Influence of Luddism on innovation diffusion

Mellor, Andrew; Mobilia, Mauro; Redner, S.; Rucklidge, Alastair M.; Ward, Jonathan A.

doi:10.1103/physreve.92.012806

Cited by 21 publications

(13 citation statements)

References 47 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Nowadays contagion has taken on a broader meaning; it refers to any sort of process that can spread infectiously from node to node through a network [1][2][3][4][5][6][7]. Along with communicable diseases [8][9][10][11][12][13][14][15], examples of contagions include rumors [16], misinformation [17], ideas [18], innovations [19][20][21], bank failures [22], and electrical blackouts [23].…”

Section: Introductionmentioning

confidence: 99%

Descendant distributions for the impact of mutant contagion on networks

Juul

Strogatz

2020

Phys. Rev. Research

View full text Add to dashboard Cite

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.

show abstract

Section: Introductionmentioning

confidence: 99%

Descendant distributions for the impact of mutant contagion on networks

Juul

Strogatz

2020

Phys. Rev. Research

View full text Add to dashboard Cite

show abstract

“…One can also consider contrarian individuals in the context of economic markets, such as in work by Sznajd-Weron and Weron [58], who studied an Ising model on a rectangular lattice to model advertising in duopoly markets. More recent work related to contrarian agents, in addition to [47][48][49], includes that of Mellor et al [59], who examined a population in which nodes can either adopt a product or become "luddites", who oppose the spread of innovation. They found that luddites greatly limit adoption if the adoption rate is high but not if it is low.…”

Section: Introductionmentioning

confidence: 99%

“…In our model, both conformists and hipsters first choose to buy some product or form an opinion, and then they choose which one to adopt. In their study of the effect of luddites, Mellor et al [59] assumed that the probability of a node becoming a luddite is proportional to the rate of change in the density of adopters of its neighbors. This resembles our choice that a node's neighborhood influences whether or not it chooses to adopt a product, bit it differs from the fact that our nodes are either inherently a conformist or inherently a hipster.…”

Section: Introductionmentioning

confidence: 99%

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

Juul

Porter

2019

Phys. Rev. E

View full text Add to dashboard Cite

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.

show abstract

“…Dynamical processes on networks are one of the main topics in network science (Barrat et al 2008;Castellano et al 2009;Newman 2003;Porter and Gleeson 2016). Numerous applications have been modelled as dynamical processes on networks, including epidemics (Kiss et al 2017;Pastor-Satorras et al 2015), magnetism (Glauber 1963), opinion dynamics (Galam 2002;Sood and Redner 2005;Sznajd-Weron and Sznajd 2000), diffusion of innovations (Bass 1969;Mellor et al 2015;Melnik et al 2013;Watts 2002), rumour spread (Daley and Kendall 1964;Goldenberg et al 2001;Kempe et al 2003), meme popularity (Gleeson et al 2014), cultural polarisation (Axelrod 1997;Castellano et al 2000), racial segregation (Schelling 1969;1971), stock market trading (Kirman 1993), cascading failures Haldane and May 2011;Motter and Lai 2002) and language evolution (Baronchelli et al 2006;Bonabeau et al 1995;Castelló et al 2006). The mathematical analysis of such models has highlighted the rich yet subtle dependence of dynamical phenomena on network topology (Newman 2010;Porter and Gleeson 2016;Durrett 2007).…”

Section: Introductionmentioning

confidence: 99%

Exact analysis of summary statistics for continuous-time discrete-state Markov processes on networks using graph-automorphism lumping

Ward

López‐García

2019

Appl Netw Sci

Self Cite

View full text Add to dashboard Cite

We propose a unified framework to represent a wide range of continuous-time discrete-state Markov processes on networks, and show how many network dynamics models in the literature can be represented in this unified framework. We show how a particular sub-set of these models, referred to here as single-vertex-transition (SVT) processes, lead to the analysis of quasi-birth-and-death (QBD) processes in the theory of continuous-time Markov chains. We illustrate how to analyse a number of summary statistics for these processes, such as absorption probabilities and first-passage times. We extend the graph-automorphism lumping approach [Kiss, Miller, Simon, Mathematics of Epidemics on Networks, 2017; Simon, Taylor, Kiss, J. Math. Bio. 62(4), 2011], by providing a matrix-oriented representation of this technique, and show how it can be applied to a very wide range of dynamical processes on networks. This approach can be used not only to solve the master equation of the system, but also to analyse the summary statistics of interest. We also show the interplay between the graph-automorphism lumping approach and the QBD structures when dealing with SVT processes. Finally, we illustrate our theoretical results with examples from the areas of opinion dynamics and mathematical epidemiology.

show abstract

Influence of Luddism on innovation diffusion

Cited by 21 publications

References 47 publications

Descendant distributions for the impact of mutant contagion on networks

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

Exact analysis of summary statistics for continuous-time discrete-state Markov processes on networks using graph-automorphism lumping

Contact Info

Product

Resources

About