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成部分之间相互作用的结构决定的，而不是由组成部分的详细属性决定的。该项目将开发一种利用网络结构的新方法，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）广泛地表征组件。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受到生物化学反应网络的指导，这些反应网络已经演变成基因调控、细胞信号传导和生物合成途径中的几种有效电路模式。智力优势：该项目的第一部分将追求基于被动的生化反应网络方法，该方法包含并显着加强循环互连结构的数学生物学中现有的稳定性标准。由于无源性是这种稳定性准则的核心，我们将能够获得其他网络拓扑的广义准则，例如代谢网络中的分支通路。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来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，利用许多生物和工程网络中固有的集群结构。这种技术依赖于由结构而不是由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将引进一门名为“工程和生物学中的非线性现象”的本科课程和一门名为“动力系统网络”的研究生课程，这两门课程都将是高度跨学科和研究导向的。他将继续从代表性不足的群体中招收研究生，并在“新愿景计划”（New Visions Program）中与高中生合作。“新愿景计划”是伦斯勒理工学院（Rensselaer Polytechnic Institute）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领域的职业。

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.