Community Detection And Dynamics in Temporal Networks

许多当前科学感兴趣的系统是由相互作用的元素组成的，可以表示为网络。重要的例子包括互联网、联系网络、航线，但也包括广泛的生物系统。收集大量关系数据集的能力从根本上改变了对网络的看法，并导致了统计方法的发展，从而可以从网络的总体结构中提取重要信息。尽管取得了许多成功，但网络科学的标准工具往往忽视了网络的内在动力学性质。在许多情况下，网络不是静态的实体，而是它们的边缘在时间上受到限制，并且可以随时间而变化。时间网络的概念是用来研究这种时间依赖的网络。这个项目的主要目的是探索网络的结构和动态之间的相互作用如何影响扩散过程，并利用由此产生的扩散约束，以揭示其内部的动态社区结构。这种方法旨在加强我们对网络上的动态和网络的动态是如何相互关联的理解，并建立在为静态网络设计的算法之上，例如马尔可夫稳定性，其中扩散对于探索系统的多尺度结构至关重要，并有助于定义节点的中心性和网络的嵌入。该项目将受到来自一系列学科的真实数据的测试和启发，最终旨在加深我们对时间网络及其与图形信号处理关系的数学知识，并开发新的算法来揭示网络中随时间演变的重要结构。

Many systems of current scientific interest are made of elements in interaction and can be represented as networks. Important examples include the Internet, contact networks, airline routes but also a wide range of biological systems. The capacity to collect large data-sets of relational data has radically changed the way networks are considered and has led to the development of statistical methods allowing for the extraction of significant information from their overall structure. Despite its many successes, standard tools of network science often overlook the intrinsic dynamical nature of networks. In many situations, networks are not static entities but their edges are instead limited in time and can change over time. The concept of temporal networks is used to study such time-dependent networks. The main purpose of this project is to explore how the interplay between the structure and dynamics of networks affects diffusive processes, and to exploit the resulting constraints on diffusion in order to uncover their inner dynamical community structure. This approach searches to strengthen ou understanding of how the dynamics on and of the network are inter-related, and builds on algorithms designed for static networks, such as Markov stability, where diffusion is known to be essential to explore the multi-scale structure of the system, and to help defining the centrality of nodes and the embedding of networks. The project will be tested and inspired by real-world data from a range of disciplines, and will ultimately aim at deepening our mathematical knowledge of temporal networks and their relation to graph signal processing, and at developing novel algorithms to uncover significant structures in networks evolving in time.