The Viral Adoption of Web Applications: Twitter’s Story
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Web Information Applications: Technologies: Twitter’s Twitter’s Story Story
Outline Background Descriptive Statistics Modeling Simulation
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
Background Epidemic Models
SI, SIR, etc.
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
Networks
Diffusion of Innovations
Percolation, SI
Threshold, Bass Model
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The Viral Adoption of Information Technologies: Twitter’s Story
Questions What roll does geography play in diffusion? What is a more accurate way to incorporate mass media?
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
Data
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
*Meeyoung Cha - KAIST
Number
Time
Place
3.5 million
March 2006 August 2009
City
5
The Viral Adoption of Information Technologies: Twitter’s Story
Space: Aggregate Dynamics New users, search and news volume per week 1 Adoption News Google Search
Users / Volume
0.8 0.6 0.4 0.2 0
May 06
Nov 06
Jun 07
Dec 07
Jul 08
Jan 09
Aug 09
Cumulative new users, search and news volume 1
Users / Volume
0.8
Adoption News Google Search
0.6 0.4 0.2 0 May 06
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
Nov 06
Jun 07
Dec 07
6
Jul 08
Jan 09
Aug 09
The Viral Adoption of Information Technologies: Twitter’s Story
Time: Media Influence
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
Space: Local Dynamics New Users per week 600 Denver, CO Ann Arbor, MI Arlington, VA
500
Users
400 300 200 100 0
May 06
Nov 06
Jun 07
Dec 07
Jul 08
Jan 09
Aug 09
Jul 08
Jan 09
Aug 09
Cumulative users 10000 Denver, CO Ann Arbor, MI Arlington, VA
Users
8000 6000 4000 2000 0
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
May 06
Nov 06
Jun 07
Dec 07
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The Viral Adoption of Information Technologies: Twitter’s Story
Time: Critical Mass
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
Time: Types
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
dt dM = αI · (1 + cos(ωt)) dt
Modeling Adoption: Analytically dS = −βSI − γM dt dI = +βSI + γM SI-M MODEL dt dM = αI · (1 + cos(ωt)) dt
VII.
DEL
(8)
(9)
dS = −βSI dt dI = +βSI dt
1 1 + e−βt
I(t)(10) =
dS SI Model Bass Model BASS MODEL = −βSI
VIII.
dS = −βSI dt dI = +βSI dt
IX. VIII. CONCLUSION USION
dt dI = +βSI dt
1 I(t) = 1 + e−βt
CONCLUSION
Logistic growth
(10)
(11) (12)
� I(11) (t) = α + βI(t) 1− I(t) (12)
(13)
Seeding External influence
R. Muhamad, D. C. Medina, [1] andD. P. J. S. Watts, Dodds, Proceedings of theD.National R. Muhamad, C. Medina, and P. S. Dodds, Proceedings of t
1] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proceedings of the National
ciences of the United States of America 102, 11157 (Augustof2005), ISSN 0027Academy of Sciences the United States of America 102, 11157 (August 2005),
Academy of Sciences of the United States of America 102, 11157 (August 2005), ISSN 0027-
/dx.doi.org/10.1073/pnas.0501226102.
8424, http://dx.doi.org/10.1073/pnas.0501226102.
Toole 8424, http://dx.doi.org/10.1073/pnas.0501226102. ndJameson D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN The Viral Adoption Biology of Information232, Technologies: Story Marta Gonzalez 11 [2] P. S. Dodds and D. J. Watts, Journal of Theoretical 587 Twitter’s (February tp://dx.doi.org/10.1016/j.jtbi.2004.09.006. 2]Tuesday, P. S. Dodds June 21, 2011 and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN
Modeling Adoption: Simulation I
M
NETWORK
S I
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
I
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The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Simulation I
Make Network
size, degree, geography, type
S
10%, Poisson, Power-law/pop. Early/Reg I
Dynamics
• • •
Seed infection Inf. nodes try to inf. nbr. Media infects
Analysis
• • •
Probabilistic - Many runs Fit parameters to data. What parameters matter?
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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M I
The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Results Giant Component Size vs. Homopholy
Giant Component Size
1 0.8 0.6 0.4 0.2 0
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
Biased Unbiased
0
0.2
0.4 0.6 Homopholy
14
0.8
1
The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Results 4
14
real Biased − No Media Unbiased − No Media Biased − Media
12 10 Users
Parameters
Simulation: No Media | Fit to crit. mass
x 10
B = .0035 No/Exog. Media Biased/Unbiased Geography
8 6 4 2 0
0
20
40
60
80
100
120
140
160
180
Critical Mass Achievement Prediction
Time
160 Biased | !r = .003 Unbiased | !r = .01
6
x 10
real Biased − No Media Unbiased − No Media Biased − Media
2
Users
150
1.5
Sim. Critical Mass Achievement
2.5
1
140
130
120
0.5 110
0
0
20
40
60
80
100
120
140
160
Time
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
15
180
100 100
110
120 130 140 Real Critical Mass Achievement
150
160
The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Results Parameters
Critical Mass Achievement Prediction 160 Biased | !r = .003
B = .0035 No/Exog. Media Biased/Unbiased Geography
Unbiased | ! = .01 r
Sim. Critical Mass Achievement
150
140
130
120
110
100 100
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
110
120 130 140 Real Critical Mass Achievement
150
16
160
The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Results
Users
150 140
Adopters Media 0.5
130
0
120
1
110 100 90 100
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
160
17
0
20
40
60
80
100
120 140 160
Cumulative Adoption
0.5
0 110 120 130 140 150 Real Critical Mass Achievement
B = .0035 a = .15 Poisson, Geography Endog. Media
Media and Adoption per unit time
1
Users
Simulated Critical Mass Achievement
160
Critical Mass Achievement
Parameters
0
20
40
60
80 100 Time
120 140 160
The Viral Adoption of Information Technologies: Twitter’s Story
Modeling Adoption: Results Parameters
Insights
Social
• •
Preferences correlated with demographics. Homopholy plays a large roll in local spread.
Geography
• •
Geographically biased friendships matter. Different areas respond to influences differently.
Media
• • •
Not all news is the same. Hyper-influencials vs. mass media. Media affects are very strong, on par with word-of mouth. Endog. media responds to adoption rates.
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
Selected References [Bass, 1969]Bass, F. M. (1969, January). A new product growth for model consumer durables. MANAGEMENT SCIENCE 15(5), 215–227. [Watts et al., 2005]Watts, D. J., R. Muhamad, D. C. Medina, and P. S. Dodds (2005, August). Multiscale, resurgent epidemics in a hierarchical metapopulation model. Proceedings of the National Academy of Sciences of the United States of America 102(32), 11157–11162 [Valente, 1995]Valente, T. W. (1995, January). Network Models of the Diffusion of Innovations (Quantitative Methods in Communication Subseries). Hampton Press (NJ). [Leskovec et al., 2007]Leskovec, J., L. A. Adamic, and B. A. Huberman (2007, May). The dynamics of viral marketing. ACM Trans. Web 1. [Liben-Nowell et al., 2005]Liben-Nowell, D., J. Novak, R. Kumar, P. Raghavan, and A. Tomkins (2005, August). Geographic routing in social networks. Proceedings of the National Academy of Sciences of the United States of America 102(33), 11623–11628.
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
THANK YOU
Jameson Toole Marta Gonzalez Tuesday, June 21, 2011
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The Viral Adoption of Information Technologies: Twitter’s Story
