为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式...为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。展开更多
The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)metho...The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.展开更多
A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue prob...A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).展开更多
Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular s...Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.展开更多
During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive...During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.展开更多
To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approxima...To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.展开更多
Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase appro...Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase approximation.This approach successfully highlights the dominance of the chiral p-wave pairing between electrons with the same spin and valley index at low densities,while also predicting the superconducting range in agreement with experimental findings.Furthermore,we examine the characteristics of distinct superconducting regions:SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations,whereas SC4 displays zero-momentum spin-singlet superconductivity.展开更多
LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the...LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.展开更多
State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constraine...State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constrained solution,which not only offers flexibility by activating constraints just during specific time periods of interest to the user,but also successfully accommodates different types of constraint boundaries.The innovative shifting functions are proposed to facilitate seamless transitions between constrained and unconstrained operational phases,resulting in more user-friendly design and implementation.By blending an improved shifting transformation into intermittent constraint design,we construct a universal barrier function upon the constrained states,with which our control strategy removes the limitations on constraint functions and completely obviates the feasibility conditions.Furthermore,a modified fuzzy approximator driven by the prediction error rather than the tracking error achieves decoupling of the control and estimation loops,which not only ensures the estimation performance,but also facilitates proof of stability.Finally,the effectiveness of the proposed scheme is assessed by numerical simulation.展开更多
文摘为构建综合能源系统安全域(integrated energy system security region,IESSR),该文提出一种基于多项式混沌展开(polynomial chaos expansion,PCE)的IESSR边界(IESR boundary,IESSRB)近似方法,借助该方法可得IESSRB的多项式逼近表达式。首先,根据IESSRB的边界拓扑特性,构建系统的IESSR边界点搜索优化模型;然后,根据PCE,对IESSR边界点搜索优化模型进行参数化处理,构建IESSRB搜索的参数化优化模型;进一步地,根据IESSRB搜索的参数化优化模型的KKT条件,将IESSRB的参数化优化模型转化为高维参数化非线性方程组;在此基础上,借助广义Galerkin投影构建关于近似IESSRB的多项式逼近系数的Galerkin投影方程组,通过求解该方程组可得IESSRB的多项式逼近系数,从而获得IESSRB的多项式逼近表达式;为进一步降低Galerkin投影方程组求解复杂度,提出多项式分段近似IESSRB方法,在提高IESSRB近似精度的同时,提升了IESSRB近似的计算效率;最后,通过IES E39-G20测试系统和IES E118-G96测试系统对所提方法进行分析、验证。结果表明,所提方法可实现IESSR的准确、有效构建。
基金supported by the National Natural Science Foundation of China[grant number 12001266]the Humanities and Social Science Projects ofMinistry of Education of China[grant number 19YJCZH166]supported by the National Natural Science Foundation of China[grant numbers 12271168 and 12531013].
文摘The integrated nested Laplace approximation(INLA)algorithm provides a computationally efficient approach for approximate Bayesian inference,overcoming the limitations of traditional Markov chain Monte Carlo(MCMC)methods.This paper reviews INLA algorithm and provides a systematic review of six key books that explore the theoretical foundations,practical implementations,and diverse applications of INLA.These six books cover spatial and spatio-temporal modelling,general Bayesian inference,SPDE-based spatial analysis,geospatial health data,regression modelling,and dynamic time series.In addition,these books highlight the versatility of INLA method in handling complex models while maintaining high computational efficiency.This paper begins with an introduction to the INLA method and algorithm,followed by a systematic review of six key publications in the field.
基金supported by the National Natural Science Foundation of China(12401482)the second author was supported by the National Natural Science Foundation of China(12371371,12261160361,11971366)supported by the Open Research Fund of Hubei Key Laboratory of Computational Science,Wuhan University.
文摘A new quadrilateral edge element method is proposed and analyzed for Maxwell equations.This proposed method is based on Duan-Liang quadrilateral element(Math.Comp.73(2004),pp.1–18).When applied to the eigenvalue problem,the method is spectral-correct and spurious-free.Stability and error estimates are obtained,including the interpolation error estimates and the error estimates between the finite element solution and the exact solution.The method is suitable for singular solution as well as smooth solution,and consequently,the method is valid for nonconvex domains which may have a number of reentrant corners.Of course,the method is suitable for arbitrary quadrilaterals(under the usual shape-regular condition).
基金Supported by the Natural Science Foundation of Shandong Province (No.ZR2023MA031)the Natural Science Foundation of China (No.12201619)。
文摘Submodular optimization is primarily applied in multi-agent systems for tasks such as resource allocation,task assignment,collaborative decision-making,and optimization problems.Maximization of optimizing submodular set functions attracts much attention since the 1970s.A large body of work has been done using approximation algorithms.When the dimension of the independent variable of the set function changes from one tok,it is called ak-submodular set function.Thek-submodular set function,a generalization of the classical submodular set function,arises in diverse fields with varied applications.In many practical scenarios,quantifying the degree of closeness to submodularity becomes essential,leading to concepts such as approximately submodular set functions and the diminishing-return(DR) ratio.This paper investigates ak-dimensional set function under matroid constraints,which may lack full submodularity.Instead,we focus on an approximately non-ksubmodular set function characterized by its DR ratio.Employing a greedy algorithmic approach,we derive an approximation guarantee for this problem.Notably,when the DR ratio is set to one,our results align with existing findings in the literature.Experimental results demonstrate the superiority of our algorithm over the baselines.
基金supported by the National Natural Sci‐ence Foundation of China(Grant No.62306325)。
文摘During the use of robotics in applications such as antiterrorism or combat,a motion-constrained pursuer vehicle,such as a Dubins unmanned surface vehicle(USV),must get close enough(within a prescribed zero or positive distance)to a moving target as quickly as possible,resulting in the extended minimum-time intercept problem(EMTIP).Existing research has primarily focused on the zero-distance intercept problem,MTIP,establishing the necessary or sufficient conditions for MTIP optimality,and utilizing analytic algorithms,such as root-finding algorithms,to calculate the optimal solutions.However,these approaches depend heavily on the properties of the analytic algorithm,making them inapplicable when problem settings change,such as in the case of a positive effective range or complicated target motions outside uniform rectilinear motion.In this study,an approach employing a high-accuracy and quality-guaranteed mixed-integer piecewise-linear program(QG-PWL)is proposed for the EMTIP.This program can accommodate different effective interception ranges and complicated target motions(variable velocity or complicated trajectories).The high accuracy and quality guarantees of QG-PWL originate from elegant strategies such as piecewise linearization and other developed operation strategies.The approximate error in the intercept path length is proved to be bounded to h^(2)/(4√2),where h is the piecewise length.
基金The National Natural Science Foundation of China(No.62172443).
文摘To address the issue that static densest subgraph mining algorithms often exhibit low efficiency when handling large scale dynamic graphs,this paper proposes a heuristic approximation algorithm.The algorithm approximates the densest k-subgraphs of the entire graph through four steps:partitioning the large-scale dynamic graph,constructing a partial set of the densest k-subgraphs,heuristically merging the subgraph sets,and finally extracting the densest k-subgraphs.This approach significantly reduces the computational time for large-scale dynamic graphs while simultaneously improving the quality of the resulting subgraphs.This algorithm is applicable to various definitions of“density”and can accommodate diverse requirements on the number of edges.When integrated with existing static densest subgraph detection algorithms,it achieves scalability and computational efficiency.Theoretical analysis demonstrates that the optimal density of the densest k-subgraphs extracted by the proposed algorithm reaches 0.9.To evaluate the performance of the algorithm,experiments were conducted on four billion-scale datasets:Friendster,Orkut,YouTube,and DBLP.The results indicate that the proposed algorithm outperforms static methods in both runtime efficiency and subgraph quality on large-scale dynamic graphs.
基金supported by the National Natural Science Foundation of China (Grant Nos.12447125,12234016,and 12174317)the New Cornerstone Science Foundation。
文摘Motivated by the recent experimental discovery of superconductivity in rhombohedral tetralayer graphene,we investigate the pairing mechanism arising from the density–density interactions within the random-phase approximation.This approach successfully highlights the dominance of the chiral p-wave pairing between electrons with the same spin and valley index at low densities,while also predicting the superconducting range in agreement with experimental findings.Furthermore,we examine the characteristics of distinct superconducting regions:SC1 and SC2 exhibit chiral finite-momentum superconductivity with pronounced phase fluctuations,whereas SC4 displays zero-momentum spin-singlet superconductivity.
基金supported by the Scientific Research Project of Colleges and Universities in Anhui Province(2024AH050016)supported by the NSFC(12171172).The third author was supported by the NSFC(12201476)the Fundamental Research Funds for the Central Universities.
文摘LetΨ={ψn}n≥1 be an iterated function system(IFS)on[0,1]with attractor J.Associated with each x∈J,there is a sequence{ωn(x)}n≥1 consisting of integers,called the digit sequence of x,such that■((1))We revisit the Borel-Bernstein theorem in a d-decaying Gauss-like IFS,and completely characterize the metrical properties of the set■whereΦ:ℕ→ℝis a positive function.
基金supported by the Fundamental Research Funds for the Central Universities(N2404005)the National Key Research and Development Program of China(2018YFA0702200)+2 种基金Liaoning Revitalization Talents Program(XLYC1801005)the National Natural Science Foundation of China(U23B20118)the Nature Science Foundation of Liaoning Province of China(2022JH25/10100008)。
文摘State constraints in nonlinear systems are commonly pursued by resorting to barrier functions,which enforce constraints over the entire duration of system operation.We propose a universal intermittent state-constrained solution,which not only offers flexibility by activating constraints just during specific time periods of interest to the user,but also successfully accommodates different types of constraint boundaries.The innovative shifting functions are proposed to facilitate seamless transitions between constrained and unconstrained operational phases,resulting in more user-friendly design and implementation.By blending an improved shifting transformation into intermittent constraint design,we construct a universal barrier function upon the constrained states,with which our control strategy removes the limitations on constraint functions and completely obviates the feasibility conditions.Furthermore,a modified fuzzy approximator driven by the prediction error rather than the tracking error achieves decoupling of the control and estimation loops,which not only ensures the estimation performance,but also facilitates proof of stability.Finally,the effectiveness of the proposed scheme is assessed by numerical simulation.
