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建立了包含心房肌、心室肌、房室腔、室间隔并考虑心室肌分层结构的心电图元胞自动机模型.利用所建立的模型，仿真了电信号在心脏中的传导，计算了正常和缺血情况下的场点电势走势.数值结果表明：正常情况下，模拟所得的场点电势呈现与标准心电图一致的P波、QRS波群、T波和J波；在心内膜下肌细胞缺血情况下，出现T波倒置的现象；在心外膜下肌细胞缺血情况下，T波变得高耸；在透壁缺血情况下，T波提前形成，QT间期缩短.将正常和异常情况下的场点电势走势与临床结果进行了对比，并分析了其形成与持续机制.研究结果可为准确阐明心电图与心肌细胞电活动之间的关系、探讨心电图的产生与持续机制提供参考.How to evaluate the node spreading ability and how to find influential nodes in complex networks are crucial to controlling diseases and rumors, accelerating or hindering information from diffusing, and designing effective advertising strategies for viral marketing, etc. At present, many indicators based on the shortest path, such as closeness centrality, betweenness centrality and the (SP) index have been proposed to evaluate node spreading influence. The shortest path indicates that the information transmission path between nodes always selects the optimal mode. However, information does not know the ideal route from one place to another. The message does not flow only along geodesic paths in most networks, and information transmission path may be any reachable path between nodes. In the network with high clustering coefficient, the local high clustering of the nodes is beneficial to the large-scale dissemination of information. If only the information is transmitted according to the optimal propagation mode, which is the shortest path propagation, the ability to disseminate the node information would be underestimated, and thus the sorting precision of node spreading influence is reduced. By taking into account the transmission rate and the reachable path between a node and its three-step inner neighbors, we design an improved method named ASP to generate ranking list to evaluate the node spreading ability. We make use of the susceptible-infected-recovered (SIR) spreading model with tunable transmission rate to check the effectiveness of the proposed method on six real-world networks and three artificial networks generated by the Lancichinetii-Fortunato-Radicchi (LFR) benchmark model. In the real data sets, the proposed algorithm can achieve a better result than other metrics in a wide range of transmission rate, especially in networks with high clustering coefficients. The experimental results of the three LFR benchmark datasets show that the relative accuracy of ranking result of the ASP index and the SP index changes with the sparseness of the network and the information transmission rate. When the information dissemination rate is small, SP index is slightly better than the ASP index. The reason for this result is that when the transmission rate is small, the node influence is close to the degree. However, when the transmission rate is greater, the accuracy of the ASP index is higher than those of other indicators. This work can shed light on how the local clustering exerts an influence on the node propagation.
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Keywords:
- complex network /
- spreading influence /
- information spreading probability /
- transmission path
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[40] Knight W R 1966 J. Amer. Statist. Assoc. 61 436
[41] Newman M E J 2006 Phys. Rev. E 74 036104
[42] Guimera R, Danon L, Diaz-Guilera A, Giralt F, Arenas A 2003 Phys. Rev. E 68 065103
[43] Jeong H, Mason S P, Barabasi A, Oltvai Z N 2001 Nature 1 41
[44] Xie N 2006 M.S. Dissertation (Bristol:University of Bristol)
[45] Spring N, Mahajan R, Wetherall D 2002 IEEEACM Trans. Netw. 1 2
[46] Lancichinetti A, Fortunato S, Radicchi F 2008 Phys. Rev. E 78 046110
-
[1] Dorogovtsev S N, Mendes J F F, Samukhin A N 2000 Phys. Rev. Lett. 85 4633
[2] L L Y, Medo M, Yeung C H, Zhang Y C, Zhang Z K, Zhou T 2012 Phys. Rep. 59 1
[3] Papadopoulos F, Kitsak M, Serrano M A, Boguna M, Krioukov D 2012 Nature 489 537
[4] Tang J, Piera M A, Guasch T 2016 Transport Res. C 67 357
[5] Barabsi A L, Albert R 1999 Science 286 509
[6] Watts D J, Strogatz S H 1998 Nature 393 440
[7] L L Y, Chen D B, Zhou T 2011 New J. Phys. 13 123005
[8] Medo M, Zhang Y C, Zhou T 2009 Europhys. Lett. 88 38005
[9] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[10] Albert R, Barabsi A L 2002 Rev. Modern Phys. 74 47
[11] Castellano C, Fortunato S, Loreto V 2009 Rev. Modern Phys. 81 591
[12] Yang J, Yao C, Ma W, Chen G 2010 Physica A 389 859
[13] Morone F, Makse H A 2015 Nature 524 65
[14] Zhang J X, Chen D B, Zhao Z D 2016 Sci. Rep. 6
[15] Albert R, Jeong H, Barabsi A L 1999 Nature 401 130
[16] Chen D B, Lu L Y, Shang M S, Zhang Y C, Zhou T 2012 Physica A 391 1777
[17] Stephenson K, Zelen M 1989 Soc. Netw. 1 11
[18] Borgatti S P 2005 Soc. Netw. 27 55
[19] Sabidussi G 1966 Psychometrika 31 581
[20] Freeman L C 1977 Sociometry 40 35
[21] Kleinberg J M 1999 JACM 46 604
[22] Brin S, Page L 1998 Comput. Networks. Isdn. 30 107
[23] Radicchi F, Fortunato S, Markines B, Vespignani A 2009 Phys. Rev. E 80 056103
[24] L L Y, Zhang Y C, Yeung C H, Zhou T 2011 PLoS ONE 6 e21202
[25] L L Y, Zhou T, Zhang Q M, Stanley H E 2016 Nat. Commun. 7 10168
[26] Kitsak M, Gallos L K, Havlin S, Liljeros F, Muchnik L, Stanley H E, Makse H A 2010 Nat. Phys. 6 888
[27] Bae J, Kim S 2014 Physica A 395 549
[28] Liu Y, Tang M, Zhou T, Do Y 2016 Physica A 452 289
[29] Duan J M, Shang M S, Cai S M, Zhang Y X 2015 Acta Phys. Sin. 64 200501 (in Chinese)[段杰明, 尚明生, 蔡世民, 张玉霞2015物理学报64 200501]
[30] Liu J G, Lin J H, Guo Q, Zhou T 2016 Sci. Rep. 6 21380
[31] Liu J G, Ren Z M, Guo Q, Wang B H 2013 Acta Phys. Sin. 62 178901 (in Chinese)[刘建国, 任卓明, 郭强, 汪秉宏2013物理学报62 178901]
[32] Ren X L, L L Y 2014 Chin. Sci. Bull. 59 1175 (in Chinese)[任晓龙, 吕琳媛2014科学通报59 1175]
[33] L L Y, Chen D B, Ren X L, Zhang Q M, Zhang Y C, Zhou T 2016 Phys. Rep. 650 1
[34] Bao Z K, Ma C, Xiang B B, Zhang H F 2017 Physica A 468 391
[35] Newman M E J 2005 Soc. Netw. 27 39
[36] Fowler J H, Christakis N A 2008 Br. Med. J. 337 a2338
[37] Newman M E J 2002 Phys. Rev. E 66 016128
[38] Pastor-Satorras R, Vespignani A 2001 Phys. Rev. Lett. 86 3200
[39] Kendall M G 1945 Biometrika 33 239
[40] Knight W R 1966 J. Amer. Statist. Assoc. 61 436
[41] Newman M E J 2006 Phys. Rev. E 74 036104
[42] Guimera R, Danon L, Diaz-Guilera A, Giralt F, Arenas A 2003 Phys. Rev. E 68 065103
[43] Jeong H, Mason S P, Barabasi A, Oltvai Z N 2001 Nature 1 41
[44] Xie N 2006 M.S. Dissertation (Bristol:University of Bristol)
[45] Spring N, Mahajan R, Wetherall D 2002 IEEEACM Trans. Netw. 1 2
[46] Lancichinetti A, Fortunato S, Radicchi F 2008 Phys. Rev. E 78 046110
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