104,973 research outputs found
On the behavior of threshold models over finite networks
We study a model for cascade effects over finite networks based on a deterministic binary linear threshold model. Our starting point is a networked coordination game where each agent's payoff is the sum of the payoffs coming from pairwise interaction with each of the neighbors. We first establish that the best response dynamics in this networked game is equivalent to the linear threshold dynamics with heterogeneous thresholds over the agents. While the previous literature has studied such linear threshold models under the assumption that each agent may change actions at most once, a study of best response dynamics in such networked games necessitates an analysis that allows for multiple switches in actions. In this paper, we develop such an analysis. We establish that agent behavior cycles among different actions in the limit, we characterize the length of such limit cycles, and reveal bounds on the time steps required to reach them. We finally propose a measure of network resilience that captures the nature of the involved dynamics. We prove bounds and investigate the resilience of different network structures under this measure.Irwin Mark Jacobs and Joan Klein Jacobs Presidential FellowshipSiebel ScholarshipUnited States. Air Force Office of Scientific Research (Grant FA9550-09-1-0420)United States. Army Research Office (Grant W911NF-09-1-0556
Outage Capacity and Optimal Transmission for Dying Channels
In wireless networks, communication links may be subject to random fatal
impacts: for example, sensor networks under sudden power losses or cognitive
radio networks with unpredictable primary user spectrum occupancy. Under such
circumstances, it is critical to quantify how fast and reliably the information
can be collected over attacked links. For a single point-to-point channel
subject to a random attack, named as a \emph{dying channel}, we model it as a
block-fading (BF) channel with a finite and random delay constraint. First, we
define the outage capacity as the performance measure, followed by studying the
optimal coding length such that the outage probability is minimized when
uniform power allocation is assumed. For a given rate target and a coding
length , we then minimize the outage probability over the power allocation
vector \mv{P}_{K}, and show that this optimization problem can be cast into a
convex optimization problem under some conditions. The optimal solutions for
several special cases are discussed.
Furthermore, we extend the single point-to-point dying channel result to the
parallel multi-channel case where each sub-channel is a dying channel, and
investigate the corresponding asymptotic behavior of the overall outage
probability with two different attack models: the independent-attack case and
the -dependent-attack case. It can be shown that the overall outage
probability diminishes to zero for both cases as the number of sub-channels
increases if the \emph{rate per unit cost} is less than a certain threshold.
The outage exponents are also studied to reveal how fast the outage probability
improves over the number of sub-channels.Comment: 31 pages, 9 figures, submitted to IEEE Transactions on Information
Theor
Griffiths phases and localization in hierarchical modular networks
We study variants of hierarchical modular network models suggested by Kaiser
and Hilgetag [Frontiers in Neuroinformatics, 4 (2010) 8] to model functional
brain connectivity, using extensive simulations and quenched mean-field theory
(QMF), focusing on structures with a connection probability that decays
exponentially with the level index. Such networks can be embedded in
two-dimensional Euclidean space. We explore the dynamic behavior of the contact
process (CP) and threshold models on networks of this kind, including
hierarchical trees. While in the small-world networks originally proposed to
model brain connectivity, the topological heterogeneities are not strong enough
to induce deviations from mean-field behavior, we show that a Griffiths phase
can emerge under reduced connection probabilities, approaching the percolation
threshold. In this case the topological dimension of the networks is finite,
and extended regions of bursty, power-law dynamics are observed. Localization
in the steady state is also shown via QMF. We investigate the effects of link
asymmetry and coupling disorder, and show that localization can occur even in
small-world networks with high connectivity in case of link disorder.Comment: 18 pages, 20 figures, accepted version in Scientific Report
Thresholds for epidemic spreading in networks
We study the threshold of epidemic models in quenched networks with degree
distribution given by a power-law. For the susceptible-infected-susceptible
(SIS) model the activity threshold lambda_c vanishes in the large size limit on
any network whose maximum degree k_max diverges with the system size, at odds
with heterogeneous mean-field (HMF) theory. The vanishing of the threshold has
not to do with the scale-free nature of the connectivity pattern and is instead
originated by the largest hub in the system being active for any spreading rate
lambda>1/sqrt{k_max} and playing the role of a self-sustained source that
spreads the infection to the rest of the system. The
susceptible-infected-removed (SIR) model displays instead agreement with HMF
theory and a finite threshold for scale-rich networks. We conjecture that on
quenched scale-rich networks the threshold of generic epidemic models is
vanishing or finite depending on the presence or absence of a steady state.Comment: 5 pages, 4 figure
Collective versus hub activation of epidemic phases on networks
We consider a general criterion to discern the nature of the threshold in
epidemic models on scale-free (SF) networks. Comparing the epidemic lifespan of
the nodes with largest degrees with the infection time between them, we propose
a general dual scenario, in which the epidemic transition is either ruled by a
hub activation process, leading to a null threshold in the thermodynamic limit,
or given by a collective activation process, corresponding to a standard phase
transition with a finite threshold. We validate the proposed criterion applying
it to different epidemic models, with waning immunity or heterogeneous
infection rates in both synthetic and real SF networks. In particular, a waning
immunity, irrespective of its strength, leads to collective activation with
finite threshold in scale-free networks with large exponent, at odds with
canonical theoretical approaches.Comment: Revised version accepted for publication in PR
Disease Spreading in Structured Scale-Free Networks
We study the spreading of a disease on top of structured scale-free networks
recently introduced. By means of numerical simulations we analyze the SIS and
the SIR models. Our results show that when the connectivity fluctuations of the
network are unbounded whether the epidemic threshold exists strongly depends on
the initial density of infected individuals and the type of epidemiological
model considered. Analytical arguments are provided in order to account for the
observed behavior. We conclude that the peculiar topological features of this
network and the absence of small-world properties determine the dynamics of
epidemic spreading.Comment: 7 pages, 6 figures. EPJ styl
Epidemic processes in complex networks
In recent years the research community has accumulated overwhelming evidence
for the emergence of complex and heterogeneous connectivity patterns in a wide
range of biological and sociotechnical systems. The complex properties of
real-world networks have a profound impact on the behavior of equilibrium and
nonequilibrium phenomena occurring in various systems, and the study of
epidemic spreading is central to our understanding of the unfolding of
dynamical processes in complex networks. The theoretical analysis of epidemic
spreading in heterogeneous networks requires the development of novel
analytical frameworks, and it has produced results of conceptual and practical
relevance. A coherent and comprehensive review of the vast research activity
concerning epidemic processes is presented, detailing the successful
theoretical approaches as well as making their limits and assumptions clear.
Physicists, mathematicians, epidemiologists, computer, and social scientists
share a common interest in studying epidemic spreading and rely on similar
models for the description of the diffusion of pathogens, knowledge, and
innovation. For this reason, while focusing on the main results and the
paradigmatic models in infectious disease modeling, the major results
concerning generalized social contagion processes are also presented. Finally,
the research activity at the forefront in the study of epidemic spreading in
coevolving, coupled, and time-varying networks is reported.Comment: 62 pages, 15 figures, final versio
Epidemic spreading in evolving networks
A model for epidemic spreading on rewiring networks is introduced and
analyzed for the case of scale free steady state networks. It is found that
contrary to what one would have naively expected, the rewiring process
typically tends to suppress epidemic spreading. In particular it is found that
as in static networks, rewiring networks with degree distribution exponent
exhibit a threshold in the infection rate below which epidemics die
out in the steady state. However the threshold is higher in the rewiring case.
For no such threshold exists, but for small infection rate
the steady state density of infected nodes (prevalence) is smaller for rewiring
networks.Comment: 7 pages, 7 figure
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