Based on the tropical cyclone(TC) observations in the western North Pacific from 2000 to 2008, this paper adopts the particle swarm optimization(PSO) algorithm of evolutionary computation to optimize one comprehensive...Based on the tropical cyclone(TC) observations in the western North Pacific from 2000 to 2008, this paper adopts the particle swarm optimization(PSO) algorithm of evolutionary computation to optimize one comprehensive classification rule, and apply the optimized classification rule to the forecasting of TC intensity change. In the process of the optimization, the strategy of hierarchical pruning has been adopted in the PSO algorithm to narrow the search area,and thus to enhance the local search ability, i.e. hierarchical PSO algorithm. The TC intensity classification rule involves core attributes including 12-HMWS, MPI, and Rainrate which play vital roles in TC intensity change. The testing accuracy using the new mined rule by hierarchical PSO algorithm reaches 89.6%. The current study shows that the novel classification method for TC intensity change analysis based on hierarchic PSO algorithm is not only easy to explain the source of rule core attributes, but also has great potential to improve the forecasting of TC intensity change.展开更多
The famous F5 algorithm for computing Grobner basis was presented by Faugere in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm i...The famous F5 algorithm for computing Grobner basis was presented by Faugere in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger＇s style such that it is easy to understand and implement. In order to describe F5B, we introduce F5-reduction, which keeps the signature of labeled polynomials unchanged after reduction. The equivalence between F5 and F5B is also shown. At last, some versions of the F5 algorithm are illustrated.展开更多
GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than F5. In this paper, the authors generalize GVW algorithm and presen...GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than F5. In this paper, the authors generalize GVW algorithm and present an algorithm to compute a Grobner bases for ideal when the coefficient ring is a principal ideal domain. K展开更多
Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 a...Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G2V algorithm, to compute SAGBI-Grbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Grbner bases. We have implemented our new algorithm in Maple , and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm.展开更多
基金National Natural Science Foundation of China(41201045)Jiangsu Qing Lan Project(2016)Natural Science Foundation of Jiangsu Province(BK20151458)
文摘Based on the tropical cyclone(TC) observations in the western North Pacific from 2000 to 2008, this paper adopts the particle swarm optimization(PSO) algorithm of evolutionary computation to optimize one comprehensive classification rule, and apply the optimized classification rule to the forecasting of TC intensity change. In the process of the optimization, the strategy of hierarchical pruning has been adopted in the PSO algorithm to narrow the search area,and thus to enhance the local search ability, i.e. hierarchical PSO algorithm. The TC intensity classification rule involves core attributes including 12-HMWS, MPI, and Rainrate which play vital roles in TC intensity change. The testing accuracy using the new mined rule by hierarchical PSO algorithm reaches 89.6%. The current study shows that the novel classification method for TC intensity change analysis based on hierarchic PSO algorithm is not only easy to explain the source of rule core attributes, but also has great potential to improve the forecasting of TC intensity change.
文摘The famous F5 algorithm for computing Grobner basis was presented by Faugere in 2002. The original version of F5 is given in programming codes, so it is a bit difficult to understand. In this paper, the F5 algorithm is simplified as F5B in a Buchberger＇s style such that it is easy to understand and implement. In order to describe F5B, we introduce F5-reduction, which keeps the signature of labeled polynomials unchanged after reduction. The equivalence between F5 and F5B is also shown. At last, some versions of the F5 algorithm are illustrated.
基金supported by the National Natural Science Foundation of China under Grant Nos.11071062,11271208Scientific Research Fund of Hunan Province Education Department under Grant Nos.10A033,12C0130
文摘GVW algorithm was given by Gao, Wang, and Volny in computing a Grobuer bases for ideal in a polynomial ring, which is much faster and more simple than F5. In this paper, the authors generalize GVW algorithm and present an algorithm to compute a Grobner bases for ideal when the coefficient ring is a principal ideal domain. K
文摘Faugère and Rahmany have presented the invariant F5 algorithm to compute SAGBI-Grbner bases of ideals of invariant rings. This algorithm has an incremental structure, and it is based on the matrix version of F5 algorithm to use F5 criterion to remove a part of useless reductions. Although this algorithm is more efficient than the Buchberger-like algorithm, however it does not use all the existing criteria (for an incremental structure) to detect superfluous reductions. In this paper, we consider a new algorithm, namely, invariant G2V algorithm, to compute SAGBI-Grbner bases of ideals of invariant rings using more criteria. This algorithm has a new structure and it is based on the G2V algorithm; a variant of the F5 algorithm to compute Grbner bases. We have implemented our new algorithm in Maple , and we give experimental comparison, via some examples, of performance of this algorithm with the invariant F5 algorithm.
