Problems in Complex Network Dynamics

该奖项是根据2009年美国复苏和再投资法案(公法111-5)资助的。技术总结该奖项支持网络统计物理的理论研究和教育。研究将集中在网络动力学和三个重要问题上：(1)对于给定的网络结构，如何设计网络上的动力学以优化期望的特性？(2)网络结构如何影响或影响网络的动力学？(3)网络如何组装或如何组装以获得期望的动力学，以及类似地，它们如何或可以调整或进化以优化期望的动态特征？通过回答这些问题，PI旨在改变对自然网络和工程网络动力学的理解，并改变新的和现有网络的设计和控制。自然网络无处不在，从颗粒状物质延伸到生物细胞和系统的各个方面。PI旨在回答有关凝聚态和生物系统中紧急行为的基本问题。这些问题是许多跨越学科的技术和科学问题的核心。第一组问题涉及两个重要的优化问题：1)如何在交通拥堵时对复杂网络上的传输进行最佳路由。通过最大化任何节点的介数来获得该问题的解决方案，并将其与真实世界的数据进行比较。2.)通过根据网络的静态或动态行为最大化模块化来检测复杂网络中的社区。PI将寻求算法改进和统计方法来解释结果。作为这些群落检测方法的应用，PI将研究小鼠的微小RNA表达数据，以帮助了解它们的生物学功能。第二组问题研究复杂网络的自适应动力学，其中网络的拓扑和网络上的动力学同时随着彼此的响应而进化。PI将对真菌网络的生长进行建模。由于营养物质的位置和在整个网络中有效运输营养物质的能力，真菌适应了它们的结构。PI将探索布尔网络中运河化的进化发展。管道化是在发育有机体中发现的一种重要的健壮性形式。第三组问题将研究随机矩阵理论在复杂网络动力学中的应用。具体地说，我们将研究各种随机矩阵系综中的扰动矩阵如何影响系综的光谱性质。光谱特性控制着复杂系统的许多基本结构和动力学特性。将要研究的系综包括那些描述各种结构的复杂网络的系综。此外，随机矩阵理论的统计预测将用于理解其他两组问题的结果。该奖项有助于休斯顿大学在计算和网络科学方面的多学科努力。它为学生提供跨学科的学习体验；他们将接受广泛适用的分析和计算技能培训。这项研究将与来自德国、澳大利亚和休斯顿的不同的国际理论家和实验者小组合作完成。国际学生联合会坚定地致力于让代表人数不足的群体的学生参与这一项目，其中包括妇女、少数民族和残疾人。非技术总结该奖项支持理论研究和教育，重点是制定管理网络中出现的现象的原则，并立即应用于生物系统和材料。网络的概念是一个抽象的概念，它能够表示和分析各种复杂的交互系统。常见的例子包括电网、电话线、互联网和社交网络，如那些描述熟人、合作和恐怖分子的网络。许多生物系统、材料和物理系统可以被视为网络结构，从而更深入地了解它们的基本性质。PI旨在发现适用于不同物理系统的网络动力学的基本原理。PI将专注于凝聚态物理和生物学交界处的问题，以及实现这一目标的更传统的统计物理主题。这项研究是理论和计算的，可能会对不同的复杂系统和跨学科产生影响。该奖项有助于休斯顿大学在计算和网络科学方面的多学科努力。它为学生提供跨学科的学习体验；他们将接受广泛适用的分析和计算技能培训。这项研究将与来自德国、澳大利亚和休斯顿的不同的国际理论家和实验者团队合作完成。国际学生联合会坚定地致力于让代表人数不足的群体的学生参与这一项目，其中包括妇女、少数民族和残疾人。

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5).TECHNICAL SUMMARYThis award supports theoretical research and education on the statistical physics of networks. The research will be focused on network dynamics, and on three important questions: (1) For a given network structure, how can the dynamics on the network be designed to optimize desired properties? (2) How does network structure effect, or influence, the dynamics of networks? (3) How are networks assembled, or how can they be assembled, in order to have desired dynamics, and, similarly, how do, or can, they adapt or evolve to optimize desired dynamical features? By answering these questions, the PI aims to transform understanding of the dynamics of natural and engineered networks, and transform the design and control of new and existing networks. Natural networks are ubiquitous, extending from granular materials to aspects of biological cells and systems. The PI aims to answer fundamental questions about emergent behavior in condensed matter and biological systems. These questions lie at the heart of many of the technological and scientific questions that cut across disciplines. The first set of problems concerns two important optimization problems: 1.) How to best route transport on complex networks when there is congested traffic. Solutions of this problem obtained by maximizing the betweenness of any node will be explored and compared to real-world data. 2.) Community detection in complex networks through maximizing modularity based on either static or dynamic behavior of the network. The PI will pursue an algorithmic improvement and a statistical approach to interpreting the results. As an application for these community detection methods, the PI will study micro RNA expression data in mice in order to help understand their biological function.The second set of problems studies adaptive dynamics of complex networks in which the topology of the network and the dynamics on the network simultaneously evolve in response to each other. The PI will model the growth of fungus networks. Funguses adapt their structure due to the location of nutrients and the ability to transport nutrients effectively throughout the network. The PI will explore the evolutionary development of canalization in Boolean networks. Canalization is an important form of robustness found in developmental organisms.The third set of problems will study the application of random matrix theory to the dynamics of complex networks. Specifically, we will investigate how perturbing matrices in various random matrix ensembles affects the spectral properties of the ensembles. Spectral properties control many of the essential structural and dynamical properties of complex systems. The ensembles that will be studied include those describing complex networks of various structures. Additionally, the statistical predictions of random matrix theory will be applied to understand the results obtained for the other two sets of problems.This award contributes to multi-disciplinary efforts at the University of Houston in Computational and Network Science. It provides an interdisciplinary learning experience for students; they will be trained in broadly applicable analytical and computational skills. The research will be done collaboratively with a diverse, international group of theorists, and experimentalists from Germany, Australia, and Houston. The PI is strongly committed to involving students from under-represented groups in this project, including women, ethnic minorities, and persons with disabilities. NON-TECHNICAL SUMMARYThis award supports theoretical research and education with a focus to develop the principles that govern phenomena that emerge in networks with immediate application to biological systems and materials. The notion of a network is an abstract concept that enables the representation and analysis of diverse complex interacting systems. Common examples include the power-grid, phone lines, the Internet, and social networks, such as those describing acquaintanceships, collaborations, and terrorists. Many biological systems and materials and physical systems can be viewed to be structured as networks leading to deeper insights into their fundamental nature. The PI aims to discover fundamental principles of the dynamics of networks that will apply to diverse physical systems. The PI will focus on problems at the interface of condensed matter physics and biology and more traditional topics of statistical physics to achieve this goal. The research is theoretical and computational and may have impact on diverse complex systems and across disciplines. This award contributes to multi-disciplinary efforts at the University of Houston in Computational and Network Science. It provides an interdisciplinary learning experience for students; they will be trained in broadly applicable analytical and computational skills. The research will be done collaboratively with a diverse, international group of theorists, and experimentalists from Germany, Australia and Houston. The PI is strongly committed to involving students from under-represented groups in this project, including women, ethnic minorities, and persons with disabilities.