method(MoM) generates lower tail approximation, which is inaccuracy when the gamma random variables are replaced by the lognormal random variables. The channel parameters of composite NG shadow fading based on the method of minimizing the Kullback-Leibler(KL) divergence were estimated and a closed-form expression for the system bit error rate(BER) was derived in this paper. The simulation results show that the KL estimated parameters solve the lower tail approximation problem, and the replacement effect of the lognormal function by the gamma function is better than the MoM when the shading parameters are around the typical value of 4 dB-9 dB. Moreover, the KL method has a lower mean square error(MSE) value for the channel analysis.
