In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very we...In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very weak condition.展开更多
An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the ...An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.展开更多
In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equa...In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X n+1 = f ( X n )?, are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.展开更多
基金The first author is supported by a grant from Postdoctoral Science Research Program (0701049C) of Jiangsu Provincethe second author is partially supported by the NSF (10571086) of Chinathe National Basic Research Program-973 Program (2007CB814800) of China
文摘In this paper we define the pre-image topological pressure for a sequence of subadditive continuous functions on the compact metric space. And we also give a subadditive pre-image variational principle under a very weak condition.
基金Project supported by the National Science and Technology Major Project of China(No.2012EX01027001-002)the Fun-damental Research Funds for the Central Universities,China
文摘An important issue involved in kernel methods is the pre-image problem. However, it is an ill-posed problem, as the solution is usually nonexistent or not unique. In contrast to direct methods aimed at minimizing the distance in feature space, indirect methods aimed at constructing approximate equivalent models have shown outstanding performance. In this paper, an indirect method for solving the pre-image problem is proposed. In the proposed algorithm, an inverse mapping process is constructed based on a novel framework that preserves local linearity. In this framework, a local nonlinear transformation is implicitly conducted by neighborhood subspace scaling transformation to preserve the local linearity between feature space and input space. By extending the inverse mapping process to test samples, we can obtain pre-images in input space. The proposed method is non-iterative,and can be used for any kernel functions. Experimental results based on image denoising using kernel principal component analysis(PCA) show that the proposed method outperforms the state-of-the-art methods for solving the pre-image problem.
文摘In this work, we analyzed the impact of interventions on populations which exhibit unimodal dynamics. The six landmarks that characterize the “shape” of the unimodal reproduction curve f ( x ) of the difference equation, X n+1 = f ( X n )?, are defined and used in order to examine and determine the behavior of dynamics of populations. By using the Li-Yorke criterion for determination of chaos we propose a qualitative intervention rule that can be applied without any explicit population equation. This proposed strategy for intervention brings out many interesting behaviors in population dynamics. A qualitative decision rule can be applied with a straight edge without any population equation and therefore offers a robust strategy for the management of populations.
