The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling an...The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling and an inner product were introduced in the space of homogeneous polynomials. Theorems were established for the explicit expression of the simplest normal forms in terms of the coefficients of both the conventional normal forms of Hopf and generalized Hopf bifurcation systems. A symbolic manipulation was designed to perform the calculation of the coefficients of the simplest normal forms using Mathematica. The original ordinary differential equation was required in the input and the simplest normal form could be obtained as the output. Finally, the simplest normal forms of 6-dimensional generalized Hopf singularity of type 2 and 5-dimensional Hopf bifurcation system were discussed by executing the program. The output showed that the 5th- and 9th-order terms remained in 6-dimensional generalized Hopf singularity of type 2 and the 3rd- and 5th-order terms remained in 5-dimensional Hopf bifurcation system.展开更多
Ambiguous expression is a common phenomenon in facial expression recognition(FER).Because of the existence of ambiguous expression,the effect of FER is severely limited.The reason maybe that the single label of the da...Ambiguous expression is a common phenomenon in facial expression recognition(FER).Because of the existence of ambiguous expression,the effect of FER is severely limited.The reason maybe that the single label of the data cannot effectively describe complex emotional intentions which are vital in FER.Label distribution learning contains more information and is a possible way to solve this problem.To apply label distribution learning on FER,a label distribution expression recognition algorithm based on asymptotic truth value is proposed.Under the premise of not incorporating extraneous quantitative information,the original information of database is fully used to complete the generation and utilization of label distribution.Firstly,in training part,single label learning is used to collect the mean value of the overall distribution of data.Then,the true value of data label is approached gradually on the granularity of data batch.Finally,the whole network model is retrained using the generated label distribution data.Experimental results show that this method can improve the accuracy of the network model obviously,and has certain competitiveness compared with the advanced algorithms.展开更多
基金National Natural Science Foundation of China (No 10372068)
文摘The coefficients of the simplest normal forms of both high-dimensional generalized Hopf and high-dimensional Hopf bifurcation systems were discussed using the adjoint operator method. A particular nonlinear scaling and an inner product were introduced in the space of homogeneous polynomials. Theorems were established for the explicit expression of the simplest normal forms in terms of the coefficients of both the conventional normal forms of Hopf and generalized Hopf bifurcation systems. A symbolic manipulation was designed to perform the calculation of the coefficients of the simplest normal forms using Mathematica. The original ordinary differential equation was required in the input and the simplest normal form could be obtained as the output. Finally, the simplest normal forms of 6-dimensional generalized Hopf singularity of type 2 and 5-dimensional Hopf bifurcation system were discussed by executing the program. The output showed that the 5th- and 9th-order terms remained in 6-dimensional generalized Hopf singularity of type 2 and the 3rd- and 5th-order terms remained in 5-dimensional Hopf bifurcation system.
基金National Youth Natural Science Foundation of China(No.61806006)Innovation Program for Graduate of Jiangsu Province(No.KYLX160-781)Project Supported by Jiangsu University Superior Discipline Construction Project。
文摘Ambiguous expression is a common phenomenon in facial expression recognition(FER).Because of the existence of ambiguous expression,the effect of FER is severely limited.The reason maybe that the single label of the data cannot effectively describe complex emotional intentions which are vital in FER.Label distribution learning contains more information and is a possible way to solve this problem.To apply label distribution learning on FER,a label distribution expression recognition algorithm based on asymptotic truth value is proposed.Under the premise of not incorporating extraneous quantitative information,the original information of database is fully used to complete the generation and utilization of label distribution.Firstly,in training part,single label learning is used to collect the mean value of the overall distribution of data.Then,the true value of data label is approached gradually on the granularity of data batch.Finally,the whole network model is retrained using the generated label distribution data.Experimental results show that this method can improve the accuracy of the network model obviously,and has certain competitiveness compared with the advanced algorithms.
