Amorphous computation, random graphs and complex biological networks

在这个“信息时代”，计算、通信和海量信息处理已成为现代社会的面包和黄油。互联网、网络和流行的点对点网络都是我们正在见证的从本地的集中式计算机到相对低功率的个人资源的大规模分布式网络的过渡的例子。这些是我们对未来无定形计算机的第一次瞥见。更广泛地说，无定形计算机包括通过灵活且不断变化的交互网络连接的任何大规模计算单元或过程网络。它们可能是成群的微型机器人，也可能是监测气候或污染的大型传感器阵列。这种自组织分布式系统共有的一个至关重要的特征是，期望的计算会出现，而不是明确地预先编程。向无定形计算的过渡带来了巨大的潜力和风险(例如困扰互联网的病毒流行)。为了利用无定形计算的优势和避免危险，从根本上说，需要新的方法来应对复杂性。为此，我们计划一方面开发适当的数学模型和工具，另一方面从成功的系统中获得适当的工程原理。无定形计算机的统一特征之一是它们活跃的网络结构。因此，对于它们的描述，自然的数学实体是图：具有节点(处理器)和边(连接)的结构。由于无定形计算机的网络结构本质上是非规定的，因此对随机图的研究特别有前途。为了将随机图理论扩展到现实世界的应用，需要开发新的数学，包括新的随机图族，模拟其生长和动态的新工具，以及分析这些图上发生的动态的新方法。该提案的一个关键部分是开发这些工具，并将其应用于非晶态计算机的特定模型，最终应用于真实系统(如P2P网络和传感器阵列)。非晶态计算的挑战之一是找到有用的类比，以洞察手头系统的需求、能力和限制。在这个提案中，我们将从生物系统和它们执行的强大计算中获得灵感。生物功能的计算方面几乎在任何任务中都能找到：从进化到发育，再到信息处理，在组织的每个层面上都很明显，包括大分子(例如蛋白质折叠)、细胞(例如蛋白质和基因的调节网络)和更高层次(神经网络和神经系统)。生物系统由微小的、嘈杂的和相对不可靠的组件组成，其效果和效率令人惊讶。与人类设计的计算机不同，它们也是动态和高度适应性的机器。它们通常是分布式和去中心化的，每个组件都遵循一套基于其环境的本地规则来确定其操作。它是从简单和不可靠的元素集合中出现的功能和连贯的整体，我们希望为自己的工程目的而捕获这些元素。

In this ``information age'', computation, communication and massive information handling have become the bread and butter of modern society. Internet networks, the web, and popular peer-to-peer networks are all examples of the transition we are witnessing from local, centralised computers to massive distributed networks of relatively low-power individual resources. These are our first glimpses of the amorphous computers of the future. More generally, amorphous computers include any large-scale network of computational units or processes that are connected through a flexible and constantly changing network of interactions. These may be swarms of microscopic robots or large sensor-arrays that monitor climate or pollution. The critically important feature common to these kinds of self-organising distributed systems is that the desired computation emerges and is not explicitly preprogrammed.The transition to amorphous computing brings with it enormous potential as well as risk (such as the virus epidemics that plague the internet). To exploit the advantages and avoid the dangers of amorphous computing, fundamentally new ways of coping with complexity are needed. To do so we plan to develop appropriate mathematical models and tools, on the one hand, and to derive appropriate engineering principles inspired by successful systems, on the other.One of the unifying features of amorphous computers is their active network structure. Thus, a natural mathematical entity for their description is the graph: a structure with nodes (processors) and edges (connections). Since by their very nature, the network structure of amorphous computers is non-prescribed, the study of random graphs is especially promising. To extend the theory of random graphs to real-world applications, new mathematics needs to be developed, including new families of random graphs, new tools for simulating their growth and dynamics and new methods for analysing the dynamics that takes place on these graphs. A key part of this proposal is the development of these tools and their application to specific models of amorphous computers, and ultimately to real systems (such as P2P networks and sensor arrays).One of the challenges of amorphous computing is to find useful analogies that provide insight into the requirements, capabilities and limitations of the systems at hand. In this proposal, we will draw inspiration from biological systems and the powerful computation they perform. Computational aspects of biological functions are found in almost any task: from evolution, though development, to information processing, and are evident on every level of organisation, including macro-molecules (e.g., protein folding), cells (e.g., regulatory networks of proteins and genes) and higher (neural networks and nervous systems). Built of microscopic, noisy and relatively unreliable components, biological systems are surprisingly effective and efficient. Unlike human-engineered computers, they are also dynamic and highly adaptive machines. They are typically distributed and decentralised, with each component following a set of local rules based on its environment to determine its actions. It is the emergence of a functional and coherent whole from an ensemble of simple and unreliable elements that we would like to capture for our own engineering purposes.