MOLTEN: Mathematics Of Large Technological Evolving Networks

人际关系很重要。在研究自然、技术、商业和社会科学时，关注各个组成部分之间的相互作用模式往往是有意义的。例如，在英国的数字经济活动中，在能源领域出现了大型复杂的网络：连接电力供应商和用户，在电信领域：连接移动电话用户，在交通领域：连接火车站、机场或港口，在万维网领域：连接网页，在单线社交网络中连接网友，在零售贸易领域：将不同产品的销售连接到同一客户。计算能力的提高使得收集、存储和分析大型数据集成为可能，尤其是在快速消费品（谁买了什么）、电信（谁给谁打电话）、移动设备（谁去了哪里）、在线社交网络（谁给谁发过推特）和能源（谁什么时候开机）等领域。作为理解和量化这些大型网络并提取有用信息的一种手段，网络科学的跨学科领域已经出现。通过关注潜在的连通性，数学技术可以用来解决常见的问题：我们能发现强连接个体的集群吗？这将允许我们将网络分解成有意义的子单元。当添加或删除链接时，网络属性是否会改变？这决定了对攻击/疾病/故障的稳健性/效率和进化中的稳定性。是否有些个人或联系特别重要？“枢纽”是指拥有高质量连接的个人（例如，b谷歌排名靠前的网页），“捷径”是指连接不同子网的链接，“瓶颈”是指可能过载的特定链接。我们能建立数学模型来重现复杂网络的特征吗？给定观察到的输出（例如动态通信网络中的排队时间），我们能否发现复杂系统中潜在的、隐藏的连通性？本提案旨在通过解决迄今为止很少受到数学界关注的重要特性，为这一重要领域增加价值。技术网络随着时间的推移而变化，这种动态因素具有重要的影响。例如，如果A今天给B打电话，B明天给C打电话，那么信息可能从A传递给C，但不是从C传递给A。因此，立即缺乏对称性，使现有的许多理论过时了。此外，我们今天看到的连接模式明天可能会有所不同。因此，未来存在内在的不确定性。在本提案中，我们将开发新的数学技术来研究与数字经济相关的动态发展网络的类型，使研究人员能够发现重要的参与者，量化网络的效率并预测未来的行为。这些想法在学术界之外提供了直接的好处，使我们能够解决诸如：谁是重要的广播者或信息接收者？我们的广告活动应该针对谁？下周或明年的网络会是什么样子？今天有什么可疑活动吗？哪些网络用户看起来未成年？哪些客户可能改变品牌忠诚度？谣言或病毒传播的速度有多快？改变用户的网络收费方式会产生什么影响？我们的目标是通过开发一种新的、基础的数学框架，直接导致有用的计算机软件，为这些问题开发出实用的、定量的解决方案。为了确保结果能够立即产生效益，我们组建了一个由非学术专家组成的团队，他们在业务中使用大型技术网络。这些人将提供真实的数据集，提出具体的挑战，并在整个项目中定期提供反馈和建议。

Connections are important. In studying nature, technology, commerce and the social sciences it often makes sense to focus on the pattern of interactions between individual components. Within the UK's Digital Economy activities, for example, large, complex networks arisein energy: connecting power suppliers and users,in telecommunications: connecting mobile phone users,in transport: connecting train stations, airports or ports,in the World Wide Web: connecting web pages,in one-line social networking connecting cyberfriends, in retail trade: connecting sales of different products to the same customer.Improvements in computing power have made it possible to gather, store and analyze large data sets, especially in the areas of fast moving consumer goods (who bought what), telecommunications (who phoned who), mobile devices (who travelled where) , on-line social networks (who Twittered to who) and energy (who switched on when). The interdisciplinary field of Network Science has emerged as a means to understand and quantify these large networks and to extract useful information. By focussing on the underlying connectivity, mathematical techniques can be used to address common questions:Can we discover clusters of strongly connected individuals? This would allow us to break the network down into meaningful subunits.Do the network properties change when links are added or removed? This determines robustness/efficiency to attack/disease/malfunction and stability under evolution.Are some individuals or links especially important? `Hubs' are individuals with high-quality connections (e.g. web pages highly ranked by Google), `short-cuts' are links that join distinct subnetworks and `bottlenecks' are specific links that may become overloaded.Can we develop mathematical models that reproduce the features of a complex network?Given observed output (such as queuing times in a dynamic communication network) can we discover underlying, hidden, connectivity in a complex system?This proposal aims to add value to this important area by addressing an important feature that has fo far received very little attention from the mathematical community. Technological networks vary over time, and this dynamic element has important consequences. For example, if A phones B today and B phones C tomorrow, then a message may pass from A to C, but not from C to A. So there is an immediate lack of symmetry that makes much of the existing theory obsolete. .Moreover, the patterns of connectivity that we see today may be different tomorrow. So there is built-in uncertainty about the future. In this proposal we will develop new mathematical techniques to study the type of dynamically evolving networks that are relevant in the Digital Economy, allowing researchers to discover the important players, quantify the efficiency of a network and predict future behaviour. These ideas offer immediate benefits outside academia, allowing us to tackle questions such as: who are the important broadcasters or receivers of information? who should we target our advertising campaign at? what will the network look like next week or next year? is there any suspicious activity today? which networks users appear to be underage? which customers are likely to change brand loyalty? how quickly will a rumour or virus spread? what would be the effect of changing the way that customers are charged for network usage? Our objectives are to develop to practical, quantitative solutions to these issues by developing a new, underpinning mathematical framework that leads directly to useful computer software. In order to make sure that the results will have immediate benefit, we have put together a team of non-academic experts who use large technological networks in their businesses. These people will provide realistic data sets, pose specific challenges and provide regular feedback and advice throughout the project.