In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the exi...In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.展开更多
In this short note we study how two colors, red and blue, painted on a given graph are evolved randomly according to a transition rule which aims to simulate how people influence each other. We shall also calculate th...In this short note we study how two colors, red and blue, painted on a given graph are evolved randomly according to a transition rule which aims to simulate how people influence each other. We shall also calculate the probability that the evolution will be trapped eventually using the martingale method.展开更多
Nonlinear least trimmed squares （NLTS） estimator is a very important kind of nonlinear robust estimator, which is widely used for recovering an ideal high-quality signal from contaminated data. However, the NLTS est...Nonlinear least trimmed squares （NLTS） estimator is a very important kind of nonlinear robust estimator, which is widely used for recovering an ideal high-quality signal from contaminated data. However, the NLTS estimator has not been widely used because it is hard to compute, This paper develops an algorithm to compute the NLTS estimator based on a random differential evolution （DE） strategy. The strategy which uses random DE schemes and control variables improves the DE performance. The simulation results demonstrate that the algorithm gives better performance and is more convenient than existing computing algorithms for the NLTS estimator. The algorithm makes the NLTS estimator easy to apply in practice, even for large data sets, e.g. in a data mining context.展开更多
Searching the global optimal value in heat exchanger network synthesis (HENS) becomes more difficult along with the increasing scale of cases.In structural opitimization model,such as stage-wise superstructure,solutio...Searching the global optimal value in heat exchanger network synthesis (HENS) becomes more difficult along with the increasing scale of cases.In structural opitimization model,such as stage-wise superstructure,solution domain can be enlarged by adding the stages of network,which would involve multiple integer and continuous variables in optimization and result in a decreasing computational efficiency.Thus,a new nodes-based model with stream splits is proposed,which can promote the quality of result and decrease time consumption at the same time.The characteristic of this model is that it changes the matching mode of heat exchangers by setting the number of nodes on streams to quantify the positions of heat exchangers.The proposed nodes-based model has more flexibility in generating and eliminating the heat exchangers and strong ductility in exploring the solution domain.The random walk with compulsive evolution is modified for enhancing its searching ability and applying modified random walk algorithm with compulsive evolution (RWCE) into the new proposed model.The obtained results of Case 1,Case 2 and Case 3 are superior to those reported in the literature,which decreases 106 USD·a-1,1253 USD·a-1,23 444 USD·a-1,respectively,verifying the robust effectiveness of this new model in solving HENS problem.展开更多
基金Partially supported by the National Natural Science Foundation of China,Grant No.69874003
文摘In this paper we consider a random evolution equation with small perturbations, and show how to construct coupled solutions to the equation. As applications, we prove the Feller continuity of the solutions and the existence and uniqueness of invariant measures. Furthermore, we establish a large deviations principle for the family of invariant measures as the perturbations tend to zero.
文摘In this short note we study how two colors, red and blue, painted on a given graph are evolved randomly according to a transition rule which aims to simulate how people influence each other. We shall also calculate the probability that the evolution will be trapped eventually using the martingale method.
基金the Key Technologies Research and Development Program of the Tenth Five-Year Plan of China (No. 2001609A12)
文摘Nonlinear least trimmed squares （NLTS） estimator is a very important kind of nonlinear robust estimator, which is widely used for recovering an ideal high-quality signal from contaminated data. However, the NLTS estimator has not been widely used because it is hard to compute, This paper develops an algorithm to compute the NLTS estimator based on a random differential evolution （DE） strategy. The strategy which uses random DE schemes and control variables improves the DE performance. The simulation results demonstrate that the algorithm gives better performance and is more convenient than existing computing algorithms for the NLTS estimator. The algorithm makes the NLTS estimator easy to apply in practice, even for large data sets, e.g. in a data mining context.
基金We would like to thank the financial support in partfrom the National Natural Science Foundation of China(51176125)National Natural Science Foundation of China(21978171)Capacity Building Plan for some Non-military Universities and Colleges of Shanghai Scientific Committee(16060502600).
文摘Searching the global optimal value in heat exchanger network synthesis (HENS) becomes more difficult along with the increasing scale of cases.In structural opitimization model,such as stage-wise superstructure,solution domain can be enlarged by adding the stages of network,which would involve multiple integer and continuous variables in optimization and result in a decreasing computational efficiency.Thus,a new nodes-based model with stream splits is proposed,which can promote the quality of result and decrease time consumption at the same time.The characteristic of this model is that it changes the matching mode of heat exchangers by setting the number of nodes on streams to quantify the positions of heat exchangers.The proposed nodes-based model has more flexibility in generating and eliminating the heat exchangers and strong ductility in exploring the solution domain.The random walk with compulsive evolution is modified for enhancing its searching ability and applying modified random walk algorithm with compulsive evolution (RWCE) into the new proposed model.The obtained results of Case 1,Case 2 and Case 3 are superior to those reported in the literature,which decreases 106 USD·a-1,1253 USD·a-1,23 444 USD·a-1,respectively,verifying the robust effectiveness of this new model in solving HENS problem.
