A Structurally-Based Approach to Nonlinear Analysis and Design of Networks

目的：各种自然和技术网络的动态行为是由组件之间的相互作用结构决定的，而不是由组件的详细属性决定的。该项目将开发一种新的方法，利用网络结构，同时通过与集成行为相关的基本属性（如被动性和时间尺度）广泛表征组件。这种基于结构的方法将弥合非线性系统技术和高阶复杂网络模型之间的差距。寻找重要的网络结构将引导生化反应网络已演变成几个有效的电路模式，在基因调控，细胞信号，和biosynthetic pathways.智力优点：本项目的第一部分将追求一个被动为基础的方法，生化反应网络，包括和显着加强现有的稳定性标准，在数学生物学的循环互连结构。由于无源性是这个稳定性判据的核心，我们将能够获得其他网络拓扑结构的通用判据，例如代谢网络中的分支路径。下一个研究课题是验证网络模型的无源性，并修改所提出的稳定性准则，以考虑时间延迟。最后一个主题是使用被动属性，以确保对空间分布模型中的扩散不稳定性的鲁棒性。该项目的第二部分将开发一种新的模型简化技术，该技术利用了许多生物和工程网络中固有的聚类结构。该技术依赖于由网络结构而不是网络的特定参数引起的时间尺度分离，并且特别有希望用于马尔可夫链的降阶。更广泛的影响：PI将引入一门名为“工程和生物学中的非线性现象”的本科课程和一门名为“动态系统网络”的研究生课程，这两门课程都是高度跨学科的，以研究为导向。他将继续从代表性不足的群体中招收研究生，并与高中生一起参加新视野计划，这是伦斯勒理工学院和当地学区的联合研究和教育计划，旨在吸引有才华的学生从事科学和技术职业。

Objective:The dynamic behavior of various natural and technological networks is dictated by the structure of interactions between the components rather than by detailed properties of the components. This project will develop a new approach that exploits the network structure while broadly characterizing the components by their essential properties, such as passivity and time scales, that are relevant to the ensemble behavior. This structurally based approach will bridge the gap between nonlinear systems techniques and high order, complex network models. The search for important network structures will be guided by biochemical reaction networks which have evolved into several efficient circuit patterns in gene regulation, cell signaling, and biosynthetic pathways.Intellectual Merit:The first part of this project will pursue a passivity based approach to biochemical reaction networks that encompass and significantly strengthen an existing stability criterion in mathematical biology for cyclic interconnection structures. Because passivity is at the core of this stability criterion, we will be able to obtain generalized criteria for other network topologies, such as branched pathways in metabolic networks. The next research topic is verification of passivity properties in network models and modification of the proposed stability criteria to account for time delays. The final topic is the use of passivity properties to ensure robustness against diffusive instabilities in spatially distributed models. The second part of the project will develop a novel model reduction technique that exploits a clustered structure inherent in numerous biological and engineering networks. This technique relies on a timescale separation induced by the structure rather than by the specific parameters of the network, and is particularly promising for order reduction of Markov chains.Broader Impacts:The PI will introduce an undergraduate level course entitled Nonlinear Phenomena in Engineering and Biology¡± and a graduate level course entitled Networks of Dynamic Systems, both of which will be highly interdisciplinary and research oriented. He will continue to recruit graduate students from underrepresented groups and to work with high school students in the New Visions Program a joint research and education program of Rensselaer Polytechnic Institute and local school districts that aims to attract talented students to careers in science and technology.