EAGER: Stochastic Synchronization and Coordination Problems in Complex Networks with Time Delays

Rensselaer Polytechnic Institute, Troy NY

Investigators

Abstract

TECHNICAL SUMMARY The Division of Materials Research and the Division of Mathematical Sciences contribute funds to this EAGER award. Synchronization, coordination, and balancing resources in networks are complex tasks and they are very sensitive to time delays. The PI will investigate the impact of time delays in stochastic network synchronization and coordination problems, which are present in most natural and engineered network-coupled systems. Delays can be attributed to both nonzero transmission times between the nodes and to non-zero time for the node to process and act. Time delays can have profound implications for the stability of signal and communication-driven systems at all scales, ranging from transport through disordered materials to cell kinetics and growth, neuronal networks, and genetic regulatory networks, to info-social and communication networks, leading to the emergence of optimization and trade-offs between low-connectivity/poor-communication and high-connectivity/frequent-communication instabilities. Building on recent advances in statistical physics and network science, it is precisely the combination of these three key ingredients - networks, noise, and time delays, which provides avenues for cross-cutting applications, and significant advance. The PI will also investigate fundamental statistical properties of extreme fluctuations in stochastic networks synchronization problems with time delays. Extreme fluctuations not only play an important role in disordered materials, but in infrastructure and information networks as well. Due to constrained costs, these networks are often designed to operate just below their capacity. Thus, in addition to the average load in the network, knowing the typical size and the distribution of the extreme fluctuations is of great importance from a system-design viewpoint, since system delays or global failures are often triggered by extreme events occurring on an individual node. The education and training of students and postdocs in simulations and modeling with applications in statistical physics and random networks are integral parts of the proposed research. Students and postdocs supported by this grant will be part of a larger interdisciplinary collaborative environment that facilitates collaborations within the university and with other universities in the United States. The PI will also be engaged in outreach activities, primarily through classroom interaction with high-school students which target science-oriented high-school students in the Albany, New York area. NON-TECHNICAL SUMMARY The Division of Materials Research and the Division of Mathematical Sciences contribute funds to this EAGER award. The formal concept of networks involves nodes interconnected by links and provides a potentially insightful avenue to analyze natural and engineered systems. The internet and power grid are familiar examples of networks. The dynamical properties of networks are of increasing interest in the application of this concept to materials, biological systems such as cells and the brain, as well as in predicting the response of the power grid and other infrastructure networks to rapid changes in demand or component failure. The PI will combine the methods of statistical mechanics with network theory to investigate the role of time delays in networks in which individual nodes change their properties but interact only with their local neighbors. The large number of interacting nodes in most complex systems of interest from neurons in the brain to atoms in materials, leads to challenging problems. The theoretical advances in this project may enable progress on difficult problems, most notably in materials and biological systems and have impact on mathematics and statistics. The education and training of students and postdocs in simulations and modeling with applications in statistical physics and random networks are integral parts of the proposed research. Students and postdocs supported by this grant will be part of a larger interdisciplinary collaborative environment that facilitates collaborations within the university and with other universities in the United States. The PI will also be engaged in outreach activities, primarily through classroom interaction with high-school students which target science-oriented high-school students in the Albany, New York area.