Theory and applications of higher-order network models

高阶网络模型理论与应用

• 批准号: 2434800
• 金额: --
• 依托单位: University of Strathclyde
• 依托单位国家: 英国
• 项目类别: Studentship
• 财政年份: 2020
• 资助国家: 英国
• 起止时间: 2020 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=studentship-2434800
• 关键词: Theory; applications; higher; order; network

Networks (or graphs) provide a useful modelling tool to describe very different complex systems, from brains and ecosystems to social organisations, financial markets, transportation systems, and power grids, to name a few. Since these complex systems consist of entities that interact or relate to each other, network models represent them as graphs where the components are described as vertices and the edges capture pairwise (dyadic) interactions between them. One of the main strengths of these models is in their ability to relate the structure of systems to their dynamic; for example, a communication network of a community of people may provide insights into how a new idea spreads across the members of such a community, since the network is the mean that allows the information to flow. On the other hand, a fundamental shortcoming of current network models is their inability to appropriately capture higher-order interactions, i.e., those interactions that occur between more than two components. For example, consider three people, named A, B, and C, that collaborate together. A standard network would model this triadic interaction using three pairs, namely (A, B), (B, C), and (C, A). However, the relationship between these people would be better represented using a single interaction, (A,B,C), that standard network model cannot store. This exemplifies something that has become more and more apparent with the advent of big data and the growing evidence that these often present several instances of group-based interactions, which standard network models fail to capture. The aim of this project is to model, describe, and apply new classes of network models that effectively capture higher-order interactions occurring in complex systems; this will in turn allow for a better understading of the behavior and dynamics of such systems. A key reason for the limited number of higher-order network models is that data is often collected in a pairwise format: higher-order information is disregarded at the data-collection stage. However, this limitation can sometimes be overcome by using the metadata accompaining the experimental information; For example, collaborative relationships among more than two authors can be recovered by looking at the authors list of the papers they have co-authored. The main modelling tool that will be used is simplicial complexes from algebraic topology. Simplices generalize line segments in higher-dimensional spaces and thus can be effectively used to represent many-body interactions. A simplicial complex is then just a collection of 'connected' simplices. The theory developed will provide a theoretical framework for analytical tools that will allow to quantify the importance of components within the network, as well as to identify large-scale structures (e.g., clusters of densely connected components) in terms of higher-order interactions. The theory will be equipped with a set of computationally efficient algorithms that will ensure wide applicability of the introduced techniques, especially for large datasets. The developed techniques will be tested against standard network models and other available higher-order representations of networks, including tensor representations.This studentship will contribute to understanding how to incorporate and take advantage of higher-order information in networks modelling complex systems. It will develop mathematical, statistical, and computational tools for analysis of higher-order interactions and open up novel data analytics for relational data. The wide applicability of the theory and algorithmics developed will allow testing on publicly available real-world data.

网络（或图形）提供了一种有用的建模工具来描述非常不同的复杂系统，从大脑和生态系统到社会组织、金融市场、交通系统和电网等等。由于这些复杂系统由彼此交互或相关的实体组成，因此网络模型将它们表示为图形，其中组件被描述为顶点，边捕获它们之间的成对（二元）交互。这些模型的主要优势之一是能够将系统结构与其动态联系起来。例如，人们社区的通信网络可以提供有关新想法如何在该社区成员之间传播的见解，因为网络是允许信息流动的手段。另一方面，当前网络模型的一个根本缺点是它们无法正确捕获高阶交互，即发生在两个以上组件之间的交互。例如，考虑三个人，分别为 A、B 和 C，他们一起协作。标准网络将使用三对（即（A，B）、（B，C）和（C，A））来模拟这种三元交互。然而，使用标准网络模型无法存储的单个交互（A，B，C）可以更好地表示这些人之间的关系。这说明了随着大数据的出现而变得越来越明显的事情，并且越来越多的证据表明，这些通常呈现出标准网络模型无法捕获的基于群体的交互的几个实例。该项目的目标是建模、描述和应用新型网络模型，以有效捕获复杂系统中发生的高阶交互；这反过来将有助于更好地理解此类系统的行为和动态。高阶网络模型数量有限的一个关键原因是数据通常以成对格式收集：在数据收集阶段忽略高阶信息。然而，有时可以通过使用实验信息附带的元数据来克服这种限制；例如，可以通过查看他们共同撰写的论文的作者列表来恢复两个以上作者之间的合作关系。将使用的主要建模工具是代数拓扑中的单纯复形。单纯形概括了高维空间中的线段，因此可以有效地用于表示多体相互作用。单纯复形只是“相连”单纯形的集合。所开发的理论将为分析工具提供一个理论框架，该框架将允许量化网络内组件的重要性，以及根据高阶交互来识别大规模结构（例如，密集连接组件的集群）。该理论将配备一套计算高效的算法，以确保所引入技术的广泛适用性，特别是对于大型数据集。所开发的技术将针对标准网络模型和其他可用的网络高阶表示（包括张量表示）进行测试。该学生奖学金将有助于理解如何在复杂系统建模的网络中合并和利用高阶信息。它将开发数学、统计和计算工具来分析高阶交互，并为关系数据开辟新颖的数据分析。所开发的理论和算法的广泛适用性将允许对公开的真实世界数据进行测试。