Symmetry and the Dynamics of Complex Networks and Systems

该奖项支持研究和教育，以了解对称性在包含许多相互作用元素的系统动力学中的作用，特别是复杂网络，以及如何使用对称性来理解它们的行为。将处理三组根本性的重要问题。第一组问题涉及使用对称性来理解和表征复杂网络的自适应动力学，其中网络的拓扑结构和网络上的动力学同时相互响应而进化。进化布尔网络模型作为具有简单而非平凡的自适应动力学的典型例子进行了研究。对称在复杂系统的鲁棒性和适应性的进化发展中的作用也将被检查。第二组问题的重点是对称对复杂系统特征值谱的影响。具体来说，我们将识别和分析图对称对复杂网络的拉普拉斯谱的影响，以及对主要特征值的极值行为的影响。PI还将应用随机矩阵理论的思想来系统地分析和表征复杂网络的动力学。第三组问题涉及开发有效的算法，以便对由各种类型的约束定义的网络集合进行适当的采样。这些算法很重要，因为为了正确地对许多网络集成进行统计研究，它们被广泛需要。这项工作将是计算性和分析性的。统计和数学物理的工具和方法将贯穿始终。这些结果对于物理学界来说将是重要的和变革性的，因为它们将回答有关复杂系统中集体行为的基本问题。它们对更广泛的科学界也很重要，因为所提出的问题是其他学科所研究的许多技术和科学问题的核心。该奖项还支持休斯顿大学在计算和网络科学方面正在进行的多学科努力。与这一倡议相关的是，最近在研究生物理课程中增加了核心要求，为此，PI开发并教授了一系列以研究为基础的课程来满足这些要求。此外，PI将开发和教授一门新的多学科研究生课程，以更广泛地教育学生网络科学的最新进展。该奖项还将用于支持将接受广泛应用的分析和计算技能培训的研究生。这项工作将与一个不同的国际科学家小组合作完成。该奖项支持理论研究和教育，重点是发展应用于生物系统和材料的网络中出现的管理现象的原则。网络是一个抽象的概念，它能够表示和分析各种复杂的相互作用的系统。常见的例子包括电网、电话线、互联网和社会网络，例如描述熟人、合作和恐怖分子的网络。许多生物系统、材料和物理系统都可以被看作是网络结构，从而更深入地了解它们的基本性质。PI将专注于对称在连接不同物理系统的网络动力学中的作用。对称在许多自然现象中扮演着重要的组织原则。为了实现这一目标，PI将专注于凝聚态物理和生物学的界面问题，以及更传统的统计物理主题。这项工作将是计算性和分析性的，将解决的问题范围从基本问题到在分析和应用现实世界的实验数据中出现的问题。在整个过程中，将使用统计和数学物理的工具和方法。这些结果对更广泛的科学界来说将是重要的，因为所提出的问题是其他学科研究的许多技术和科学问题的核心。该奖项还支持休斯顿大学在计算和网络科学方面正在进行的多学科努力。与这一倡议相关的是，最近在研究生物理课程中增加了核心要求，为此，PI开发并教授了一系列以研究为基础的课程来满足这些要求。此外，PI将开发和教授一门新的多学科研究生课程，以更广泛地教育学生网络科学的最新进展。该奖项还将用于支持将接受广泛应用的分析和计算技能培训的研究生。这项工作将与一个不同的国际科学家小组合作完成。

TECHNICAL SUMMARYThis award supports research and education to understand the role that symmetry has in the dynamics of systems containing many interacting elements, especially of complex networks, and how symmetry may be used to understand their behavior. Three sets of fundamentally important problems in will be addressed. The first set of problems concerns using symmetry to understand and characterize the 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. Evolutionary Boolean network models are studied as prototypical examples with simple, yet nontrivial, adaptive dynamics. The role of symmetry in evolutionary development of robustness and adaptability in complex systems will also be examined. The second set of problems focuses on the effects of symmetry on the eigenvalue spectra of complex systems. Specifically, we will identify and analyze the effects of graph symmetry on the spectrum of the Laplacian of complex networks, and on the extreme value behavior of leading eigenvalues. The PI will also apply ideas of random matrix theory to systematically analyze and characterize the dynamics of complex networks. The third set of problems involves developing efficient algorithms for the proper sampling of network ensembles defined by various types of constraints. These algorithms are important because they are widely needed in order to properly make statistical studies of many network ensembles. The work will be both computational and analytical. Tools and methods of statistical and mathematical physics will be used throughout. The results will be important and transformative to the physics community because they will answer fundamental questions about collective behavior in complex systems. They will also be important to the broader scientific community because the proposed problems are at the heart of many of the technological and scientific questions investigated by of other disciplines.This award also supports the on-going multi-disciplinary efforts at the University of Houston in both Computational and Network Science. Related to this initiative are recently added core requirements in the graduate physics curriculum, for which the PI has developed and teaches a series of research-based courses to satisfy those requirements. Additionally, the PI will develop and teach a new multidisciplinary graduate course to more broadly educate students about recent advances in Network Science. The award will also be used to support graduate students who will be trained in broadly applicable analytic and computational skills. This work will be done collaboratively with a diverse international group of scientists.NON-TECHNICAL SUMMARYThis award supports theoretical research and education with a focus to develop the principles that govern phenomena that emerge in networks with application to biological systems and materials. 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 will focus on the role of symmetry in the dynamics of networks that will connect diverse physical systems. Symmetry plays an important role as an organizing principle for a wide range of natural phenomena. 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 work will be both computational and analytical, and the problems that will be addressed range from ones that are fundamental to those that arise in the analysis and application of the ideas to real world experimental data. Throughout, tools and methods of statistical and mathematical physics will be used. The results will be important to the broader scientific community because the proposed problems are at the heart of many of the technological and scientific questions investigated by of other disciplines.This award also supports the on-going multi-disciplinary efforts at the University of Houston in both Computational and Network Science. Related to this initiative are recently added core requirements in the graduate physics curriculum, for which the PI has developed and teaches a series of research-based courses to satisfy those requirements. Additionally, the PI will develop and teach a new multidisciplinary graduate course to more broadly educate students about recent advances in Network Science. The award will also be used to support graduate students who will be trained in broadly applicable analytic and computational skills. This work will be done collaboratively with a diverse international group of scientists.