Complex contagions with timers

Oh, Se‐Wook; Porter, Mason A.

doi:10.1063/1.4990038

Cited by 20 publications

(17 citation statements)

References 71 publications

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“…Because all binary models, mentioned above, have been extensively investigated for years, many modifications and extensions of their original formulations have been proposed; a short review on modifications of the majorityvote model can be found in [29], on the Watts threshold model in [30], on the q-voter model in [31] and on the Galam model comprehensive review has been written by the author of the model [32,33]. Among many extensions, going into different directions, the introduction of an additional type of the social response was particularly interesting from the point of view of social/psychological sciences, as well as the theory of non-equilibrium phase transitions.…”

Section: Introductionmentioning

confidence: 99%

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Nowak

Sznajd-Weron

2019

Complexity

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We study two variants of the modified Watts threshold model with a noise (with nonconformity, in the terminology of social psychology) on a complete graph. Within the first version, a noise is introduced via so-called independence, whereas in the second version anticonformity plays the role of a noise, which destroys the order. The modified Watts threshold model, studied here, is homogeneous and posses an up-down symmetry, which makes it similar to other binary opinion models with a single-flip dynamics, such as the majority-vote and the q-voter models. Because within the majority-vote model with independence only continuous phase transitions are observed, whereas within the q-voter model with independence also discontinuous phase transitions are possible, we ask the question about the factor, which could be responsible for discontinuity of the order parameter. We investigate the model via the mean-field approach, which gives the exact result in the case of a complete graph, as well as via Monte Carlo simulations. Additionally, we provide a heuristic reasoning, which explains observed phenomena. We show that indeed, if the threshold r = 0.5, which corresponds to the majority-vote model, an order-disorder transition is continuous. Moreover, results obtained for both versions of the model (one with independence and the second one with anticonformity) give the same results, only rescaled by the factor of 2. However, for r > 0.5 the jump of the order parameter and the hysteresis is observed for the model with independence, and both versions of the model give qualitatively different results.

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Section: Introductionmentioning

confidence: 99%

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Nowak

Sznajd-Weron

2019

Complexity

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“…The epidemic trees analyzed in this paper, along with their associated pathways of contagion, have been studied previously in diverse disciplines. They have been called adoption paths [20], dissemination trees [40,41], spreading patterns [42], causal trees of disease transmission [43], diffusion structure patterns [44], the structure of diffusion events [45], and epidemic trees [46]. We have chosen to adopt the term "epidemic trees," although it comes with a significant caveat: Generally, the graph of the propagation paths for a contagion need not be a directed tree; in the case of a complex contagion [47], where each child node has two or more parents, the graph could be a directed graph with no cycles.…”

Section: Discussionmentioning

confidence: 99%

Descendant distributions for the impact of mutant contagion on networks

Juul

Strogatz

2020

Phys. Rev. Research

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Contagion, broadly construed, refers to anything that can spread infectiously from peer to peer. Examples include communicable diseases, rumors, misinformation, ideas, innovations, bank failures, and electrical blackouts. Sometimes, as in the 1918 Spanish flu epidemic, a contagion mutates at some point as it spreads through a network. Here, using a simple susceptible-infected model of contagion, we explore the downstream impact of a single mutation event. Assuming that this mutation occurs at a random node in the contact network, we calculate the distribution of the number of "descendants," d, downstream from the initial "patient zero" mutant. We find that the tail of the distribution decays as d −2 for complete graphs, random graphs, small-world networks, networks with block-like structure, and other infinite-dimensional networks. This prediction agrees with the observed statistics of memes propagating and mutating on Facebook and is expected to hold for other effectively infinite-dimensional networks, such as the global human contact network. In a wider context, our approach suggests a possible starting point for a mesoscopic theory of contagion. Such a theory would focus on the paths traced by a spreading contagion, thereby furnishing an intermediate level of description between that of individual nodes and the total infected population. We anticipate that contagion pathways will hold valuable lessons, given their role as the conduits through which single mutations, innovations, or failures can sweep through a network as a whole.

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“…In this case, the presence of a single hipster node increases the expected fraction of nodes who adopt product B at steady state from 0 nodes to half of the nodes. The main idea is that early adopters can influence later adopters in a way that depends on the adoption paths that are available [40]. Moreover, although the expected fraction of product-B adopters is 1/2, a realization will be equally likely to result in any number of product-B adopters, because every node is equally likely to be the hipster.…”

Section: Major Impact Of Few Individuals: Approximation On K-regumentioning

confidence: 99%

“…For a spreading process on a network, one can construct a dissemination tree, which describes how a contagion spreads through the network [40]. For a k-regular tree with only vulnerable nodes, the dissemination tree is the same k-regular tree, except that all edges are directed from the center towards the periphery.…”

Section: Major Impact Of Few Individuals: Approximation On K-regumentioning

confidence: 99%

“…When considering a node for updating, if the fraction of its neighbors that are adopters is at least as large as its threshold, it becomes an adopter itself. There are numerous variants and generalizations of the WTM, including ones with adoption thresholds that are based on the number (rather than the fraction) of adopted neighbors [12,39], ones with multiple adoption stages [26], ones with "synergy" from other nearby adopters [28], and ones with timers in addition to adoption thresholds [40].…”

Section: Introductionmentioning

confidence: 99%

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Hipsters on networks: How a minority group of individuals can lead to an antiestablishment majority

Juul

Porter

2019

Phys. Rev. E

Self Cite

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The spread of opinions, memes, diseases, and "alternative facts" in a population depends both on the details of the spreading process and on the structure of the social and communication networks on which they spread. One feature that can change spreading dynamics substantially is heterogeneous behavior among different types of individuals in a social network. In this paper, we explore how antiestablishment nodes (e.g., hipsters) influence the spreading dynamics of two competing products. We consider a model in which spreading follows a deterministic rule for updating node states (which describe which product has been adopted) in which an adjustable fraction pHip of the nodes in a network are hipsters, who choose to adopt the product that they believe is the less popular of the two. The remaining nodes are conformists, who choose which product to adopt by considering which products their immediate neighbors have adopted. We simulate our model on both synthetic and real networks, and we show that the hipsters have a major effect on the final fraction of people who adopt each product: even when only one of the two products exists at the beginning of the simulations, a very small fraction of hipsters in a network can still cause the other product to eventually become the more popular one. To account for this behavior, we construct an approximation for the steadystate adoption fraction on k-regular trees in the limit of few hipsters. Additionally, our simulations demonstrate that a time delay τ in the knowledge of the product distribution in a population, as compared to immediate knowledge of product adoption among nearest neighbors, can have a large effect on the final distribution of product adoptions. Using a local-tree approximation, we derive an analytical estimate of the spreading of products and obtain good agreement if a sufficiently small fraction of the population consists of hipsters. In all networks, we find that either of the two products can become the more popular one at steady state, depending on the fraction of hipsters in the network and on the amount of delay in the knowledge of the product distribution. Our simple model and analysis may help shed light on the road to success for anti-establishment choices in elections, as such success -and qualitative differences in final outcomes between competing products, political candidates, and so on -can arise rather generically in our model from a small number of antiestablishment individuals and ordinary processes of social influence on normal individuals.

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Complex contagions with timers

Cited by 20 publications

References 71 publications

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Homogeneous Symmetrical Threshold Model with Nonconformity: Independence versus Anticonformity

Descendant distributions for the impact of mutant contagion on networks

Hipsters on networks: How a minority group of individuals can lead to an antiestablishment majority

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