Symmetry and the Dynamics of Complex Networks and Systems

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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.