Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective...Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.展开更多
As the underlying foundation of a digital twin network(DTN),digital twin channel(DTC)can accurately depict the electromagnetic wave propagation in the air interface to support the DTN-based 6G wireless network.Since e...As the underlying foundation of a digital twin network(DTN),digital twin channel(DTC)can accurately depict the electromagnetic wave propagation in the air interface to support the DTN-based 6G wireless network.Since electromagnetic wave propagation is affected by the environment,constructing the relationship between the environment and radio wave propagation is the key to implementing DTC.In the existing methods,the environmental information inputted into the neural network has many dimensions,and the correlation between the environment and the channel is unclear,resulting in a highly complex relationship construction process.To solve this issue,we propose a unified construction method of radio environment knowledge(REK)inspired by the electromagnetic wave property to quantify the propagation contribution based on easily obtainable location information.An effective scatterer determination scheme based on random geometry is proposed which reduces redundancy by 90%,87%,and 81%in scenarios with complete openness,impending blockage,and complete blockage,respectively.We also conduct a path loss prediction task based on a lightweight convolutional neural network(CNN)employing a simple two-layer convolutional structure to validate REK’s effectiveness.The results show that only 4 ms of testing time is needed with a prediction error of 0.3,effectively reducing the network complexity.展开更多
Receptor-like kinases(RLKs)play key roles in regulating various physiological aspects in plant growth and development.In Arabidopsis thaliana,there are at least 223 leucine-rich repeat(LRR)RLKs.The functions of the ma...Receptor-like kinases(RLKs)play key roles in regulating various physiological aspects in plant growth and development.In Arabidopsis thaliana,there are at least 223 leucine-rich repeat(LRR)RLKs.The functions of the majority of RLKs in the LRR XI subfamily were previously revealed.Only three RLKs were not characterized.Here we report that two independent triple mutants of these RLKs,named ROOT ELONGATION RECEPTOR KINASES(REKs),exhibit increased cell numbers in the root apical meristem and enhanced cell size in the elongation and maturation zones.The promoter activities of a number of Quiescent Center marker genes are significantly up-regulated in the triple mutant.However,the promoter activities of several marker genes known to control root stem cell niche activities are not altered.RNA-seq analysis revealed that a number of cell wall remodeling genes are significantly up-regulated in the triple mutant.Our results suggest that these REKs play key roles in regulating root development likely via negatively regulating the expression of a number of key cell wall remodeling genes.展开更多
基金supported by the National Natural Science Foundations of China(Nos.11571171,62073161,and 61473148)。
文摘Tikhonov regularization is a powerful tool for solving linear discrete ill-posed problems.However,effective methods for dealing with large-scale ill-posed problems are still lacking.The Kaczmarz method is an effective iterative projection algorithm for solving large linear equations due to its simplicity.We propose a regularized randomized extended Kaczmarz(RREK)algorithm for solving large discrete ill-posed problems via combining the Tikhonov regularization and the randomized Kaczmarz method.The convergence of the algorithm is proved.Numerical experiments illustrate that the proposed algorithm has higher accuracy and better image restoration quality compared with the existing randomized extended Kaczmarz(REK)method.
基金supported by the National Key R&D Program of China(No.2023YFB2904803)the National Natural Science Foundation of China(Nos.62341128,62201087,and 62101069)+2 种基金the National Science Fund for Distinguished Young Scholars,China(No.61925102)the Beijing Natural Science Foundation,China(No.L243002)the Beijing University of Posts and Telecommunications-China Mobile Research Institute Joint Innovation Center。
文摘As the underlying foundation of a digital twin network(DTN),digital twin channel(DTC)can accurately depict the electromagnetic wave propagation in the air interface to support the DTN-based 6G wireless network.Since electromagnetic wave propagation is affected by the environment,constructing the relationship between the environment and radio wave propagation is the key to implementing DTC.In the existing methods,the environmental information inputted into the neural network has many dimensions,and the correlation between the environment and the channel is unclear,resulting in a highly complex relationship construction process.To solve this issue,we propose a unified construction method of radio environment knowledge(REK)inspired by the electromagnetic wave property to quantify the propagation contribution based on easily obtainable location information.An effective scatterer determination scheme based on random geometry is proposed which reduces redundancy by 90%,87%,and 81%in scenarios with complete openness,impending blockage,and complete blockage,respectively.We also conduct a path loss prediction task based on a lightweight convolutional neural network(CNN)employing a simple two-layer convolutional structure to validate REK’s effectiveness.The results show that only 4 ms of testing time is needed with a prediction error of 0.3,effectively reducing the network complexity.
基金supported by the National Natural Science Foundation of China(31720103902 and 32030005)the 111 Project from the Department of Science and Technology(B16022)。
文摘Receptor-like kinases(RLKs)play key roles in regulating various physiological aspects in plant growth and development.In Arabidopsis thaliana,there are at least 223 leucine-rich repeat(LRR)RLKs.The functions of the majority of RLKs in the LRR XI subfamily were previously revealed.Only three RLKs were not characterized.Here we report that two independent triple mutants of these RLKs,named ROOT ELONGATION RECEPTOR KINASES(REKs),exhibit increased cell numbers in the root apical meristem and enhanced cell size in the elongation and maturation zones.The promoter activities of a number of Quiescent Center marker genes are significantly up-regulated in the triple mutant.However,the promoter activities of several marker genes known to control root stem cell niche activities are not altered.RNA-seq analysis revealed that a number of cell wall remodeling genes are significantly up-regulated in the triple mutant.Our results suggest that these REKs play key roles in regulating root development likely via negatively regulating the expression of a number of key cell wall remodeling genes.
