INSPIRE Track 1: Geometry and Physics of Network Dynamics

INSPIRE奖的部分资金来自计算机信息科学与工程局计算机和网络系统部的网络技术和系统计划、数学和物理科学局物理部的数学物理计划和数学和物理科学局的多学科活动办公室。两个相互脱节的科学领域的两个重大挑战是网络动力学预测和量子引力理论。缺乏对驱动许多复杂网络动态的基本规律的了解，从而导致我们无法预测和控制它们的行为，这是许多重要的实际问题几十年来仍未解决的原因之一。缺乏完整的量子引力理论，统一了所有基本的相互作用，这可能是继爱因斯坦之后物理学中最基本的问题。最近的结果表明，这两个问题实际上可能通过双曲空间和德西特空间之间的几何对偶而密切相关-前者反映了复杂网络的潜在几何，后者代表了宇宙中时空的渐近几何-该项目通过推导网络动力学的基本定律，既解决了重大挑战，又推动了这两个领域的科学进步。该项目研究的主要假设是，人们可以将物理学中用于研究自然界中所有基本相互作用的正则方法扩展并应用于一大类物理系统-复杂网络。该项目的一部分集中于寻找定义哈密顿网络动力学方程的哈密顿算符，并对照真实网络的动力学验证推导出的方程。这些方程预计会比引力理论中的相应方程更简单。该项目的其他部分集中在根据导出的方程建立预测这种动力学的工具，并调查这种动力学、它在德西特/共形场理论对应(DS/CFT)背景下的共形不变性和网络导航之间的联系，这可能会导致对宇宙学中暗能量问题的不同解释。这个跨学科的项目结合了数学物理和网络研究的概念和方法，将物理学中的正则方法扩展到复杂网络，以促进我们对其动力学的理解，并探索在网络科学中应用理论概念是否将促进我们对暗能量的理解。因此，这个项目通过假设哈密顿动力学和网络动力学之间的基本联系开辟了令人兴奋的新研究方向，到目前为止，这种联系一直被认为是完全无关的。因此，这个变革性的项目挑战了传统的观点，即物理学中的正则方法在研究复杂网络方面都无用，网络科学也没有任何东西可以提供理论物理。更广泛的影响：许多在科学和社会中具有更广泛影响的问题被阻止在网络动态预测上。例如疾病治疗、药物设计和各种链接预测问题，这些都是网络动态预测的子问题。总体而言，大脑、互联网和宇宙等不同系统之间的连接吸引了普通公众，培养了创造性思维，并吸引了更广泛、更多样化的学生进入科学和工程领域。

This INSPIRE award is partially funded by the Networking Technology and Systems Program in the Division of Computer and Network Systems in the Directorate for Computer Information Science and Engineering; the Mathematical Physics Program in the Division of Physics in the Directorate for Mathematical and Physical Sciences; and the Office of Multidisciplinary Activities in the Directorate for Mathematical and Physical Sciences.Two grand challenges in two disjoint fields of science are network dynamics prediction and quantum gravity theory. The lack of understanding of fundamental laws driving the dynamics of many complex networks, and consequently our inability to predict and control their behavior, are among the reasons why many practical problems of great significance remain unsolved for decades. The lack of a complete theory of quantum gravity, unifying all the fundamental interactions, is perhaps the most fundamental problem in physics after Einstein. Motivated by the recent results suggesting that the two problems might in fact be intimately related via a geometric duality between hyperbolic and de Sitter spaces---the former reflecting the latent geometry of complex networks, the latter representing the asymptotic geometry of spacetime in the universe---this project addresses both grand challenges and advances science in both fields by deriving fundamental laws of network dynamics. The main hypothesis that the project investigates is that one can extend and apply the canonical approach in physics used to study all the fundamental interactions in nature to a wide class of physical systems---complex networks. One part of the project focuses on finding Hamiltonians defining Hamilton's equations of network dynamics, and validating the derived equations against the dynamics of real networks. These equations are expected to be simpler than the corresponding equations in gravitational theories. Other parts of the project focus on building tools to predict this dynamics based on the derived equations, and investigating connections between this dynamics, its conformal invariance in the de Sitter/conformal field theory correspondence (dS/CFT) context, and network navigability that may lead to a different interpretation of the dark energy problem in cosmology. This interdisciplinary project combines concepts and methods from mathematical physics and network research by extending the canonical approach in physics to complex networks to advance our understanding of their dynamics, and to explore whether applying theoretical concepts in network science will advance our understanding of dark energy. This project thus opens exciting new research directions by hypothesizing a fundamental connection between Hamiltonian dynamics and network dynamics that until now have been considered completely unrelated. The transformative project thus challenges the conventional wisdom that neither the canonical approach in physics can be useful in studying complex networks, nor network science has anything to offer theoretical physics. Broader Impact: Many problems of broader impacts in science and society are blocked on network dynamics prediction. Examples include disease treatment, drug design, and a variety of link-prediction problems, which are sub-problems of network dynamics prediction. In general, connections between systems as different as the brain, the Internet, and the universe, appeal to general public, foster creative thinking, and attract wider and more diverse circles of students to science and engineering.