Dynamics of Asynchronous Networks, Adaptation and Visualization

该项目将发展异步和自适应网络的数学理论，作为模式识别、复杂动态可视化和“定性”计算的总体方案的一部分。这项工作将结合受计算神经科学启发的自适应网络的思想，特别是Spike-Timing Dependent Plasticity (STDP)，以及在研究具有多个时间尺度的动力系统的统计特性中发展起来的数学技术。我们允许异步动态（没有全局时钟）；具体来说，网络的节点可能不会同步更新（在每个时间步）。特别感兴趣的是一个非常有前途的全局异步本地同步（GALS）网络架构的进一步开发，它将随机性（来自节点动态）与松散（草率）异步逻辑结合起来。总体而言，该研究将利用网络动力学数学在研究动力系统统计特性方面发展起来的数学技术，并以数值模拟和实验为指导。许多物理、电子和生物系统可以通过相互作用的微分方程和地图网络来建模。最现实的模型允许随机性、不连续性、时间延迟和异步——可能没有全局时钟，因此网络节点可能不会同步更新（相比之下，行星围绕太阳的运动是同步的：所有行星都在不断移动，并通过重力与所有其他行星相互作用）。异步是许多最新技术以及复杂生物系统（如大脑）的一个特征。该项目将开发涉及随机、异步和确定性动态混合的网络动力学新模型。作为工作的一部分，提出了改进和开发现有的新型可视化工具，目的是识别复杂网络动力学中的关键动态特征，例如大型网络中的同步模式。开发高速模式识别和学习的新自适应方法具有重要的潜在应用意义。

The project will develop the mathematical theories of asynchronous and adaptive networks as part of a general scheme for pattern recognition, visualization of complex dynamics and 'qualitative' computing. The work will combine ideas on adaptive networks inspired by computational neuroscience, notably Spike-Timing Dependent Plasticity (STDP), with mathematical techniques developed in the study of statistical properties of dynamical systems with multiple time scales. We allow for asynchronous dynamics (no global clock); specifically, nodes of the network may not be updated synchronously (at each time step). Of special interest is the further development of a very promising Globally Asynchronous Locally Synchronous (GALS) network architecture that combines randomness (coming from node dynamics) with a loose (sloppy) asynchronous logic. Overall, the research will use mathematical techniques developed in the study of statistical properties of dynamical systems with the mathematics of network dynamics and be guided by numerical simulation and experimentation.Many physical, electrical and biological systems can be modeled by networks of interacting differential equations and maps. The most realistic models allow for randomness, discontinuity, time delays and asynchrony - there may be no global clock and so the nodes of the network may not be updated synchronously (by way of contrast, the motion of the planets round the sun is synchronous: all the planets continually move and interact, via gravity, with all the other planets). Asynchrony is a characteristic feature of much recent technology as well as of complex biological systems, such as the brain. The project will develop new models for network dynamics that involve a mix of random, asynchronous and deterministic dynamics. As part of the work, it is proposed to refine and develop existing novel visualization tools with the aim of identifying key dynamical features in complex network dynamics, such as patterns of synchronization in large networks. Of great potential significance in applications is the development of new adaptive methods for high speed pattern recognition and learning.