How Global Directionality and Hierarchy shape the Structure and Function of Directed Complex Networks

我的博士学位涉及有向复杂网络的研究，以及应用一种名为营养分析的方法来研究这些系统，这些系统可以是各种各样的食物网、神经网络、社交网络、互联网或经济。营养分析衡量这些系统的全球定向组织，并根据节点在层次结构中的位置提供节点的本地排名。在我的博士学位期间，我一直在应用这些方法来研究定向复杂系统的各个方面。我发表了关于各种主题的作品。我们研究了在有向Hopfield神经网络中，全局方向性和层次结构如何影响存储和恢复模式的能力，以及信息呈现层次结构中的位置如何影响网络回忆模式的能力。我们还给出了一些分析结果，这些结果表明，如何使用营养分析和在打破全局方向性并激发强连通分量的边上的渗流理论来预测实有向网络中强连通的出现。我们还研究了有向系统中的影响力和可影响性的概念，并展示了网络影响力的动态和结构概念与营养分析所测量的系统的有向有序性之间的相关性。我们还在研究基于节点适应度差异分布的网络生成模型，以解释有序结构是如何在有向系统中产生的。

My PhD concerned the study of directed complex networks and the application of a method known as Trophic Analysis to study these systems which can be as diverse as food webs, neural networks, social networks, the internet or economies. Trophic Analysis measures the global directional organisation of these systems as well as providing a local ranking of the nodes by their place in the hierarchical structure. Throughout my PhD I have been applying these methods to study various facets of directed complex systems. I have published work on a variety of topics. We studied how in directed Hopfield Neural Networks the global directionality and hierarchy can influence the ability to store and recover patterns as well as the fact that the location in the hierarchy of information presentation can affect the ability of networks to recall the pattern. We also showed some analytical results which show how emergence of strong connectivity in real directed networks can be predicted using Trophic Analysis and by using percolation theory on the edges which break the global directionality and incite the strongly connected component. We also have worked on the notion of influence and influenceability in a directed systems and showed the correlation between dynamical and structural notions of network influence and the directed ordering of the system as measured by Trophic Analysis. We are also working on notions to explain how ordered structures arise in directed systems by working on network generative models based on node fitness difference distributions.