This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the...This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.展开更多
Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control s...Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.展开更多
In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given se...In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.展开更多
China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families ...China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families spend more outlay on cultural products and services.Within this flourishing industry,many museums caught development opportunities and began to get profit through successfully promoting their own cultural and creative products.However,it is unusual that Emperor Qinshihuang’s Mausoleum Site Museum,enjoying high social status and a reputation for world cultural heritage as well as a national 5A level tourist attraction,regretfully,did not achieve noticeable achievements in this area.Therefore,based on STP theory,the purpose of this paper is to study the reasons why this museum fails to fulfill its potential in promising cultural and creative industry and give some suggestions to the development and promotion of its cultural and creative goods.展开更多
An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds ...An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.展开更多
Boolean satisfiability (SAT) is widely used as a solver engine in electronic design automation (EDA). Typically, SAT is used to determine whether one or more groups of variables can be combined to form a true formula....Boolean satisfiability (SAT) is widely used as a solver engine in electronic design automation (EDA). Typically, SAT is used to determine whether one or more groups of variables can be combined to form a true formula. All solutions SAT (AllSAT) is a variant of the SAT problem. In the fields of formal verification and pattern generation, AllSAT is particularly useful because it efficiently enumerates all possible solutions. In this paper, a semi-tensor product (STP) based AllSAT solver is proposed. The solver can solve instances described in both the conjunctive normal form (CNF) and circuit form. The implementation of our method differs from incremental enumeration because we do not add blocking conditions for existing solutions, but rather compute the matrices to obtain all the solutions in one pass. Additionally, the logical matrices support a variety of logic operations. Results from experiments with MCNC benchmarks using CNF-based and circuit-based forms show that our method can accelerate CPU time by 8.1x (238x maximum) and 19.9x (72x maximum), respectively.展开更多
The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders an...The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases.Three different types of hyperdeterminants are introduced and certain properties are revealed.The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed.Finally,these results are applied to dynamical systems.展开更多
文摘This paper investigates the networked evolutionary model based on snow-drift game with the strategy of rewards and penalty. Firstly, by using the semi-tensor product of matrices approach, the mathematical model of the networked evolutionary game is built. Secondly, combined with the matrix expression of logic, the mathematical model is expressed as a dynamic logical system and next converted into its evolutionary dynamic algebraic form. Thirdly, the dynamic evolution process is analyzed and the final level of cooperation is discussed. Finally, the effects of the changes in the rewarding and penalty factors on the level of cooperation in the model are studied separately, and the conclusions are verified by examples.
基金supported by the National Natural Science Foundation of China (62273201,62173209,72134004,62303170)the Research Fund for the Taishan Scholar Project of Shandong Province of China (TSTP20221103)。
文摘Set stabilization is one of the essential problems in engineering systems, and self-triggered control(STC) can save the storage space for interactive information, and can be successfully applied in networked control systems with limited communication resources. In this study, the set stabilization problem and STC design of Boolean control networks are investigated via the semi-tensor product technique. On the one hand, the largest control invariant subset is calculated in terms of the strongly connected components of the state transition graph, by which a graph-theoretical condition for set stabilization is derived. On the other hand, a characteristic function is exploited to determine the triggering mechanism and feasible controls. Based on this, the minimum-time and minimum-triggering open-loop, state-feedback and output-feedback STCs for set stabilization are designed,respectively. As classic applications of self-triggered set stabilization, self-triggered synchronization, self-triggered output tracking and self-triggered output regulation are discussed as well. Additionally, several practical examples are given to illustrate the effectiveness of theoretical results.
基金the National Natural Science Foundation of China under Grants 61673012 and 11971240,respectively。
文摘In this paper,a criterion for the partially symmetric game(PSG)is derived by using the semitensor product approach.The dimension and the basis of the linear subspace composed of all the PSGs with respect to a given set of partial players are calculated.The testing equations with the minimum number are concretely determined,and the computational complexity is analysed.Finally,two examples are displayed to show the theoretical results.
基金This paper is funded by the Innovation and Entrepreneurship Training Program for college students in Guangdong Province(No.2019126220004).
文摘China’s booming economy and the growing demand of urban middle class are creating a favorable situation for the development of domestic cultural and creative industry.The consumption pattern has changed and families spend more outlay on cultural products and services.Within this flourishing industry,many museums caught development opportunities and began to get profit through successfully promoting their own cultural and creative products.However,it is unusual that Emperor Qinshihuang’s Mausoleum Site Museum,enjoying high social status and a reputation for world cultural heritage as well as a national 5A level tourist attraction,regretfully,did not achieve noticeable achievements in this area.Therefore,based on STP theory,the purpose of this paper is to study the reasons why this museum fails to fulfill its potential in promising cultural and creative industry and give some suggestions to the development and promotion of its cultural and creative goods.
基金This work was supported partly by the National Natural Science Foundation of China(NSFC)(Nos.62073315,62103305)the Shanghai Pujiang Program(No.21PJ 1413100)China Postdoctoral Science Foundation(Nos.2021M703423,2022T150686).
文摘An equivalent definition of hypermatrices is introduced.The matrix expression of hypermatrices is proposed.Using permu-tation matrices,the conversion between different matrix expressions is revealed.The various kinds of contracted products of hypermatrices are realized by semi-tensor products(STP)of matrices via matrix expressions of hypermatrices.
基金supported in part by the National Natural Science Foundation of China under Grant No.61871242in part by the State Key Laboratory of ASIC(Application Specific Integrated Circuit)&System of China under Grant No.2021KF008.
文摘Boolean satisfiability (SAT) is widely used as a solver engine in electronic design automation (EDA). Typically, SAT is used to determine whether one or more groups of variables can be combined to form a true formula. All solutions SAT (AllSAT) is a variant of the SAT problem. In the fields of formal verification and pattern generation, AllSAT is particularly useful because it efficiently enumerates all possible solutions. In this paper, a semi-tensor product (STP) based AllSAT solver is proposed. The solver can solve instances described in both the conjunctive normal form (CNF) and circuit form. The implementation of our method differs from incremental enumeration because we do not add blocking conditions for existing solutions, but rather compute the matrices to obtain all the solutions in one pass. Additionally, the logical matrices support a variety of logic operations. Results from experiments with MCNC benchmarks using CNF-based and circuit-based forms show that our method can accelerate CPU time by 8.1x (238x maximum) and 19.9x (72x maximum), respectively.
基金supported partly by the National Natural Science Foundation of China under Grant Nos.62073315 and 62103305Shanghai Pujiang Program under Grant No.21PJ 1413100China Postdoctoral Science Foundation under Grant Nos.2021M703423 and 2022T150686。
文摘The semi-tensor product(STP)of matrices is generalized to multidimensional arrays,called the compound product of hypermatrices.The product is first defined for three-dimensional hypermatrices with compatible orders and then extended to general cases.Three different types of hyperdeterminants are introduced and certain properties are revealed.The Lie groups and Lie algebras corresponding to the hypermatrix products are constructed.Finally,these results are applied to dynamical systems.
