Fixed Mobile Convergence (FMC) is the focus of the future communications network development,on which the industry has kept strengthening its relevant research. However,before a large scale of implementation,there are...Fixed Mobile Convergence (FMC) is the focus of the future communications network development,on which the industry has kept strengthening its relevant research. However,before a large scale of implementation,there are still lots of key issues to be explored. The adoption of IP Multimedia Subsystem (IMS) architecture to replace the real-time services in the traditional application needs to solve the Quality of Service (QoS) problem in the IP domain,unify the method that the fixed and mobile users of the traditional circuit domain access IMS,complete the mapping of circuit domain service flow to IMS,guarantee the security of IMS bearer network,transform the traditional operation mode,and set up a new pattern adaptable to the convergence.展开更多
For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation r...For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.展开更多
In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transforma...In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.展开更多
In this article,we investigate a stochastic Galerkin method for the Maxwell equations with random inputs.The generalized Polynomial Chaos(gPC)expansion technique is used to obtain a deterministic system of the gPC exp...In this article,we investigate a stochastic Galerkin method for the Maxwell equations with random inputs.The generalized Polynomial Chaos(gPC)expansion technique is used to obtain a deterministic system of the gPC expansion coefficients.The regularity of the solution with respect to the random is analyzed.On the basis of the regularity results,the optimal convergence rate of the stochastic Galerkin approach for Maxwell equations with random inputs is proved.Numerical examples are presented to support the theoretical analysis.展开更多
A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential tha...A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.展开更多
The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differenti...The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.展开更多
A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. Wh...A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straightline-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations.展开更多
Federated learning(FL)is a distributed machine learning(ML)framework where several clients cooperatively train an ML model by exchanging the model parameters without directly sharing their local data.In FL,the limited...Federated learning(FL)is a distributed machine learning(ML)framework where several clients cooperatively train an ML model by exchanging the model parameters without directly sharing their local data.In FL,the limited number of participants for model aggregation and communication latency are two major bottlenecks.Hierarchical federated learning(HFL),with a cloud-edge-client hierarchy,can leverage the large coverage of cloud servers and the low transmission latency of edge servers.There are growing research interests in implementing FL in vehicular networks due to the requirements of timely ML training for intelligent vehicles.However,the limited number of participants in vehicular networks and vehicle mobility degrade the performance of FL training.In this context,HFL,which stands out for lower latency,wider coverage and more participants,is promising in vehicular networks.In this paper,we begin with the background and motivation of HFL and the feasibility of implementing HFL in vehicular networks.Then,the architecture of HFL is illustrated.Next,we clarify new issues in HFL and review several existing solutions.Furthermore,we introduce some typical use cases in vehicular networks as well as our initial efforts on implementing HFL in vehicular networks.Finally,we conclude with future research directions.展开更多
This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-lev...This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.展开更多
As a promising edge learning framework in future 6G networks,federated learning(FL)faces a number of technical challenges due to the heterogeneous network environment and diversified user behaviors.Data imbalance is o...As a promising edge learning framework in future 6G networks,federated learning(FL)faces a number of technical challenges due to the heterogeneous network environment and diversified user behaviors.Data imbalance is one of these challenges that can significantly degrade the learning efficiency.To deal with data imbalance issue,this work proposes a new learning framework,called clustered federated learning with weighted model aggregation(weighted CFL).Compared with traditional FL,our weighted CFL adaptively clusters the participating edge devices based on the cosine similarity of their local gradients at each training iteration,and then performs weighted per-cluster model aggregation.Therein,the similarity threshold for clustering is adaptive over iterations in response to the time-varying divergence of local gradients.Moreover,the weights for per-cluster model aggregation are adjusted according to the data balance feature so as to speed up the convergence rate.Experimental results show that the proposed weighted CFL achieves a faster model convergence rate and greater learning accuracy than benchmark methods under the imbalanced data scenario.展开更多
文摘Fixed Mobile Convergence (FMC) is the focus of the future communications network development,on which the industry has kept strengthening its relevant research. However,before a large scale of implementation,there are still lots of key issues to be explored. The adoption of IP Multimedia Subsystem (IMS) architecture to replace the real-time services in the traditional application needs to solve the Quality of Service (QoS) problem in the IP domain,unify the method that the fixed and mobile users of the traditional circuit domain access IMS,complete the mapping of circuit domain service flow to IMS,guarantee the security of IMS bearer network,transform the traditional operation mode,and set up a new pattern adaptable to the convergence.
基金the Major State Basic Research Program of China(19990328)NNSF of China(19871051,19972039) the Doctorate Foundation of the State Education Commission
文摘For compressible two-phase displacement problem, a kind of upwind operator splitting finite difference schemes is put forward and make use of operator splitting, of calculus of variations, multiplicative commutation rule of difference operators, decomposition of high order difference operators and prior estimates are adopted. Optimal order estimates in L 2 norm are derived to determine the error, in the approximate solution.
基金supported by the State Key Program of National Natural Science Foundation of China(11931003)the National Natural Science Foundation of China(41974133,11671157)。
文摘In this paper,a Jacobi-collocation spectral method is developed for a Volterraintegro-differential equation with delay,which contains a weakly singular kernel.We use a function transformation and a variable transformation to change the equation into a new Volterra integral equation defined on the standard interval[-1,1],so that the Jacobi orthogonal polynomial theory can be applied conveniently.In order to obtain high order accuracy for the approximation,the integral term in the resulting equation is approximated by Jacobi spectral quadrature rules.In the end,we provide a rigorous error analysis for the proposed method.The spectral rate of convergence for the proposed method is established in both the L^(∞)-norm and the weighted L^(2)-norm.
基金Supported by NSFC (91430107/11771138/11171104)the Construct Program of the Key Discipline in Hunan+4 种基金partially supported by Scientific Research Fund of Hunan Provincial Education Department (19B325/19C1059)Hunan International Economics University (2017A05)supported by NSFC (11771137)the Construct Program of the Key Discipline in Hunan Provincea Scientific Research Fund of Hunan Provincial Education Department (16B154)。
文摘In this article,we investigate a stochastic Galerkin method for the Maxwell equations with random inputs.The generalized Polynomial Chaos(gPC)expansion technique is used to obtain a deterministic system of the gPC expansion coefficients.The regularity of the solution with respect to the random is analyzed.On the basis of the regularity results,the optimal convergence rate of the stochastic Galerkin approach for Maxwell equations with random inputs is proved.Numerical examples are presented to support the theoretical analysis.
基金supported by the National Natural Science Foundation of China(Grant Nos.11201169,11271195,and 41231173)the Project of Graduate Education Innovation of Jiangsu Province,China(Grant No.CXLX13 366)
文摘A local energy conservation law is proposed for the Klein--Gordon-Schrrdinger equations, which is held in any local time-space region. The local property is independent of the boundary condition and more essential than the global energy conservation law. To develop a numerical method preserving the intrinsic properties as much as possible, we propose a local energy-preserving （LEP） scheme for the equations. The merit of the proposed scheme is that the local energy conservation law can hold exactly in any time-space region. With the periodic boundary conditions, the scheme also possesses the discrete change and global energy conservation laws. A nonlinear analysis shows that the LEP scheme converges to the exact solutions with order O（τ2 ＋ h2）. The theoretical properties are verified by numerical experiments.
基金supported the Natural Science Foundation of Shandong Province(ZR2016AM08)Natural Science Foundation of Hunan Province(2018JJ2028)National Natural Science Foundation of China(11871312).
文摘The numerical simulation of a three-dimensional semiconductor device is a fundamental problem in information science. The mathematical model is defined by an initialboundary nonlinear system of four partial differential equations: an elliptic equation for electric potential, two convection-diffusion equations for electron concentration and hole concentration, and a heat conduction equation for temperature. The first equation is solved by the conservative block-centered method. The concentrations and temperature are computed by the block-centered upwind difference method on a changing mesh, where the block-centered method and upwind approximation are used to discretize the diffusion and convection, respectively. The computations on a changing mesh show very well the local special properties nearby the P-N junction. The upwind scheme is applied to approximate the convection, and numerical dispersion and nonphysical oscillation are avoided. The block-centered difference computes concentrations, temperature, and their adjoint vector functions simultaneously.The local conservation of mass, an important rule in the numerical simulation of a semiconductor device, is preserved during the computations. An optimal order convergence is obtained. Numerical examples are provided to show efficiency and application.
基金Project supported by the National Natural Science Foundation of China(Grant Nos.71071044,71001001,71201041,and 11247291)the Doctoral Program of the Ministry of Education of China(Grant Nos.20110111120023 and 20120111120022)+2 种基金the Postdoctoral Fund Project of China(Grant No.2013M530295)the National Basic Research Program of China(Grant No.2012CB725404)1000 Plan for Foreign Talent,China(Grant No.WQ20123400070)
文摘A delayed chasing model is proposed to simulate the chase behavior in the queue, where each member regards the closest one ahead as the target, and the leader is attracted to a target point with slight fluctuation. When the initial distances between neighbors possess an identical low value, the fluctuating target of the leader can cause an amplified disturbance in the queue. After a long period of time, the queue recovers the stable state from the disturbance, forming a straightline-like pattern again, but distances between neighbors grow. Whether the queue can keep stable or not depends on initial distance, desired velocity, and relaxation time. Furthermore, we carry out convergence analysis to explain the divergence transformation behavior and confirm the convergence conditions, which is in approximate agreement with simulations.
基金sponsored in part by the National Key R&D Program of China under Grant No. 2020YFB1806605the National Natural Science Foundation of China under Grant Nos. 62022049, 62111530197, and 61871254+1 种基金OPPOsupported by the Fundamental Research Funds for the Central Universities under Grant No. 2022JBXT001
文摘Federated learning(FL)is a distributed machine learning(ML)framework where several clients cooperatively train an ML model by exchanging the model parameters without directly sharing their local data.In FL,the limited number of participants for model aggregation and communication latency are two major bottlenecks.Hierarchical federated learning(HFL),with a cloud-edge-client hierarchy,can leverage the large coverage of cloud servers and the low transmission latency of edge servers.There are growing research interests in implementing FL in vehicular networks due to the requirements of timely ML training for intelligent vehicles.However,the limited number of participants in vehicular networks and vehicle mobility degrade the performance of FL training.In this context,HFL,which stands out for lower latency,wider coverage and more participants,is promising in vehicular networks.In this paper,we begin with the background and motivation of HFL and the feasibility of implementing HFL in vehicular networks.Then,the architecture of HFL is illustrated.Next,we clarify new issues in HFL and review several existing solutions.Furthermore,we introduce some typical use cases in vehicular networks as well as our initial efforts on implementing HFL in vehicular networks.Finally,we conclude with future research directions.
文摘This paper considers the one-dimensional dissipative cubic nonlinear SchrSdinger equation with zero Dirichlet boundary conditions on a bounded domain. The equation is discretized in time by a linear implicit three-level central difference scheme, which has analogous discrete conservation laws of charge and energy. The convergence with two orders and the stability of the scheme are analysed using a priori estimates. Numerical tests show that the three-level scheme is more efficient.
文摘As a promising edge learning framework in future 6G networks,federated learning(FL)faces a number of technical challenges due to the heterogeneous network environment and diversified user behaviors.Data imbalance is one of these challenges that can significantly degrade the learning efficiency.To deal with data imbalance issue,this work proposes a new learning framework,called clustered federated learning with weighted model aggregation(weighted CFL).Compared with traditional FL,our weighted CFL adaptively clusters the participating edge devices based on the cosine similarity of their local gradients at each training iteration,and then performs weighted per-cluster model aggregation.Therein,the similarity threshold for clustering is adaptive over iterations in response to the time-varying divergence of local gradients.Moreover,the weights for per-cluster model aggregation are adjusted according to the data balance feature so as to speed up the convergence rate.Experimental results show that the proposed weighted CFL achieves a faster model convergence rate and greater learning accuracy than benchmark methods under the imbalanced data scenario.
