Collaborative Research: Random Dynamics on Networks

合作研究：网络随机动力学

• 批准号: 1802516
• 负责人: Daniel Tartakovsky
• 金额: $ 23.06万
• 依托单位: Stanford University
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2017
• 资助国家: 美国
• 起止时间: 2017-07-01 至 2018-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1802516&HistoricalAwards=false
• 关键词: Collaborative; Research; Random; Dynamics; Networks

Transport and distribution networks come in a number of forms, from animal cardiovascular and respiratory systems to communication and industrial infrastructures. Practical issues abound: prediction of local spikes, estimation of perfusion, and impact of structural changes such as vessel occlusion. The complexity of such phenomena can be illustrated by the well-known Braess' paradox: adding links to a transportation network might not improve the operation of the system! In spite of recent successes, our understanding of network flows is usually limited to small deterministic problems, while most applications correspond to large uncertain ones. The goal of this project is to enable improved predictions in biological and technological transport and diffusion networks. For instance, can one predict how cerebral blood flow will be affected if one of the carotids becomes narrow or blocked? Will the vasculature allow for re-routing? If so, with what probability and how fast? The main challenge in this research project is the presence of uncertainties. For many applications, only partial information about the systems is available. For instance the size or even the presence of a specific vessel might be uncertain or the status of a router unknown. The analysis of such problems requires the creation of novel mathematical tools and numerical methods to describe how uncertainties propagate through vast and complex networks. The computational tools to be constructed will provide information, usually probabilistic in nature, regarding phenomena that are difficult, expensive, or impossible to measure.

运输和分销网络有多种形式，从动物心血管和呼吸系统到通信和工业基础设施。实际问题比比皆是：局部峰值的预测，灌注的估计以及结构变化（如血管遮挡）的影响。这种现象的复杂性可以通过著名的布拉斯（Braess）的悖论来说明：添加到运输网络的链接可能无法改善系统的运行！尽管最近取得了成功，但我们对网络流的理解通常仅限于小的确定性问题，而大多数应用程序对应于大型不确定问题。该项目的目的是为了改善生物和技术运输和扩散网络的预测。例如，如果其中一种颈动脉变窄或阻塞，是否可以预测脑血流将如何影响？脉管系统是否允许重新穿线？如果是这样，有什么概率和多快？ 该研究项目的主要挑战是存在不确定性。对于许多应用程序，只有有关系统的部分信息。例如，特定容器的大小甚至存在可能是不确定的，也可能是路由器未知的状态。对此类问题的分析需要创建新颖的数学工具和数值方法，以描述不确定性如何通过庞大而复杂的网络传播。要构建的计算工具将提供有关困难，昂贵或无法衡量的现象的信息，通常本质上是概率的。