【作者】 周斌；

【导师】 汪秉宏；

【作者基本信息】 中国科学技术大学 ， 理论物理， 2015， 博士

【摘要】 双向选择在人类的日常生活中是非常普遍的。为了研究隐藏在人类双向选择行为背后的机制和规律,我们建立了一个关于任意双向选择系统的最小模型,并且得到了这个模型的解析解。模型包括了三个影响双向选择的主要因素,分别是双向选择双方各自的个体总数k1,k2和双向选择双方个体所共有的可供选择的总特性数n。在三种不同的条件下,我们对模型的精确解释式作了近似分析,得到了更简洁的函数关系：配对成功率P和相关变量成简单的反比例关系,并和模型的仿真结果是一致的。现实中男女之间爱情选择是典型的双向选择问题,为了验证模型在现实中的有效性,我们搜集了现实中82组关于相亲大会的实证数据。由于相亲大会提供的数据信息不完整,只提供了参加的总人数和配对成功总对数,并没有提供详细的男女双方各自的人数,所以我们无法用模型和实证数据做精确的对比,我们只能把模型和实证数据做一个粗糙的验证,我们发现大多数实证数都落在了模型可以预测的范围内,但是当参加相亲大会的总人数相对较少时,会有少量实证数据落在模型所能预测的区域范围之外,我们对此做出了合理的解释。因此总体上讲,实证数据理论上验证了模型的合理性,如此一个简单的双向选择模型对了解现实中双向选择系统的内在机制有一定的价值和现实意义。上面的研究属于双向选择在复杂系统和网络科学领域的一个基础性初步研究。其双向选择机制是建立在一个全联通网络上。为了进一步加深对双向选择课题的研究,我们将双向选择机制拓展到了任意一个网络上,包括主流的网络模型(ER随机网络,WS小世界网络,BA无标度网络)以及现实中的网络。并且给出了模型在任意一个网络上的解析解,模型仿真结果和模型的数学解析结果吻合的非常好,说明了解析结果的精确性和正确性。我们主要选做了双向选择机制在三个主流网络上的研究：ER随机网络,WS小世界网络,BA无标度网络。经过研究发现,一个个体的邻居的数量和状态直接决定了个体的匹配成功率,而且网络的平均度越高,个体的匹配概率也越高。在三个主流网络模型中,我们发现WS小世界网络的拓扑结构最有利于匹配,而BA无标度网络的拓扑结果最不利于匹配。WS小世界网络是在以现实中社交网络为基础上研究建立起来的,那么我们的双向选择机制研究可以暗示现实中社交网络的演化形成很可能遵守着有利于异性个体之间的匹配这一基本规则。此研究工作对现实中的双向选择研究更进了一步,让我们对双向选择的基础研究从一开始的特殊性网络(全联通网络)拓展到任意一个网络上,我们认为这对后续关于现实中双向选择现象的理论和应用研究有一定的意义和作用。更多还原

【Abstract】 Two-way selection is wide-spread in nature and society, such as the marriages be-tween men and women, the conclusion of contracts between job hunters and recruiters, and the trade between buyers and sellers. We propose a model of two-way selection system and provide its exact solution. Defining two basic relative ratios:η for the ra-tio of selection quantities from both sides, and ξ for the ratio of the total number of states to the smaller number of two sides, we find the matching rate P of two-way se-lections trends toward an inverse proportion to either η or ξ under different conditions, in agreement with the numerical simulations. Eighty-two pieces of news of real-world matchmaking fairs are collected from the Internet. We surprisingly notice that, most of the empirical data of the matchmaking fairs, the typical real-world two-way selections, are included in the range predicted by our model, implying such a simple model is help-ful for understanding dynamics mechanism of real-world two-way selection system and would be valuable to the real life.A bidirectional selection model we described above has been presented to investi-gate the factors influencing the matching rate. The model is presented on the Globally coupled network. But the real networks often are not the Globally coupled network, and the average degree are often far smaller than the number of nodes in the real net-work. In addition, many real complex networks have emerged some common charac-teristics, such as small world phenomena, scale-free properties with power-law degree distributions. Therefore some famous networks’models with real networks charac-teristics have been proposed, for instance:Nearest-neighbor coupled network model, WS small world network model, ER random network model and BA scale-free network model, etc. Therefore, we should deeply study the matching of two-way selection sys-tem on complex networks. We demonstrated theoretically that the rate of successfully matching is affected greatly by individuals’neighborhoods in social networks, regard-less of the type of networks. Furthermore, it is found that the high average degree of networks contributes to increasing rates of successful matches. The matching perfor-mance in different types of networks has been quantitatively investigated, revealing that the small-world networks reinforces the matching rate more than scale-free networks at given average degree. In addition, our analysis is consistent with the modeling result, which provides the theoretical understanding of underlying mechanisms of matching in complex networks.更多还原