87,551 research outputs found
2D pattern evolution constrained by complex network dynamics
Complex networks have established themselves along the last years as being
particularly suitable and flexible for representing and modeling several
complex natural and human-made systems. At the same time in which the
structural intricacies of such networks are being revealed and understood,
efforts have also been directed at investigating how such connectivity
properties define and constrain the dynamics of systems unfolding on such
structures. However, lesser attention has been focused on hybrid systems,
\textit{i.e.} involving more than one type of network and/or dynamics. Because
several real systems present such an organization (\textit{e.g.} the dynamics
of a disease coexisting with the dynamics of the immune system), it becomes
important to address such hybrid systems. The current paper investigates a
specific system involving a diffusive (linear and non-linear) dynamics taking
place in a regular network while interacting with a complex network of
defensive agents following Erd\"os-R\'enyi and Barab\'asi-Albert graph models,
whose nodes can be displaced spatially. More specifically, the complex network
is expected to control, and if possible to extinguish, the diffusion of some
given unwanted process (\textit{e.g.} fire, oil spilling, pest dissemination,
and virus or bacteria reproduction during an infection). Two types of pattern
evolution are considered: Fick and Gray-Scott. The nodes of the defensive
network then interact with the diffusing patterns and communicate between
themselves in order to control the spreading. The main findings include the
identification of higher efficiency for the Barab\'asi-Albert control networks.Comment: 18 pages, 32 figures. A working manuscript, comments are welcome
A topological approximation of the nonlinear Anderson model
We study the phenomena of Anderson localization in the presence of nonlinear
interaction on a lattice. A class of nonlinear Schrodinger models with
arbitrary power nonlinearity is analyzed. We conceive the various regimes of
behavior, depending on the topology of resonance-overlap in phase space,
ranging from a fully developed chaos involving Levy flights to pseudochaotic
dynamics at the onset of delocalization. It is demonstrated that quadratic
nonlinearity plays a dynamically very distinguished role in that it is the only
type of power nonlinearity permitting an abrupt localization-delocalization
transition with unlimited spreading already at the delocalization border. We
describe this localization-delocalization transition as a percolation
transition on a Cayley tree. It is found in vicinity of the criticality that
the spreading of the wave field is subdiffusive in the limit
t\rightarrow+\infty. The second moment grows with time as a powerlaw t^\alpha,
with \alpha = 1/3. Also we find for superquadratic nonlinearity that the analog
pseudochaotic regime at the edge of chaos is self-controlling in that it has
feedback on the topology of the structure on which the transport processes
concentrate. Then the system automatically (without tuning of parameters)
develops its percolation point. We classify this type of behavior in terms of
self-organized criticality dynamics in Hilbert space. For subquadratic
nonlinearities, the behavior is shown to be sensitive to details of definition
of the nonlinear term. A transport model is proposed based on modified
nonlinearity, using the idea of stripes propagating the wave process to large
distances. Theoretical investigations, presented here, are the basis for
consistency analysis of the different localization-delocalization patterns in
systems with many coupled degrees of freedom in association with the asymptotic
properties of the transport.Comment: 20 pages, 2 figures; improved text with revisions; accepted for
publication in Physical Review
Universality classes in nonequilibrium lattice systems
This work is designed to overview our present knowledge about universality
classes occurring in nonequilibrium systems defined on regular lattices. In the
first section I summarize the most important critical exponents, relations and
the field theoretical formalism used in the text. In the second section I
briefly address the question of scaling behavior at first order phase
transitions. In section three I review dynamical extensions of basic static
classes, show the effect of mixing dynamics and the percolation behavior. The
main body of this work is given in section four where genuine, dynamical
universality classes specific to nonequilibrium systems are introduced. In
section five I continue overviewing such nonequilibrium classes but in coupled,
multi-component systems. Most of the known nonequilibrium transition classes
are explored in low dimensions between active and absorbing states of
reaction-diffusion type of systems. However by mapping they can be related to
universal behavior of interface growth models, which I overview in section six.
Finally in section seven I summarize families of absorbing state system
classes, mean-field classes and give an outlook for further directions of
research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs
included. Scheduled for publication in Reviews of Modern Physics in April
200
Affinity Paths and Information Diffusion in Social Networks
Widespread interest in the diffusion of information through social networks
has produced a large number of Social Dynamics models. A majority of them use
theoretical hypothesis to explain their diffusion mechanisms while the few
empirically based ones average out their measures over many messages of
different content. Our empirical research tracking the step-by-step email
propagation of an invariable viral marketing message delves into the content
impact and has discovered new and striking features. The topology and dynamics
of the propagation cascades display patterns not inherited from the email
networks carrying the message. Their disconnected, low transitivity, tree-like
cascades present positive correlation between their nodes probability to
forward the message and the average number of neighbors they target and show
increased participants' involvement as the propagation paths length grows. Such
patterns not described before, nor replicated by any of the existing models of
information diffusion, can be explained if participants make their pass-along
decisions based uniquely on local knowledge of their network neighbors affinity
with the message content. We prove the plausibility of such mechanism through a
stylized, agent-based model that replicates the \emph{Affinity Paths} observed
in real information diffusion cascades.Comment: 11 pages, 7 figure
Universality classes in nonequilibrium lattice systems
This work is designed to overview our present knowledge about universality
classes occurring in nonequilibrium systems defined on regular lattices. In the
first section I summarize the most important critical exponents, relations and
the field theoretical formalism used in the text. In the second section I
briefly address the question of scaling behavior at first order phase
transitions. In section three I review dynamical extensions of basic static
classes, show the effect of mixing dynamics and the percolation behavior. The
main body of this work is given in section four where genuine, dynamical
universality classes specific to nonequilibrium systems are introduced. In
section five I continue overviewing such nonequilibrium classes but in coupled,
multi-component systems. Most of the known nonequilibrium transition classes
are explored in low dimensions between active and absorbing states of
reaction-diffusion type of systems. However by mapping they can be related to
universal behavior of interface growth models, which I overview in section six.
Finally in section seven I summarize families of absorbing state system
classes, mean-field classes and give an outlook for further directions of
research.Comment: Updated comprehensive review, 62 pages (two column), 29 figs
included. Scheduled for publication in Reviews of Modern Physics in April
200
A Comparison of Spatial-based Targeted Disease Containment Strategies using Mobile Phone Data
Epidemic outbreaks are an important healthcare challenge, especially in
developing countries where they represent one of the major causes of mortality.
Approaches that can rapidly target subpopulations for surveillance and control
are critical for enhancing containment processes during epidemics.
Using a real-world dataset from Ivory Coast, this work presents an attempt to
unveil the socio-geographical heterogeneity of disease transmission dynamics.
By employing a spatially explicit meta-population epidemic model derived from
mobile phone Call Detail Records (CDRs), we investigate how the differences in
mobility patterns may affect the course of a realistic infectious disease
outbreak. We consider different existing measures of the spatial dimension of
human mobility and interactions, and we analyse their relevance in identifying
the highest risk sub-population of individuals, as the best candidates for
isolation countermeasures. The approaches presented in this paper provide
further evidence that mobile phone data can be effectively exploited to
facilitate our understanding of individuals' spatial behaviour and its
relationship with the risk of infectious diseases' contagion. In particular, we
show that CDRs-based indicators of individuals' spatial activities and
interactions hold promise for gaining insight of contagion heterogeneity and
thus for developing containment strategies to support decision-making during
country-level pandemics
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