The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between t...The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.展开更多
In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both h...In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.展开更多
基金Supported by the National Natural Science Foundation of China (No.60277101, No.60301003, No.60431020), Beijing Foundation (No.3052005), and Beijing Munici-pal Commission of Education Project (KM200410005030).
文摘The hypersphere support vector machine is a new algorithm in pattern recognition. By studying three kinds of hypersphere support vector machines, it is found that their solutions are identical and the margin between two classes of samples is zero or is not unique. In this letter, a new kind of hypersphere support vector machine is proposed. By introducing a parameter n(n>1), a unique solution of the margin can be obtained. Theoretical analysis and experimental results show that the proposed algorithm can achieve better generaliza-tion performance.
文摘In this paper, we consider a sex-structured predator prey model with strongly coupled nonlinear reaction diffusion. Using the Lyapunov functional and Leray Schauder degree theory, the existence and stability of both homogenous and heterogenous steady-states are investigated. Our results demonstrate that the unique homogenous steady-state is locally asymptotically stable for the associated ODE system and PDE system with self-diffusion. With the presence of the cross-diffusion, the homogeneous equilibrium is destabilized, and a heterogenous steady-state emerges as a consequence. In addition, the conditions guaranteeing the emergence of Turing patterns are derived.