Voters, Games, and Epidemics on Random Graphs

随机图上的选民、游戏和流行病

基本信息

批准号：
1809967
负责人：
Richard Durrett
金额：
$ 29.97万
依托单位：
Duke University
依托单位国家：
美国
项目类别：
Continuing Grant
财政年份：
2018
资助国家：
美国
起止时间：
2018-07-01 至 2023-05-31
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=1809967&HistoricalAwards=false
关键词：
Voters Games Epidemics Random Graphs

项目摘要

The main focus of this research will be on spatial random processes. Motivated by applications in ecology we will consider processes that take place in two and three dimensional space. We will also study processes that take place on random graphs, which provide models for social networks. We will consider the spread of information and of diseases through these structures. In addition we will study of the behavior of evolutionary games, which were introduced many years ago to help understand animal behavior and have recently been used to understand the interactions of different cell types in cancer modeling. Despite the fact that it has been clearly established that spatial structure changes the outcome of evolutionary games, most applications assume homogeneous mixing and use the replicator equation to determine the dynamics. Having a well developed theory that predicts the behavior of spatial games will be useful for applications. Much of this theory has been developed under the assumption of weak selection, so it is important to understand whether the results are valid when selection is not weak.Work will be carried out on evolutionary games, variants of the voter model, coalescing random walk, and epidemics. These processes will in most cases take place on static random graphs generated by the configuration model in which vertices are assigned i.i.d. degrees, but in one situation we will let the states of an SIS epidemic and the graph co-evolve. The degree heterogeneity of random graphs forces the development of new techniques in order to extend results known on the d-dimensional lattice. In addition, new phenomena occur on these structures, such as rigorously provable discontinuous phase transitions. Specific research goals include (i) Study the rate of decay of the density of coalescing random walks on a random graph. (ii) Disprove physicists? claim that the critical infection probability on a finite graph is 1 over the largest eigenvalue of the adjacency matrix. (iii) Show that the critical threshold of the SIS is positive if the degree distribution has an exponential tail. (iv) Study SIR and SIS models on evolving graphs where susceptible individuals cut their ties to infected neighbors and rewire to a randomly chosen individual. In the SIR version we want to determine the critical value. In the SIS case we want to show that when the rewiring rate is fixed and the infection rate is varied there is a discontinuous phase transition.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

这项研究的主要重点将放在空间随机过程上。在生态学中的应用中，我们将考虑在两个维度和三维空间中发生的过程。我们还将研究在随机图上进行的过程，这些过程为社交网络提供了模型。我们将通过这些结构考虑信息和疾病的传播。此外，我们还将研究进化游戏的行为，这些行为是在许多年前引入的，目的是帮助了解动物行为，并最近被用来了解癌症模型中不同细胞类型的相互作用。尽管已经明确确定空间结构改变了进化游戏的结果，但大多数应用程序都假设混合并使用复制器方程来确定动力学。拥有一个良好发展的理论来预测空间游戏的行为将对应用程序有用。该理论的大部分是根据弱选择的假设发展的，因此重要的是要了解当选择不弱时结果是否有效。在大多数情况下，这些过程将发生在由配置模型生成的静态随机图上，其中分配了顶点。学位，但在一种情况下，我们将让SIS流行和图形的状态共同进化。随机图的程度异质性迫使新技术的发展，以扩展在D维晶格上已知的结果。此外，这些结构上发生了新现象，例如严格证明的不连续相变。具体的研究目标包括（i）研究在随机图上合并随机行走密度的衰减率。（ii）反驳物理学家？声称有限图上的关键感染概率在邻接矩阵的最大特征值上为1。（iii）表明，如果程度分布有指数式尾巴，则SIS的临界阈值为正。（iv）在不断发展的图表上研究SIR和SIS模型，在这些图表中，敏感的个体削减了与受感染的邻居的联系，并重新连接到随机选择的个体。在SIR版本中，我们要确定临界值。在SIS案例中，我们想表明，当重新布线固定且感染率变化时，会有不连续的相过渡。该奖项反映了NSF的法定任务，并且认为值得通过基金会的智力优点评估来获得支持，并具有更广泛的影响。