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

材料研究部和数学科学部为EAGER奖提供资金。同步、协调和平衡网络中的资源是一项复杂的任务，它们对时间延迟非常敏感。PI将研究随机网络同步和协调问题中的时间延迟的影响，这些问题存在于大多数自然和工程网络耦合系统中。延迟可以归因于节点之间的非零传输时间和节点处理和动作的非零时间。时间延迟可以在所有尺度上对信号和通信驱动系统的稳定性产生深远的影响，从通过无序材料的运输到细胞动力学和生长，神经元网络和遗传调控网络，再到信息社会和通信网络，导致低连通性/差通信和高连通性/频繁通信不稳定性之间的优化和权衡的出现。基于统计物理学和网络科学的最新进展，正是这三个关键因素-网络，噪声和时间延迟的组合，为交叉应用提供了途径，并取得了重大进展。PI还将研究具有时间延迟的随机网络同步问题中极端波动的基本统计特性。 极端涨落不仅在无序材料中起着重要作用，而且在基础设施和信息网络中也起着重要作用。由于成本有限，这些网络通常被设计为仅在低于其容量的情况下运行。因此，除了网络中的平均负载之外，从系统设计的角度来看，了解极端波动的典型大小和分布是非常重要的，由于系统延迟或全局故障通常由单个节点上发生的极端事件触发。学生和博士后在模拟和建模方面的教育和培训以及统计物理和随机网络的应用是建议的研究。由该补助金支持的学生和博士后将成为一个更大的跨学科合作环境的一部分，促进大学内部以及与美国其他大学的合作。PI还将参与外展活动，主要是通过与高中生的课堂互动，目标是奥尔巴尼的理科高中生，纽约地区。技术总结材料研究部和数学科学部为EAGER奖提供资金。网络的正式概念涉及通过链接互连的节点，并提供了一个潜在的有洞察力的途径来分析自然和工程系统。 互联网和电网是网络的常见例子。 网络的动力学性质在将这一概念应用于材料、生物系统（如细胞和大脑）以及预测电网和其他基础设施网络对需求或组件故障的快速变化的响应方面越来越感兴趣。 PI将联合收割机与网络理论的统计力学方法相结合，以研究网络中的时间延迟的作用，其中单个节点改变其属性，但只与其本地邻居相互作用。 从大脑中的神经元到材料中的原子，大多数复杂系统中的大量相互作用的节点导致了具有挑战性的问题。该项目的理论进展可能会使困难问题取得进展，特别是在材料和生物系统方面，并对数学和统计学产生影响。在统计物理和随机网络中应用模拟和建模的学生和博士后的教育和培训是拟议研究的组成部分。由该补助金支持的学生和博士后将成为一个更大的跨学科合作环境的一部分，促进大学内部以及与美国其他大学的合作。PI还将参与外展活动，主要是通过与高中生的课堂互动，目标是纽约地区奥尔巴尼的理科高中生。

TECHNICAL SUMMARYThe 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 SUMMARYThe 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.