Inference and Complexity in Composite Connected Systems

缺乏处理相互作用子组件网络上的复杂性和紧急行为的原则性方法已被英国研究委员会和欧盟确定为未来重大需求的关键瓶颈领域。这项建议解决了复合系统的一个特别苛刻的领域：相互作用子组件的复杂系统，其中子组件之间存在局部相互作用的组合，以及不同规模的较长范围的相互作用。研究复杂性的传统方法通常基于大规模的基于主体的模拟或耦合的非线性确定性或随机微分方程的数值解。然而，由于这些方法具有大规模、高度非线性和固有的复合多层次相互作用，很可能无法为此类系统提供通用的洞察力以及健壮、原则性和可靠的解决方案。由于参数的敏感性、外部观测性和大规模的复杂性，直接计算方法不能可靠地用于组合系统的建模，因此，我们提出了一个基于内在分布和近似概率方法的框架。我们将用来描述复杂系统中的不确定性、信息传递和紧急特性的方法是基于复杂连通图的。分析这类图表的技术将源于统计物理方法的扩展，即将高维联合分布分解为更简单的、可计算的量。该方案的新颖性来自于对呈现这种复合特征的系统的关注：局部和远程、稀疏和密集、子组件之间的弱和强相互作用的组合。我们对利用信息系统中可以用这种图来描述的复杂性感兴趣，但我们正在利用物理学的技术，并将它们修改为适用于复杂系统的推理和分析。该框架将产生关于一般系统的新的见解和基本工具和技术，这些将适用于当前许多重要的现实世界问题，包括：码分多址编码方法、自组织传感器网络、分布式交通灯管理、嵌入式智能传感器、和大脑皮层功能。

A lack of principled approaches for dealing with complexity and emergent behaviour on networks of interacting subcomponents has been identified as a key bottleneck area of significant future demand both by UK research councils and the EU.This proposal tackles a particularly demanding area of composite systems: complex systems of interacting subcomponents where there is a combination of local interactions between subcomponents, together with a different scale of longer range interactions.Traditional methods to study complexity are based typically on large scale agent-based simulations or on numerical solutions of coupled non-linear deterministic or stochastic differential equations. However, being of a large scale, highly non-linear and inherently of composite multi-level interactions, these methods are likely to be unsuccessful in providing generic insight as well as robust, principled and reliable solutions for such systems. Due to sensitivity of parameterisation, external observation, and massive scale, reliable direct computational approaches to composite systems' modelling are unfeasible.Instead, we propose a framework based on inherently distributive and approximative probabilistic approaches. The methods we will use to describe uncertainty, information transfer and emergent properties in complex systems are based on complex connected graphs. The techniques for analysing such graphs will derive from extensions of methods in statistical physics to decompose high dimensional joint distributions into simpler, computable quantities. The novelty of the proposal stems from the focus on systems which exhibit this composite character: a combination of localised and long range, sparse and dense, weak and strong interactions between subcomponents in such graphs.We are interested in exploiting complexity in information systems which can be described by such graphs, but we are utilising techniques from physics and modify them to be applicable to inference in, and analysis of, complex systems.This framework will lead to new insights and fundamental tools and techniques on generic systems which will be applicable to many important current real world problems, including: CDMA coding methods, ad-hoc sensor networks, distributive traffic-lights management, embedded intelligent sensors, and cortical functioning.