This document discusses mathematical modeling of cascades on networks. It describes modeling techniques like branching processes that can be used to model how information spreads through social networks. Several examples are provided of modeling hashtag cascades on Twitter, the spreading of apps on Facebook, and retweet cascades from an Irish marriage referendum. The document lists collaborators from various universities and companies that contribute to this research.

1. Applying advances in mathematics and
statistics research for science and industry1
Mathema'cal
modelling
of
cascades
on
networks
James
P.
Gleeson
MACSI,
Department
of
Mathema:cs
and
Sta:s:cs,
University
of
Limerick
www.ul.ie/gleeson
james.gleeson@ul.ie
@gleesonj

2. Applying advances in mathematics and
statistics research for science and industry2
What
is
mathema'cal
modelling?

3. Applying advances in mathematics and
statistics research for science and industry3
Computa'onal
Social
Science

4. Applying advances in mathematics and
statistics research for science and industry4
Popularity
of
hashtags
associated
with
the
Spanish
15M
protest
movement

5. Applying advances in mathematics and
statistics research for science and industry5
Mathema'cal
modelling
of
informa'on
cascades
J.
P.
Gleeson
et
al.,
“Effects
of
network
structure,
compe::on
and
memory
:me
on
social
spreading
phenomena”,
Physical
Review
X,
6,
021019
(2016)
[Open]

6. Applying advances in mathematics and
statistics research for science and industry6
Mathema'cal
techniques:
branching
processes
J.
P.
Gleeson
et
al.,
“Effects
of
network
structure,
compe::on
and
memory
:me
on
social
spreading
phenomena”,
Physical
Review
X,
6,
021019
(2016)
[Open]

7. Applying advances in mathematics and
statistics research for science and industry7
Hashtag
cascades
on
TwiEer
J.
P.
Gleeson
et
al.,
“Effects
of
network
structure,
compe::on
and
memory
:me
on
social
spreading
phenomena”,
Physical
Review
X,
6,
021019
(2016)
[Open]

8. Applying advances in mathematics and
statistics research for science and industry8
The
spreading
of
apps
on
Facebook
J.
P.
Gleeson,
D.
Cellai,
et
al.,
“A
simple
genera:ve
model
of
collec:ve
online
behavior”,
Proceedings
of
the
Na:onal
Academy
of
Sciences
USA,
111,
10411
(2014)
[Open]

9. Applying advances in mathematics and
statistics research for science and industry9
Retweet
cascades
from
the
2015
Irish
marriage
referendum
D.
J.
P.
O’Sullivan
et
al.,
“Integra:ng
sen:ment
and
social
structure
to
determine
preference
alignments:
The
Irish
Marriage
Referendum”,
arXiv:1701.00289

10. Applying advances in mathematics and
statistics research for science and industry10
Summary
Collaborators:
§ David
O’Sullivan,
UL
§ Kevin
O’Sullivan,
UL
§ Yamir
Moreno,
Zaragoza
§ Raquel
A
Baños,
Zaragoza
§ Jonathan
Ward,
Leeds
§ William
Lee,
Portsmouth
§ Mariano
Beguerisse-­‐Díaz,
Oxford
§ Felix
Reed-­‐Tsochas,
Oxford
§ J-­‐P
Onnela,
Harvard
§ Mason
A
Porter,
UCLA
§ Guillermo
Hernández,
Sinnia
§ Sergey
Melnik,
LoyaltyOne
§ Davide
Cellai,
Idiro
Analy:cs

11. Applying advances in mathematics and
statistics research for science and industry11

12. Applying advances in mathematics and
statistics research for science and industry12
Mathema'cal
modelling
of
cascades
on
networks
James
P.
Gleeson
MACSI,
Department
of
Mathema:cs
and
Sta:s:cs,
University
of
Limerick
www.ul.ie/gleeson
james.gleeson@ul.ie
@gleesonj