Stochastic Spatial Models: on Complex Networks, Coevolution, and Modeling Cancer

随机空间模型：关于复杂网络、共同进化和癌症建模

• 批准号: 1305997
• 负责人: Richard Durrett
• 金额: $ 16.5万
• 依托单位: Duke University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-15 至 2015-08-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1305997&HistoricalAwards=false
• 关键词: Stochastic; Spatial; Models; Complex; Networks

Research will be carried out on various aspects of stochastic spatial models taking place on regular lattices and on complex networks. (i) With Ted Cox and Ed Perkins, the author has studied voter model perturbations. This work will be the starting point for studying evolutionary games with weak selection in order to try to resolve some recent conjectures of Martin Nowak. (ii) The proposer has studied various processes on random regular graphs in joint work with Shirhsendu Chatterjee. The main thrust of the new work will consider process on graphs with more general degree distributions, but we will also consider models in which a threshold of more than one neighbor with a different opinion is needed for an individual to change. (iii) A third theme is to study networks in which the state of the system and the connections in the network coevolve. This work leads to difficult questions about stochastic evolutions on the space of all labeled graphs.The world around us is spatially structured. In biological systems, organisms and infections only spread over short distances. Social systems have a network structure that is described by a graph with vertices being individuals and edges between those that interact. Connections between individuals may extend over large physical distances, but diseases, opinions, and new technologies spreading due to the interactions between an individual and their neighbors in the graph. Most mathematical analyses ignore spatial or network structure because its inclusion greatly complicates the analysis. However, as our past work with Simon Levin and others has shown, incorporating spatial structure changes the outcome of ecological competition. Our new work will focus on how spatial structure changes the impact of frequency dependent selection, and how the network structure of a social system changes the behavior of processes that occur in it. The models are idealized but the results give valuable insights about real systems.

研究将进行随机空间模型的各个方面发生在规则的格子和复杂的网络。(i)作者与Ted考克斯和艾德帕金斯一起研究了选民模型扰动。这项工作将是研究弱选择进化博弈的起点，以解决马丁·诺瓦克最近的一些问题。(ii)提出者在与Shirhsendu Chatterjee的联合工作中研究了随机正则图上的各种过程。新工作的主要重点将考虑具有更一般度分布的图上的过程，但我们也将考虑其中需要一个以上具有不同意见的邻居的阈值来改变个体的模型。(iii)第三个主题是研究系统状态和网络连接共同进化的网络。这项工作导致了困难的问题，随机演化的空间上的所有标记图。我们周围的世界是空间结构。在生物系统中，有机体和感染只在短距离内传播。社会系统有一个网络结构，它由一个图来描述，图中的顶点是个体，边是相互作用的个体。个体之间的联系可能跨越很大的物理距离，但疾病、观点和新技术的传播是由于个体与图中邻居之间的相互作用。大多数数学分析都忽略了空间或网络结构，因为包含它会使分析变得非常复杂。然而，正如我们过去与西蒙·莱文（Simon Levin）等人的研究所表明的那样，整合空间结构会改变生态竞争的结果。我们的新工作将集中在空间结构如何改变频率依赖选择的影响，以及社会系统的网络结构如何改变其中发生的过程的行为。模型是理想化的，但结果提供了关于真实的系统的有价值的见解。