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AF: Small: Natural Algorithms and Dynamic Networks

AF：小：自然算法和动态网络

基本信息

批准号：
2006125
负责人：
Bernard Chazelle
金额：
$ 40万
依托单位：
Princeton University
依托单位国家：
美国
项目类别：
Standard Grant
财政年份：
2020
资助国家：
美国
起止时间：
2020-07-01 至 2023-06-30
项目状态：
已结题

来源：
https://www.nsf.gov/awardsearch/showAward?AWD_ID=2006125&HistoricalAwards=false
关键词：
AF Small Natural Algorithms Dynamic

项目摘要

The emergence of large-scale order from local interactions is a theme common to computing and living systems. The field of natural algorithms seeks to discover the fundamental principles that underlie this phenomenon in all its remarkable diversity. Can simple algorithmic rules explain how birds flock, how termites cooperate, how opinions polarize, how oscillators self-synchronize, how languages evolve through iterated learning, or how robustness emerges from adaptive systems? Beyond providing answers to these specific questions, the broader ambition of this project is to build bridges between the fields of algorithms and dynamical systems. Nearly all of the processes under consideration involve dynamic networks whose nodes represent autonomous agents interacting under time-varying topologies. It is often crucial to perform dimension reduction on such systems in a manner respectful of the dynamics. This task is approached through the lens of “semantic renormalization,” a process that involves clustering dynamic graphs hierarchically. The theme of the project is highly multidisciplinary and forms the basis of graduate seminars and undergraduate projects with participation from computer science, mathematics, statistics, neuroscience, genomics, evolutionary biology, and mechanical engineering. The project draws upon a wide range of techniques from areas as diverse as dynamical systems, machine learning, statistical mechanics, and network theory. It consists of four main parts: (a) “iterated learning” features students who, acting as Bayesian agents, learn from teachers and then, in turn, become teachers themselves; (b) “dynamic random walks” model random walks over graphs whose topology changes over time via a feedback loop; (c) “opinion dynamics” investigates how autonomous agents can reach consensus through mutual, constrained interaction; (d) “averaging systems” are coupled dynamical systems driven by convex combination updates over embedded dynamic networks.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.

局部交互产生大规模秩序是计算和生命系统的共同主题。自然算法领域致力于发现这种现象的显着多样性背后的基本原理。简单的算法规则能否解释鸟类如何成群、白蚁如何合作、意见如何两极分化、振荡器如何自同步、语言如何通过迭代学习进化，或者自适应系统如何产生鲁棒性？除了提供这些具体问题的答案之外，该项目更广泛的目标是在算法和动力系统领域之间建立桥梁。几乎所有正在考虑的过程都涉及动态网络，其节点代表在时变拓扑下交互的自主代理。以尊重动力学的方式对此类系统进行降维通常至关重要。这项任务是通过“语义重整化”的视角来完成的，该过程涉及对动态图进行分层聚类。该项目的主题是高度多学科的，构成研究生研讨会和本科生项目的基础，计算机科学、数学、统计学、神经科学、基因组学、进化生物学和机械工程的参与。该项目借鉴了动力系统、机器学习、统计力学和网络理论等不同领域的广泛技术。它由四个主要部分组成：（a）“迭代学习”的特点是学生充当贝叶斯代理，向教师学习，然后自己成为教师； (b) “动态随机游走”对拓扑结构通过反馈循环随时间变化的图进行随机游走模型； (c) “意见动态”研究自主主体如何通过相互的、有约束的互动达成共识； (d) “平均系统”是由嵌入动态网络上的凸组合更新驱动的耦合动态系统。该奖项反映了 NSF 的法定使命，并通过使用基金会的智力价值和更广泛的影响审查标准进行评估，被认为值得支持。