CDI Type II: Complex Dynamics in the Internet: A Computational Analytic Approach

了解互联网和其他大型网络的动态行为是一个令人生畏的问题。传统方法试图捕获互联网？的详细行为，但随后与系统的斗争？的压倒性的复杂性。在另一个极端，强调大尺度而忽略细节的模型更容易处理，但经常忽略实际工程问题所需的功能，特别是当动态而不是静态行为是一个重要的问题时。这项研究通过分析和计算技术的新融合开发了一种快乐的媒介。 探讨了三个重要问题。 第一个是关于互联网的整体效率和稳定性;第二个是开发改进传感器网络功能的方法（可用于监测环境变化的小型传感器的大型阵列）;第三个重点是通过激励用户以有利于整体的方式行事来提高大型协作计算系统的质量。它的？计算分析为广泛的复杂网络创建有效模型的方法。在这种策略中，计算技术与分析技术交织在一起，使用诸如？无方程建模？？化学工程和统计物理学中的数值重整化。该方法是从根本上跨学科的，具有统一和扩展多尺度分析方法的能力，这些方法适用于动力系统理论，数学物理和理论生物学等不同领域。 预计这里创建的技术的副产品，并将调查涉及复杂网络的其他重要问题，包括互联网上的路由，神经网络的同步，以及全球金融网络的稳定性。

Understanding the dynamical behavior of the Internet and other large networks is a daunting problem. Traditional approaches try to capture the Internet?s detailed behavior at a granular level, but then struggle with the system?s overwhelming complexity. At the other extreme, models that emphasize the large scale while ignoring fine details are more tractable, but frequently neglect features needed for practical engineering issues, especially when dynamical rather than static behaviors are an important concern. This research develops a happy medium through a novel fusion of analytical and computational techniques. Three important problems are explored. The first concerns the overall efficiency and stability of the Internet; the second develops methods for improving the functioning of sensor networks (large arrays of small sensors that can be used to monitor environmental changes); and the third focuses on improving the quality of large cooperative computing systems by providing incentives for users to behave in ways that benefit the whole.The potentially transformative aspect of this research lies in its ?computational-analytic? approach to creating effective models for a wide range of complex networks. In this strategy, computational techniques are interlaced with analytical ones, using such methods as ?equation-free modeling?? from chemical engineering and numerical renormalization from statistical physics. The approach is radically interdisciplinary, with the power to unify and extend multi-scale analytical methods adapted from such diverse fields as dynamical systems theory, mathematical physics and theoretical biology. Spin-offs of the techniques created here are expected and will be investigated for other important problems involving complex networks, including routing on the Internet, synchronization in neural networks, and stability in global financial networks.