Pub Date : 2024-10-29DOI: 10.1038/s44260-024-00018-8
Akshay Verma, Richard Sear, Neil Johnson
Local or national politics can be a catalyst for potentially dangerous hate speech. But with a third of the world’s population eligible to vote in 2024 elections, we need an understanding of how individual-level hate multiplies up to the collective global scale. We show, based on the most recent U.S. presidential election, that offline events are associated with rapid adaptations of the global online hate universe that strengthens both its network-of-networks structure and the types of hate content that it collectively produces. Approximately 50 million accounts in hate communities are drawn closer to each other and to a broad mainstream of billions. The election triggered new hate content at scale around immigration, ethnicity, and antisemitism that aligns with conspiracy theories about Jewish-led replacement. Telegram acts as a key hardening agent; yet, it is overlooked by U.S. Congressional hearings and new E.U. legislation. Because the hate universe has remained robust since 2020, anti-hate messaging surrounding global events (e.g., upcoming elections or the war in Gaza) should pivot to blending multiple hate types while targeting previously untouched social media structures.
{"title":"How U.S. Presidential elections strengthen global hate networks","authors":"Akshay Verma, Richard Sear, Neil Johnson","doi":"10.1038/s44260-024-00018-8","DOIUrl":"10.1038/s44260-024-00018-8","url":null,"abstract":"Local or national politics can be a catalyst for potentially dangerous hate speech. But with a third of the world’s population eligible to vote in 2024 elections, we need an understanding of how individual-level hate multiplies up to the collective global scale. We show, based on the most recent U.S. presidential election, that offline events are associated with rapid adaptations of the global online hate universe that strengthens both its network-of-networks structure and the types of hate content that it collectively produces. Approximately 50 million accounts in hate communities are drawn closer to each other and to a broad mainstream of billions. The election triggered new hate content at scale around immigration, ethnicity, and antisemitism that aligns with conspiracy theories about Jewish-led replacement. Telegram acts as a key hardening agent; yet, it is overlooked by U.S. Congressional hearings and new E.U. legislation. Because the hate universe has remained robust since 2020, anti-hate messaging surrounding global events (e.g., upcoming elections or the war in Gaza) should pivot to blending multiple hate types while targeting previously untouched social media structures.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-6"},"PeriodicalIF":0.0,"publicationDate":"2024-10-29","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00018-8.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142525750","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-07DOI: 10.1038/s44260-024-00019-7
Aparna Ananthasubramaniam, David Jurgens, Daniel M. Romero
{"title":"Author Correction: Networks and identity drive the spatial diffusion of linguistic innovation in urban and rural areas","authors":"Aparna Ananthasubramaniam, David Jurgens, Daniel M. Romero","doi":"10.1038/s44260-024-00019-7","DOIUrl":"10.1038/s44260-024-00019-7","url":null,"abstract":"","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-1"},"PeriodicalIF":0.0,"publicationDate":"2024-10-07","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00019-7.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142383563","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-03DOI: 10.1038/s44260-024-00016-w
Kunal Bhattacharya, Chandreyee Roy, Tuomas Takko, Anna Rotkirch, Kimmo Kaski
We studied residential clustering and mobility of ethnic minorities using a theoretical framework based on null models of spatial distributions and movements of populations. Using microdata from population registers we compared the patterns of clustering amongst various socioethnic groups living in and around the capital region of Finland. The models enabled us to connect the factors influencing intraurban migration to the spatial patterns that have developed over time. The observed clustering seems to be a combined effect of fertility and the tendency to migrate locally. The models also highlight the importance of factors like proximity to the city centre, neighbourhood income levels, and similarity of socioeconomic profiles. While the demonstrated relationship between clustering, mobility, and fertility is based on a limited number of observations, it could serve as a motivation for future research in different urban settings. Overall, these insights are expected to contribute to our understanding of demographic dynamics in culturally diverse environments.
{"title":"Urban residential clustering and mobility of ethnic groups: impact of fertility","authors":"Kunal Bhattacharya, Chandreyee Roy, Tuomas Takko, Anna Rotkirch, Kimmo Kaski","doi":"10.1038/s44260-024-00016-w","DOIUrl":"10.1038/s44260-024-00016-w","url":null,"abstract":"We studied residential clustering and mobility of ethnic minorities using a theoretical framework based on null models of spatial distributions and movements of populations. Using microdata from population registers we compared the patterns of clustering amongst various socioethnic groups living in and around the capital region of Finland. The models enabled us to connect the factors influencing intraurban migration to the spatial patterns that have developed over time. The observed clustering seems to be a combined effect of fertility and the tendency to migrate locally. The models also highlight the importance of factors like proximity to the city centre, neighbourhood income levels, and similarity of socioeconomic profiles. While the demonstrated relationship between clustering, mobility, and fertility is based on a limited number of observations, it could serve as a motivation for future research in different urban settings. Overall, these insights are expected to contribute to our understanding of demographic dynamics in culturally diverse environments.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-9"},"PeriodicalIF":0.0,"publicationDate":"2024-10-03","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00016-w.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142368732","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-10-01DOI: 10.1038/s44260-024-00015-x
Zhuoying Xu, Yingjun Zhu, Binbin Hong, Xinlin Wu, Jingwen Zhang, Mufeng Cai, Da Zhou, Yu Liu
This study employs the recently developed Ladderpath approach, within the broader category of Algorithmic Information Theory (AIT), which characterizes the hierarchical and nested relationships among repeating substructures, to explore the structure-function relationship in neural networks, multilayer perceptrons (MLP), in particular. The metric order-rate η, derived from the approach, is a measure of structural orderliness: when η is in the middle range (around 0.5), the structure exhibits the richest hierarchical relationships, corresponding to the highest complexity. We hypothesize that the highest structural complexity correlates with optimal functionality. Our experiments support this hypothesis in several ways: networks with η values in the middle range show superior performance, and the training processes tend to naturally adjust η towards this range; additionally, starting neural networks with η values in this middle range appears to boost performance. Intriguingly, these findings align with observations in other distinct systems, including chemical molecules and protein sequences, hinting at a hidden regularity encapsulated by this theoretical framework.
本研究在算法信息论（AIT）的大范畴内采用了最近开发的阶梯路径方法（Ladderpath approach），该方法描述了重复子结构之间的层次和嵌套关系，以探索神经网络（尤其是多层感知器（MLP））中的结构-功能关系。从该方法中得出的度量秩率 η 是结构有序性的一个度量：当 η 处于中间范围（约 0.5）时，结构表现出最丰富的层次关系，相当于最高的复杂性。我们假设，最高的结构复杂度与最佳功能相关。我们的实验从几个方面支持了这一假设：η 值处于中间范围的网络表现出更优越的性能，而训练过程往往会自然地将 η 调整到这一范围；此外，以 η 值处于中间范围的神经网络作为起点似乎也能提高性能。耐人寻味的是，这些发现与其他不同系统（包括化学分子和蛋白质序列）中的观察结果一致，暗示了这一理论框架所包含的隐藏规律性。
{"title":"Correlating measures of hierarchical structures in artificial neural networks with their performance","authors":"Zhuoying Xu, Yingjun Zhu, Binbin Hong, Xinlin Wu, Jingwen Zhang, Mufeng Cai, Da Zhou, Yu Liu","doi":"10.1038/s44260-024-00015-x","DOIUrl":"10.1038/s44260-024-00015-x","url":null,"abstract":"This study employs the recently developed Ladderpath approach, within the broader category of Algorithmic Information Theory (AIT), which characterizes the hierarchical and nested relationships among repeating substructures, to explore the structure-function relationship in neural networks, multilayer perceptrons (MLP), in particular. The metric order-rate η, derived from the approach, is a measure of structural orderliness: when η is in the middle range (around 0.5), the structure exhibits the richest hierarchical relationships, corresponding to the highest complexity. We hypothesize that the highest structural complexity correlates with optimal functionality. Our experiments support this hypothesis in several ways: networks with η values in the middle range show superior performance, and the training processes tend to naturally adjust η towards this range; additionally, starting neural networks with η values in this middle range appears to boost performance. Intriguingly, these findings align with observations in other distinct systems, including chemical molecules and protein sequences, hinting at a hidden regularity encapsulated by this theoretical framework.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2024-10-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00015-x.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142360064","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-09-02DOI: 10.1038/s44260-024-00009-9
Aparna Ananthasubramaniam, David Jurgens, Daniel M. Romero
Cultural innovation (e.g., music, beliefs, language) tends to be adopted regionally. The geographic area where innovation is adopted is often attributed to one of two factors: (i) speakers adopting new behaviors that signal their demographic identities (i.e., an identity effect), or (ii) these behaviors spreading through homophilous networks (i.e., a network effect). In this study, we show that network and identity play complementary roles in determining where new language is adopted; thus, modeling the diffusion of lexical innovation requires incorporating both network and identity. We develop an agent-based model of cultural adoption, and validate geographic properties in our simulations against a dataset of innovative words that we identify from a 10% sample of Twitter (e.g., fleeky, birbs, ubering). Using our model, we are able to directly test the roles of network and identity by comparing a model that combines network and identity against simulated network-only and identity-only counterfactuals. We show that both effects influence different mechanisms of diffusion. Specifically, network principally drives spread among urban counties via weak-tie diffusion, while identity plays a disproportionate role in transmission among rural counties via strong-tie diffusion. Diffusion between urban and rural areas, a key component in innovation spreading nationally, requires both network and identity. Our work suggests that models must integrate both factors in order to understand and reproduce the adoption of innovation.
文化创新（如音乐、信仰、语言）往往在地区范围内采用。创新被采用的地理区域通常归因于以下两个因素之一：(i) 说话者采用了表明其人口身份的新行为（即身份效应），或 (ii) 这些行为通过同亲网络传播（即网络效应）。在本研究中，我们发现网络和身份在决定新语言在何处被采用方面起着互补作用；因此，建立词汇创新传播模型需要同时考虑网络和身份。我们建立了一个基于代理的文化采用模型，并在模拟中根据我们从 Twitter 的 10% 样本中识别出的创新词数据集（例如，fleeky、birbs、ubering）验证了地理属性。利用我们的模型，我们能够通过将网络和身份相结合的模型与模拟的纯网络和纯身份反事实进行比较，直接检验网络和身份的作用。我们发现，这两种效应影响着不同的传播机制。具体来说，网络主要通过弱联系扩散推动城市县域之间的传播，而身份则通过强联系扩散在农村县域之间的传播中发挥着不成比例的作用。城市和农村地区之间的扩散是创新在全国范围内传播的一个关键组成部分，它既需要网络，也需要身份。我们的工作表明，模型必须整合这两个因素，才能理解和再现创新的采用。
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Pub Date : 2024-09-02DOI: 10.1038/s44260-024-00013-z
Robert Jankowski, Pegah Hozhabrierdi, Marián Boguñá, M. Ángeles Serrano
In existing models and embedding methods of networked systems, node features describing their qualities are usually overlooked in favor of focusing solely on node connectivity. This study introduces FiD-Mercator, a model-based ultra-low dimensional reduction technique that integrates node features with network structure to create D-dimensional maps of complex networks in a hyperbolic space. This embedding method efficiently uses features as an initial condition, guiding the search of nodes’ coordinates toward an optimal solution. The research reveals that downstream task performance improves with the correlation between network connectivity and features, emphasizing the importance of such correlation for enhancing the description and predictability of real networks. Simultaneously, hyperbolic embedding’s ability to reproduce local network properties remains unaffected by the inclusion of features. The findings highlight the necessity for developing network embedding techniques capable of exploiting such correlations to optimize both network structure and feature association jointly in the future.
在现有的网络系统模型和嵌入方法中，描述其质量的节点特征通常被忽视，而只关注节点的连接性。本研究介绍的 FiD-Mercator 是一种基于模型的超低维缩减技术，它将节点特征与网络结构相结合，在双曲空间中创建复杂网络的 D 维映射。这种嵌入方法有效地将特征作为初始条件，引导节点坐标的搜索走向最优解。研究发现，下游任务的性能会随着网络连通性和特征之间的相关性而提高，从而强调了这种相关性对于增强真实网络的描述和可预测性的重要性。同时，双曲嵌入再现局部网络属性的能力不受包含特征的影响。这些发现突出表明，未来有必要开发能够利用这种相关性的网络嵌入技术，以共同优化网络结构和特征关联。
{"title":"Feature-aware ultra-low dimensional reduction of real networks","authors":"Robert Jankowski, Pegah Hozhabrierdi, Marián Boguñá, M. Ángeles Serrano","doi":"10.1038/s44260-024-00013-z","DOIUrl":"10.1038/s44260-024-00013-z","url":null,"abstract":"In existing models and embedding methods of networked systems, node features describing their qualities are usually overlooked in favor of focusing solely on node connectivity. This study introduces FiD-Mercator, a model-based ultra-low dimensional reduction technique that integrates node features with network structure to create D-dimensional maps of complex networks in a hyperbolic space. This embedding method efficiently uses features as an initial condition, guiding the search of nodes’ coordinates toward an optimal solution. The research reveals that downstream task performance improves with the correlation between network connectivity and features, emphasizing the importance of such correlation for enhancing the description and predictability of real networks. Simultaneously, hyperbolic embedding’s ability to reproduce local network properties remains unaffected by the inclusion of features. The findings highlight the necessity for developing network embedding techniques capable of exploiting such correlations to optimize both network structure and feature association jointly in the future.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-11"},"PeriodicalIF":0.0,"publicationDate":"2024-09-02","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00013-z.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"142117961","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1038/s44260-024-00010-2
Maximilian M. Nguyen
We expand the calculation of the upper bound on epidemic overshoot in SIR models to account for nonlinear incidence. We lay out the general procedure and restrictions to perform the calculation analytically for nonlinear functions in the number of susceptibles. We demonstrate the procedure by working through several examples and also numerically study what happens to the upper bound on overshoot when nonlinear incidence manifests in the form of epidemic dynamics over a contact network. We find that both steeper incidence terms and larger contact heterogeneity can increase the range of communicable diseases at which the overshoot remains a relatively large public health hazard.
我们扩展了 SIR 模型中流行病超调上限的计算方法，以考虑非线性发生率。我们列出了针对易感者数量的非线性函数进行分析计算的一般程序和限制条件。我们通过几个例子演示了这一过程，并用数值方法研究了当非线性发生率以接触网络上流行动态的形式出现时，超调的上限会发生什么变化。我们发现，更陡峭的发病率项和更大的接触异质性都会扩大传染病的范围，在这种情况下，过冲仍会对公共健康造成相对较大的危害。
{"title":"Upper bounds on overshoot in SIR models with nonlinear incidence","authors":"Maximilian M. Nguyen","doi":"10.1038/s44260-024-00010-2","DOIUrl":"10.1038/s44260-024-00010-2","url":null,"abstract":"We expand the calculation of the upper bound on epidemic overshoot in SIR models to account for nonlinear incidence. We lay out the general procedure and restrictions to perform the calculation analytically for nonlinear functions in the number of susceptibles. We demonstrate the procedure by working through several examples and also numerically study what happens to the upper bound on overshoot when nonlinear incidence manifests in the form of epidemic dynamics over a contact network. We find that both steeper incidence terms and larger contact heterogeneity can increase the range of communicable diseases at which the overshoot remains a relatively large public health hazard.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-7"},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00010-2.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968459","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-08-01DOI: 10.1038/s44260-024-00014-y
Cristian Axenie, Oliver López-Corona, Michail A. Makridis, Meisam Akbarzadeh, Matteo Saveriano, Alexandru Stancu, Jeffrey West
Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system’s output response to input variability. Systems may respond poorly to perturbations (fragile) or benefit from perturbations (antifragile). In this manuscript, we review a range of applications of antifragility theory in technical systems (e.g., traffic control, robotics) and natural systems (e.g., cancer therapy, antibiotics). While there is a broad overlap in methods used to quantify and apply antifragility across disciplines, there is a need for precisely defining the scales at which antifragility operates. Thus, we provide a brief general introduction to the properties of antifragility in applied systems and review relevant literature for both natural and technical systems’ antifragility. We frame this review within three scales common to technical systems: intrinsic (input–output nonlinearity), inherited (extrinsic environmental signals), and induced (feedback control), with associated counterparts in biological systems: ecological (homogeneous systems), evolutionary (heterogeneous systems), and interventional (control). We use the common noun in designing systems that exhibit antifragile behavior across scales and guide the reader along the spectrum of fragility–adaptiveness–resilience–robustness–antifragility, the principles behind it, and its practical implications.
{"title":"Antifragility in complex dynamical systems","authors":"Cristian Axenie, Oliver López-Corona, Michail A. Makridis, Meisam Akbarzadeh, Matteo Saveriano, Alexandru Stancu, Jeffrey West","doi":"10.1038/s44260-024-00014-y","DOIUrl":"10.1038/s44260-024-00014-y","url":null,"abstract":"Antifragility characterizes the benefit of a dynamical system derived from the variability in environmental perturbations. Antifragility carries a precise definition that quantifies a system’s output response to input variability. Systems may respond poorly to perturbations (fragile) or benefit from perturbations (antifragile). In this manuscript, we review a range of applications of antifragility theory in technical systems (e.g., traffic control, robotics) and natural systems (e.g., cancer therapy, antibiotics). While there is a broad overlap in methods used to quantify and apply antifragility across disciplines, there is a need for precisely defining the scales at which antifragility operates. Thus, we provide a brief general introduction to the properties of antifragility in applied systems and review relevant literature for both natural and technical systems’ antifragility. We frame this review within three scales common to technical systems: intrinsic (input–output nonlinearity), inherited (extrinsic environmental signals), and induced (feedback control), with associated counterparts in biological systems: ecological (homogeneous systems), evolutionary (heterogeneous systems), and interventional (control). We use the common noun in designing systems that exhibit antifragile behavior across scales and guide the reader along the spectrum of fragility–adaptiveness–resilience–robustness–antifragility, the principles behind it, and its practical implications.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2024-08-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00014-y.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141968458","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-11DOI: 10.1038/s44260-024-00012-0
Michael W. Macy, Boleslaw K. Szymanski, Janusz A. Hołyst
The centennial of the Ising model marks a century of interdisciplinary contributions that extend well beyond ferromagnets, including the evolution of language, volatility in financial markets, mood swings, scientific collaboration, the persistence of unintended neighborhood segregation, and asymmetric hysteresis in political polarization. The puzzle is how anything could be learned about social life from a toy model of second order ferromagnetic phase transitions on a periodic network. Our answer points to Ising’s deeper contribution: a bottom-up modeling approach that explores phase transitions in population behavior that emerge spontaneously through the interplay of individual choices at the micro-level of interactions among network neighbors.
{"title":"The Ising model celebrates a century of interdisciplinary contributions","authors":"Michael W. Macy, Boleslaw K. Szymanski, Janusz A. Hołyst","doi":"10.1038/s44260-024-00012-0","DOIUrl":"10.1038/s44260-024-00012-0","url":null,"abstract":"The centennial of the Ising model marks a century of interdisciplinary contributions that extend well beyond ferromagnets, including the evolution of language, volatility in financial markets, mood swings, scientific collaboration, the persistence of unintended neighborhood segregation, and asymmetric hysteresis in political polarization. The puzzle is how anything could be learned about social life from a toy model of second order ferromagnetic phase transitions on a periodic network. Our answer points to Ising’s deeper contribution: a bottom-up modeling approach that explores phase transitions in population behavior that emerge spontaneously through the interplay of individual choices at the micro-level of interactions among network neighbors.","PeriodicalId":501707,"journal":{"name":"npj Complexity","volume":" ","pages":"1-8"},"PeriodicalIF":0.0,"publicationDate":"2024-07-11","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"https://www.nature.com/articles/s44260-024-00012-0.pdf","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"141597210","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":0,"RegionCategory":"","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"OA","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2024-07-02DOI: 10.1038/s44260-024-00011-1
Thomas F. Varley
In the last decade, there has been an explosion of interest in the field of multivariate information theory and the study of emergent, higher-order interactions. These “synergistic” dependencies reflect information that is in the “whole” but not any of the “parts.” Arguably the most successful framework for exploring synergies is the partial information decomposition (PID). Despite its considerable power, the PID has a number of limitations that restrict its general applicability. Subsequently, other heuristic measures, such as the O-information, have been introduced, although these measures typically only provide a summary statistic of redundancy/synergy dominance, rather than direct insight into the synergy itself. To address this issue, we present an alternative decomposition that is synergy-first, scales much more gracefully than the PID, and has a straightforward interpretation. We define synergy as that information encoded in the joint state of a set of elements that would be lost following the minimally invasive perturbation on any single element. By generalizing this idea to sets of elements, we construct a totally ordered “backbone” of partial synergy atoms that sweeps the system’s scale. This approach applies to the entropy, the Kullback-Leibler divergence, and by extension, to the total correlation and the single-target mutual information (thus recovering a “backbone” PID). Finally, we show that this approach can be used to decompose higher-order interactions beyond information theory by showing how synergistic combinations of edges in a graph support global integration via communicability. We conclude by discussing how this perspective on synergistic structure can deepen our understanding of part-whole relationships in complex systems.
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