29 research outputs found
The Multidimensional Study of Viral Campaigns as Branching Processes
Viral campaigns on the Internet may follow variety of models, depending on
the content, incentives, personal attitudes of sender and recipient to the
content and other factors. Due to the fact that the knowledge of the campaign
specifics is essential for the campaign managers, researchers are constantly
evaluating models and real-world data. The goal of this article is to present
the new knowledge obtained from studying two viral campaigns that took place in
a virtual world which followed the branching process. The results show that it
is possible to reduce the time needed to estimate the model parameters of the
campaign and, moreover, some important aspects of time-generations relationship
are presented.Comment: In proceedings of the 4th International Conference on Social
Informatics, SocInfo 201
Why Do Cascade Sizes Follow a Power-Law?
We introduce random directed acyclic graph and use it to model the
information diffusion network. Subsequently, we analyze the cascade generation
model (CGM) introduced by Leskovec et al. [19]. Until now only empirical
studies of this model were done. In this paper, we present the first
theoretical proof that the sizes of cascades generated by the CGM follow the
power-law distribution, which is consistent with multiple empirical analysis of
the large social networks. We compared the assumptions of our model with the
Twitter social network and tested the goodness of approximation.Comment: 8 pages, 7 figures, accepted to WWW 201
Uncovering the dynamics of citations of scientific papers
We demonstrate a comprehensive framework that accounts for citation dynamics
of scientific papers and for the age distribution of references. We show that
citation dynamics of scientific papers is nonlinear and this nonlinearity has
far-reaching consequences, such as diverging citation distributions and runaway
papers. We propose a nonlinear stochastic dynamic model of citation dynamics
based on link copying/redirection mechanism. The model is fully calibrated by
empirical data and does not contain free parameters. This model can be a basis
for quantitative probabilistic prediction of citation dynamics of individual
papers and of the journal impact factor.Comment: 18 pages, 7 figure
Random Walks on Stochastic Temporal Networks
In the study of dynamical processes on networks, there has been intense focus
on network structure -- i.e., the arrangement of edges and their associated
weights -- but the effects of the temporal patterns of edges remains poorly
understood. In this chapter, we develop a mathematical framework for random
walks on temporal networks using an approach that provides a compromise between
abstract but unrealistic models and data-driven but non-mathematical
approaches. To do this, we introduce a stochastic model for temporal networks
in which we summarize the temporal and structural organization of a system
using a matrix of waiting-time distributions. We show that random walks on
stochastic temporal networks can be described exactly by an
integro-differential master equation and derive an analytical expression for
its asymptotic steady state. We also discuss how our work might be useful to
help build centrality measures for temporal networks.Comment: Chapter in Temporal Networks (Petter Holme and Jari Saramaki
editors). Springer. Berlin, Heidelberg 2013. The book chapter contains minor
corrections and modifications. This chapter is based on arXiv:1112.3324,
which contains additional calculations and numerical simulation
Infrequent social interaction can accelerate the spread of a persuasive idea
We study the spread of a persuasive new idea through a population of
continuous-time random walkers in one dimension. The idea spreads via social
gatherings involving groups of nearby walkers who act according to a biased
"majority rule": After each gathering, the group takes on the new idea if more
than a critical fraction of them
already hold it; otherwise they all reject it. The boundary of a domain where
the new idea has taken hold expands as a traveling wave in the density of new
idea holders. Our walkers move by L\'{e}vy motion, and we compute the wave
velocity analytically as a function of the frequency of social gatherings and
the exponent of the jump distribution. When this distribution is sufficiently
heavy tailed, then, counter to intuition, the idea can propagate faster if
social gatherings are held less frequently. When jumps are truncated, a
critical gathering frequency can emerge which maximizes propagation velocity.
We explore our model by simulation, confirming our analytical results
Temporal interactions facilitate endemicity in the susceptible-infected-susceptible epidemic model
Data of physical contacts and face-to-face communications suggest temporally
varying networks as the media on which infections take place among humans and
animals. Epidemic processes on temporal networks are complicated by complexity
of both network structure and temporal dimensions. Theoretical approaches are
much needed for identifying key factors that affect dynamics of epidemics. In
particular, what factors make some temporal networks stronger media of
infection than other temporal networks is under debate. We develop a theory to
understand the susceptible-infected-susceptible epidemic model on arbitrary
temporal networks, where each contact is used for a finite duration. We show
that temporality of networks lessens the epidemic threshold such that
infections persist more easily in temporal networks than in their static
counterparts. We further show that the Lie commutator bracket of the adjacency
matrices at different times is a key determinant of the epidemic threshold in
temporal networks. The effect of temporality on the epidemic threshold, which
depends on a data set, is approximately predicted by the magnitude of a
commutator norm.Comment: 8 figures, 1 tabl