合作竞争网的特例特性及统一规律研究
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摘要
本论文主要探讨了世界语言网络的构建、网络性质以及模型。在深入研究某个系统(世界语言网络)基础之上,本文倾向于研究合作--竞争网络中哪种性质在竞争中起关键作用,即独特性在竞争中的重要作用;以及研究合作--竞争网络中不同系统的基本单元在合作中遵从的统一规律,即二方组和三方组遵从的统一规律,这也是本论文要报道的内容之一。
复杂网络中常用二分图来描述一类网络,这类网络中包含两类节点:一类节点是参与某种活动、事件或者组织的“参与者”,另一类是节点就是它们参与的活动、事件或者组织(称为“项目”)。在世界语言网络中我们把语言看成“参与者”,把语言所在的国家看成“项目”。在这类网络研究中,若只是关心参与者的相互作用,常常把二分图向参与者投影。在这篇论文中着重关注语言间的相互作用关系,所以把二分图向语言这类节点投影,同时用语言的人数表示语言的点权(表征世界语言使用人数的不均匀性),这样我们便得到了含权的世界语言网络。在世界语言网络构建起来后,我们研究了它的网络拓扑性质,发现其点强度分布具有显著的特征,即在点强度分布中我们可以清晰的看到世界语言分为截然的两类(即世界语言的二元性),我们称为活跃的语言和不活跃的语言。这在传统的语言研究中未曾发现和提及。为了更好的理解世界语言的二元性,提出一个小小的语言模型来说明世界语言演化的可能动力学机制。这个模型首先考虑最简化的情况,即不考虑语言人口因素的影响,在得到理想的结果后,再进一步细化即考虑语言人口因素对语言演化的影响。在这种情形下,解析得到的世界语言网的点强度分布同实证可以很好的吻合,同时这个模型还可以解析地得到世界语言网络的其它统计性质并与实证很好的符合。这说明本文的研究抓住了世界语言演化的关键因素,在一定程度上说明所建模型是可靠的。
在复杂网络研究中,合作网络和合作--竞争网络受到广泛关注。好多专家、学者给出了许多真知灼见,但是都只是定性的阐述并没有定量的来描述这些系统。在本文的工作中,定量地阐述了合作--竞争网络中一个广为人们接受的思想,即在竞争中独特性是非常重要的。为了定量的描述这一思想,提出了两个统计量:竞争力和独特性,解析后发现两者在一般情况下是相等的。这意味着独特性可以完全决定竞争力。为了验证得到的结果,把它应用到地方高校系统中,发现它的实证结果和解析结果是一致。这很好地说明了本文提出的两个物理量是很有价值的并对现实有很好的指导意义。
论文的最后汇报了二方组、三方组在合作中遵从的统一规律。这一研究是针对不同的系统进行的,虽然研究的系统横跨了不同学科门类,但是它们的二方组和三方组项目度分布却遵从统一的规律,即我们科研组倡导的“漂移幂律”分布(Shifted Power Law)。这一工作是对前面工作的加深和拓展,因此也是汇报的重点之一。
This thesis mainly reports the construction, properties and model of world languages network. On the basis of profound in research of a particular system (network of world languages) , we are inclined to investigate the property which plays key role in the process of competition, i.e. the key role of uniqueness in the competition, and research the basic units in different collaboration-competition systems and find the law which the units obey. That is the unified rule which dyads and triads follow. These are the contents we report here as well.
In the complex networks, we usually use bipartite graphs to describe a kind of networks. In this kind of networks, there are two sets of nodes, one is called“actors”in which take part events, activities, or organizations (i.e., the participants) and the other is called“acts”(i.e., events, activities, organizations). In the network of world languages, we view languages as“actors”and countries or regions as“acts”. In this kind of networks, if we only concern the interaction between actors, a projected single-mode (unipartite) network is often used (projected to the actor set). In this paper, we just pay attention to the relationship between languages, so we project the network into the language set. Meanwhile we use the population of a language to denote the node’s weight (that means the nonuniformity of language’s population). In this way we get weighted network of world languages. We investigate the topology properties of the world language network after the network is constructed. And we found the distribution of strength has distinct trait.That is the world languages can be divided into two kinds clearly from the figure of the language’s strength distribution(i.e. the duality of world languages). We call them active languages and inactive languages. That did not find and mention in traditional language research. In order to understand the duality of world languages better, we propose a minimal model to explain the may mechanism dynamics of world languages’evolution. The model gets ideal outcome in the most simple condition without considering the factor of language population. Then we consider the influence of language population and fine the model further. The analytic strength distribution of world language network fits the empirical investigation well. Meanwhile the model can get other statistic properties analytically and fits the empirical investigation as well. That show we catch the key factor of world languages’evolution, and in a certain degree show our model can stand up.
In the research of complex networks, collaboration networks and collaboration-competition networks attract a lot of attention. Many experts and scholars propose a lot of brilliant ideas, but these ideas are just qualitative description and do not present quantitative one. In our study, we present a quantitative expression of a well accepted idea about collaboration and competition: uniqueness is important in competition. In order to quantify this expression, we suggest two new statistical quantity called“competition ability”and“uniqueness”. We analyze the relationship of the two quantity and find they are equal in ordinary case. This means that uniqueness completely drives the competition. In order to check our outcome, we apply it to regional university system and find the empirical investigation in accord with our analytic outcome. That shows the two quantity we proposed is valuable and can give good advice to our real life.
In the end of the thesis, we report the unified law the dyads and triads obey in cooperation. This research aims at different systems. Thought the systems cross a lot of subjects, all the act degree distribution of their dyads and triads obey the same law, i.e. the“shifted power law”which is advocated by our group. This work extend our work before, therefore it is our key report as well.
复杂网络中常用二分图来描述一类网络,这类网络中包含两类节点:一类节点是参与某种活动、事件或者组织的“参与者”,另一类是节点就是它们参与的活动、事件或者组织(称为“项目”)。在世界语言网络中我们把语言看成“参与者”,把语言所在的国家看成“项目”。在这类网络研究中,若只是关心参与者的相互作用,常常把二分图向参与者投影。在这篇论文中着重关注语言间的相互作用关系,所以把二分图向语言这类节点投影,同时用语言的人数表示语言的点权(表征世界语言使用人数的不均匀性),这样我们便得到了含权的世界语言网络。在世界语言网络构建起来后,我们研究了它的网络拓扑性质,发现其点强度分布具有显著的特征,即在点强度分布中我们可以清晰的看到世界语言分为截然的两类(即世界语言的二元性),我们称为活跃的语言和不活跃的语言。这在传统的语言研究中未曾发现和提及。为了更好的理解世界语言的二元性,提出一个小小的语言模型来说明世界语言演化的可能动力学机制。这个模型首先考虑最简化的情况,即不考虑语言人口因素的影响,在得到理想的结果后,再进一步细化即考虑语言人口因素对语言演化的影响。在这种情形下,解析得到的世界语言网的点强度分布同实证可以很好的吻合,同时这个模型还可以解析地得到世界语言网络的其它统计性质并与实证很好的符合。这说明本文的研究抓住了世界语言演化的关键因素,在一定程度上说明所建模型是可靠的。
在复杂网络研究中,合作网络和合作--竞争网络受到广泛关注。好多专家、学者给出了许多真知灼见,但是都只是定性的阐述并没有定量的来描述这些系统。在本文的工作中,定量地阐述了合作--竞争网络中一个广为人们接受的思想,即在竞争中独特性是非常重要的。为了定量的描述这一思想,提出了两个统计量:竞争力和独特性,解析后发现两者在一般情况下是相等的。这意味着独特性可以完全决定竞争力。为了验证得到的结果,把它应用到地方高校系统中,发现它的实证结果和解析结果是一致。这很好地说明了本文提出的两个物理量是很有价值的并对现实有很好的指导意义。
论文的最后汇报了二方组、三方组在合作中遵从的统一规律。这一研究是针对不同的系统进行的,虽然研究的系统横跨了不同学科门类,但是它们的二方组和三方组项目度分布却遵从统一的规律,即我们科研组倡导的“漂移幂律”分布(Shifted Power Law)。这一工作是对前面工作的加深和拓展,因此也是汇报的重点之一。
This thesis mainly reports the construction, properties and model of world languages network. On the basis of profound in research of a particular system (network of world languages) , we are inclined to investigate the property which plays key role in the process of competition, i.e. the key role of uniqueness in the competition, and research the basic units in different collaboration-competition systems and find the law which the units obey. That is the unified rule which dyads and triads follow. These are the contents we report here as well.
In the complex networks, we usually use bipartite graphs to describe a kind of networks. In this kind of networks, there are two sets of nodes, one is called“actors”in which take part events, activities, or organizations (i.e., the participants) and the other is called“acts”(i.e., events, activities, organizations). In the network of world languages, we view languages as“actors”and countries or regions as“acts”. In this kind of networks, if we only concern the interaction between actors, a projected single-mode (unipartite) network is often used (projected to the actor set). In this paper, we just pay attention to the relationship between languages, so we project the network into the language set. Meanwhile we use the population of a language to denote the node’s weight (that means the nonuniformity of language’s population). In this way we get weighted network of world languages. We investigate the topology properties of the world language network after the network is constructed. And we found the distribution of strength has distinct trait.That is the world languages can be divided into two kinds clearly from the figure of the language’s strength distribution(i.e. the duality of world languages). We call them active languages and inactive languages. That did not find and mention in traditional language research. In order to understand the duality of world languages better, we propose a minimal model to explain the may mechanism dynamics of world languages’evolution. The model gets ideal outcome in the most simple condition without considering the factor of language population. Then we consider the influence of language population and fine the model further. The analytic strength distribution of world language network fits the empirical investigation well. Meanwhile the model can get other statistic properties analytically and fits the empirical investigation as well. That show we catch the key factor of world languages’evolution, and in a certain degree show our model can stand up.
In the research of complex networks, collaboration networks and collaboration-competition networks attract a lot of attention. Many experts and scholars propose a lot of brilliant ideas, but these ideas are just qualitative description and do not present quantitative one. In our study, we present a quantitative expression of a well accepted idea about collaboration and competition: uniqueness is important in competition. In order to quantify this expression, we suggest two new statistical quantity called“competition ability”and“uniqueness”. We analyze the relationship of the two quantity and find they are equal in ordinary case. This means that uniqueness completely drives the competition. In order to check our outcome, we apply it to regional university system and find the empirical investigation in accord with our analytic outcome. That shows the two quantity we proposed is valuable and can give good advice to our real life.
In the end of the thesis, we report the unified law the dyads and triads obey in cooperation. This research aims at different systems. Thought the systems cross a lot of subjects, all the act degree distribution of their dyads and triads obey the same law, i.e. the“shifted power law”which is advocated by our group. This work extend our work before, therefore it is our key report as well.
引文
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[2] A L Barabasi, R Albert, Science 286 (1999) 509.
[3] P Erdos, A Renyi, Publ. Math. Inst. Hung. Acad. Sci. 5 (1960)17.
[4]汪小帆,李翔,陈关荣,复杂网络理论及其应用,清华大学出版社,北京2006.
[5] M E J Newman, Phys. Rev. E 64 (2001) 016131.
[6] M E J Newman, Phys. Rev. E 64 (2001) 016132.
[7] Y He, X Zhu, D R He, Int. J. Mod. Phys. B 18, 17 (2004) 2595.
[8] X Zhu, Y He , D R He , Bulletin of APS 49 (2004) 1006; Y He, P Zhang, Bulletin of APS 49 (2004) 1007; Y Zhang, Y He, D R He, Bulletin of APS 49 (2004) 1008; A Sun , P Zhang , Y He , B B Su , D R He , Bulletin of APS 49 (2004)1006; J Hu, P Zhang, R Qiu, J Tang, D R He, Bulletin of APS 49 (2004) 1008.
[9] P P Zhang, K Chen, Y He, et al. Physica A 360 (2006) 599.
[10] Y M Jiang, T Xu and D R He, Inter. J. Modern Physics B 18 (2004) 2604.
[11]何阅,张培培,许田,姜玉梅,何大韧,物理学报,53 (2004) 1710.
[12]张培培,何阅,周涛,苏蓓蓓,常慧,周月平,汪秉宏,何大韧,物理学报,55 (2006) 60.
[13]何大韧,中国高等科学技术中心,CCAST——WL workshop series: Vol. 170 (I), Second National Forum on Complex Dynamical Networks, 205-212.
[14] H Chang, B B Su, Y P Zhou, D R He, Physica A 383 (2007) 687.
[1] M Nowak, D Krakauer, Proc. Natl. Acad. Sci. USA 96 (1999) 8028.
[2] R Cancho, R Sole, Proc. Natl. Acad. Sci. USA 100 (2003) 788.
[3] M A Nowak, N L Komarova, P. Niyogi, Nature 417 (2002) 611.
[4] S N Dorogovtsev, J F F Mendes, Proc. R. Soc. London Ser. B 268 (2001) 2603.
[5] S Kirby, Evolutionary Computation, IEEE Transactions on 5 ( 2001) 102.
[6] R Cancho, R Sole, Proc. Natl. Acad. Sci. USA 100 (2003) 788.
[7] G K Zipf, Human Behaviour and the Principle of Least Effort (Addison-Wesley,Cambridge,Massachusetts,1949).
[8] S Kirby, Natural language and artificial life 8 (2002) 182.
[9] H H Bulthoff, S Edelman, Proc. Natl. Acad. Sci. USA 89 (1992) 60.
[10] R Conte, Proc. Natl. Acad. Sci. USA 99 (2002) 7189.
[11] Z Solan, D Horn, E Puppin & S Edelman, Proc. Natl. Acad. Sci. USA 102 (2005) 11629.
[12] D Abrams, S Strogatz, Nature 424 (2003) 900.
[13] C Schulze, D Stauffer, Phys. Life Rev. 2 (2005) 89.
[14] R Albert, A L Barabasi, Rev. Mod. Phys. 74 (2002) 47.
[15] S N Dorogovtsev, J F F Mendes, Adv. Phys. 51 (2002) 1079.
[16] M E J Newman, SIAM Review 45 (2003) 167.
[17] S Boccaletti, et al., Phys. Rep. 424 (2006) 175.
[18] R F I Cancho, R V Sole, Proc. Natl. Acad. Sci. USA 100 (2003) 788.
[19] R V Sole, B C Murtra, et al, 2005, Santa Fe Institute Working Paper/05-12—042
[20] R Sole, Nature 434 (2005) 289.
[21] M A F Gomes, G. L. Vasconcelos, et al, Physica A 271 (1999) 489.
[22] S Wichmann, Journal of Linguistics 41 (2005) 117.
[23] http://www.ethnologue.com/.
[24] A L Barabasi, R Albert, Science 286 (1999) 509.
[25] H Chang, B B Su, Y P Zhou & D R He, Physica A 383 (2007) 687.
[26] R Pastor-Satorras, A Vazquez, A Vespignani, Phys. Rev. Lett. 87 (2001) 258701.
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