《VoterModelinAssortativeNetworks在同配网络上的一个改》由会员分享，可在线阅读，更多相关《VoterModelinAssortativeNetworks在同配网络上的一个改（19页珍藏版）》请在金锄头文库上搜索。
1、A Variant Voter Model in Assortative Networks在同配网络上的一个改进投票模型的研究潘黎明潘黎明 荣智海荣智海 王直杰王直杰Donghua UniversityOctober 2010Presented in CCCN2010, SuzhouContentsReview of the Voter Models Voter Model Invasion Process Link DynamicsIntroduction to a variant voter modelDegree correlations The variant voter model
2、in assortative networksConclusionsReview of the Voter modelsThe origin voter model (VM): (i) randomly pick a node; (ii) the node adopts the state of a random neighbor.The invasion process (IP): (i) pick a random node; (ii) the node exports its state to a random neighbor.link dynamics (LD) (i) pick a
3、 random link; (ii) one of the nodes on the link, adopts the state of the other end node. V. Sood, T. Antal, and S. Redner, Phys. Rev. E 77, 041121 (2008) T. M. Liggett, Interacting Particle Systems, (Springer-Verlag, Berlin, 2005). P. L. Krapivsky, Phys. Rev. A 45, 1067 (1992). C. Castellano, AIP Co
4、nference Proceedings 779, 1142005).Review of the Voter modelsIn uncorrelated networks, consider all the nodes of like degree to be indistinguishable, the probability of node i adopts node js opinion is: (C. M. Schneider-Mizell and L. M. Sander, J. Stat. Phys. 136, 59 (2009) ) VM: LD: IP:ni ,nj: the
5、fraction of nodes with degree i and jki,kj : the degree of node i j1: the average degreeReview of the Voter modelsIn uncorrelated networks, consider all the nodes of like degree to be indistinguishable, the probability of node i adopts node js opinion is: (C. M. Schneider-Mizell and L. M. Sander, J.
6、 Stat. Phys. 136, 59 (2009) ) VM: LD: IP:ni ,nj: the fraction of nodes with degree i and jki,kj : the degree of node i j1: the average degreeThe differences seems to be trivial, but they are fundamental.Discussion of a Variant Voter ModelA variant of the voter model with respect to the heterogeneous
7、 influence of individuals. The nodes update their state in the following two steps: (i) Select a pair of nodes using node selection (ii) The pair of nodes choose of the opinions as their common opinion. The probability of choosing is opinion as the common opinion is Han-Xin Yang, Zhi-Xi Wu, Changson
8、g Zhou, Tao Zhou and Bing-Hong Wang Phys. Rev. E 80, 046108 (2009) Discussion of a Variant Voter ModelOn uncorrelated networks, the probability of node i adopting node js opinion is: When the parameter =1, The model reduces to the origin voter modelConsensus time as a function of the parameter for d
9、ifferent GHan-Xin Yang, Zhi-Xi Wu, Changsong Zhou, Tao Zhou and Bing-Hong Wang Phys. Rev. E 80, 046108 (2009)A.-L. Barabasi and R. Albert, Science 286, 509 (1999).Degree-mixing patterns Many networks show assortative mixing on their degrees, i.e., a preference for high degree vertices to attach to o
10、ther high-degree vertices. Whereas, others show disassortative mixing: high-degree vertices attach to low-degree ones.Most social networks have assortative mixing, while technological and biological networks are disassortative. M. E. J. Newman, Phys. Rev. Lett. 89,208701,2002;The variant voter model
11、 in assortative scale-free networksSimulations in assortative scale-free networks with N=5000, and G=2Maslov, S. and Sneppen, K. (2002). Science,296,910 - 913.R. Xulvi-Brunet and I. M. Sokolov, Phys. Rev. E 70, 066102 (2004)Discussion of the situation when =0 Comparison of the =0 situation and the l
12、ink dynamics LD: Symmetric random walks on integers. =0: When an active link is selected, the probability for increasing or decreasing the 1 nodes are the same for networks of different degree-mixing coefficients, but the probability of selecting an active link are different. A plausible explanation
13、 for =0 Average degree of the final common opinion during the time process when =4.(G=2) The consensus time Tc when G=5000 whenThe number of opinion clusters during the time process when G=5000 The fraction of the final common opinion for different degree regionsNode selection The fraction of the fi
14、nal common opinion for different degree regionsLink SelectionConclusionsWe studied a variant of the voter model on assortative scale-free networks.We find that under node selection, the assortative degree mixing will resulting faster convergence speed due to that the opinion clusters around high-deg
15、ree individuals will easier to vanish.The slight difference of the way selecting a pair of nodes will change the dynamical behavior dramatically. When using the link selection, assortative-degree mixing will inhibit the consensus for some region of the parameter alpha. Further study is in progress. Thank you very much!Email:
