39,573 research outputs found
Collective Relaxation Dynamics of Small-World Networks
Complex networks exhibit a wide range of collective dynamic phenomena,
including synchronization, diffusion, relaxation, and coordination processes.
Their asymptotic dynamics is generically characterized by the local Jacobian,
graph Laplacian or a similar linear operator. The structure of networks with
regular, small-world and random connectivities are reasonably well understood,
but their collective dynamical properties remain largely unknown. Here we
present a two-stage mean-field theory to derive analytic expressions for
network spectra. A single formula covers the spectrum from regular via
small-world to strongly randomized topologies in Watts-Strogatz networks,
explaining the simultaneous dependencies on network size N, average degree k
and topological randomness q. We present simplified analytic predictions for
the second largest and smallest eigenvalue, and numerical checks confirm our
theoretical predictions for zero, small and moderate topological randomness q,
including the entire small-world regime. For large q of the order of one, we
apply standard random matrix theory thereby overarching the full range from
regular to randomized network topologies. These results may contribute to our
analytic and mechanistic understanding of collective relaxation phenomena of
network dynamical systems.Comment: 12 pages, 10 figures, published in PR
Coupled effects of local movement and global interaction on contagion
By incorporating segregated spatial domain and individual-based linkage into
the SIS (susceptible-infected-susceptible) model, we investigate the coupled
effects of random walk and intragroup interaction on contagion. Compared with
the situation where only local movement or individual-based linkage exists, the
coexistence of them leads to a wider spread of infectious disease. The roles of
narrowing segregated spatial domain and reducing mobility in epidemic control
are checked, these two measures are found to be conducive to curbing the spread
of infectious disease. Considering heterogeneous time scales between local
movement and global interaction, a log-log relation between the change in the
number of infected individuals and the timescale is found. A theoretical
analysis indicates that the evolutionary dynamics in the present model is
related to the encounter probability and the encounter time. A functional
relation between the epidemic threshold and the ratio of shortcuts, and a
functional relation between the encounter time and the timescale are
found
Cultural transmission and optimization dynamics
We study the one-dimensional version of Axelrod's model of cultural
transmission from the point of view of optimization dynamics. We show the
existence of a Lyapunov potential for the dynamics. The global minimum of the
potential, or optimum state, is the monocultural uniform state, which is
reached for an initial diversity of the population below a critical value.
Above this value, the dynamics settles in a multicultural or polarized state.
These multicultural attractors are not local minima of the potential, so that
any small perturbation initiates the search for the optimum state. Cultural
drift is modelled by such perturbations acting at a finite rate. If the noise
rate is small, the system reaches the optimum monocultural state. However, if
the noise rate is above a critical value, that depends on the system size,
noise sustains a polarized dynamical state.Comment: 11 pages, 10 figures include
Opinion formation driven by PageRank node influence on directed networks
We study a two states opinion formation model driven by PageRank node
influence and report an extensive numerical study on how PageRank affects
collective opinion formations in large-scale empirical directed networks. In
our model the opinion of a node can be updated by the sum of its neighbor
nodes' opinions weighted by the node influence of the neighbor nodes at each
step. We consider PageRank probability and its sublinear power as node
influence measures and investigate evolution of opinion under various
conditions. First, we observe that all networks reach steady state opinion
after a certain relaxation time. This time scale is decreasing with the
heterogeneity of node influence in the networks. Second, we find that our model
shows consensus and non-consensus behavior in steady state depending on types
of networks: Web graph, citation network of physics articles, and LiveJournal
social network show non-consensus behavior while Wikipedia article network
shows consensus behavior. Third, we find that a more heterogeneous influence
distribution leads to a more uniform opinion state in the cases of Web graph,
Wikipedia, and Livejournal. However, the opposite behavior is observed in the
citation network. Finally we identify that a small number of influential nodes
can impose their own opinion on significant fraction of other nodes in all
considered networks. Our study shows that the effects of heterogeneity of node
influence on opinion formation can be significant and suggests further
investigations on the interplay between node influence and collective opinion
in networks.Comment: 10 pages, 6 figures. Published in Physica A 436, 707-715 (2015
Revealing networks from dynamics: an introduction
What can we learn from the collective dynamics of a complex network about its
interaction topology? Taking the perspective from nonlinear dynamics, we
briefly review recent progress on how to infer structural connectivity (direct
interactions) from accessing the dynamics of the units. Potential applications
range from interaction networks in physics, to chemical and metabolic
reactions, protein and gene regulatory networks as well as neural circuits in
biology and electric power grids or wireless sensor networks in engineering.
Moreover, we briefly mention some standard ways of inferring effective or
functional connectivity.Comment: Topical review, 48 pages, 7 figure
The use of multilayer network analysis in animal behaviour
Network analysis has driven key developments in research on animal behaviour
by providing quantitative methods to study the social structures of animal
groups and populations. A recent formalism, known as \emph{multilayer network
analysis}, has advanced the study of multifaceted networked systems in many
disciplines. It offers novel ways to study and quantify animal behaviour as
connected 'layers' of interactions. In this article, we review common questions
in animal behaviour that can be studied using a multilayer approach, and we
link these questions to specific analyses. We outline the types of behavioural
data and questions that may be suitable to study using multilayer network
analysis. We detail several multilayer methods, which can provide new insights
into questions about animal sociality at individual, group, population, and
evolutionary levels of organisation. We give examples for how to implement
multilayer methods to demonstrate how taking a multilayer approach can alter
inferences about social structure and the positions of individuals within such
a structure. Finally, we discuss caveats to undertaking multilayer network
analysis in the study of animal social networks, and we call attention to
methodological challenges for the application of these approaches. Our aim is
to instigate the study of new questions about animal sociality using the new
toolbox of multilayer network analysis.Comment: Thoroughly revised; title changed slightl
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