Computational Methods for Studying Heterogeneous Pulse-Coupled Network Dynamics

研究异构脉冲耦合网络动力学的计算方法

• 批准号: 0914827
• 负责人: Aaditya Rangan
• 金额: $ 27万
• 依托单位: New York University
• 依托单位国家: 美国
• 项目类别: Standard Grant
• 财政年份: 2009
• 资助国家: 美国
• 起止时间: 2009-08-01 至 2013-07-31
• 项目状态: 已结题
• 来源: https://www.nsf.gov/awardsearch/showAward?AWD_ID=0914827&HistoricalAwards=false
• 关键词: Computational; Methods; Studying; Heterogeneous; Pulse

This award is funded under the American Recovery and Reinvestment Act of 2009 (Public Law 111-5). The goal of this proposal is to develop analytical and computational tools capable of addressing the architecture-specific dynamics associated with heterogeneous pulse-coupled dynamical systems. There are two major components to this proposal. First, the development of a diagrammatic subnetwork expansion will provide a systematic way of analyzing dynamic observables (such as activity rates or correlations) for the long-time dynamics associated with any pulse-coupled network. Due to the pulse-coupling of the network dynamics, each term within this diagrammatic expansion corresponds to a causal sequence of events spanning a subnetwork of the original network. Second, the development of numerical algorithms for solving delay-differential population-dynamics equations will provide a natural method for computing the terms within the subnetwork expansion, as well as for solving more general delay-differential equations.Pulse-coupled networks are a very general, and important, type of dynamical system which are often studied within the physical sciences. Indeed, any system which can be represented using a network of connected nodes which interact through instantaneous bursts of information can be formally described as a pulse-coupled network. For example, the internet, networks of neurons within the brain, and many neural networks used in computer science can all be thought of as pulse-coupled networks. One of the major questions associated with the study of any pulse-coupled network is "what does it do?" How can a complicated pulse-coupled network's dynamics be understood? The techniques to be developed within this proposal will provide a framework for analyzing the dynamics of pulse-coupled networks, casting a detailed picture of the relationship between any given pulse-coupled network's structure (i.e., how the network is built) and how that network behaves. The proposed research will aid in understanding the function of many important pulse-coupled networks studied in a variety of fields, ranging from image-processing and pattern detection to robotics and circuit design to neuroscience.

该奖项是根据2009年美国复苏和再投资法案（公法111-5）资助的。本提案的目标是开发能够处理与异构脉冲耦合动力系统相关的特定架构动力学的分析和计算工具。这个提议有两个主要组成部分。首先，图解子网络扩展的发展将提供一种系统的方法来分析与任何脉冲耦合网络相关的长期动态动态的动态可观测值（如活动率或相关性）。由于网络动力学的脉冲耦合，此图解展开中的每个项对应于跨越原始网络的子网络的事件因果序列。其次，求解延迟-微分种群动力学方程的数值算法的发展将为计算子网扩展中的项以及求解更一般的延迟-微分方程提供一种自然的方法。脉冲耦合网络是一种非常普遍和重要的动力系统类型，经常在物理科学中进行研究。实际上，任何可以用通过瞬时信息爆发相互作用的连接节点网络来表示的系统都可以正式地描述为脉冲耦合网络。例如，互联网，大脑内的神经元网络，以及计算机科学中使用的许多神经网络都可以被认为是脉冲耦合网络。与研究任何脉冲耦合网络相关的一个主要问题是“它是做什么的？”如何理解一个复杂的脉冲耦合网络的动力学？在本提案中开发的技术将为分析脉冲耦合网络的动力学提供一个框架，为任何给定的脉冲耦合网络的结构（即网络如何构建）和网络行为之间的关系绘制详细的图片。拟议的研究将有助于理解在各种领域研究的许多重要脉冲耦合网络的功能，从图像处理和模式检测到机器人和电路设计到神经科学。