3,233 research outputs found
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
Hybrid Epidemics - A Case Study on Computer Worm Conficker
Conficker is a computer worm that erupted on the Internet in 2008. It is
unique in combining three different spreading strategies: local probing,
neighbourhood probing, and global probing. We propose a mathematical model that
combines three modes of spreading, local, neighbourhood and global to capture
the worm's spreading behaviour. The parameters of the model are inferred
directly from network data obtained during the first day of the Conifcker
epidemic. The model is then used to explore the trade-off between spreading
modes in determining the worm's effectiveness. Our results show that the
Conficker epidemic is an example of a critically hybrid epidemic, in which the
different modes of spreading in isolation do not lead to successful epidemics.
Such hybrid spreading strategies may be used beneficially to provide the most
effective strategies for promulgating information across a large population.
When used maliciously, however, they can present a dangerous challenge to
current internet security protocols
A survey on Human Mobility and its applications
Human Mobility has attracted attentions from different fields of studies such
as epidemic modeling, traffic engineering, traffic prediction and urban
planning. In this survey we review major characteristics of human mobility
studies including from trajectory-based studies to studies using graph and
network theory. In trajectory-based studies statistical measures such as jump
length distribution and radius of gyration are analyzed in order to investigate
how people move in their daily life, and if it is possible to model this
individual movements and make prediction based on them. Using graph in mobility
studies, helps to investigate the dynamic behavior of the system, such as
diffusion and flow in the network and makes it easier to estimate how much one
part of the network influences another by using metrics like centrality
measures. We aim to study population flow in transportation networks using
mobility data to derive models and patterns, and to develop new applications in
predicting phenomena such as congestion. Human Mobility studies with the new
generation of mobility data provided by cellular phone networks, arise new
challenges such as data storing, data representation, data analysis and
computation complexity. A comparative review of different data types used in
current tools and applications of Human Mobility studies leads us to new
approaches for dealing with mentioned challenges
Geographic constraints on social network groups
Social groups are fundamental building blocks of human societies. While our
social interactions have always been constrained by geography, it has been
impossible, due to practical difficulties, to evaluate the nature of this
restriction on social group structure. We construct a social network of
individuals whose most frequent geographical locations are also known. We also
classify the individuals into groups according to a community detection
algorithm. We study the variation of geographical span for social groups of
varying sizes, and explore the relationship between topological positions and
geographic positions of their members. We find that small social groups are
geographically very tight, but become much more clumped when the group size
exceeds about 30 members. Also, we find no correlation between the topological
positions and geographic positions of individuals within network communities.
These results suggest that spreading processes face distinct structural and
spatial constraints.Comment: 10 pages, 5 figure
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