Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers syst...Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.展开更多
An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map nav...An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map navigation systems are expected to play more important roles in transportation systems. In order to extend current navigation systems to more applications, two fundamental problems must be resolved: the lane-level map model and lane-level route planning. This study proposes solutions to both problems. The current limitation of the lane-level map model is not its accuracy but its flexibility;this study proposes a novel seven-layer map structure, called as Tsinghua map model, which is able to support autonomous driving in a flexible and efficient way. For lane-level route planning, we propose a hierarchical route-searching algorithm to accelerate the planning process, even in the presence of complicated lane networks. In addition, we model the travel costs allocated for lane-level road networks by analyzing vehicle maneuvers in traversing lanes, changing lanes, and turning at intersections. Tests were performed on both a grid network and a real lane-level road network to demonstrate the validity and efficiency of the proposed algorithm.展开更多
In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional diss...In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.展开更多
Self-organizing map(SOM) proposed by Kohonen has obtained certain achievements in solving the traveling salesman problem(TSP).To improve Kohonen SOM,an effective initialization and parameter modification method is dis...Self-organizing map(SOM) proposed by Kohonen has obtained certain achievements in solving the traveling salesman problem(TSP).To improve Kohonen SOM,an effective initialization and parameter modification method is discussed to obtain a faster convergence rate and better solution.Therefore,a new improved self-organizing map(ISOM)algorithm is introduced and applied to four traveling salesman problem instances for experimental simulation,and then the result of ISOM is compared with those of four SOM algorithms:AVL,KL,KG and MSTSP.Using ISOM,the average error of four travelingsalesman problem instances is only 2.895 0%,which is greatly better than the other four algorithms:8.51%(AVL),6.147 5%(KL),6.555%(KG) and 3.420 9%(MSTSP).Finally,ISOM is applied to two practical problems:the Chinese 100 cities-TSP and102 counties-TSP in Shanxi Province,and the two optimal touring routes are provided to the tourists.展开更多
New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the numb...New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the number of markers may, by orders of magnitude, exceed the threshold of recombination resolution achievable for a given population size. Hence, only a small part of markers can be genuinely ordered in the map. The question is how to choose the most informative markers for building such a reliable “skeleton” map. We believe that our approach provides a solution to this difficult problem due to: a) powerful tools of discrete optimization for multilocus ordering;b) a verification procedure, which is impossible without fast and high-quality optimization, to control the map quality based on re-sampling techniques;c) an interactive algorithm of marker clustering in complicated situations caused by significant deviation of recombination rates between markers of non-homologous chromosomes from the expected 50% (referred to as quasi-linkage or pseudo-linkage);and d) an algorithm for detection and removing excessive markers to increase the stability of multilocus ordering.展开更多
The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlin...The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.展开更多
文摘Starting from the symbolic computation system Maple and Riccati equation mapping approach and a linear variable separation approach, a new family of non-traveling wave solutions of the (1 + 1)-dimensional Burgers system is derived.
基金the National Key Research and Development Program of China (2018YFB0105000)the National Natural Science Foundation of China (61773234 and U1864203)+2 种基金the Project of Tsinghua University and Toyota Joint Research Center for AI Technology of Automated Vehicle (TT2018-02)the International Science and Technology Cooperation Program of China (2016YFE0102200)the software developed in the Beijing Municipal Science and Technology Program (D171100005117001 and Z181100005918001).
文摘An increasing number of drivers are relying on digital map navigation systems in vehicles or mobile phones to select optimal driving routes in order to save time and improve safety. In the near future, digital map navigation systems are expected to play more important roles in transportation systems. In order to extend current navigation systems to more applications, two fundamental problems must be resolved: the lane-level map model and lane-level route planning. This study proposes solutions to both problems. The current limitation of the lane-level map model is not its accuracy but its flexibility;this study proposes a novel seven-layer map structure, called as Tsinghua map model, which is able to support autonomous driving in a flexible and efficient way. For lane-level route planning, we propose a hierarchical route-searching algorithm to accelerate the planning process, even in the presence of complicated lane networks. In addition, we model the travel costs allocated for lane-level road networks by analyzing vehicle maneuvers in traversing lanes, changing lanes, and turning at intersections. Tests were performed on both a grid network and a real lane-level road network to demonstrate the validity and efficiency of the proposed algorithm.
文摘In this work, with the help of the symbolic computation system Maple and the Riccati mapping approach and a linear variable separation approach, a new family of traveling wave solutions of the (2 + 1)-dimensional dissipative Zabolotskaya-Khokhlov equation (DZK) is derived. Based on the derived solitary wave solution, some novel kind wave excitations are investigated.
文摘Self-organizing map(SOM) proposed by Kohonen has obtained certain achievements in solving the traveling salesman problem(TSP).To improve Kohonen SOM,an effective initialization and parameter modification method is discussed to obtain a faster convergence rate and better solution.Therefore,a new improved self-organizing map(ISOM)algorithm is introduced and applied to four traveling salesman problem instances for experimental simulation,and then the result of ISOM is compared with those of four SOM algorithms:AVL,KL,KG and MSTSP.Using ISOM,the average error of four travelingsalesman problem instances is only 2.895 0%,which is greatly better than the other four algorithms:8.51%(AVL),6.147 5%(KL),6.555%(KG) and 3.420 9%(MSTSP).Finally,ISOM is applied to two practical problems:the Chinese 100 cities-TSP and102 counties-TSP in Shanxi Province,and the two optimal touring routes are provided to the tourists.
文摘New high throughput DNA technologies resulted in a disproportion between the high number of scored markers for the mapping populations and relatively small sizes of the genotyped populations. Correspondingly, the number of markers may, by orders of magnitude, exceed the threshold of recombination resolution achievable for a given population size. Hence, only a small part of markers can be genuinely ordered in the map. The question is how to choose the most informative markers for building such a reliable “skeleton” map. We believe that our approach provides a solution to this difficult problem due to: a) powerful tools of discrete optimization for multilocus ordering;b) a verification procedure, which is impossible without fast and high-quality optimization, to control the map quality based on re-sampling techniques;c) an interactive algorithm of marker clustering in complicated situations caused by significant deviation of recombination rates between markers of non-homologous chromosomes from the expected 50% (referred to as quasi-linkage or pseudo-linkage);and d) an algorithm for detection and removing excessive markers to increase the stability of multilocus ordering.
文摘The special kind of (G’/G)-expansion method and the new mapping method are easy and significant mathematical methods. In this paper, exact travelling wave solutions of the higher order dispersive Cubic-quintic nonlinear Schrödinger equation and the generalized nonlinear Schrödinger equation are studied by using the two methods. Finally, the solitary wave solutions, singular soliton solutions, bright and dark soliton solutions and periodic solutions of the two nonlinear Schrödinger equations are obtained. The results show that this method is effective for solving exact solutions of nonlinear partial differential equations.
