期刊
SIAM REVIEW
卷 63, 期 3, 页码 435-485出版社
SIAM PUBLICATIONS
DOI: 10.1137/20M1355896
关键词
complex systems; dependencies; graph theory; simplicial complexes; hypergraphs
资金
- Army Research Office [Falk-W911NF-18-1-0244, Grafton-W911NF-16-1-0474, DCIST-W911NF-17-20181,]
- National Science Foundation (NSF) [PHY-1554488, IIS-1926757]
- Paul G. Allen Family Foundation
- NSF [IIS-1741197]
- Combat Capabilities Development Command Army Research Laboratory [W911NF-13-2-0045]
The paper proposes a basic, domain-agnostic language to advance towards a more cohesive vocabulary for complex systems. It evaluates each step of the complex systems analysis pipeline and discusses different types of dependencies that can affect the results and the entire analysis process.
Complex systems, composed at the most basic level of units and their interactions, describe phenomena in a wide variety of domains, from neuroscience to computer science and economics. The wide variety of applications has resulted in two key challenges: the generation of many domain-specific strategies for complex systems analyses that are seldom revisited, and the compartmentalization of representation and analysis ideas within a domain due to inconsistency in complex systems language. In this work we propose basic, domain-agnostic language in order to advance toward a more cohesive vocabulary. We use this language to evaluate each step of the complex systems analysis pipeline, beginning with the system under study and data collected, then moving through different mathematical frameworks for encoding the observed data (i.e., graphs, simplicial complexes, and hypergraphs), and relevant computational methods for each framework. At each step we consider different types of dependencies; these are properties of the system that describe how the existence of an interaction among a set of units in a system may affect the possibility of the existence of another relation. We discuss how dependencies may arise and how they may alter the interpretation of results or the entirety of the analysis pipeline. We close with two real-world examples using coauthorship data and email communications data that illustrate how the system under study, the dependencies therein, the research question, and the choice of mathematical representation influence the results. We hope this work can serve as an opportunity for reflection for experienced complex systems scientists, as well as an introductory resource for new researchers.
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