We consider undirected graphs that grow through the successive combination of component sub-graphs. For any well-behaved functions defined for such graphs, taking values in a Banach space, we show that there must exist a scaling law applicable when successive copies of the same component graph are combined. Crucially, we extend the approach introduced in previous work to the successive combination of component random sub-graphs. We illustrate this by generalizing the preferential attachment operation for the combination of stochastic block models. We discuss a further wide range of random graph combination operators to which this theory now applies, indicating the ubiquity of growth scaling laws (and asymptotic decay scaling laws) within applications, where the modules are quite distinct, yet may be considered as instances drawn from the same random graph. This is a type of statistically self-similar growth process, as opposed to a deterministic growth process incorporating exact copies of the same motif, and it represents a natural, partially random, growth processes for graphs observed in the analysis of social and technology contexts.
{"title":"Scaling laws for properties of random graphs that grow via successive combination","authors":"P. Grindrod","doi":"10.1093/comnet/cnac024","DOIUrl":"https://doi.org/10.1093/comnet/cnac024","url":null,"abstract":"\u0000 We consider undirected graphs that grow through the successive combination of component sub-graphs. For any well-behaved functions defined for such graphs, taking values in a Banach space, we show that there must exist a scaling law applicable when successive copies of the same component graph are combined. Crucially, we extend the approach introduced in previous work to the successive combination of component random sub-graphs. We illustrate this by generalizing the preferential attachment operation for the combination of stochastic block models. We discuss a further wide range of random graph combination operators to which this theory now applies, indicating the ubiquity of growth scaling laws (and asymptotic decay scaling laws) within applications, where the modules are quite distinct, yet may be considered as instances drawn from the same random graph. This is a type of statistically self-similar growth process, as opposed to a deterministic growth process incorporating exact copies of the same motif, and it represents a natural, partially random, growth processes for graphs observed in the analysis of social and technology contexts.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-04-25","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"74335522","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1016/j.jco.2022.101665
T. Kühn, M. Petersen
{"title":"Approximation in periodic Gevrey spaces","authors":"T. Kühn, M. Petersen","doi":"10.1016/j.jco.2022.101665","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101665","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"78198529","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-04-01DOI: 10.1016/j.jco.2022.101667
Michael Allouche, S. Girard, E. Gobet
{"title":"A generative model for fBm with deep ReLU neural networks","authors":"Michael Allouche, S. Girard, E. Gobet","doi":"10.1016/j.jco.2022.101667","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101667","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-04-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"90586697","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-01DOI: 10.1016/j.jco.2022.101654
M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter
{"title":"Countable tensor products of Hermite spaces and spaces of Gaussian kernels","authors":"M. Gnewuch, M. Hefter, A. Hinrichs, K. Ritter","doi":"10.1016/j.jco.2022.101654","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101654","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"89191902","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-03-01DOI: 10.1016/j.jco.2022.101661
E. Novak, J. Prochno, Mario Ullrich
{"title":"Approximation and Geometry in High Dimensions","authors":"E. Novak, J. Prochno, Mario Ullrich","doi":"10.1016/j.jco.2022.101661","DOIUrl":"https://doi.org/10.1016/j.jco.2022.101661","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-03-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"86885152","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/s0885-064x(21)00079-0
E. Novak
{"title":"Michaela Szölgyenyi is the winner of the 2021 Joseph F. Traub Information-Based Complexity Young Researcher Award","authors":"E. Novak","doi":"10.1016/s0885-064x(21)00079-0","DOIUrl":"https://doi.org/10.1016/s0885-064x(21)00079-0","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"72882548","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
Pub Date : 2022-02-01DOI: 10.1016/s0885-064x(21)00078-9
Josef Dick, A. Hinrichs, E. Novak, K. Ritter, G. Wasilkowski, H. Wozniakowski
{"title":"Changes of the Editorial Board","authors":"Josef Dick, A. Hinrichs, E. Novak, K. Ritter, G. Wasilkowski, H. Wozniakowski","doi":"10.1016/s0885-064x(21)00078-9","DOIUrl":"https://doi.org/10.1016/s0885-064x(21)00078-9","url":null,"abstract":"","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-02-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"87739957","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
In the last years, vaccines debate has attracted the attention of all the social media, with an outstanding increase during COVID-19 vaccination campaigns. The topic has created at least two opposing factions, pro- and anti-vaccines, that have conflicting and incompatible narratives. However, a not negligible fraction of the population has an unclear position, as many citizens feel confused by the vast amount of information coming from both sides in the online social network. The engagement of the undecided population by the two parties has a key role in the success of the vaccination campaigns. In this article, we present three models used to describe the recruitment of the undecided population by pro-vax and no-vax factions in a three-states context. Starting from real-world data of Facebook pages previously labelled as pro-, anti-vaccines or neutral, we describe and compare three opinion dynamics models that catch different behaviours of the undecided population. The first one is a variation of the SIS model, where undecided position is considered an indifferent position, including users not interested in the discussion. Neutrals can be 'infected' by one of the two extreme factions, joining their side, and they 'recover' when they lose interest in the debate and go back to neutrality. The second model studied is a Voters model with three parties: neutral pages represent a centrist position. They lean on their original ideas, that are different from both the other parties. The last is the Bilingual model adapted to the vaccination debate: it describes a context where neutral individuals are in agreement with both pro- and anti-vax factions, with a position of compromise between the extremes ('bilingualism'). If they have a one-sided neighbourhood, the necessity (or the convenience) to agree with both parties comes out, and bi-linguists can become mono-linguists. Our results depicts an agreement between the three models: anti-vax opinion propagates more than pro-vax, thanks to an initial strategic position in the online social network (even if they start with a smaller population). While most of the pro-vaccines nodes are segregated in their own communities, no-vaccines ones are entangled at the core of the network, where the majority of the undecided population is located. In the last section, we propose and compare some policies that could be applied to the network to prevent anti-vax overcome: they lead us to conclude that censoring strategies are not effective, as well as segregating scenarios based on unfollowing decisions, while the addition of links in the network favours the containment of the pro-vax domain, reducing the distance between pro-vaxxers and undecided population.
{"title":"Ensemble of opinion dynamics models to understand the role of the undecided about vaccines","authors":"Jacopo Lenti, G. Ruffo","doi":"10.1093/comnet/cnac018","DOIUrl":"https://doi.org/10.1093/comnet/cnac018","url":null,"abstract":"In the last years, vaccines debate has attracted the attention of all the social media, with an outstanding increase during COVID-19 vaccination campaigns. The topic has created at least two opposing factions, pro- and anti-vaccines, that have conflicting and incompatible narratives. However, a not negligible fraction of the population has an unclear position, as many citizens feel confused by the vast amount of information coming from both sides in the online social network. The engagement of the undecided population by the two parties has a key role in the success of the vaccination campaigns. In this article, we present three models used to describe the recruitment of the undecided population by pro-vax and no-vax factions in a three-states context. Starting from real-world data of Facebook pages previously labelled as pro-, anti-vaccines or neutral, we describe and compare three opinion dynamics models that catch different behaviours of the undecided population. The first one is a variation of the SIS model, where undecided position is considered an indifferent position, including users not interested in the discussion. Neutrals can be 'infected' by one of the two extreme factions, joining their side, and they 'recover' when they lose interest in the debate and go back to neutrality. The second model studied is a Voters model with three parties: neutral pages represent a centrist position. They lean on their original ideas, that are different from both the other parties. The last is the Bilingual model adapted to the vaccination debate: it describes a context where neutral individuals are in agreement with both pro- and anti-vax factions, with a position of compromise between the extremes ('bilingualism'). If they have a one-sided neighbourhood, the necessity (or the convenience) to agree with both parties comes out, and bi-linguists can become mono-linguists. Our results depicts an agreement between the three models: anti-vax opinion propagates more than pro-vax, thanks to an initial strategic position in the online social network (even if they start with a smaller population). While most of the pro-vaccines nodes are segregated in their own communities, no-vaccines ones are entangled at the core of the network, where the majority of the undecided population is located. In the last section, we propose and compare some policies that could be applied to the network to prevent anti-vax overcome: they lead us to conclude that censoring strategies are not effective, as well as segregating scenarios based on unfollowing decisions, while the addition of links in the network favours the containment of the pro-vax domain, reducing the distance between pro-vaxxers and undecided population.","PeriodicalId":15442,"journal":{"name":"Journal of complex networks","volume":null,"pages":null},"PeriodicalIF":2.1,"publicationDate":"2022-01-21","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":null,"resultStr":null,"platform":"Semanticscholar","paperid":"60891333","PeriodicalName":null,"FirstCategoryId":null,"ListUrlMain":null,"RegionNum":4,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":"","EPubDate":null,"PubModel":null,"JCR":null,"JCRName":null,"Score":null,"Total":0}
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