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(a)
(b)
Fig. 1.
(a) An example of
cascade
and
ˆ
values in an information network.
(b)
Information disruption
by a challenger in an information cascade. The seed
of an established paradigm, marked in red, creates a cascade as it is cited by other
papers, while a challenger, marked in blue, disrupts the cascade of the seed.
paradigm, and a link from node 3 to 1, means paper 3 cites paper 1. This
representation can be generalized to other communication networks,
e.g.
,where
nodes are social media users sharing information with followers. The cascade
function
ˆ
(
j
)ofapaper
j
is defined as the sum of
ʱˆ
(
i
) for all papers
i
that
j
cites
and
ʱ
is a constant damping factor. For example,
ˆ
(5) =
ʱˆ
(2)+
ʱˆ
(3)+
ʱˆ
(4) =
ʱ
+2
ʱ
2
+
ʱ
2
=
ʱ
+3
ʱ
2
.Weset
ʱ
=0
.
5 in all of our experiments.
Consider Figure 1(b). The cascade
C
of the seed paper (red node) is the net-
work connecting all papers to the seed via citations. A challenger (blue node)
is a paper that advocates a new paradigm. It attracts citations from papers in
the cascade, shown as white nodes with blue background, leaving the comple-
ment cascade consisting of green nodes. When the challenger represents a non-
competing idea, though there will be papers that cite both seed and challenger,
they will not interfere with the growth of the cascade of the seed.
In contrast, a transformative challenger will disrupt the growth of the estab-
lished paradigm. Without considering the challenger, it may appear that the
established paradigm continues to prosper, as its cascade continues to grow, but
subtracting part of the cascade taken over by the challenger will reveal that the
growth of the remaining cascade (green nodes) slows. In this case, the commu-
nity's attention shifts to papers that support the challenger paradigm. This can
be measured by comparing the growth of the average
ˆ
over time for all papers
in the cascade and the papers in the complement cascade (green nodes).
Formally, a citation network is a directed graph
G
=(
V,E
)where
V
is the
set of papers and
E
is the set of edges indicating citations made by papers. A
link (
i
E
denotes that paper
j
cites paper
i
,
cite
(
j
) denotes the set of
all papers that
j
cites and
cited
(
i
)thesetofallpapersthatcite
i
.
V
t
is the set
of papers published at time
t
. We assume that if (
i
←
j
)
∈
←
j
)
∈
E
and
i
∈
V
t
and
V
t
then
t<t
. That is, no new paper should be cited by an older paper.
j
∈
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