"Complexity Science: Percolation, Networks and Information Theory"

复杂性科学发展迅速，在物理学、生物学、语言学和社会学等领域得到了广泛的应用。本提案涉及三个领域：渗流、网络和互信息。渗流是随着控制参数的变化而突然出现的远程连通性。已经详细研究了具有简单链路的单个网络上的渗流现象，但实际上大多数网络不是孤立存在的，可能具有多于一种类型的链路，或者表现出被称为广义传染的不同形式的传播。例如，基础设施和技术网络往往是耦合的或相互依存的。社会动态可以反映暴露的历史。最近，已经提出了几个渗流的推广来处理这些情况。它们表现出出乎意料的行为，与普通渗流的行为不一致。例如，目前尚不清楚耦合如何改变过渡附近击穿的性质。这些模型之间的细节和相互关系以及总体理论仍然不清楚，但它们对现实世界问题的适用性越来越明显。我们将有助于理解这些模型，并确定它们或类似模型适用的场景以及可能产生的后果。

Complexity science is rapidly evolving and finds wide application in fields as diverse as physics, biology, linguistics, and sociology. The present proposal deals with three areas: percolation, networks, and mutual information. Percolation is the sudden emergence of long-range connectivity as a control parameter is varied. Percolation phenomena on individual networks with simple links have been studied in detail but in reality most networks do not exist in isolation, may have more than one type of link, or exhibit different forms of propagation referred to as generalized contagion. For example infrastructure and technological networks are often coupled or 'interdependent'. Social dynamics can reflect the history of exposure. Recently, several generalizations of percolation have been proposed to deal with these situations. They exhibit unexpected behaviour, inconsistent with that of ordinary percolation. It is not clear, for example, how coupling can change the nature of breakdown near the transition. The details and interrelationships between these models as well as an overarching theory are still unclear, but their applicability to real world problems is increasingly evident. We will contribute to understanding these models and identify scenarios to which they or similar models apply and what the consequences might be.