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The Why, How, and When of Representations for Complex Systems
SIAM Review ( IF 10.8 ) Pub Date : 2021-08-05 , DOI: 10.1137/20m1355896 Leo Torres , Ann S. Blevins , Danielle Bassett , Tina Eliassi-Rad
SIAM Review ( IF 10.8 ) Pub Date : 2021-08-05 , DOI: 10.1137/20m1355896 Leo Torres , Ann S. Blevins , Danielle Bassett , Tina Eliassi-Rad
SIAM Review, Volume 63, Issue 3, Page 435-485, January 2021.
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.
中文翻译：
复杂系统表示的原因、方式和时间
SIAM 评论，第 63 卷，第 3 期，第 435-485 页，2021 年 1 月。
复杂系统由最基本的单元及其相互作用组成，描述了从神经科学到计算机科学和经济学等广泛领域的现象。各种各样的应用程序导致了两个关键挑战：为复杂系统分析生成许多特定领域的策略，这些策略很少被重新审视，以及由于复杂系统语言的不一致而导致域内表示和分析思想的划分。在这项工作中，我们提出了基本的、领域不可知的语言，以便朝着更有凝聚力的词汇发展。我们使用这种语言来评估复杂系统分析管道的每个步骤，从正在研究的系统和收集的数据开始，然后通过不同的数学框架对观察到的数据（即图形、单纯复形和超图），以及每个框架的相关计算方法。在每一步，我们都会考虑不同类型的依赖关系；这些是系统的属性，描述了系统中一组单元之间相互作用的存在如何影响另一个关系存在的可能性。我们讨论了依赖关系如何产生以及它们如何改变结果的解释或整个分析管道。我们以两个使用合着数据和电子邮件通信数据的真实示例结束，这些示例说明了所研究的系统、其中的依赖关系、研究问题以及数学表示的选择如何影响结果。我们希望这项工作可以成为经验丰富的复杂系统科学家进行反思的机会，
更新日期：2021-08-07
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.
中文翻译：
复杂系统表示的原因、方式和时间
SIAM 评论，第 63 卷，第 3 期，第 435-485 页，2021 年 1 月。
复杂系统由最基本的单元及其相互作用组成，描述了从神经科学到计算机科学和经济学等广泛领域的现象。各种各样的应用程序导致了两个关键挑战：为复杂系统分析生成许多特定领域的策略，这些策略很少被重新审视，以及由于复杂系统语言的不一致而导致域内表示和分析思想的划分。在这项工作中，我们提出了基本的、领域不可知的语言，以便朝着更有凝聚力的词汇发展。我们使用这种语言来评估复杂系统分析管道的每个步骤，从正在研究的系统和收集的数据开始，然后通过不同的数学框架对观察到的数据（即图形、单纯复形和超图），以及每个框架的相关计算方法。在每一步，我们都会考虑不同类型的依赖关系；这些是系统的属性，描述了系统中一组单元之间相互作用的存在如何影响另一个关系存在的可能性。我们讨论了依赖关系如何产生以及它们如何改变结果的解释或整个分析管道。我们以两个使用合着数据和电子邮件通信数据的真实示例结束，这些示例说明了所研究的系统、其中的依赖关系、研究问题以及数学表示的选择如何影响结果。我们希望这项工作可以成为经验丰富的复杂系统科学家进行反思的机会，
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