The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator.The proposed approach combines a newly developed loss function with an innovative neural network a...The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator.The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the problem.These improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded domains.The authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger operators.As an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.展开更多
In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled ...In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation functions.In addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling points.As this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical interpretation.Finally,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the PILNs.To the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.展开更多
VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities.It calls Bertini or MMCRSolver for finding approximate real solutions and then applies...VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities.It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2(AIVISS)to verify the existence of a double solution(a singular solution of an arbitrary multiplicity)of a slightly perturbed polynomial system.展开更多
Gas turbine engines must be operated by means of control,and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention.The pape...Gas turbine engines must be operated by means of control,and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention.The paper considers the multivariable decoupling problems of aero-engines by using a compound controller,which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints.Two controllers are involved in the compound controller.One is a fully actuated controller and the other is classical feedback controller.In order to use fully actuated control and maintain the accuracy of engine model,a full state scheduling linear parameter-varying(LPV)modeling method is proposed based on fuzzy neural network weights.For a general input matrix of the system,its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system.Combined with a feedback controller and control limiter,the control synthesis is achieved.The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach.展开更多
The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In ...The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In particular,the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao,et al.at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu,et al.at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks.Consequently,at this state of the art,whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly,that is,the number of terms.Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now.Some effective cube construction methods were proposed for experimental cube attacks,but not applicable to division property based cube attacks.In this paper,the authors propose a heuristic cube criterion and a cube sieve algorithm,which can be combined with the three-subset division property to recover a number of superpolies.Applied to815-round Trivium,the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48.The success rate is 94.56%.There are 165 non-constant superpolies with degree less than 14.In order to demonstrate the significance of the new algorithm,the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium.The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.展开更多
This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile...This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile potential matrix,the bases of incomplete-profile potential game subspace(GPΩ)and incomplete-profile non-strategic game subspace(NΩ)are obtained.Then the bases of incomplete-profile pure potential game subspace(PΩ)and incomplete-profile pure harmonic game subspace(HΩ)are also revealed.These bases offer an expression for the orthogonal decomposition.Finally,an example is provided to verify the theoretical results.展开更多
In this paper,the formation control problem is investigated for a team of uncertain underactuated surface vessels(USVs)based on a directed graph.Considering the risk of collision and the limited communication range of...In this paper,the formation control problem is investigated for a team of uncertain underactuated surface vessels(USVs)based on a directed graph.Considering the risk of collision and the limited communication range of USVs,the prescribed performance control(PPC)methodology is employed to ensure collision avoidance and connectivity maintenance.An event-triggered mechanism is designed to reasonably use the limited communication resources.Moreover,neural networks(NNs)and an auxiliary variable are constructed to deal with the problems of uncertain nonlinearities and underactuation,respectively.Then,an event-triggered formation control scheme is proposed to ensure that all signals of the closed-loop system are uniformly ultimately bounded(UUB).Finally,simulation results are presented to demonstrate the effectiveness of the proposed control scheme.展开更多
A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy sensors.This paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from act...A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy sensors.This paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from actions,and privacy enforcement in such a context.First,the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter.Next,the authors consider a rational decision-maker that forms a private belief(posterior distribution)on the state of the world by filtering private information.The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent.In the setting of adversarial systems,the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions.Applications range from financial portfolio investments to life science decision systems.展开更多
Motivated by a medical study that attempts to analyze the relationship between growth curves and other variables and to measure the association among multiple growth curves,the authors develop a functional multiple-ou...Motivated by a medical study that attempts to analyze the relationship between growth curves and other variables and to measure the association among multiple growth curves,the authors develop a functional multiple-outcome model to decompose the total variation of multiple functional outcomes into variation explained by independent variables with time-varying coefficient functions,by latent factors and by noise.The latent factors are the hidden common factors that influence the multiple outcomes and are found through the combined functional principal component analysis approach.Through the coefficients of the latent factors one may further explore the association of the multiple outcomes.This method is applied to the multivariate growth data of infants in a real medical study in Shanghai and produces interpretable results.Convergence rates for the proposed estimates of the varying coefficient and covariance functions of the model are derived under mild conditions.展开更多
Coal is essential to ensure China’s energy security.The sudden or gradual change of coal price reflects the degree of disequilibrium or expected disequilibrium of coal supply and demand,which will not be conducive to...Coal is essential to ensure China’s energy security.The sudden or gradual change of coal price reflects the degree of disequilibrium or expected disequilibrium of coal supply and demand,which will not be conducive to energy security.Therefore,it is important to analyze the change points of coal price and explore the reason of the price fluctuation.This paper analyses the coal price from January2008 to June 2019 as the perspective of the financial market.Firstly,the PPM-DBSCAN model is used to identify the mutation point of coal price fluctuation.Secondly,path analysis is used to extract the core driving factors that affect coal price.Thirdly,the authors construct a time-varying and time-lag effect analysis model for structural changes of coal price based on the TVP-VAR model.The results show that there are 11 mutation points of coal price fluctuation.Financial market factors,coal supply and demand and alternative factors are the reasons of coal price mutation.The authors find that the imbalance of coal supply and demand in traditional view cannot fully explain the fluctuation of coal price.The impact of the financial market and non-thermal power generation have more influence on the coal price.展开更多
Based on the rational univariate representation of zero-dimensional polynomial systems,Tan and Zhang proposed the rational representation theory for solving a high-dimensional polynomial system,which uses so-called ra...Based on the rational univariate representation of zero-dimensional polynomial systems,Tan and Zhang proposed the rational representation theory for solving a high-dimensional polynomial system,which uses so-called rational representation sets to describe all the zeros of a high-dimensional polynomial system.This paper is devoted to giving an improvement for the rational representation.The idea of this improvement comes from a minimal Dickson basis used for computing a comprehensive Grobner system of a parametric polynomial system to reduce the number of branches.The authors replace the normal Grobner basis G satisfying certain conditions in the original algorithm(Tan-Zhang’s algorithm)with a minimal Dickson basis G_(m) of a Grobner basis for the ideal,where G_(m) is smaller in size than G.Based on this,the authors give an improved algorithm.Moreover,the proposed algorithm has been implemented on the computer algebra system Maple.Experimental data and its performance comparison with the original algorithm show that it generates fewer branches and the improvement is rewarding.展开更多
This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed poin...This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.展开更多
This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase.The authors first construct a stabilizing...This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase.The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics.Then,a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms.Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem,which guarantees the global asymptotical stability of the resulting switched system.Obviously,the proposed control approach can improvemore the transient state,compared to a feedback linearization based on only one diffeomorphism.Simulation studies illustrate the effectiveness of the suggested approach.展开更多
The discrete-time model of plague is deduced by zero-order holder based on the continuoustime model.Due to the existence of stochastic disturbances,the stochastic model is given corresponding to the discrete-time mode...The discrete-time model of plague is deduced by zero-order holder based on the continuoustime model.Due to the existence of stochastic disturbances,the stochastic model is given corresponding to the discrete-time model.The state estimation and noise reduction of the stochastic model are achieved by designing Kalman filter.Nuclear norm minimization is to structure the low-rank matrix approximation instead of the singular value decomposition in the process of subspace system identification.According to the plague data from the World Health Organization,the system matrices and noise intensity of the model are identified.Simulations are carried out to show the higher approximation capability of the proposed method.展开更多
This paper formulates a novel integrated measure for energy market efficiency,by investigating different aspects of the market performance.Different from most existing models focusing on one certain aspect,the novel m...This paper formulates a novel integrated measure for energy market efficiency,by investigating different aspects of the market performance.Different from most existing models focusing on one certain aspect,the novel measure especially takes into consideration the self-similarity(or system memo ability or long-term persistence)via fractality,the attractor properties in phase-space via chaos,and disorder state of data dynamics via entropy.In the proposed method,the most popular data analysis techniques of multi-fractal detrended fluctuation analysis,correlation dimension,and sample entropy are respectively conducted on the market returns to capture the corresponding features,and the entropy weight method is then used to generate the final integrated index.For illustration and verification,the proposed measure is applied to three typical energy markets analyses.The empirical results find that natural gas market and crude oil market are much more efficient than carbon market.展开更多
For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σi2= f(ui), the design points(xi, ti, ui) are known and nonrandom, g(·) and f(·) are de?ned on the closed interval [0, ...For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σi2= f(ui), the design points(xi, ti, ui) are known and nonrandom, g(·) and f(·) are de?ned on the closed interval [0, 1]. When f(·) is known, we investigate the asymptotic normality for wavelet estimators of β and g(·) under {ei, 1 ≤ i ≤ n} is a sequence of identically distributed α-mixing errors;when f(·) is unknown, the asymptotic normality for wavelet estimators of β, g(·) and f(·) are established under independent errors. A simulation study is provided to illustrate the feasibility of the theoretical result that the authors derived.展开更多
In this paper,iterative learning control(ILC)is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths.Using the two-dimensional Kalman filtering techniq...In this paper,iterative learning control(ILC)is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths.Using the two-dimensional Kalman filtering technique,the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix.It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges.The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method.Numerical simulations are provided to verify the effectiveness of the proposed framework.展开更多
This paper considers the optimal control problem of a single train,which is formulated as an optimal control problem of nonlinear systems with switching controller.The switching sequence and the switching time are dec...This paper considers the optimal control problem of a single train,which is formulated as an optimal control problem of nonlinear systems with switching controller.The switching sequence and the switching time are decision variables to be chosen optimally.Generally speaking,it is very difficult to solve this problem analytically due to its nonlinear nature,the complexity of the controller,and the existence of system state and control input constraints.To obtain the numerical solution,by introducing binary functions for every value of the control input,relaxing the binary functions,and imposing a penalty function on the relaxation,the problem is transformed into a parameter optimization problem,which can be efficiently solved by using any gradient-based numerical approach.Then,the authors propose an adaptive numerical approach to solve this problem.Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem.Finally,an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches.展开更多
In order to avoid the overcharge and overdischarge damages, and to improve the lifetime of the lithium-ion batteries, it is essential to keep the cell voltages in a battery pack at the same level,i.e., battery equaliz...In order to avoid the overcharge and overdischarge damages, and to improve the lifetime of the lithium-ion batteries, it is essential to keep the cell voltages in a battery pack at the same level,i.e., battery equalization. Based on the bi-directional modified Cuk converter, variable universe fuzzy controllers are proposed to adaptively maintain equalizing currents between cells of a serially connected battery pack in varying conditions. The inputs to the fuzzy controller are the voltage differences and the average voltages of adjacent cell pairs. A large voltage difference requires large equalizing current while adjacent cells both with low/high voltages can only stand small discharge/charge currents. Compared with the conventional fuzzy control method, the proposed method differs in that the universe can shrink or expand as the effects of the input changes. This is important as the input may change in a small range. Simulation results demonstrate that the proposed variable universe fuzzy control method has fast equalization speed and good adaptiveness for varying conditions.展开更多
Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the imp...Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.展开更多
基金supported by the National Natural Science Foundation of China under Grant Nos.12371438 and 12326336.
文摘The authors present a novel deep learning method for computing eigenvalues of the fractional Schrödinger operator.The proposed approach combines a newly developed loss function with an innovative neural network architecture that incorporates prior knowledge of the problem.These improvements enable the proposed method to handle both high-dimensional problems and problems posed on irregular bounded domains.The authors successfully compute up to the first 30 eigenvalues for various fractional Schrödinger operators.As an application,the authors share a conjecture to the fractional order isospectral problem that has not yet been studied.
基金supported by the National Natural Science Foundation of China under Grant Nos.11975143 and 12105161.
文摘In this paper,physics-informed liquid networks(PILNs)are proposed based on liquid time-constant networks(LTC)for solving nonlinear partial differential equations(PDEs).In this approach,the network state is controlled via ordinary differential equations(ODEs).The significant advantage is that neurons controlled by ODEs are more expressive compared to simple activation functions.In addition,the PILNs use difference schemes instead of automatic differentiation to construct the residuals of PDEs,which avoid information loss in the neighborhood of sampling points.As this method draws on both the traveling wave method and physics-informed neural networks(PINNs),it has a better physical interpretation.Finally,the KdV equation and the nonlinear Schr¨odinger equation are solved to test the generalization ability of the PILNs.To the best of the authors’knowledge,this is the first deep learning method that uses ODEs to simulate the numerical solutions of PDEs.
基金supported by the National Key Research Project of China under Grant No.2018YFA0306702the National Natural Science Foundation of China under Grant Nos.12171159,12071467 and 61772203Shanghai Trusted Industry Internet Software Collaborative Innovation Center。
文摘VerifyRealRoots is a Matlab package for computing and verifying real solutions of polynomial systems of equations and inequalities.It calls Bertini or MMCRSolver for finding approximate real solutions and then applies AINLSS to verify the existence of a regular solution of a polynomial system or applies AINLSS2(AIVISS)to verify the existence of a double solution(a singular solution of an arbitrary multiplicity)of a slightly perturbed polynomial system.
基金supported by National Science and Technology Major Project(2017-V-0010-0060,2017-V-0013-0065,J2019-V-0010-0104),Original exploration project of National Natural Science Foundation of China(62250056)Major Basic Research of Natural Science Foundation of Shandong Province(ZR2021ZD14)+2 种基金High-Level Talent Team Project of Qingdao West Coast New Area(RCTD-JC-2019-05)Key Research and Development Program of Shandong Province(2020CXGC01208)National Natural Science Foundation of China(51506176).
文摘Gas turbine engines must be operated by means of control,and how to achieve multivariable control decoupling with aero-engine control constraints is an open thorny issue attracting increasingly more attention.The paper considers the multivariable decoupling problems of aero-engines by using a compound controller,which originates from the fact that it is impossible to eliminate all the nonlinear dynamics of system to obtain desired constant linear closed-loop system by using full actuated control because of modeling errors and some physical constraints.Two controllers are involved in the compound controller.One is a fully actuated controller and the other is classical feedback controller.In order to use fully actuated control and maintain the accuracy of engine model,a full state scheduling linear parameter-varying(LPV)modeling method is proposed based on fuzzy neural network weights.For a general input matrix of the system,its generalized inverse is applied to design fully actuated controller to result in a pseudolinear system.Combined with a feedback controller and control limiter,the control synthesis is achieved.The simulation shows that the proposed method is possessed of a better decoupling and tracking effect compared with traditional control approach.
基金supported by the National Natural Science Foundation of China under Grant No.61672533。
文摘The cube attack proposed by Dinur and Shamir is one of the most important key-recovery attacks against Trivium.Recently division property based cube attacks have been extensively studied and significantly improved.In particular,the MILP modeling technique for the three-subset division property without unknown subset proposed by Hao,et al.at EUROCRYPT 2020 and the new technique with nested monomial predictions proposed by Hu,et al.at ASIACRYPT 2021 are best techniques to recover exact superpolies in division property based cube attacks.Consequently,at this state of the art,whether a superpoly can be recovered in division property based cube attacks is mainly decided by the scale of the superpoly,that is,the number of terms.Hence the choice for proper cubes corresponding to low-complexity superpolies is more critical now.Some effective cube construction methods were proposed for experimental cube attacks,but not applicable to division property based cube attacks.In this paper,the authors propose a heuristic cube criterion and a cube sieve algorithm,which can be combined with the three-subset division property to recover a number of superpolies.Applied to815-round Trivium,the authors recovered 417 superpolies from 441 cubes obtained by our algorithm of sizes between 41 and 48.The success rate is 94.56%.There are 165 non-constant superpolies with degree less than 14.In order to demonstrate the significance of the new algorithm,the authors tested the best superpoly recovery technique at EUROCRYPT 2020 using random cubes of similar sizes on 815-round Trivium.The experimental result shows that no cube could be completely recovered within a given period of time because the superpolies for random cubes are too complex.
基金the Natural Science Foundation of Hebei Province under Grant Nos.F2021202032,A2019202205the Cultivation of Postgraduate Students Innovation Ability of Hebei Province under Grant No.CXZZSS2021045。
文摘This work studies the orthogonal decomposition of the incomplete-profile normal finite game(IPNFG)space using the method of semi-tensor product(STP)of matrices.Firstly,by calculating the rank of the incomplete-profile potential matrix,the bases of incomplete-profile potential game subspace(GPΩ)and incomplete-profile non-strategic game subspace(NΩ)are obtained.Then the bases of incomplete-profile pure potential game subspace(PΩ)and incomplete-profile pure harmonic game subspace(HΩ)are also revealed.These bases offer an expression for the orthogonal decomposition.Finally,an example is provided to verify the theoretical results.
基金partially supported by the National Natural Science Foundation of China under Grant Nos.62033003,62003098,61973091the Local Innovative and Research Teams Project of Guangdong Special Support Program under Grant No.2019BT02X353the China Postdoctoral Science Foundation under Grant Nos.2019M662813 and 2020T130124。
文摘In this paper,the formation control problem is investigated for a team of uncertain underactuated surface vessels(USVs)based on a directed graph.Considering the risk of collision and the limited communication range of USVs,the prescribed performance control(PPC)methodology is employed to ensure collision avoidance and connectivity maintenance.An event-triggered mechanism is designed to reasonably use the limited communication resources.Moreover,neural networks(NNs)and an auxiliary variable are constructed to deal with the problems of uncertain nonlinearities and underactuation,respectively.Then,an event-triggered formation control scheme is proposed to ensure that all signals of the closed-loop system are uniformly ultimately bounded(UUB).Finally,simulation results are presented to demonstrate the effectiveness of the proposed control scheme.
基金the Wallenberg AIAutonomous Systems and Software Program(WASP)the Swedish Research Council and the Swedish Research Council Research Environment NewLEADS under contract 2016-06079。
文摘A hidden Markov model(HMM)comprises a state with Markovian dynamics that can only be observed via noisy sensors.This paper considers three problems connected to HMMs,namely,inverse filtering,belief estimation from actions,and privacy enforcement in such a context.First,the authors discuss how HMM parameters and sensor measurements can be reconstructed from posterior distributions of an HMM filter.Next,the authors consider a rational decision-maker that forms a private belief(posterior distribution)on the state of the world by filtering private information.The authors show how to estimate such posterior distributions from observed optimal actions taken by the agent.In the setting of adversarial systems,the authors finally show how the decision-maker can protect its private belief by confusing the adversary using slightly sub-optimal actions.Applications range from financial portfolio investments to life science decision systems.
基金supported by the National Natural Science Foundation of China under Grant Nos.11771146,11831008,81530086,11771145,11871252the 111 Project(B14019)Program of Shanghai Subject Chief Scientist under Grant No.14XD1401600。
文摘Motivated by a medical study that attempts to analyze the relationship between growth curves and other variables and to measure the association among multiple growth curves,the authors develop a functional multiple-outcome model to decompose the total variation of multiple functional outcomes into variation explained by independent variables with time-varying coefficient functions,by latent factors and by noise.The latent factors are the hidden common factors that influence the multiple outcomes and are found through the combined functional principal component analysis approach.Through the coefficients of the latent factors one may further explore the association of the multiple outcomes.This method is applied to the multivariate growth data of infants in a real medical study in Shanghai and produces interpretable results.Convergence rates for the proposed estimates of the varying coefficient and covariance functions of the model are derived under mild conditions.
基金supported by the National Natural Science Foundation of China under Grant No.71874133“Special Support Program for High-Level Talents”Youth Top Talent Program of Shaanxi Province,China。
文摘Coal is essential to ensure China’s energy security.The sudden or gradual change of coal price reflects the degree of disequilibrium or expected disequilibrium of coal supply and demand,which will not be conducive to energy security.Therefore,it is important to analyze the change points of coal price and explore the reason of the price fluctuation.This paper analyses the coal price from January2008 to June 2019 as the perspective of the financial market.Firstly,the PPM-DBSCAN model is used to identify the mutation point of coal price fluctuation.Secondly,path analysis is used to extract the core driving factors that affect coal price.Thirdly,the authors construct a time-varying and time-lag effect analysis model for structural changes of coal price based on the TVP-VAR model.The results show that there are 11 mutation points of coal price fluctuation.Financial market factors,coal supply and demand and alternative factors are the reasons of coal price mutation.The authors find that the imbalance of coal supply and demand in traditional view cannot fully explain the fluctuation of coal price.The impact of the financial market and non-thermal power generation have more influence on the coal price.
基金supported by the National Natural Science Foundation of China under Grant No.11801558the Chinese Universities Scientific Funds under Grant No.15059002the CAS Key Project QYZDJ-SSWSYS022。
文摘Based on the rational univariate representation of zero-dimensional polynomial systems,Tan and Zhang proposed the rational representation theory for solving a high-dimensional polynomial system,which uses so-called rational representation sets to describe all the zeros of a high-dimensional polynomial system.This paper is devoted to giving an improvement for the rational representation.The idea of this improvement comes from a minimal Dickson basis used for computing a comprehensive Grobner system of a parametric polynomial system to reduce the number of branches.The authors replace the normal Grobner basis G satisfying certain conditions in the original algorithm(Tan-Zhang’s algorithm)with a minimal Dickson basis G_(m) of a Grobner basis for the ideal,where G_(m) is smaller in size than G.Based on this,the authors give an improved algorithm.Moreover,the proposed algorithm has been implemented on the computer algebra system Maple.Experimental data and its performance comparison with the original algorithm show that it generates fewer branches and the improvement is rewarding.
基金supported by the National Natural Sciences Foundation of People’s Republic of China under Grants Nos.11861072 and 11361072.
文摘This paper considers a class of quaternion-valued Hopfield neural networks with mixed time-varying delays and leakage delays.By utilizing the exponential dichotomy of linear differential equations,Banach’s fixed point theorem and differential inequality techniques,the authors obtain some sufficient conditions to ensure the existence and global exponential stability of almost automorphic solutions for this class of quaternion-valued neural networks.The results are completely new.Finally,the authors give an example to illustrate the feasibility of the results.
文摘This paper investigates the problem of robust stabilization of a class of switched nonlinear system with uncertain dynamics where each subsystem represents a non-minimum phase.The authors first construct a stabilizing sliding mode controller for each subsystem to stabilize individually its own unstable internal dynamics.Then,a switching strategy is introduced to select the most appropriate diffeomorphism through an infinity of diffeomorphisms.Sufficient conditions are specifically given for the exponential stability and the exponential upper bound of the trajectory of the switched subsystem,which guarantees the global asymptotical stability of the resulting switched system.Obviously,the proposed control approach can improvemore the transient state,compared to a feedback linearization based on only one diffeomorphism.Simulation studies illustrate the effectiveness of the suggested approach.
基金supported by the National Natural Science Foundation of China under Grant Nos.61374137and 61773106the State Key Laboratory of Integrated Automation of Process Industry TechnologyResearch Center of National Metallurgical Automation Fundamental Research Funds under Grant No.2013ZCX02-03.
文摘The discrete-time model of plague is deduced by zero-order holder based on the continuoustime model.Due to the existence of stochastic disturbances,the stochastic model is given corresponding to the discrete-time model.The state estimation and noise reduction of the stochastic model are achieved by designing Kalman filter.Nuclear norm minimization is to structure the low-rank matrix approximation instead of the singular value decomposition in the process of subspace system identification.According to the plague data from the World Health Organization,the system matrices and noise intensity of the model are identified.Simulations are carried out to show the higher approximation capability of the proposed method.
基金supported by the Major Program of the National Fund of Philosophy and Social Science of China under Grant No.18ZDA106
文摘This paper formulates a novel integrated measure for energy market efficiency,by investigating different aspects of the market performance.Different from most existing models focusing on one certain aspect,the novel measure especially takes into consideration the self-similarity(or system memo ability or long-term persistence)via fractality,the attractor properties in phase-space via chaos,and disorder state of data dynamics via entropy.In the proposed method,the most popular data analysis techniques of multi-fractal detrended fluctuation analysis,correlation dimension,and sample entropy are respectively conducted on the market returns to capture the corresponding features,and the entropy weight method is then used to generate the final integrated index.For illustration and verification,the proposed measure is applied to three typical energy markets analyses.The empirical results find that natural gas market and crude oil market are much more efficient than carbon market.
基金supported by the National Natural Science Foundation of China under Grant Nos.11271189,11461057Science Foundation of Guangxi Education Department under Grant No.2019KY0646+1 种基金2019 Youth Teacher Research,the Development Fund Project of Guangxi University of Finance and Economics under Grant No.2019QNB07the Discipline Project of School of Information and Statistics of Guangxi University of Finance and Economics under Grant No.2019XTZZ07
文摘For the heteroscedastic regression model Yi = xiβ + g(ti) + σiei, 1 ≤ i ≤ n, where σi2= f(ui), the design points(xi, ti, ui) are known and nonrandom, g(·) and f(·) are de?ned on the closed interval [0, 1]. When f(·) is known, we investigate the asymptotic normality for wavelet estimators of β and g(·) under {ei, 1 ≤ i ≤ n} is a sequence of identically distributed α-mixing errors;when f(·) is unknown, the asymptotic normality for wavelet estimators of β, g(·) and f(·) are established under independent errors. A simulation study is provided to illustrate the feasibility of the theoretical result that the authors derived.
基金supported by the National Natural Science Foundation of China under Grant Nos.61673045and 11661016。
文摘In this paper,iterative learning control(ILC)is considered to solve the tracking problem of time-varying linear stochastic systems with randomly varying trial lengths.Using the two-dimensional Kalman filtering technique,the authors can establish a recursive framework for designing the learning gain matrix along both time and iteration axes by optimizing the trace of input error covariance matrix.It is strictly proved that the input error converges to zero asymptotically in mean square sense and thus the tracking error covariance converges.The extensions to that prior distribution of nonuniform trial lengths is unknown are also investigated with an asymptotical estimation method.Numerical simulations are provided to verify the effectiveness of the proposed framework.
基金supported by the Chinese National Natural Science Foundation under Grant Nos.61563011,61473158,61703012,and 61374006the Ph.D Research Fund of Guizhou Normal University under Grant No.11904–0514170
文摘This paper considers the optimal control problem of a single train,which is formulated as an optimal control problem of nonlinear systems with switching controller.The switching sequence and the switching time are decision variables to be chosen optimally.Generally speaking,it is very difficult to solve this problem analytically due to its nonlinear nature,the complexity of the controller,and the existence of system state and control input constraints.To obtain the numerical solution,by introducing binary functions for every value of the control input,relaxing the binary functions,and imposing a penalty function on the relaxation,the problem is transformed into a parameter optimization problem,which can be efficiently solved by using any gradient-based numerical approach.Then,the authors propose an adaptive numerical approach to solve this problem.Convergence results indicate that any optimal solution of the parameter optimization problem is also an optimal solution of the original problem.Finally,an optimal control problem of a single train illustrates that the adaptive numerical approach proposed by us is less time-consuming and obtains a better cost function value than the existing approaches.
基金supported by the National Natural Science Foundation of China under Grant Nos.61433013 and 61621002
文摘In order to avoid the overcharge and overdischarge damages, and to improve the lifetime of the lithium-ion batteries, it is essential to keep the cell voltages in a battery pack at the same level,i.e., battery equalization. Based on the bi-directional modified Cuk converter, variable universe fuzzy controllers are proposed to adaptively maintain equalizing currents between cells of a serially connected battery pack in varying conditions. The inputs to the fuzzy controller are the voltage differences and the average voltages of adjacent cell pairs. A large voltage difference requires large equalizing current while adjacent cells both with low/high voltages can only stand small discharge/charge currents. Compared with the conventional fuzzy control method, the proposed method differs in that the universe can shrink or expand as the effects of the input changes. This is important as the input may change in a small range. Simulation results demonstrate that the proposed variable universe fuzzy control method has fast equalization speed and good adaptiveness for varying conditions.
基金supported by the National Natural Science Foundation of China under Grant No.61174081
文摘Impulse observability and impulse controllability of regular degenerate evolution systems are discussed by using functional analysis and operator theory in Banach space. Necessary and sufficient conditions for the impulse observability and impulse controllability of the system are obtained. This research is theoretically important for studying the design of the degenerate evolution system.
