INNOVATION SPREADING: A PROCESS ON MULTIPLE SCALES János Kertész Central European University Center for Network Science Lorentz Centre, Leiden, 2013

In collaboration with: Márton Karsai Northeastern University  Université de Lyon Gerardo Iñiguez Kimmo Kaski Aalto University Ando Sabbas Skype Research Labs Marlon Dumas Tartu University

Outline -Role of innovations in economy -Innovation diffusion -Skype data and network characteristics -Mean field theory of spreading -Predictions, scenarios and correlations with global characteristics -Summary, to do

Role of innovation in economy Equilibrium theories: Static view. There are needs (demand), which can be satisfied by supply of goods and services at the price determined by their balance. Change one parameter and assume smooth dependence. Economic growth: Non-equilibrium. Increasing productivity, new products, new demand. (Schumpeter’s “creative destruction”). Key element: Innovation Innovation: creation of novel values through invention, ideas, technologies, processes.

In 1898 the first international urban planning conference convened in New York. One topic dominated discussion: manure. Cities all over the world, including Sydney, were experiencing the same problem. Unable to see any solution to the manure crisis, the delegates abandoned the conference after three days instead of the scheduled ten days. Then, quite quickly, the crisis passed as millions of horses were replaced by millions of motor vehicles. Cars were cheaper to own and operate than horse-drawn vehicles, both for the individual and for society. In 1900, 4,192 cars were sold in the US; by 1912 that number had risen to 356,000. In 1912, traffic counts in New York showed more cars than horses for the first time.

Invention is not enough, success is needed! (see, e.g., typing keyboard as a counterexample) Spreading (diffusion) of innovations For success the innovation has to spread through the target population. Verbal theory (E.M. Rogers) Innovators: 2.5% Early Adopters: 13.5% Early majority: 34% Late majority 34% Laggards 16%

Spreading mechanism Network effects are crucial Mahajan, Muller and Bass (1990 ) Adoption ratep: probability of adoption m: market potential

Diffusion networks -Two effects: peer communication and mass media -Social learning theory (“microscopic” mechanism) -Sociological aspects (Opinion leadership, homophily as a barrier) -Analogies and differences to epidemic spreading -SOCIAL NETWORK STRUCTURE, cascading on networks

Mathematical models for (epidemic) spreading Nodes can be in different states Susceptible (S)  Target population for innovation: not yet adopters Infected (I)  Adopters Recovered (R)  Terminated Different rates describe the transitions between these states, depending on the microscopic details of the process. In epidemics, if I meets S, S  I, I  R spontaneously, R  S sometimes etc. Accordingly, there are families of spreading models: SI SIR SIRS etc. Huge amount of literature (e.g. Barrat, Barthelémy, Vespignani book)

Effect of the network structure on spreading Network of social contacts has nontrivial mesoscale structure: There are strongly wired communities con- nected by weak ties “The strength of weak ties” Granovetter 1976 Onnela et al. PNAS, 2007

Diffusion of information Knowledge of information diffusion based on unweighted networks Use the empirical network to study diffusion on a weighted network: Does the local relationship between topology and tie strength have an effect? Spreading simulation: infect one node with new information (1) Empirical: p ij  w ij (2) Reference: p ij  Spreading significantly faster on the reference (average weight) network Information gets trapped in communities in the real network SI dynamics Reference Empirical

Diffusion of information Where do individuals get their information? Majority of both weak and strong ties have subordinate role as information sources! ReferenceEmpirical The importance of intermediate ties!

Correlations influence spreading -Topology (community structure) -Weight-topology -Daily pattern -Bursty dynamics -Link-link dynamic correlations Karsai et al. PRE (R) 2011

Correlations influence spreading Event stamps based simulation Reference systems by appropriate shuffling. Dominant decelerating effect Weight-topology + burstiness

Innovation spreading in the society Data from Skype: Information about: -Basic service network -Adoption of additional services -Data about location (IP)

Social network layer

Online social network layer

Online service network layer unknown

Separation of time scales

Skype slides missing

Summary Innovations are crucial for understanding the dynamics of the economy Diffusion of innovation is a mechanism with parallels and differences to spreading of diseases Network correlations influence spreading speed significantly Skype data are ideal to study diffusion of innovation, which can be modeled as adoption and terminating process Basic processes are: Spontaneous adoption, peer pressure, temporal halt and terminating We verified that pear pressure is proportional to the rate of adopting neighbors Mean field works surprisingly well Correlations with country characteristics

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