The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its i...The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its invariant measure are of interest.In this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound.With a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.展开更多
The reconfigurable intelligent surface(RIS),which is composed of multiple passive reflective components,is now considered as an effective mean to improve security performance in wireless communications,as it can enhan...The reconfigurable intelligent surface(RIS),which is composed of multiple passive reflective components,is now considered as an effective mean to improve security performance in wireless communications,as it can enhance the signal of legitimate users and suppress the power leakage at eavesdroppers by adjusting signal phases.In this paper,we maximize the downlink ergodic secrecy sum rate of a RIS-aided multi-user system over Rician fading channels,where we assume that only imperfect channel state information(CSI)is available at the base station(BS).Firstly,we obtain the deterministic approximate expression for the ergodic secrecy sum rate by resorting to the large-system approximation theory.Then the problem is formulated to maximize the downlink ergodic secrecy sum rate by optimizing the regularization coefficient of regularized zero-forcing(RZF)precoding and the phase-shifting matrix of the RIS.By using the particle swarm optimization(PSO)method,we propose an alternate optimization(AO)algorithm to solve this non-convex problem.Finally,the numerical simulations illustrate the accuracy of our large-system approximate expression as well as the effectiveness of the proposed algorithm.展开更多
In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obta...In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.展开更多
In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.
In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general g...In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.展开更多
Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the s...Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.展开更多
In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed al...In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order oracles.To encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search condition.Otherwise,a small step size will be taken to help induce desired good properties.Then we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain conditions.We also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen output.Furthermore,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high probability.At last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.展开更多
Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on th...Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks.展开更多
Extreme learning machine （ELM） is a learning algorithm for generalized single-hidden-layer feed-forward networks （SLFNs）. In order to obtain a suitable network architecture, Incremental Extreme Learning Machine （...Extreme learning machine （ELM） is a learning algorithm for generalized single-hidden-layer feed-forward networks （SLFNs）. In order to obtain a suitable network architecture, Incremental Extreme Learning Machine （I-ELM） is a sort of ELM constructing SLFNs by adding hidden nodes one by one. Although kinds of I-ELM-class algorithms were proposed to improve the convergence rate or to obtain minimal training error, they do not change the construction way of I-ELM or face the over-fitting risk. Making the testing error converge quickly and stably therefore becomes an important issue. In this paper, we proposed a new incremental ELM which is referred to as Length-Changeable Incremental Extreme Learning Machine （LCI-ELM）. It allows more than one hidden node to be added to the network and the existing network will be regarded as a whole in output weights tuning. The output weights of newly added hidden nodes are determined using a partial error-minimizing method. We prove that an SLFN constructed using LCI-ELM has approximation capability on a universal compact input set as well as on a finite training set. Experimental results demonstrate that LCI-ELM achieves higher convergence rate as well as lower over-fitting risk than some competitive I-ELM-class algorithms.展开更多
对于O+NH反应,在~3A″和~1A″势能面(Guadagnini R,Schatz G C,Walch S P.Global potential energysurface for the lowest^1 A′,~3A″,and^1A″states of HNO[J].J.Chem.Phys.,1995,10:774)上,我们运用coupled state or centrifugal s...对于O+NH反应,在~3A″和~1A″势能面(Guadagnini R,Schatz G C,Walch S P.Global potential energysurface for the lowest^1 A′,~3A″,and^1A″states of HNO[J].J.Chem.Phys.,1995,10:774)上,我们运用coupled state or centrifugal sudden(CS)近似和close coupling or Coriolis coupled(CC)方法进行了量子动力学计算.通过比较两种方法得到的总的反应几率,我们发现对于两个势能面上的标题反应,CS近似是失效的.我们还讨论了用CS和CC方法得到的速率常数,并进行了结果比较.展开更多
基金partially supported by the National Key R&D Program of China,Project No.2020YFA0712000NSFC Grant No.12031013 and 12171013.
文摘The stochastic growth-fragmentation model describes the temporal evolution of a structured cell population through a discrete-time and continuous-state Markov chain.The simulations of this stochastic process and its invariant measure are of interest.In this paper,we propose a numerical scheme for both the simulation of the process and the computation of the invariant measure,and show that under appropriate assumptions,the numerical chain converges to the continuous growth-fragmentation chain with an explicit error bound.With a triangle inequality argument,we are also able to quantitatively estimate the distance between the invariant measures of these two Markov chains.
基金the National Natural Science Foundation of China.92067201the National Natural Science Foundation of China.62071247+2 种基金the National Natural Science Foundation of China.62171240the National Natural Science Foundation of China.62171231Jiangsu Provincial Key Research and Development Program.BE2020084-4
文摘The reconfigurable intelligent surface(RIS),which is composed of multiple passive reflective components,is now considered as an effective mean to improve security performance in wireless communications,as it can enhance the signal of legitimate users and suppress the power leakage at eavesdroppers by adjusting signal phases.In this paper,we maximize the downlink ergodic secrecy sum rate of a RIS-aided multi-user system over Rician fading channels,where we assume that only imperfect channel state information(CSI)is available at the base station(BS).Firstly,we obtain the deterministic approximate expression for the ergodic secrecy sum rate by resorting to the large-system approximation theory.Then the problem is formulated to maximize the downlink ergodic secrecy sum rate by optimizing the regularization coefficient of regularized zero-forcing(RZF)precoding and the phase-shifting matrix of the RIS.By using the particle swarm optimization(PSO)method,we propose an alternate optimization(AO)algorithm to solve this non-convex problem.Finally,the numerical simulations illustrate the accuracy of our large-system approximate expression as well as the effectiveness of the proposed algorithm.
文摘In the present paper we introduce the q analogue of the Baskakov Beta operators. We establish some direct results in the polynomial weighted space of continuous functions defined on the interval [0, ∞）. Then we obtain point-wise estimate, using the Lipschitz type maximal function.
基金supported by the National Nature Science Foundation of China(No.11571362)Fundamental Research Funds for the Central Universities(No.2652018054).
文摘In the present note,we consider the problem:how many interpolation nodes can be deleted from the Newman-type rational function such that the convergence rate still achieve.
基金Supported by Institute of Mathematics,State Academy of Sciences,Pyongyang,Democratic Peoples Republic of Korea。
文摘In this paper,we consider the 3-D Cauchy problem for the diffusion approximation model in radiation hydrodynamics.The existence and uniqueness of global solutions is proved in perturbation framework,for more general gases including ideal poly tropic gas.Moreover,the optimal time decay rates are obtained for higher-order spatial derivatives of density,velocity,temperature,and radiation field.
基金Supported by National Natural Science Foundation of China (61662036)。
文摘Alternating direction method of multipliers(ADMM)receives much attention in the recent years due to various demands from machine learning and big data related optimization.In 2013,Ouyang et al.extend the ADMM to the stochastic setting for solving some stochastic optimization problems,inspired by the structural risk minimization principle.In this paper,we consider a stochastic variant of symmetric ADMM,named symmetric stochastic linearized ADMM(SSL-ADMM).In particular,using the framework of variational inequality,we analyze the convergence properties of SSL-ADMM.Moreover,we show that,with high probability,SSL-ADMM has O((ln N)·N^(-1/2))constraint violation bound and objective error bound for convex problems,and has O((ln N)^(2)·N^(-1))constraint violation bound and objective error bound for strongly convex problems,where N is the iteration number.Symmetric ADMM can improve the algorithmic performance compared to classical ADMM,numerical experiments for statistical machine learning show that such an improvement is also present in the stochastic setting.
基金supported by the National Natural Science Foundation of China (Nos.11731013,11871453 and 11971089)Young Elite Scientists Sponsorship Program by CAST (No.2018QNRC001)+1 种基金Youth Innovation Promotion Association,CASFundamental Research Funds for the Central Universities,UCAS.
文摘In this paper,we study a stochastic Newton method for nonlinear equations,whose exact function information is difficult to obtain while only stochastic approximations are available.At each iteration of the proposed algorithm,an inexact Newton step is first computed based on stochastic zeroth-and first-order oracles.To encourage the possible reduction of the optimality error,we then take the unit step size if it is acceptable by an inexact Armijo line search condition.Otherwise,a small step size will be taken to help induce desired good properties.Then we investigate convergence properties of the proposed algorithm and obtain the almost sure global convergence under certain conditions.We also explore the computational complexities to find an approximate solution in terms of calls to stochastic zeroth-and first-order oracles,when the proposed algorithm returns a randomly chosen output.Furthermore,we analyze the local convergence properties of the algorithm and establish the local convergence rate in high probability.At last we present preliminary numerical tests and the results demonstrate the promising performances of the proposed algorithm.
文摘Recently,Li[16]introduced three kinds of single-hidden layer feed-forward neural networks with optimized piecewise linear activation functions and fixed weights,and obtained the upper and lower bound estimations on the approximation accuracy of the FNNs,for continuous function defined on bounded intervals.In the present paper,we point out that there are some errors both in the definitions of the FNNs and in the proof of the upper estimations in[16].By using new methods,we also give right approximation rate estimations of the approximation by Li’s neural networks.
基金This work was partially supported by the National Natural Science Foundation of China under Grant Nos. 61673159 and 61370144, and the Natural Science Foundation of Hebei Province of China under Grant No. F2016202145.
文摘Extreme learning machine （ELM） is a learning algorithm for generalized single-hidden-layer feed-forward networks （SLFNs）. In order to obtain a suitable network architecture, Incremental Extreme Learning Machine （I-ELM） is a sort of ELM constructing SLFNs by adding hidden nodes one by one. Although kinds of I-ELM-class algorithms were proposed to improve the convergence rate or to obtain minimal training error, they do not change the construction way of I-ELM or face the over-fitting risk. Making the testing error converge quickly and stably therefore becomes an important issue. In this paper, we proposed a new incremental ELM which is referred to as Length-Changeable Incremental Extreme Learning Machine （LCI-ELM）. It allows more than one hidden node to be added to the network and the existing network will be regarded as a whole in output weights tuning. The output weights of newly added hidden nodes are determined using a partial error-minimizing method. We prove that an SLFN constructed using LCI-ELM has approximation capability on a universal compact input set as well as on a finite training set. Experimental results demonstrate that LCI-ELM achieves higher convergence rate as well as lower over-fitting risk than some competitive I-ELM-class algorithms.
文摘对于O+NH反应,在~3A″和~1A″势能面(Guadagnini R,Schatz G C,Walch S P.Global potential energysurface for the lowest^1 A′,~3A″,and^1A″states of HNO[J].J.Chem.Phys.,1995,10:774)上,我们运用coupled state or centrifugal sudden(CS)近似和close coupling or Coriolis coupled(CC)方法进行了量子动力学计算.通过比较两种方法得到的总的反应几率,我们发现对于两个势能面上的标题反应,CS近似是失效的.我们还讨论了用CS和CC方法得到的速率常数,并进行了结果比较.
