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Jingdong book

复杂系统与复杂网络

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本书为学习和研究复杂网络的初学者们阐述了必要的基础知识;为使用复杂网络工具研究复杂系统的非物理同行们提供了物理工作者的观点和方法;为高校师生和学术界的青年朋友们介绍了复杂网络与复杂系统科学的一些最新研究进展。
Content Description

《复杂系统与复杂网络》从研究复杂系统的角度来介绍复杂网络。作为一本入门引导,前五章介绍一些复杂系统理论的基础知识,包括熵、计算机与信息、非平衡统计物理学、耗散结构与协同学、临界现象与自组织临界性、混沌、元胞自动机模型、复杂性的定义与量度、有关的统计物理学方法、博弈论、数理统计、图论等。第六、第七章介绍复杂网络的一些基础知识,包括描述网络拓扑结构的统计性质以及一些有影响的网络演化模型。在第八、第九、第十章中介绍了网络上的物理传输过程、生命网络和合作网络与合作一竞争网络。其中侧重介绍了作者群体的工作。另外,《复杂系统与复杂网络》阐述了作者们对复杂网络研究前景的一些看法,特别是在第十一章中介绍了关于复杂网络动力学框架的一些最新研究。
《复杂系统与复杂网络》可作为复杂系统与复杂网络研究方向的研究生教材,也可作为相关领域研究人员的参考书。
Catalogue

第一章 漫谈复杂性与复杂系统
1.1 熵
1.2 计算机与信息
1.3 算法复杂性
1.4 非平衡统计物理学、耗散结构与协同学
1.5 临界现象与自组织临界现象
1.6 混沌
1.7 原胞自动机
1.8 描述复杂性与统计复杂性
第一章参考文献
第二章 一些有关复杂网络研究的统计物理学方法
2.1 连续相变的平均场理论
2.2 自组织临界现象的平均场理论
2.3 流行病传播的平均场理论简介
2.4 主方程
2.5 生成函数
2.6 率方程
第二章参考文献
第三章 博弈论及演化网络博弈
3.1 基本概念
3.2 完全信息静态博弈与纳什均衡
3.3 完全信息动态博弈与子博弈精炼纳什均衡
3.4 不完全信息静态博弈与贝叶斯纳什均衡
3.5 不完全信息动态博弈与精炼贝叶斯纳什均衡
3.6 合作博弈
3.7 演化网络博弈
3.8 城市公交网络的网络操纵者博弈模型
第三章参考文献
第四章 数理统计简介
4.1 一些基本概念
4.2 统计假设及其检验
4.3 一元线性回归
4.4 回归的一些问题
4.5 漫谈数据的采集与处理
第四章参考文献
附录
第五章 图论简介
5.1 一些基本概念
5.2 图的连通性
5.3 树图
5.4 最短道路问题
5.5 图的矩阵描述
5.6 有向图
5.7 二分图
5.8 网络流
第五章参考文献
第六章 复杂网络的统计描述
6.1 平均距离、谐平均距离、效率与脆弱性
6.2 集群系数、圈系数、富人集团系数、集团度
6.3 度、度分布、度相关性
6.4 边权网及边权的一些统计性质
6.5 二分图的二分度
6.6 中心度与中心化
6.7 谱分析
6.8 模体
6.9 群落、派系与层次
6.10 度分布熵、目标熵以及不同的网络信息熵
6.11 多标度分形的分数维谱
6.12 漫谈复杂网络的统计描述
第六章参考文献
第七章 一些网络演化模型
7.1 ER随机网模型
7.2 WS小世界网模型
7.3 BA无标度网模型
7.4 BA无标度网模型的主方程解
7.5 BA无标度网模型的率方程解
7.6 部分优选、部分随机选择模型
7.7 局域世界模型
7.8 赋权演化网络的BBV模型
7.9 可调集群系数的HK模型及其改进模型
7.10 JGN社会网络模型
7.11 自组织耦合演化模型
7.12 其他运用统计物理学方法的模型研究
第七章参考文献
第八章 复杂网络上的物理传输过程
8.1 流行病传播的基本模型
8.2 复杂网络上的流行病传播
8.3 复杂网络上的舆论传播
8.4 群落网结构对流行病传播的影响
8.5 动态群落网上的流行病传播
8.6 因特网上的信息包传递
8.7 因特网上交通堵塞的控制
8.8 交通数据的去趋势涨落分析
8.9 复杂网络上的粒子输运
8.10 粒子输运的平均场方法
8.11 加权复杂网络上的粒子输运
8.12 简单网络上能量输运
8.13 复杂网络上能量输运
展望
第八章参考文献
第九章 一些生命网络的研究
9.1 大脑功能网络
9.2 两态小动物群体网络
9.3 生物分子网络
第九章参考文献
第十章 合作网络与合作一竞争网络
10.1 简介
10.2 比较早期的合作网实证研究
10.3 合作网的项目大小分布和项目度分布
10.4 合作网的同类性与项目度分布的相关性
10.5 二分图投影的资源分配方法
10.6 近期关于合作网络的实证研究
10.7 关于合作一竞争网络的研究
第十章参考文献
第十一章 网络动力学的一些探索
11.1 布尔网络、信息距离及一些复杂网络的非线性动力学
11.2 最小作用量原理与网络形态的自然选择
11.3 图的动力学谱分析
第十一章参考文献
Book Abstract

第一章 漫谈复杂性与复杂系统
从20世纪末以来,不少物理学工作者一直在寻求描述复杂系统的概念和理论,力图把物理学的适用领域推广到复杂系统。近十年来,复杂网络成为被寄予希望的一种描述工具。然而,要把复杂网络与复杂系统的研究很好地结合,首先要知道什么是复杂,什么是复杂系统、简单系统以及复杂性。这可能也是古往今来许多智者反复思考过的问题。除了定性的回答之外,几十年来,许多科学家致力于建立定量的定义,希望利用这样的定义来定量计算各种系统的复杂程度,从而比较不同系统复杂程度的大小。他们的成果尽管都还没有得到公认,但是很可能是建立复杂系统理论的必经阶段之一。这类研究论文数量相当多,已经提出的定义五花八门,有些很难搞懂,更难计算,要在本章中全面介绍不大可能,然而,这些研究发展的大趋势是一致的,都是从20世纪中叶以来物理学及一些别的科学分支的一些大进展延拓开来的。我们认为与复杂网络研究直接关联的正是这些大进展带来的物理学新理解,而不是个别的复杂性定义。因此,本章将主要介绍这些大进展,对复杂性定义仅按照我们的看法选择一小部分进行简介。知道这些知识对读者们理解本书以后介绍的内容很可能是必要的。由于本章各节的内容都涉及一门大学科,这里不可避免地只能作科普性的介绍,就当是在以后各章理论内容之前的一段比较轻松的阅读吧。
Introduction

十年之前(1998年6月4日),Nature发表了两位年轻的物理学家(D.J.Watts和s.H.Strogatz)关于网络的一篇论文。一年多之后(1999年10月15日),Science又发表了另外两位年轻的物理学家(A.L.Barabasi和R.Albert)关于网络的另一篇论文。这两篇论文引发了关于复杂网络的研究热潮。这个潮流席卷全球,涉及数学、力学、物理学、计算科学、管理科学、系统科学、社会科学、金融经济科学等许多科学领域,以及交通运输、能源传输、通信工程、电子科学,甚至医学、烹饪等许多应用学科。至今(2008年3月),D.J.Watts和S.H.Strogatz的论文被SCI收录的论文引用5670次;A.L Barabasi和R.Albert的论文被引用3275次。
人们把周围的许多系统(天然的或者人造的,例如交通网、电力网、人际关系网等)看作网络由来已久,运用数学的一个分支——“图论”对这些系统进行研究也已经有百年以上的历史。上述两篇文章的重要之处在于作者发现许多实际网络具有一些共同的拓扑统计性质,即“小世界性”和“无标度性”。这些性质既不同于规则网络,也不同于随机网络,正像近几十年来物理学家认为“复杂位于规则与随机之间”一样,所以大家把实际网络称为“复杂网络”。所谓小世界性是指实际网络具有比规则网络小得多的平均节点间距离和比随机网络大得多的平均集群系数(即邻点之间也相邻,形成紧密集团的比例);而无标度性则指实际网络中节点邻边数取一个定值的概率分布函数是幂函数(规则网的这个分布是函数,而随机网是正态分布)。这个幂函数标志基本单元与其邻居相互作用能力的极其不均匀分布。更加引人注目的是:_论文的作者提出了解释这些独特规律的网络演化模型,而且运用统计物理学方法从这些模型解析地得出了这些独特规律。这些模型的思想简单明白、直观合理。产生小世界性的机制就是一部分基本单元之间相互作用的远程性、跳跃性和随机性;产生无标度性的机制就是基本单元建立相互作用的“优选”(或者称为“富者更富”)法则。这是第一次把统计物理学的思想和方法引进网络或者图论的研究,因此,若与传统的图论或网络理论比较,也许可以说当前的复杂网络研究的特征就是统计物理学的进入,所以应该把统计物理学列入复杂网络研究的基础知识之中。

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Jingdong book