The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cart...The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.展开更多
In this paper,we study the complicated dynamics of general Morris-Lecar model with the impact of Cl<sup>-</sup> fluctuations on firing patterns of this neuron model. After adding Cl<sup>-</sup>...In this paper,we study the complicated dynamics of general Morris-Lecar model with the impact of Cl<sup>-</sup> fluctuations on firing patterns of this neuron model. After adding Cl<sup>-</sup> channel in the original Morris-Lecar model, the dynamics of the original model such as its bifurcations of equilibrium points would be changed and they occurred at different values compared to the primary model. We discover these qualitative changes in the point of dynamical systems and neuroscience. We will conduct the co-dimension two bifurcations analysis with respect to different control parameters to explore the complicated behaviors for this new neuron model.展开更多
One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper ...One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper provides further insights from another perspective that a co-dimensional matrix pair(shortly co-dim matrix pair)forms a building unit and a hierarchy of such building units sets up the BYY system.The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair,which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning.Besides updating typical algorithms of factor analysis(FA),binary FA(BFA),binary matrix factorization(BMF),and nonnegative matrix factorization(NMF)to share such a mechanism,we are also led to(a)a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA(LFA);(b)an alternative formulation of graph Laplacian based linear manifold learning;(c)a codecomposition of data and covariance for learning regularization and data integration;and(d)a co-dim matrix pair based generalization of temporal FA and state space model.Moreover,with help of a co-dim matrix pair in Hadamard product,we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model.Furthermore,we address that these advances provide with new tools for network biology studies,including learning transcriptional regulatory,Protein-Protein Interaction network alignment,and network integration.展开更多
基金Funded by the National Science Foundation of China （No. 40501053）, the Hong Kong RGC Project （PolyU 5228/06E）, and the Key Laboratory of Geo-informatics of State Bureau of Surveying and Mapping （No. 200635）.
文摘The description of line-line topological relations is still an unsolved issue although much effort has been done. The problem is involved in many practical applications such as spatial query, spatial analysis and cartographic generalization. To develop a sound and effective approach to describe line-line relations, it is first necessary to define the topology of an individual line, i.e., local topology. The concept of connective degree is used for the identification of topological differences in the geometric structure of a line. The general topological definition of a line is given, i.e., endpoints set and interior point set. This definition can be applied to the embedded spaces of different dimensions, whether co-dimension is equal to or larger than zero. On this basis, a generic model called the 4 intersection-and-difference is set up for the description of basic line-line topological relations, upon which a conceptual neighborhood graph is built with consideration of topological distance, it is concluded that the proposed model can represent the property of topological changes, and basic relations between line segments in IR^1 and IR^2.
文摘In this paper,we study the complicated dynamics of general Morris-Lecar model with the impact of Cl<sup>-</sup> fluctuations on firing patterns of this neuron model. After adding Cl<sup>-</sup> channel in the original Morris-Lecar model, the dynamics of the original model such as its bifurcations of equilibrium points would be changed and they occurred at different values compared to the primary model. We discover these qualitative changes in the point of dynamical systems and neuroscience. We will conduct the co-dimension two bifurcations analysis with respect to different control parameters to explore the complicated behaviors for this new neuron model.
基金supported by the General Research Fund from Research Grant Council of Hong Kong(Project No.CUHK4180/10E)the National Basic Research Program of China(973 Program)(No.2009CB825404).
文摘One paper in a preceding issue of this journal has introduced the Bayesian Ying-Yang(BYY)harmony learning from a perspective of problem solving,parameter learning,and model selection.In a complementary role,the paper provides further insights from another perspective that a co-dimensional matrix pair(shortly co-dim matrix pair)forms a building unit and a hierarchy of such building units sets up the BYY system.The BYY harmony learning is re-examined via exploring the nature of a co-dim matrix pair,which leads to improved learning performance with refined model selection criteria and a modified mechanism that coordinates automatic model selection and sparse learning.Besides updating typical algorithms of factor analysis(FA),binary FA(BFA),binary matrix factorization(BMF),and nonnegative matrix factorization(NMF)to share such a mechanism,we are also led to(a)a new parametrization that embeds a de-noise nature to Gaussian mixture and local FA(LFA);(b)an alternative formulation of graph Laplacian based linear manifold learning;(c)a codecomposition of data and covariance for learning regularization and data integration;and(d)a co-dim matrix pair based generalization of temporal FA and state space model.Moreover,with help of a co-dim matrix pair in Hadamard product,we are led to a semi-supervised formation for regression analysis and a semi-blind learning formation for temporal FA and state space model.Furthermore,we address that these advances provide with new tools for network biology studies,including learning transcriptional regulatory,Protein-Protein Interaction network alignment,and network integration.
