Problems in Complex Network Dynamics

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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.