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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
The Viral Adoption of Web Applications: Twitter’s Story
1Jameson TooleMarta Gonzalez The Viral Adoption of Web Applications: Twitter’s Story
Tuesday, June 21, 2011
The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
Outline
The Viral Adoption of Information Technologies: Twitter’s Story
Background
Descriptive Statistics
Modeling Simulation
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
BackgroundEpidemic Models
Networks Diffusion of Innovations
SI, SIR, etc. Percolation, SI Threshold, Bass Model
The Viral Adoption of Information Technologies: Twitter’s Story3
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
Questions
The Viral Adoption of Information Technologies: Twitter’s Story4
What roll does geography play in diffusion?
What is a more accurate way to incorporate mass media?
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
DataNumber Time Place
3.5 million March 2006 - August 2009
City
5
*Meeyoung Cha - KAIST
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Space: Aggregate Dynamics
May 06 Nov 06 Jun 07 Dec 07 Jul 08 Jan 09 Aug 090
0.2
0.4
0.6
0.8
1U
sers
/ Vo
lum
eNew users, search and news volume per week
AdoptionNewsGoogle Search
May 06 Nov 06 Jun 07 Dec 07 Jul 08 Jan 09 Aug 090
0.2
0.4
0.6
0.8
1
Use
rs /
Volu
me
Cumulative new users, search and news volume
AdoptionNewsGoogle Search
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
Time: Media Influence
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
Space: Local Dynamics
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May 06 Nov 06 Jun 07 Dec 07 Jul 08 Jan 09 Aug 090
100
200
300
400
500
600
User
s
New Users per week
May 06 Nov 06 Jun 07 Dec 07 Jul 08 Jan 09 Aug 090
2000
4000
6000
8000
10000
User
s
Cumulative users
Denver, COAnn Arbor, MIArlington, VA
Denver, COAnn Arbor, MIArlington, VA
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Time: Critical Mass
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Time: Types
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
Modeling Adoption: Analytically
11Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story
SI Model Bass Model
Logistic growthSeeding
External influence
VI. SI-M MODEL
dS
dt= −βSI − γM (8)
dI
dt= +βSI + γM (9)
dM
dt= αI · (1 + cos(ωt)) (10)
VII. SI-M MODEL
dS
dt= −βSI (11)
dI
dt= +βSI (12)
VIII. CONCLUSION
[1] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proceedings of the National
Academy of Sciences of the United States of America 102, 11157 (August 2005), ISSN 0027-
8424, http://dx.doi.org/10.1073/pnas.0501226102.
[2] P. S. Dodds and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN
00225193, http://dx.doi.org/10.1016/j.jtbi.2004.09.006.
[3] C. Moore and M. E. J. Newman, Physical Review E 61, 5678 (May 2000), http://dx.doi.
org/10.1103/PhysRevE.61.5678.
[4] M. E. J. Newman, I. Jensen, and R. M. Ziff, Physical Review E 65, 021904+ (Jan 2002),
http://dx.doi.org/10.1103/PhysRevE.65.021904.
[5] B. Karrer and M. E. J. Newman, Physical Review E 82, 016101+ (Jul 2010), http://dx.
doi.org/10.1103/PhysRevE.82.016101.
[6] The online version of Richard Dawkins’ terminology describing ideas and beliefs that spread
from person to person.
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VI. SI-M MODEL
dS
dt= −βSI − γM (8)
dI
dt= +βSI + γM (9)
dM
dt= αI · (1 + cos(ωt)) (10)
VII. SI-M MODEL
dS
dt= −βSI (11)
dI
dt= +βSI (12)
I(t) =1
1 + e−βt(13)
VIII. CONCLUSION
[1] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proceedings of the National
Academy of Sciences of the United States of America 102, 11157 (August 2005), ISSN 0027-
8424, http://dx.doi.org/10.1073/pnas.0501226102.
[2] P. S. Dodds and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN
00225193, http://dx.doi.org/10.1016/j.jtbi.2004.09.006.
[3] C. Moore and M. E. J. Newman, Physical Review E 61, 5678 (May 2000), http://dx.doi.
org/10.1103/PhysRevE.61.5678.
[4] M. E. J. Newman, I. Jensen, and R. M. Ziff, Physical Review E 65, 021904+ (Jan 2002),
http://dx.doi.org/10.1103/PhysRevE.65.021904.
[5] B. Karrer and M. E. J. Newman, Physical Review E 82, 016101+ (Jul 2010), http://dx.
doi.org/10.1103/PhysRevE.82.016101.
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VI. SI-M MODEL
dS
dt= −βSI − γM (8)
dI
dt= +βSI + γM (9)
dM
dt= αI · (1 + cos(ωt)) (10)
VII. SI-M MODEL
dS
dt= −βSI (11)
dI
dt= +βSI (12)
I(t) =1
1 + e−βt(13)
VIII. BASS MODEL
I �(t)
1− I(t)= α + βI(t) (14)
IX. CONCLUSION
[1] D. J. Watts, R. Muhamad, D. C. Medina, and P. S. Dodds, Proceedings of the National
Academy of Sciences of the United States of America 102, 11157 (August 2005), ISSN 0027-
8424, http://dx.doi.org/10.1073/pnas.0501226102.
[2] P. S. Dodds and D. J. Watts, Journal of Theoretical Biology 232, 587 (February 2005), ISSN
00225193, http://dx.doi.org/10.1016/j.jtbi.2004.09.006.
[3] C. Moore and M. E. J. Newman, Physical Review E 61, 5678 (May 2000), http://dx.doi.
org/10.1103/PhysRevE.61.5678.
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez 12Jameson TooleMarta Gonzalez The Viral Adoption of Information Technologies: Twitter’s Story
S
II
IM
Modeling Adoption: Simulation
NETWORK
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta GonzalezJameson TooleMarta Gonzalez
S
II
IM
Modeling Adoption: Simulation
Make Network
size, degree, geography, type10%, Poisson, Power-law/pop. Early/Reg
Dynamics• Seed infection• Inf. nodes try to inf. nbr.• Media infects
Analysis• Probabilistic - Many runs• Fit parameters to data.• What parameters matter?
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Modeling Adoption: Results
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0 0.2 0.4 0.6 0.8 10
0.2
0.4
0.6
0.8
1
Homopholy
Gia
nt C
ompo
nent
Siz
e
Giant Component Size vs. Homopholy
BiasedUnbiased
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Modeling Adoption: Results
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Parameters
B = .0035No/Exog. Media
Biased/Unbiased Geography
0 20 40 60 80 100 120 140 160 1800
2
4
6
8
10
12
14x 104
Time
Use
rs
Simulation: No Media | Fit to crit. mass
realBiased − No MediaUnbiased − No MediaBiased − Media
0 20 40 60 80 100 120 140 160 1800
0.5
1
1.5
2
2.5x 106
Time
Use
rs
realBiased − No MediaUnbiased − No MediaBiased − Media
100 110 120 130 140 150 160100
110
120
130
140
150
160
Real Critical Mass Achievement
Sim
. Crit
ical
Mas
s Ac
hiev
emen
t
Critical Mass Achievement Prediction
Biased | !r = .003Unbiased | !r = .01
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Modeling Adoption: Results
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Parameters
B = .0035No/Exog. Media
Biased/Unbiased Geography
100 110 120 130 140 150 160100
110
120
130
140
150
160
Real Critical Mass Achievement
Sim
. Crit
ical
Mas
s Ac
hiev
emen
t
Critical Mass Achievement Prediction
Biased | !r = .003Unbiased | !r = .01
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Modeling Adoption: Results
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Parameters
B = .0035a = .15
Poisson, GeographyEndog. Media
0 20 40 60 80 100 120 140 1600
0.5
1
Use
rs
Media and Adoption per unit time
0 20 40 60 80 100 120 140 1600
0.5
1
Time
Use
rs
Cumulative Adoption
100 110 120 130 140 150 16090
100
110
120
130
140
150
160
Real Critical Mass Achievement
Sim
ulat
ed C
ritic
al M
ass
Achi
evem
ent
Critical Mass Achievement
AdoptersMedia
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Modeling Adoption: Results
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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.
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[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.
Selected References
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The Viral Adoption of Information Technologies: Twitter’s StoryJameson TooleMarta Gonzalez
THANK YOU
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