Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given da...Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.展开更多
A negative example shows that the model given by Mason Iri is used to prove that the relationship between the minimum flow problem and the Hamiltonian path problem in a (directed) network, is not rigorous. A new model...A negative example shows that the model given by Mason Iri is used to prove that the relationship between the minimum flow problem and the Hamiltonian path problem in a (directed) network, is not rigorous. A new model called minimum spanning flow in a network is established to revise the old one. It is proved that the problem of determining whether there is a Hamiltonian path from a specified vertex s to another t on a given digraph can be reducible at polynomial time to the problem of constructing a minimum spanning flow in a two-terminal extended network s,t , with the unit capacity for all arcs.展开更多
The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of graphs are obtained according to their edge connectivities. ...The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of graphs are obtained according to their edge connectivities. All the bounds in this paper are tight.Moreover, for each integer k between one and the upper bound, there are infinitely many graphs with the decay number k.展开更多
Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of E...Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.展开更多
Reading is an effective means to cultivate junior high school students＇ comprehensive ability of using English and plays an important role in English study. Schema theory is a scientific reading theory advocated by m...Reading is an effective means to cultivate junior high school students＇ comprehensive ability of using English and plays an important role in English study. Schema theory is a scientific reading theory advocated by modern teaching, and it regards the reading comprehension as a process that readers＇ knowledge and skills interact with the information in the reading material. In this paper, a questionnaire is conducted to reveal the fact that students lack schemata in reading and then a proposal that language schema, content schema, and form schema be integrated to activate students＇ existing schemata in the process of reading is put forward展开更多
Networks are a class of general systems represented by becomes a weighted graph visualizing the constraints imposed their UC-structure. Suppressing the nature of elements the network by interconnections rather than th...Networks are a class of general systems represented by becomes a weighted graph visualizing the constraints imposed their UC-structure. Suppressing the nature of elements the network by interconnections rather than the elements themselves. These constraints follow generalized Kirchhoff＇s laws derived from physical constraints. Once we have a graph; then the working environment becomes the graph-theory. An algorithm derived from graph theory is developed within the paper in order to analyze general networks. The algorithm is based on computing all the spanning trees in the graph G with an associated weight. This weight is the product ofadmittance＇s of the edges forming the spanning tree. In the first phase this algorithm computes a depth first spanning tree together with its cotree. Both are used as parents for controlled generation of off-springs. The control is represented in selecting the off-springs that were not generated previously. While the generation of off-springs, is based on replacement of one or more tree edges by cycle edges corresponding to cotree edges. The algorithm can generate a frequency domain analysis of the network.展开更多
The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main r...The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.展开更多
基金Supported by the Key National Natural Science Foundation of China(61035003)~~
文摘Graph-theoretical approaches have been widely used for data clustering and image segmentation recently. The goal of data clustering is to discover the underlying distribution and structural information of the given data, while image segmentation is to partition an image into several non-overlapping regions. Therefore, two popular graph-theoretical clustering methods are analyzed, including the directed tree based data clustering and the minimum spanning tree based image segmentation. There are two contributions： （1） To improve the directed tree based data clustering for image segmentation, （2） To improve the minimum spanning tree based image segmentation for data clustering. The extensive experiments using artificial and real-world data indicate that the improved directed tree based image segmentation can partition images well by preserving enough details, and the improved minimum spanning tree based data clustering can well cluster data in manifold structure.
文摘A negative example shows that the model given by Mason Iri is used to prove that the relationship between the minimum flow problem and the Hamiltonian path problem in a (directed) network, is not rigorous. A new model called minimum spanning flow in a network is established to revise the old one. It is proved that the problem of determining whether there is a Hamiltonian path from a specified vertex s to another t on a given digraph can be reducible at polynomial time to the problem of constructing a minimum spanning flow in a two-terminal extended network s,t , with the unit capacity for all arcs.
基金Supported by the NSFC(10201022)Supported by the NSFCBJ(1012003)
文摘The decay number of a connected graph is defined to be the minimum number of the components of the cotree of the graph. Upper bounds of the decay numbers of graphs are obtained according to their edge connectivities. All the bounds in this paper are tight.Moreover, for each integer k between one and the upper bound, there are infinitely many graphs with the decay number k.
基金Natural Science Foundation of Fujian Province of ChinaGrant number:C0710036 and E0610023
文摘Using both the wavelet decomposition and the phase space embedding, the phase trajectories of electroencephalogram (EEG) is described. It is illustrated based on the present work,that is,the wavelet decomposition of EEG is essentially a projection of EEG chaotic attractor onto the wavelet space opened by wavelet filter vectors, which is in correspondence with the phase space embedding of the same EEG. In other words, wavelet decomposition and phase space embedding are equivalent in methodology. Our experimental results show that in both the wavelet space and the embedded space the structure of phase trajectory of EEG is similar to each other. These results demonstrate that wavelet decomposition is effective on characterizing EEG time series.
文摘Reading is an effective means to cultivate junior high school students＇ comprehensive ability of using English and plays an important role in English study. Schema theory is a scientific reading theory advocated by modern teaching, and it regards the reading comprehension as a process that readers＇ knowledge and skills interact with the information in the reading material. In this paper, a questionnaire is conducted to reveal the fact that students lack schemata in reading and then a proposal that language schema, content schema, and form schema be integrated to activate students＇ existing schemata in the process of reading is put forward
文摘Networks are a class of general systems represented by becomes a weighted graph visualizing the constraints imposed their UC-structure. Suppressing the nature of elements the network by interconnections rather than the elements themselves. These constraints follow generalized Kirchhoff＇s laws derived from physical constraints. Once we have a graph; then the working environment becomes the graph-theory. An algorithm derived from graph theory is developed within the paper in order to analyze general networks. The algorithm is based on computing all the spanning trees in the graph G with an associated weight. This weight is the product ofadmittance＇s of the edges forming the spanning tree. In the first phase this algorithm computes a depth first spanning tree together with its cotree. Both are used as parents for controlled generation of off-springs. The control is represented in selecting the off-springs that were not generated previously. While the generation of off-springs, is based on replacement of one or more tree edges by cycle edges corresponding to cotree edges. The algorithm can generate a frequency domain analysis of the network.
基金supported by The National Basic Research Development Program of China(No.2009CB42115)the National Natural Science foundation of China(No.40901289),and WWF China
基金Supported by the National Science Foundation of China under Grant Nos.11235003 and 11475023National Social Sciences Foundation of China under Grant No.14BZX078+1 种基金the Research Fund for the Doctoral Program of Higher Education of Chinathe Undergraduate Training Program of Beijing
文摘The axiomatization of physical theories is a fundamental issue of science. The first-order axiomatic system SpecR el for special relativity proposed recently by Andr′eka et al. is not enough to explain all the main results in the theory, including the twin paradox and energy-mass relation. In this paper, from a four-dimensional spacetime perspective, we introduce the concepts of world-line, proper time and four-momentum to our axiomatic system SpecR el^+. Then we introduce an axiom of mass(Ax Mass) and take four-momentum conservation as an axiom(Ax CFM)in SpecR el^+. It turns out that the twin paradox and energy-mass relation can be derived from SpecR el+logically. Hence,as an extension of SpecR el, SpecR el^+is a suitable first-order axiomatic system to describe the kinematics and dynamics of special relativity.
