This award supports research and education aimed to find fundamental principles that govern the behavior of complex systems, an important and challenging problem. A complex system often consists of components that each behave in a well-defined way, but when combined display new distinctly different behavior that is more than the sum of the individual behaviors. The new behavior is said to be emergent. The components of complex systems often have heterogeneous properties and interactions. Examples abound in nature, ranging from the brain and the regulatory systems of cells in biology, to social networks and ecosystems, and from interdependent infrastructure networks in engineering to atmospheric and oceanic dynamics. A principal difficulty in understanding many complex systems is that their dynamics is driven by external mechanisms that prevent them from reaching the steady state of equilibrium. Thus, the foundational principles that govern equilibrium systems, discovered over a century ago, typically do not apply to them. The analogous principles of driven, non-equilibrium systems are poorly understood, necessitating the need for finding the foundational principles of the behavior of non-equilibrium systems and for understanding the range of their possible behavior. This award supports research to address this problem by focusing on three different types of non-equilibrium complex systems and their generalizations. Each system is motivated as a model that captures the essence of real neural, biological or social behavior, and so, understanding their specific properties is important. The goal is either to develop or enhance mathematical methods and tools that can be used generally to study co-evolving complex systems, and thus, to gain transformational insight into complicated systems such as the human brain.The work on each of the systems will build on recent preliminary results obtained by the investigators in their ongoing research effort. The research will be both analytical and computational, and will range from fundamental problems in mathematical physics, to the analysis and application of the fundamental ideas to real - world experimental data.
The funded activities will significantly contribute to ongoing efforts at the University of Houston in both Computational and Network Science. These efforts foster interdisciplinary collaboration within the University and with local industry. The PI and his group will participate in outreach activities for the community each year. The PI will also continue to teach multidisciplinary graduate courses he has designed to broadly educate students about recent advances in both Computation and Network Science. The grant will also support the PI's service as a faculty facilitator in the continuing education training each year for 20 teachers without a physics background that teach physics to approximately 3000 students in high-need school districts in the Houston area. It will also support the Co-PI's collaboration on a new text that teaches physics to students in the biological sciences. His focus is on explaining the central role that understanding systems far from equilibrium plays in all biological organisms. The graduate students supported by the grant will be trained in broadly applicable analytic and computational skills that will prepare them for a wide range of career opportunities. They will also contribute to the planned educational and outreach activities. Involving people from under-represented groups in this work will also be a focus.
This award supports research and education aimed to find fundamental principles that govern the behavior of complex systems. A principal difficulty in understanding many complex systems is that their dynamics is driven by exogenous mechanisms, preventing them from reaching thermal equilibrium. Unlike equilibrium statistical mechanics, the principles of nonequilibrium statistical mechanics remain poorly understood. Yet, such systems are ubiquitous, ranging from the neural, genetic, and metabolic regulatory systems in biology, to population dynamics and competition in social systems and ecosystems, and from interdependent infrastructure networks to atmospheric/oceanic dynamics at the global scale. Establishing the foundational principles of nonequilibrium statistical mechanics as they apply to complex systems would transform not only our understanding of nature, but also our ability to control it. In order to establish the principles of nonequilibrium statistical mechanics, it is helpful to understand the range of possible behavior in complex systems, driven far from equilibrium. A particularly challenging set of such systems to understand is those in which two or more distinct components co-evolve in an interdependent manner. Systems structured as complex networks that have interdependent dynamics in both node- and link- degrees of freedom are prime examples of co-evolving complex systems.
The research will involve three sets of simple model network systems that capture the essence of non-equilibrium behavior found in nature. These models are also chosen because they can be efficiently simulated numerically, and have some aspects that can be understood analytically. The PIs will combine careful simulations with analytic calculations, to gain insight into both fundamental issues in non-equilibrium statistical mechanics, and to develop deeper understanding of the intriguing phenomena displayed in real-world systems. The first set of projects will study the co-evolutionary dynamics of social network models consisting of interacting agents endowed with a temperament as either introverts or extroverts. Game-theoretic node dynamics will be combined interdependently with link dynamics due to the temperament of the nodes. These models merge two paradigms of non-equilibrium statistical mechanics, one for the node dynamics and the other for the link dynamics, to explore new co-evolutionary phenomena. The second set of projects will study the adaptive dynamics of Boolean networks in which both nodes and links co-evolve. They are prototypical examples of heterogeneous complex systems and as such present distinct challenges to their understanding. They were originally proposed as simple models of genetic regulatory systems, and recently have become widely used as simple models of neural systems. Understanding the co-evolution of the network structure and the rules of node behavior of these models may unlock keys to understanding neural function. Finally, the third set of projects will extend the PI's recent work on the co-evolutionary dynamics leading to Emergent Speciation, a novel method of biological speciation that may be a root cause of the origin of the species.
