Complex Networks and Complex Processes

这笔赠款支持统计物理的理论研究。本研究分为两个部分。第一部分将研究网络的性质。网络在我们的生活中无处不在，范围从互联网到生物和社交网络。应用统计物理学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，本研究侧重于研究异质网络的结构和动力学特性，并应用首通道统计学来解释基本的复杂过程。智力优势：异质网络的一个显著特征是每个节点的度(连接的链路数量)具有广泛的分布。此功能会对这些网络和底层网络结构上发生的物理过程产生深远的影响。在该项目的第一部分，将研究如何在最初包含竞争的友好和不友好的结对互动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的共识形成动力学，其中潜在的广度分布控制着动力学。在网络结构的主题上，将研究非稀疏网络上的大波动现象。此外，还将调查专业化的动态，在这种情况下，最初的同质网络随着其增长而变得更加模块化，这是一个普遍存在的过程，是科学进步和社会组织的本质基础。对于所有这些例子，主方程方法将是我们主要的调查工具。在这项研究的第二部分，来自首通道统计的经典方法将被应用于具有生物学和基本分支的各种随机过程。一个这样的例子是细胞分裂的统计，其中复制衰老(本质上是细胞死亡)由每个细胞中包含的端粒的长度决定。在每个细胞分裂时，每个子细胞中的端粒长度减少，当端粒长度达到零时细胞死亡。首次通过的想法将被用来确定细胞群体的寿命分布。另一项研究工作将致力于了解竞争种群中社会多样性的机制，在这种机制中，个体代理人可以通过与不太适合的代理人竞争来获得适应性，或者由于不活动而失去适应性。这些相互作用导致了健康空间中的随机行走，其跳跃概率取决于健康。关于这个随机过程的基本问题，例如由这样的代理人组成的社会是平等主义的还是内在的不公平的，将被解决。最后，我们将研究最简单的“活塞”问题--一个有限的一维间隔，其中一个大质量粒子将两个轻得多的粒子分开。这个理想化的系统展示了非常丰富的动力学，可以通过构造到等价台球系统的映射和利用首次通过的想法来理解。这种方法将被扩展到对包含许多粒子的真实活塞系统以及粒子发生非弹性碰撞的情况下的洞察。波及影响：这项研究是研究生广泛参与的理想选择。其中许多问题相对容易概念化，而且这些项目的重要方面不需要广泛的正式背景就能使学生变得富有成效。适当的调查方法包括分析和数值的健康组合，从而为学生提供广泛的理论培训。因此，概述的项目将为几名研究生的博士论文研究提供基础，从而为研究生教育做出重大贡献。此外，几名拥有外部资金的国际博士后研究员最近在波士顿大学花了1-2年的时间从事与赠款相关的项目，从而极大地利用了NSF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)和圣达菲研究所(SFI)合作进行。一些项目是过去一年驻留在LANL期间由PI发展的科学互动的自然结果。关于意见动态和社会多样性的项目，特别是关于社会多样性的项目，与SFI目前的重点很好地契合，并为与该机构的物理和社会科学家进行合作研究提供了一个自然的部分。

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.