In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide...In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.展开更多
For three consecutive years, ZTE has been the fastest growing optical network vendor in the world. Our WDM equipment gives extra high transmission capacity over long distances at the same time as optimizing your optic...For three consecutive years, ZTE has been the fastest growing optical network vendor in the world. Our WDM equipment gives extra high transmission capacity over long distances at the same time as optimizing your optical fibre resources.展开更多
In this paper,the acceleratingly growing network model with intermittent processes is proposed.In thegrowing network,there exist both accelerating and intermittent processes.The network is grown from the number ofnode...In this paper,the acceleratingly growing network model with intermittent processes is proposed.In thegrowing network,there exist both accelerating and intermittent processes.The network is grown from the number ofnodes m<sub>o</sub> and the number of links added with each new node is a nonlinearly increasing function m+aN<sup>β</sup>（t）f（t）,whereN（t） is the number of nodes present at time t.f（t） is the periodic and bistable function with period T,whose values are1 and 0 indicating accelerating and intermittent processes,respectively.Here we denote the ratio r of acceleration timeto whole one.We study the degree distribution p（k） of the model,focusing on the dependence of p（k） on the networkparameters τ,T,m,α,N,and β.It is found that there exists a phase transition point,k<sub>c</sub> such that if k【k<sub>c</sub>,then p（k）obeys a power-law distribution with exponent -γ<sub>1</sub>,while if k】k<sub>c</sub>,then p（k） exhibits a power-law distribution withexponent-γ<sub>2</sub>.Moreover,the exponents γ<sub>1</sub> and γ<sub>2</sub> are independent of τ,T,m,a,and N,while they depend only onthe parameter β.More interesting,the phase transition point is described by k<sub>c</sub>=aN<sup>β</sup>,which is equal to the value atwhich p（k） is maximum in GM model.展开更多
From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provi...From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.展开更多
基金supported by the National Natural Science Foundation (11071258, 60874083, 10872119, 10901164)
文摘In this article, we focus on discussing the degree distribution of the DMS model from the perspective of probability. On the basis of the concept and technique of first-passage probability in Markov theory, we provide a rigorous proof for existence of the steady-state degree distribution, mathematically re-deriving the exact formula of the distribution. The approach based on Markov chain theory is universal and performs well in a large class of growing networks.
文摘For three consecutive years, ZTE has been the fastest growing optical network vendor in the world. Our WDM equipment gives extra high transmission capacity over long distances at the same time as optimizing your optical fibre resources.
基金The project supported by National Natural Science Foundation of China under Grant Nos.70571017 and 10247005the Innovation Project of Guangxi Graduate Education under Grant No.2006106020809M36
文摘In this paper,the acceleratingly growing network model with intermittent processes is proposed.In thegrowing network,there exist both accelerating and intermittent processes.The network is grown from the number ofnodes m<sub>o</sub> and the number of links added with each new node is a nonlinearly increasing function m+aN<sup>β</sup>（t）f（t）,whereN（t） is the number of nodes present at time t.f（t） is the periodic and bistable function with period T,whose values are1 and 0 indicating accelerating and intermittent processes,respectively.Here we denote the ratio r of acceleration timeto whole one.We study the degree distribution p（k） of the model,focusing on the dependence of p（k） on the networkparameters τ,T,m,α,N,and β.It is found that there exists a phase transition point,k<sub>c</sub> such that if k【k<sub>c</sub>,then p（k）obeys a power-law distribution with exponent -γ<sub>1</sub>,while if k】k<sub>c</sub>,then p（k） exhibits a power-law distribution withexponent-γ<sub>2</sub>.Moreover,the exponents γ<sub>1</sub> and γ<sub>2</sub> are independent of τ,T,m,a,and N,while they depend only onthe parameter β.More interesting,the phase transition point is described by k<sub>c</sub>=aN<sup>β</sup>,which is equal to the value atwhich p（k） is maximum in GM model.
基金supported by the National Natural Science Foundation of China (No. 10671212)
文摘From the perspective of probability, the stability of a modified Cooper- Frieze model is studied in the present paper. Based on the concept and technique of the first-passage probability in the Markov theory, we provide a rigorous proof for the exis- tence of the steady-state degree distribution, and derive the explicit formula analytically. Moreover, we perform extensive numerical simulations of the model, including the degree distribution and the clustering.
