INSPIRE Track 1: Geometry and Physics of Network Dynamics

INSPIRE 轨道 1：网络动力学的几何和物理

• 批准号: 1344289
• 负责人: Dmitri Krioukov
• 金额: $ 73.5万
• 依托单位: University of California-San Diego
• 依托单位国家: 美国
• 项目类别: Continuing Grant
• 财政年份: 2013
• 资助国家: 美国
• 起止时间: 2013-09-15 至 2014-06-30
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=1344289&HistoricalAwards=false
• 关键词: INSPIRE; Track; Geometry; Physics; Network

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.

该 INSPIRE 奖的部分资金由计算机信息科学与工程理事会计算机和网络系统部的网络技术和系统项目资助；数学和物理科学局物理系的数学物理项目；两个互不相交的科学领域面临的两大挑战是网络动力学预测和量子引力理论。由于缺乏对驱动许多复杂网络动态的基本规律的理解，因此我们无法预测和控制它们的行为，这是许多具有重大意义的实际问题几十年来仍未得到解决的原因之一。缺乏统一所有基本相互作用的完整量子引力理论，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性密切相关——前者反映了复杂网络的潜在几何形状，后者代表了宇宙中时空的渐近几何形状——该项目通过推导网络动力学的基本定律，解决了这两个领域的巨大挑战并推动了科学发展。该项目研究的主要假设是，人们可以将用于研究自然界中所有基本相互作用的物理学经典方法扩展到并应用到一类广泛的物理系统——复杂网络。该项目的一部分重点是寻找定义网络动力学汉密尔顿方程的哈密顿量，并根据真实网络的动力学验证导出的方程。 这些方程预计比引力理论中的相应方程更简单。 该项目的其他部分侧重于构建工具来根据导出的方程预测这种动力学，并研究这种动力学之间的联系、其在德西特/共形场论对应（dS/CFT）背景下的共形不变性，以及可能导致对宇宙学中暗能量问题的不同解释的网络导航性。 这个跨学科项目结合了数学物理学和网络研究的概念和方法，通过将物理学的规范方法扩展到复杂网络，以增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会增进我们对暗能量的理解。 因此，该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，而迄今为止，这些联系一直被认为是完全不相关的。 因此，这一变革性项目挑战了传统观点，即物理学中的规范方法在研究复杂网络时毫无用处，网络科学也无法提供理论物理学。 更广泛的影响：许多对科学和社会产生更广泛影响的问题都被网络动态预测所阻碍。 例子包括疾病治疗、药物设计和各种链接预测问题，它们是网络动态预测的子问题。总的来说，大脑、互联网和宇宙等不同系统之间的联系对公众有吸引力，培养创造性思维，并吸引更广泛、更多样化的学生进入科学和工程领域。