【作者】 王伟；

【导师】 高辉；

【作者基本信息】 电子科技大学 ， 计算机软件与理论， 2017， 博士

【摘要】 在现实世界中,计算机病毒、信息、谣言、健康行为和金融风险等传播现象都可以描述为复杂网络上的传播动力学。根据不同的研究对象,传播动力学可分为三类:生物传播、社会传播和社会—生物传播。生物传播主要关注计算机病毒和传染性疾病这类简单传播动力学,社会传播主要研究行为和金融风险这类具有加强效应的复杂传播动力学,而社会—生物传播主要研究信息—疾病共演化过程。传播动力学旨在揭示真实传播现象的演化机制和规律,并建立合理的数学模型,进一步预测和控制动力学过程。本论文将分三部分研究以上三类动力学。本文第一部分研究复杂网络上的生物传播,系统地研究理论方法在预测传播范围和爆发阈值时的准确性。平均场类型(MFL)方法、淬火平均场(QMF)方法和动态信息传递(DMP)方法是预测爆发阈值的三类常用理论方法。对于任意网络上的生物传播,利用以上三类理论方法通常会得到不同的爆发阈值,而它们的关联性和准确性还尚未知晓。因此,通过分析SIR模型在无关联配置网络和56个真实网络上的传播,本文首先研究三类方法所预测的理论阈值之间的关联性和准确性。对于无关联配置网络,MFL方法和DMP方法的理论阈值相同,并且更接近于真实阈值。对于56个真实网络,在大多数情况下,DMP方法的理论阈值更接近于真实阈值。然而,对于大多数正关联网络、特征向量局域于核的网络和高集群系数的网络,MFL方法所得的理论阈值最接近于真实阈值。对于权重网络上的生物传播,准确的理论方法仍然欠缺。鉴于此,我们还拓展一套准确的边权划分方法来研究具有任意度分布和权重分布网络上的生物传播,发现度分布异质性促进疾病爆发,而权重分布异质性抑制疾病爆发。进一步,本文提出一个基于边权移除的疾病控制策略,发现偏好地免疫高权重边更利于控制疾病传播,尤其是对于度分布均匀且权重分布异质性强的网络。对于具有任意度分布和权重分布的网络,理论值和模拟值很吻合。研究结论不仅加深了人们对现有理论方法的认识和理解,更为发展准确的理论方法提供了新思路。本文第二部分研究复杂网络上的社会传播。由于采纳行为时需要判断其可靠性和合法性,因此加强效应是社会传播中一个至关重要的机制。非冗余信息记忆对加强效应的影响极大,但目前仍然缺乏系统地研究。鉴于此,本文系统地研究网络结构和动力学参量对基于非冗余信息记忆社会传播的影响。首先提出一个基于非冗余信息记忆加强效应的社会传播模型,并拓展一套准确的边划分方法来描述该模型。通过研究传播阈值模型,我们发现行为采纳比例随信息传递率呈连续增长或非连续增长。值得注意的是,系统存在一个交叉现象:行为采纳增长形式从连续增长变为非连续增长。减小采纳阈值、增大初始感染态比例或增强度分布异质性,交叉现象就会出现。考虑到不同个体之间采纳阈值的差异性,进一步研究采纳阈值的异质性对社会传播的影响。在此,我们提出一个二元传播阈值模型,假设一些个体的采纳阈值较低(即“活跃者”),其余个体采纳阈值较高(即“顽固者”)。通过边划分理论和实验模拟分析,我们发现系统存在一级相变、二级相变或混合相变,并且相变之间有两种转变。当顽固者的采纳阈值较低时,增大活跃者相对比例,相变从一级转变为二级;当顽固者的采纳阈值较大时,改变活跃者比例、减小平均度或增强度分布异质性,系统相变从混合转变为二级。由于个体受到有限资源的限制,最后我们研究接触能力对社会传播影响,并拓展一套异质边划分方法,发现增加接触能力促进行为传播。系统还存在一个临界度分布指数:当度分布指数大于它时,若增加接触能力,行为采纳增长形式从连续变为非连续。研究结果加深了人们对社会传播的认识和理解,理论方法为准确刻画其它非马尔科夫动力学过程提供了一定的借鉴意义。本文第三部分研究复杂网络上的社会—生物传播。在现实世界中,生物传播和社会传播往往相互影响、共同演化,揭示它们的耦合机制、利用社会传播控制生物传播,是复杂网络上社会—生物传播的两个主要研究内容。然而,目前对以上两点的研究还较少。鉴于此,通过分析信息和疾病传播的共演化真实数据,我们首次发现了它们之间存在着非对称耦合作用:疾病传播促进信息传播,信息传播抑制疾病传播。然后,提出一个在通讯—接触耦合网络上基于简单免疫机制的信息—疾病传播模型。在模型中,假设当接触网络上的节点的耦合节点接收到了信息时,它就以一定的概率被免疫。通过异质平均场理论和实验模拟,我们发现接触网络上的疾病爆发会导致通讯网络上的信息爆发,信息扩散能够有效地增大疾病爆发阈值。此外,层间度关联会增加疾病爆发阈值。由于免疫存在风险和代价,理性的人在采取免疫措施之前时,需要多方确认自身是否有被疾病感染的可能。然而,多方确认机制对社会—生物传播的影响还未曾研究。因此,我们最后提出一个基于多源信息确认机制的信息—疾病传播模型。通过理论分析和实验模拟,我们发现信息自身传播或疾病爆发都会导致信息爆发,但疾病爆发阈值不受信息扩散影响。当指定疾病传播概率时,系统存在一个最优的信息传递概率,能极大程度地抑制疾病传播,并且动力学的时间演化过程与真实数据能定性地吻合。此外,耦合网络结构不会定性地影响上述现象。研究结果为社会—生物传播建模和分析奠定了一些基础,更为生物传播提供了新的控制手段。更多还原

【Abstract】 In real-world,the spreading of computer virus,information,rumor,healthy behavior,financial risk,etc.,can be described as spreading dynamics on complex networks.The spreading dynamics can be,based on the difference of studied objectives,classified into three categories: biological contagions,social contagions and social-biological contagions.Biological contagions mainly focus on a type of simple spreading dynamics,like computer virus and infectious diseases.Social contagions primarily investigate a type of complex spreading dynamics with reinforcement effects,such as the spreading of behavior and financial risk.Social-biological contagions principally study the coevolution of information and diseases.Spreading dynamics aims to reveal the evolution mechanisms and laws in real-world spreading phenomena,building reasonable mathematical models,and further forecasting and controlling these dynamical processes.This dissertation is divided into three sections to study the above three types of contagions.In the first section,the dissertation studies the biological contagions on complex networks,which systematically investigates the accuracy of theoretical approaches in predicting the spreading size and outbreak threshold.The mean-field like(MFL)method,the quenched mean-field(QMF)method,and the dynamical message passing(DMP)method are three types of widely used approaches to predict the outbreak threshold.For the biological contagions on a general network,three different outbreak thresholds are usually obtained when using the above three theoretical methods,while their relationships and precisions are still unclear.Thus,by studying the spreading of SIR model on uncorrelated configuration networks and 56 real-world networks,this dissertation first studies the relationships among the three approaches and the precisions of them.For the uncorrelated configuration networks,the MFL and DMP methods predict the same theoretical thresholds,and are closer to the accurate threshold.For most of the 56 real-world networks,the theoretical threshold predicted by the DMP method is closer to the accurate threshold.However,the threshold predicted by the MFL method is more closer to the accurate threshold for most of the networks with positive degree-degree correlations,an eigenvector localized on the high -core nodes,or a high level of clustering.For biological contagions on weighted networks,an accurate theoretical approach is still lacking.Thus,we generalize an accurate edge-weight-based compartmental approach to study biological contagions on networks with general degree and weight distributions,and find that the heterogeneity of degree distribution promotes disease outbreak,while the heterogeneity of weight distribution suppresses the disease spreading.Furthermore,we propose an edge-weight-based removal strategy to control the spread of disease,and find that it is effective to control the spreading of disease when preferentially remove highly weighted edges,especially for networks with homogeneous degree distribution and extremely heterogenous weight distribution.The theoretical predictions are remarkable agree with numerics for networks with general degree and weight distributions.The results not only let us have a deeper understanding about the existing approaches,but also provide some insights into developing accurate theoretical approaches.In the second section,the dissertation studies the social contagions on complex networks.Reinforcement effect is an important mechanism since individuals need to verify the credibility and legitimacy of a behavior before adopting it.Memory of nonredundant information plays an important role in reinforcement,which so far has not been studied systematically.To this end,this dissertation systematically studies the effects of network structures and dynamical parameters on social contagion model with reinforcement derived from nonredundant information memory.This dissertation first proposes a non-Markovian social contagion model with reinforcement derived from nonredundant information memory,and develops an accurate edge-based compartmental theory to describe the proposed model.By studying a spreading threshold model,we find that the growth pattern of final adoption size increases continuously or discontinuously versus information transmission probability.It’s worth noting that the system has a transition phenomenon,i.e.,the growth pattern of final adoption size can change from being discontinuous to being continuous.The transition can be triggered by decreasing individuals’ adoption threshold,increasing initial seed size,or enhancing the network heterogeneity.Since the differences among distinct individuals,the effect of the heterogeneity of adoption threshold is then studied.We herein propose a two-state spreading threshold model,and assumes that some individuals have a low adoption threshold(i.e.,“activists”)while the remaining ones hold a relatively higher adoption threshold(i.e.,“bigots”).Through the edge-based compartmental theory and numerical simulations,we find that the system has first-order,second-order,and hybrid phase transitions,and two types of crossover phenomena in phase transitions.For a relatively low adoption threshold of bigots,the phase transition changes from first-order to second-order when increasing the fraction of activists;for a relatively higher adoption threshold of bigots,the phase transition changes from hybrid to second-order when varying the fraction of activists,decreasing average degree or enhancing network heterogeneity.Since individuals are restricted by limited resources,we finally study the effects of limited contact capacity on social contagions,and generalize a heterogeneous edge-based compartmental theory,and find that enlarging the contact capacity promotes the behavior spreading.In addition,the system has a critical degree exponent.When the degree exponent is above the critical degree exponent,the growth pattern of final behavior adoption size changes from being continuous to being discontinuous by enlarging the contact capacity.The research results provide us a deeper understanding about the social contagions,and the theoretical approach has some references for establishing an accurate theory to describe other non-Markovian dynamics.In the third section,the dissertation studies the social-biological contagions on complex networks.In reality,biological contagions and social contagions are always interacting and coevolving with each other.Revealing the interacting mechanisms and controlling biological contagions by using social contagions are two mainly research contents of social-biological spreading on complex networks.However,there is still few studies about the above two research contents.Thus,by utilizing real coevolution data about information and disease,we first find that there is an asymmetrical interactions between the two dynamics: disease spreading promotes information diffusion,and information diffusion suppresses disease spreading.Then,an information-disease spreading model based on a simplified immunization mechanism on communication-contact coupled networks is proposed.In this model,assuming that a node on contact network will be immunized with a probability when its counterpart on communication network is informed.By using the heterogeneous mean-field theory and numerical simulations,we find that the disease outbreak on the contact layer induces the information outbreak on the communication layer,and the disease threshold is enlarged since the information diffusion.In addition,the structural degree correlation between the two layers increases the disease threshold.The risky and expense of immunization induce that a rational person should consider whether he is risky enough through multiple affirmations before adopting immunization strategy.However,the effects of multiple affirmations mechanism on social-biological are still lacking.Thus,we finally propose an information-disease spreading model with multiple information affirmations.By theoretical framework and numerical simulations,we find that an information outbreak can be triggered by its own spreading dynamics or by a disease outbreak,but that the disease threshold is not affected by information diffusion.For a given disease transmission probability,there is an optimal information transmission probability that markedly suppresses the disease spreading,and the time evolution of the dynamics in the proposed model qualitatively agrees with the real-world data.In addition,the phenomena are not qualitatively affected by the network structures.The research results not only provide some foundations in the modelling of social-biological spreading dynamics,but also offer new strategies for controlling biological contagions.更多还原