A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main...A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main subsystems:a converting system,an input/output system,and an operating system.The converting system is a software component that transforms the target problem into the graph coloring problem,while the operating system is designed to solve these graph coloring challenges.Comprised of 60 probe computing cards,this system is referred to as EPC60.In tackling large-scale graph coloring problems with EPC60,1003-colorable graphs were randomly selected,each consisting of 2,000 vertices.The state-of-the-art mathematical optimization solver achieved a success rate of only 6%,while EPC60 excelled with a remarkable 100%success rate.Additionally,EPC60 successfully solved two 3-colorable graphs with 1,500 and 2,000 vertices,which had eluded Gurobi’s attempts for 15 days on a standard workstation.Given the mutual reducibility of NP-complete problems in polynomial time theoretically,the EPC stands out as a universal solver for NP-complete problem.The EPC can be applied to various problems that can be abstracted as combinatorial optimization issues,making it relevant across multiple domains,including supply chain management,financial services,telecommunications,energy systems,manufacturing,and beyond.展开更多
Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical signifi...Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage.Here,we present a reconfigurable integrated photonic processor to efficiently solve a benchmark NP-complete problem,the subset sum problem.We show that in the case of successive primes,the photonic processor has genuinely surpassed electronic processors launched recently by taking advantage of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology.Moreover,we are able to program the photonic processor to tackle different problem instances,relying on the tunable integrated modules,variable split junctions,which can be used to build a fully reconfigurable architecture potentially allowing 2^(N) configurations at most.Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform,suggesting a possible practical route to solving computationally hard problems at a large scale.展开更多
We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for ...We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.展开更多
In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s phe...In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.展开更多
The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the hom...The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments.This world-wide network has yet to match the complexity of the human brain,which contains a hundred billion neurons,each with thousands of synaptic connections on average.However,it already exceeds the complexity of brains from primitive organisms,i.e.,the honey bee,which has a brain containing approximately one million neurons.In this study,we present a discussion of the computing potential of optical networks as information carriers.Using a simple fiber network,we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem,the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once.Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network,and this delay will be equal to the sum of the travel times needed to visit all of the nodes(towns).We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing.Additionally,we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.展开更多
Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery...Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.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
The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, ...The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution （QKD）, which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors＇ results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure （in case that P, NP） or infrastructures facilitating perfectly confidential communication can be constructed efficiently （in case that P = NP）.展开更多
Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(...Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].展开更多
Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2))...Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.展开更多
Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the fo...Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.展开更多
BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current statu...BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current status of family rearing,parental stress,and behavioral and emotional problems of preschool children and to analyze the mediating effect of the current status of family rearing on parental stress and behavioral/emo-tional problems.METHODS We use convenience sampling to select 258 preschool children in the physical examination center of our hospital from October 2021 to September 2023.The children and their parents were evaluated using a questionnaire survey.Pearson's correlation was used to analyze the correlation between child behavioral and emotional problems and parental stress and family rearing,and the structural equation model was constructed to test the mediating effect.RESULTS The score for behavioral/emotional problems of 258 preschool children was(27.54±3.63),the score for parental stress was(87.64±11.34),and the score for parental family rearing was(31.54±5.24).There was a positive correlation between the behavioral and emotional problems of the children and the“hostile/mandatory”parenting style;meanwhile,showed a negative correlation with the“support/participation”parenting style(all P<0.05).The intermediary effect value between the family upbringing of parents in parental stress and children's behavior problems was 29.89%.CONCLUSION Parental family upbringing has a mediating effect between parental stress and behavioral and emotional problems of children.Despite paying attention to the behavioral and emotional problems of preschool-age children,clinical medical staff should provide correct and reasonable parenting advice to their parents to promote the mental health of preschool-age children.展开更多
This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as resul...This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as result of being victimized at school by the peers. The aim was to assess and manage the child’s aggressive behavior and academic underperformance which played a significant role in the child’s low self-esteem and emotional regulation. A comprehensive assessment was conducted to rule out the difficulties and a multi-faceted intervention strategy was utilized including anger management and structured activity scheduling that helped that child to improve his academic performance as well as to learn to manage his emotional expression. Throughout 16 sessions, the intervention targeted key behavioural indicators such as emotional expression, and aggression;post-assessment results demonstrated a 22% improvement in the child’s behavioral and academic challenges. The findings suggest that a multi-faceted therapeutic approach can be effective in addressing complex issues of aggression and academic underperformance in children, highlighting the importance of integrated psychological and educational interventions.展开更多
Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either dire...Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.展开更多
This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the chara...This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.展开更多
In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,where...In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.展开更多
As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production an...As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production and processing.In view of this situation,this paper comprehensively expounded and decomposed the cultivation situation,existing problems,specific countermeasures and conclusions,so as to re-recognize them.This study provides reference materials for the sustainable and healthy development of the soybean industry.展开更多
1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4...1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4 hours,they meet at a point that is 4 kilometres away from the midpoint between their starting points.A walks faster than B.How many more kilometres per hour does A walk than B?展开更多
A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoot...A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoothing technologies.Some important properties of the proposed novel equivalent model are summarized.In addition,the stability properties of the proposed steepest descent-based neural networks for LCP are analyzed.In order to illustrate the theoretical results,we provide some numerical simulations and compare the proposed neural networks with existing neural networks based on the NCP-functions.Numerical results indicate that the performance of the proposed neural networks is effective and robust.展开更多
基金supported by the National Major Research Instrument Development Project(62427811)the Key Program of the National Natural Science Foundation of China(62332006)the General Program of the National Natural Science Foundation of China(62172014).
文摘A specialized computer named as the Electronic Probe Computer(EPC)has been developed to address large-scale NP-complete problems.The EPC employs a hybrid serial/parallel computational model,structured around four main subsystems:a converting system,an input/output system,and an operating system.The converting system is a software component that transforms the target problem into the graph coloring problem,while the operating system is designed to solve these graph coloring challenges.Comprised of 60 probe computing cards,this system is referred to as EPC60.In tackling large-scale graph coloring problems with EPC60,1003-colorable graphs were randomly selected,each consisting of 2,000 vertices.The state-of-the-art mathematical optimization solver achieved a success rate of only 6%,while EPC60 excelled with a remarkable 100%success rate.Additionally,EPC60 successfully solved two 3-colorable graphs with 1,500 and 2,000 vertices,which had eluded Gurobi’s attempts for 15 days on a standard workstation.Given the mutual reducibility of NP-complete problems in polynomial time theoretically,the EPC stands out as a universal solver for NP-complete problem.The EPC can be applied to various problems that can be abstracted as combinatorial optimization issues,making it relevant across multiple domains,including supply chain management,financial services,telecommunications,energy systems,manufacturing,and beyond.
基金supported by the National Key R&D Program of China (Grants Nos. 2019YFA0308703, 2019YFA07063022017YFA0303700)+7 种基金the National Natural Science Foundation of China (NSFC)(Grant Nos. 62235012, 12104299,61734005, 11761141014, 11690033, 11904299, and 12304342)the Innovation Program for Quantum Science and Technology(Grant Nos. 2021ZD0301500 and 2021ZD0300700)the Science and Technology Commission of Shanghai Municipality(STCSM)(Grant Nos. 20JC1416300, 2019SHZDZX01,21ZR1432800, and 22QA1404600)the Shanghai Municipal Education Commission (SMEC)(Grant No. 2017-01-07-00-02-E00049)the China Postdoctoral Science Foundation (Grant Nos. 2022T150415, 2021M692094, and 2020M671091)the Startup Fund for Young Faculty at SJTU (SFYF at SJTU)additional support from a Shanghai Talent Programsupport from the Zhiyuan Innovative Research Center of Shanghai Jiao Tong University
文摘Nondeterministic-polynomial-time(NP)-complete problems are widely involved in various reallife scenarios but are still intractable in being solved efficiently on conventional computers.It is of great practical significance to construct versatile computing architectures that solve NP-complete problems with computational advantage.Here,we present a reconfigurable integrated photonic processor to efficiently solve a benchmark NP-complete problem,the subset sum problem.We show that in the case of successive primes,the photonic processor has genuinely surpassed electronic processors launched recently by taking advantage of the high propagation speed and vast parallelism of photons and state-of-the-art integrated photonic technology.Moreover,we are able to program the photonic processor to tackle different problem instances,relying on the tunable integrated modules,variable split junctions,which can be used to build a fully reconfigurable architecture potentially allowing 2^(N) configurations at most.Our experiments confirm the potential of the photonic processor as a versatile and efficient computing platform,suggesting a possible practical route to solving computationally hard problems at a large scale.
文摘We propose the usage of formal languages for expressing instances of NP-complete problems for their application in polynomial transformations. The proposed approach, which consists of using formal language theory for polynomial transformations, is more robust, more practical, and faster to apply to real problems than the theory of polynomial transformations. In this paper we propose a methodology for transforming instances between NP-complete problems, which differs from Garey and Johnson's. Unlike most transformations which are used for proving that a problem is NP-complete based on the NP-completeness of another problem, the proposed approach is intended for extrapolating some known characteristics, phenomena, or behaviors from a problem A to another problem B. This extrapolation could be useful for predicting the performance of an algorithm for solving B based on its known performance for problem A, or for taking an algorithm that solves A and adapting it to solve B.
文摘In this paper we hybridize ant colony optimiza- tion （ACt） and river formation dynamics （RFD）, two related swarm intelligence methods. In ACt, ants form paths （prob- lem solutions） by following each other＇s pheromone trails and reinforcing trails at best paths until eventually a single path is followed. On the other hand, RFD is based on copy- ing how drops form rivers by eroding the ground and de- positing sediments. In a rough sense, RFD can be seen as a gradient-oriented version of ACt. Several previous experi- ments have shown that the gradient orientation of RFD makes this method solve problems in a different way as ACt. In particular, RFD typically performs deeper searches, which in turn makes it find worse solutions than ACt in the first exe- cution steps in general, though RFD solutions surpass ACt solutions after some more time passes. In this paper we try to get the best features of both worlds by hybridizing RFD and ACt. We use a kind of ant-drop hybrid and consider both pheromone trails and altitudes in the environment. We apply the hybrid method, as well as ACt and RFD, to solve two NP-hard problems where ACt and RFD fit in a different manner： the traveling salesman problem （TSP） and the prob- lem of the minimum distances tree in a variable-cost graph （MDV）. We compare the results of each method and we an- alyze the advantages of using the hybrid approach in each case.
基金This work was supported by the Singapore Ministry of Education Academic Research Fund Tier 3(Grant No.MOE2011-T3-1-005)the Singapore Agency for Science,Technology and Research(A*STAR,SERC Project No.1223600007)EPSRC(UK)via the Programme on Nanostructured Photonic Metamaterials.
文摘The modern information society is enabled by photonic fiber networks characterized by huge coverage and great complexity and ranging in size from transcontinental submarine telecommunication cables to fiber to the home and local segments.This world-wide network has yet to match the complexity of the human brain,which contains a hundred billion neurons,each with thousands of synaptic connections on average.However,it already exceeds the complexity of brains from primitive organisms,i.e.,the honey bee,which has a brain containing approximately one million neurons.In this study,we present a discussion of the computing potential of optical networks as information carriers.Using a simple fiber network,we provide a proof-of-principle demonstration that this network can be treated as an optical oracle for the Hamiltonian path problem,the famous mathematical complexity problem of finding whether a set of towns can be travelled via a path in which each town is visited only once.Pronouncement of a Hamiltonian path is achieved by monitoring the delay of an optical pulse that interrogates the network,and this delay will be equal to the sum of the travel times needed to visit all of the nodes(towns).We argue that the optical oracle could solve this NP-complete problem hundreds of times faster than brute-force computing.Additionally,we discuss secure communication applications for the optical oracle and propose possible implementation in silicon photonics and plasmonic networks.
基金Supported by the Natural Science Foundation of Guangxi Province(Grant Nos.2023GXNSFAA026067,2024GXN SFAA010521)the National Natural Science Foundation of China(Nos.12361079,12201149,12261026).
文摘Convex feasibility problems are widely used in image reconstruction,sparse signal recovery,and other areas.This paper is devoted to considering a class of convex feasibility problem arising from sparse signal recovery.We rst derive the projection formulas for a vector onto the feasible sets.The centralized circumcentered-reection method is designed to solve the convex feasibility problem.Some numerical experiments demonstrate the feasibility and e ectiveness of the proposed algorithm,showing superior performance compared to conventional alternating projection methods.
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.
文摘The problem of perfectly secure communication has enjoyed considerable theoretical treatment over the last decades. Results in this area include the identification of multipath transmission as a necessary ingredient, as well as quantum key distribution （QKD）, which can perfectly protect direct lines, Combining the advantages of the quantum and multipath transmission paradigm, as well as rigorously analyzing the security of such combined techniques, is possible by virtue of game-theory. Based on a game-theoretic measure of channel vulnerability, the authors prove the problem of setting up infrastructures for QKD-based multipath transmission to be NP-complete. The authors consider the problem in two flavors, both being computationally hard. Remarkably, the authors＇ results indicate that the P-vs-NP-question is only of minor effect for confidentiality, because either nowadays public-key cryptosystems remain secure （in case that P, NP） or infrastructures facilitating perfectly confidential communication can be constructed efficiently （in case that P = NP）.
基金Supported by NSFC (Nos.12471009,12301006,12001047,11901566)Beijing Natural Science Foundation (No.1242003)National Training Program of Innovation and Entrepreneurship for Undergraduates(No.202307011)。
文摘Let Pr denote an almost-prime with at most r prime factors,counted according to multiplicity.In this paper,it is proved that,for every sufficiently large even integer N,the equation N=x^(2)+p_(2)^(2)+p_(3)^(3)+p_(4)^(3)+p_(5)^(5)+_6^(5)is solvable with being an almost-prime P_(6) and the other variables primes.This result constitutes an enhancement upon the previous result of Hooley[Recent Progress in Analytic Number Theory,Vol.1(Durham,1979),London:Academic Press,1981,127-191].
基金supported by the Talent Fund of Beijing Jiaotong University(No.2020RC012)NSFC(No.11871295),supported by NSFC(No.11971476),supported by NSFC(No.12071421)。
文摘Let d(n;r_(1),q_(1),r_(2),q_(2))be the number of factorization n=n_(1)n_(2)satisfying n_i≡r_i(mod q_i)(i=1,2)andΔ(x;r_(1),q_(1),r_(2),q_(2))be the error term of the summatory function of d(n;r_(1),q_(1),r_(2),q_(2)).Suppose x≥(q_(1)q_(2))^(1+ε),1≤r_i≤q_i,and(r_i,q_i)=1(i=1,2).This paper studies the power moments and sign changes ofΔ(x;r_(1),q_(1),r_(2),q_(2)).We prove that for sufficiently large constant C,Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))changes sign in the interval[T,T+C√T]for any large T.Meanwhile,we show that for small constants c and c,there exist infinitely many subintervals of length c√log^(-7)T in[T,2T]where±Δ(q_(1)q_(2)x:r_(1),q_(1),r_(2),q_(2))>cx^(1/4)always holds.
基金supported by the National Natural Science Foundation of China(62106244)the Fundamental Research Funds for the Central Universities(WK2150110021)the University Synergy Innovation Program of Anhui Province(GXXT-2022-042).
文摘Automatically answer math word problems is a challenging task in artificial intelligence.Previous solvers constructed mathematical expressions in sequence or binary tree.However,these approaches may suffer from the following issues:Models relying on such structures exhibit fixed-order reasoning(e.g.,left-to-right),limiting flexibility and increasing error susceptibility;prior models rely on autoregressive reasoning in a single pass,accumulating minor errors(e.g.,incorrect math symbols)during generation,resulting in reduced accuracy.To address the above issues,we emulate the human“check and modify”process in reasoning and propose a unified M-tree self-correction solver(UTSCSolver)by iterative inference with self-correction mechanism.First,we use an iterative,non-autoregressive process for generating mathematical expressions,free from fixed generation orders to handle complex and diverse problems.Additionally,we design a self-correction mechanism based on alternating execution between a generator and a discriminator.This module iteratively detects and rectifies errors in generated expressions,leveraging previous iteration information for subsequent generation guidance.Experimental results show that our UTSC-Solver outperforms traditional models in accuracy on two popular datasets,while it improves the interpretability of mathematical reasoning.
基金Supported by the Shijiazhuang Science and Technology Research and Development Program,No.221460383.
文摘BACKGROUND Emotional reactions,such as anxiety,irritability,and aggressive behavior,have attracted clinical attention as behavioral and emotional problems in preschool-age children.AIM To investigate the current status of family rearing,parental stress,and behavioral and emotional problems of preschool children and to analyze the mediating effect of the current status of family rearing on parental stress and behavioral/emo-tional problems.METHODS We use convenience sampling to select 258 preschool children in the physical examination center of our hospital from October 2021 to September 2023.The children and their parents were evaluated using a questionnaire survey.Pearson's correlation was used to analyze the correlation between child behavioral and emotional problems and parental stress and family rearing,and the structural equation model was constructed to test the mediating effect.RESULTS The score for behavioral/emotional problems of 258 preschool children was(27.54±3.63),the score for parental stress was(87.64±11.34),and the score for parental family rearing was(31.54±5.24).There was a positive correlation between the behavioral and emotional problems of the children and the“hostile/mandatory”parenting style;meanwhile,showed a negative correlation with the“support/participation”parenting style(all P<0.05).The intermediary effect value between the family upbringing of parents in parental stress and children's behavior problems was 29.89%.CONCLUSION Parental family upbringing has a mediating effect between parental stress and behavioral and emotional problems of children.Despite paying attention to the behavioral and emotional problems of preschool-age children,clinical medical staff should provide correct and reasonable parenting advice to their parents to promote the mental health of preschool-age children.
文摘This case study explores the efficacy of school-based intervention to address psychosocial challenges faced by an 11-year-old adolescent. The case study aimed to decrease the agression and acting out behavior as result of being victimized at school by the peers. The aim was to assess and manage the child’s aggressive behavior and academic underperformance which played a significant role in the child’s low self-esteem and emotional regulation. A comprehensive assessment was conducted to rule out the difficulties and a multi-faceted intervention strategy was utilized including anger management and structured activity scheduling that helped that child to improve his academic performance as well as to learn to manage his emotional expression. Throughout 16 sessions, the intervention targeted key behavioural indicators such as emotional expression, and aggression;post-assessment results demonstrated a 22% improvement in the child’s behavioral and academic challenges. The findings suggest that a multi-faceted therapeutic approach can be effective in addressing complex issues of aggression and academic underperformance in children, highlighting the importance of integrated psychological and educational interventions.
基金funded by the National Key R&D Program of China(Grant No.2024YFE0102500)the National Natural Science Foundation of China(Grant No.12404568)+1 种基金the Guangzhou Municipal Science and Technology Project(Grant No.2023A03J00904)the Quantum Science Center of Guangdong-Hong Kong-Macao Greater Bay Area,China and the Undergraduate Research Project from HKUST(Guangzhou).
文摘Constraint satisfaction problems(CSPs)are a class of problems that are ubiquitous in science and engineering.They feature a collection of constraints specified over subsets of variables.A CSP can be solved either directly or by reducing it to other problems.This paper introduces the Julia ecosystem for solving and analyzing CSPs with a focus on the programming practices.We introduce some important CSPs and show how these problems are reduced to each other.We also show how to transform CSPs into tensor networks,how to optimize the tensor network contraction orders,and how to extract the solution space properties by contracting the tensor networks with generic element types.Examples are given,which include computing the entropy constant,analyzing the overlap gap property,and the reduction between CSPs.
基金supported by the Tianjin Municipal Science and Technology Program of China(No.23JCZDJC00070)。
文摘This paper focuses on the direct and inverse problems for a third-order self-adjoint differential operator with non-local potential and anti-periodic boundary conditions.Firstly,we obtain the expressions for the characteristic function and resolvent of this third-order differential operator.Secondly,by using the expression for the resolvent of the operator,we prove that the spectrum for this operator consists of simple eigenvalues and a finite number of eigenvalues with multiplicity 2.Finally,we solve the inverse problem for this operator,which states that the non-local potential function can be reconstructed from four spectra.Specially,we prove the Ambarzumyan theorem and indicate that odd or even potential functions can be reconstructed by three spectra.
基金supported by the National Natural Science Foundation of China under Grant No.12147115the Discipline(Subject)Leader Cultivation Project of Universities in Anhui Province under Grant Nos.DTR2023052 and DTR2024046+2 种基金the Natural Science Research Project of Universities in Anhui Province under Grant No.2024AH040202the Young Top Notch Talents and Young Scholars of High End Talent Introduction and Cultivation Action Project in Anhui Provincethe Scientific Research Foundation Funded Project of Chuzhou University under Grant Nos.2022qd022 and 2022qd038。
文摘In this paper,we use the Riemann-Hilbert(RH)method to investigate the Cauchy problem of the reverse space-time nonlocal Hirota equation with step-like initial data:q(z,0)=o(1)as z→-∞and q(z,0)=δ+o(1)as z→∞,whereδis an arbitrary positive constant.We show that the solution of the Cauchy problem can be determined by the solution of the corresponding matrix RH problem established on the plane of complex spectral parameterλ.As an example,we construct an exact solution of the reverse space-time nonlocal Hirota equation in a special case via this RH problem.
基金Supported by Special Fund for National Modern Agricultural Industry Technology System Construction(CARS-04-CES16).
文摘As one of the world's three major food crops and an important economic and oil crop,soybean plays a crucial role in ensuring food safety.In recent years,there are many problems in soybean cultivation,production and processing.In view of this situation,this paper comprehensively expounded and decomposed the cultivation situation,existing problems,specific countermeasures and conclusions,so as to re-recognize them.This study provides reference materials for the sustainable and healthy development of the soybean industry.
文摘1.The price of a desk is 10 times the price of a chair.The desk costs 288 yuan more than the chair.How much does one desk and one chair cost?2.A and B start from two different places and walk toward each other.After 4 hours,they meet at a point that is 4 kilometres away from the midpoint between their starting points.A walks faster than B.How many more kilometres per hour does A walk than B?
基金Supported by the National Natural Science Foundation of China(12371378,41725017,11901098).
文摘A family of neural networks is proposed to solve linear complementarity problems(LCP).The neural networks are constructed from the novel equivalent model of LCP,which is reformulated by utilizing the modulus and smoothing technologies.Some important properties of the proposed novel equivalent model are summarized.In addition,the stability properties of the proposed steepest descent-based neural networks for LCP are analyzed.In order to illustrate the theoretical results,we provide some numerical simulations and compare the proposed neural networks with existing neural networks based on the NCP-functions.Numerical results indicate that the performance of the proposed neural networks is effective and robust.
