Complex Networks and Complex Processes

这笔经费用于支持统计物理学的理论研究。本研究分为两部分。一部分将研究网络的性质。网络在我们的生活中无处不在，从互联网到生物和社会网络。应用统计物理的方法可以揭示网络的性质。研究的第二部分涉及将统计物理方法应用于更复杂的系统，如生物系统。特别是，本研究侧重于异构网络的结构和动态特性，并应用首通道统计来阐明基本的复杂过程。智力优势：异构网络的一个显著特征是每个节点的程度（附加链路的数量）具有广泛的分布。这一特征对发生在这些网络和底层网络结构上的物理过程有着深远的影响。在该项目的第一部分，将研究如何在最初包含竞争友好和不友好的成对交互的网络中实现社会平衡的问题。还将研究异质网络上选民模型共识形成的动力学，其中潜在的广泛程度分布控制着动力学。在网络结构方面，将研究非稀疏网络上的大波动现象。此外，还将研究专业化的动态，其中一个最初同质的网络随着发展而变得更加模块化，这是一个无处不在的过程，是科学进步和社会组织本质的基础。对于所有这些例子，主方程方法将是我们主要的研究工具。在本研究的第二部分，经典方法从第一通道统计将应用于不同的随机过程与生物和基础分支。一个这样的例子是细胞分裂的统计，其中复制性衰老（本质上是细胞死亡）是由每个细胞中端粒的长度决定的。每次细胞分裂时，子细胞的端粒长度减少，当端粒长度达到零时细胞死亡。第一次传代思想将被应用于确定细胞种群的寿命分布。另一项研究工作将致力于理解竞争群体中社会多样性的机制，其中个体主体可以通过与不太适合的主体竞争来获得适应性，或者由于不活动而失去适应性。这些相互作用产生了具有依赖于适应度的跳跃概率的适应度空间中的随机漫步。关于这一随机过程的基本问题，例如由这些代理人组成的社会是平等主义的还是天生不公平的，将得到解决。最后，将研究最简单的“活塞”问题——一个有限的一维区间，其中一个大质量粒子将两个轻得多的粒子分开。这个理想化的系统表现出极其丰富的动态，可以通过构造到等效台球系统的映射和利用第一通道思想来理解。这种方法将被扩展到包含许多粒子和粒子经历非弹性碰撞的真实活塞系统。更广泛的影响：该研究是理想的广泛的研究生参与。许多问题相对容易概念化，并且这些项目的重要方面在学生能够富有成效之前不需要广泛的正式背景。适当的调查方法包括分析和数字的健康组合，从而为学生提供广泛的理论训练。因此，所概述的项目将为若干研究生的博士论文研究提供基础，从而对研究生教育作出重大贡献。此外，最近有几位国际博士后利用自己的外部资金在波士顿大学度过了1-2年的时间，从事与赠款相关的项目，从而大大利用了美国国家科学基金会的资金。最后，预计一些研究将与同事和洛斯阿拉莫斯国家实验室（LANL）以及圣达菲研究所（SFI）合作进行。许多项目是PI在过去一年中在LANL居住期间发展的科学互动的自然结果。特别是关于舆论动态和社会多样性的项目，与SFI目前的重点很好地结合在一起，并为该机构的物理和社会科学家提供了一个自然的合作研究。

This grant supports theoretical research on statistical physics. The research is divided into two parts. One part will study the properties of networks. Networks are ubiquitous in our lives and range from the internet to biological and social networks. Network properties can be revealed by applying methods from statistical physics. The second part of the research deals with applying statistical physics methods to more complicated systems such as biological ones. In particular, this research is focused on structural and dynamical properties of heterogeneous networks and on applying first-passage statistics to elucidate fundamental complex processes.Intellectual Merit: A prominent feature of heterogeneous networks is that the degree of each node (the number of attached links) has a broad distribution. This feature has profound consequences for physical processes occurring on these networks and on underlying network structure. In the first part of the project, the question of how social balance is achieved in networks that initially contain competing friendly and unfriendly pair-wise interactions will be investigated. The dynamics of consensus formation for the voter model on heterogeneous networks will also be studied, where the underlying broad degree distribution controls the dynamics. On the topic of network structure, the phenomenon of large fluctuations on non-sparse networks will be studied. In addition, the dynamics of specialization will be investigated, where an initially homogeneous network becomes more modular as it grows, a ubiquitous process that underlies both the nature of scientific progress and societal organizations. For all these examples, the master equation approach will be our primary investigative tool. In the second part of this research, classical methods from first-passage statistics will be applied to diverse stochastic processes with biological and fundamental ramifications. One such example is the statistics of cell division, where replicative senescence (essentially cell death) is governed by the length of telomeres contained in each cell. Upon each cell division, the telomere lengths in each daughter cell decreases and the cell dies when telomere length reaches zero. First-passage ideas will be applied to determine the lifetime distribution of a cell population. Another research effort will be devoted to understanding mechanisms for social diversity in competitive populations, where individual agents can gain fitness by competing with less fit agents, or can lose fitness due to inactivity. These interactions give rise to a random walk in fitness space with fitness-dependent hopping probabilities. Basic question about this stochastic process, such as whether a society consisting of such agents is egalitarian or inherently unfair, will be addressed. Finally, the simplest "piston" problem - a finite one-dimensional interval where a massive particle separates two much lighter particles - will be investigated. This idealized system exhibits extremely rich dynamics that may be understood by constructing mappings to equivalent billiard systems and by exploiting first-passage ideas. This approach will be extended to develop insights for real piston systems that contain many particles and also where particles undergo inelastic collisions.Broader Impacts: The research is idealfor extensive graduate student participation. Many of the problems are relatively easy to conceptualize and important aspects of these projects do not require extensive formal background before a student can become productive. The appropriate investigative methods involve a healthy mix of analytics and numerics, thus providing broad theoretical training for students. The projects outlined will thus contribute substantially to graduate education by providing the basis for the Ph.D. thesis research of several graduate students. Additionally, several international postdoctoral fellows with their own external funding have recently spent 1-2 year periods at Boston University to work on grant-related projects, thus considerably leveraging NSF funds.Finally, it is anticipated that some of the research will be performed in collaboration with colleagues and Los Alamos National Lab (LANL) and at the Santa Fe Institute (SFI). A number of the projects are natural outgrowths of scientific interactions developed by the PI while in residence at LANL during the past year. The projects on opinion dynamics and on social diversity, in particular, mesh well with the current emphasis at SFI and provides a natural segue to collaborative research with the physical and social scientists at this institution.