5 research outputs found
Absorbing and Shattered Fragmentation Transitions in Multilayer Coevolution
We introduce a coevolution voter model in a multilayer, by coupling a
fraction of nodes across two network layers and allowing each layer to evolve
according to its own topological temporal scale. When these time scales are the
same the dynamics preserve the absorbing-fragmentation transition observed in a
monolayer network at a critical value of the temporal scale that depends on
interlayer connectivity. The time evolution equations obtained by pair
approximation can be mapped to a coevolution voter model in a single layer with
an effective average degree. When the two layers have different topological
time scales we find an anomalous transition, named shattered fragmentation, in
which the network in one layer splits into two large components in opposite
states and a multiplicity of isolated nodes. We identify the growth of the
number of components as a signature of this anomalous transition. We also find
a critical level of interlayer coupling needed to prevent the fragmentation in
a layer connected to a layer that does not fragment.Comment: 7 pages, 6 figures, last figure caption includes link to animation
Dynamical origins of the community structure of multi-layer societies
Social structures emerge as a result of individuals managing a variety of
different of social relationships. Societies can be represented as highly
structured dynamic multiplex networks. Here we study the dynamical origins of
the specific community structures of a large-scale social multiplex network of
a human society that interacts in a virtual world of a massive multiplayer
online game. There we find substantial differences in the community structures
of different social actions, represented by the various network layers in the
multiplex. Community size distributions are either similar to a power-law or
appear to be centered around a size of 50 individuals. To understand these
observations we propose a voter model that is built around the principle of
triadic closure. It explicitly models the co-evolution of node- and
link-dynamics across different layers of the multiplex. Depending on link- and
node fluctuation rates, the model exhibits an anomalous shattered fragmentation
transition, where one layer fragments from one large component into many small
components. The observed community size distributions are in good agreement
with the predicted fragmentation in the model. We show that the empirical
pairwise similarities of network layers, in terms of link overlap and degree
correlations, practically coincide with the model. This suggests that several
detailed features of the fragmentation in societies can be traced back to the
triadic closure processes.Comment: 8 pages, 6 figure
Multilayer coevolution dynamics of the nonlinear voter model
We study a coevolving nonlinear voter model on a two-layer network.
Coevolution stands for coupled dynamics of the state of the nodes and of the
topology of the network in each layer. The plasticity parameter p measures the
relative time scale of the evolution of the states of the nodes and the
evolution of the network by link rewiring. Nonlinearity of the interactions is
taken into account through a parameter q that describes the nonlinear effect of
local majorities, being q = 1 the marginal situation of the ordinary voter
model. Finally the connection between the two layers is measured by a degree of
multiplexing `. In terms of these three parameters, p, q and ` we find a rich
phase diagram with different phases and transitions. When the two layers have
the same plasticity p, the fragmentation transition observed in a single layer
is shifted to larger values of p plasticity, so that multiplexing avoids
fragmentation. Different plasticities for the two layers lead to new phases
that do not exist in a coevolving nonlinear voter model in a single layer,
namely an asymmetric fragmented phase for q > 1 and an active shattered phase
for q
1, we can find two different transitions by increasing the plasticity
parameter, a first absorbing transition with no fragmentation and a subsequent
fragmentation transition
Libro Blanco de los Sistemas Complejos Socio-tecnológicos
La Red SocioComplex está formada por la Universitat de Barcelona (coordinación), Fundación IMDEA Networks, Instituto de FÃsica Interdisciplinar y Sistemas Complejos (CSIC-Universitat Illes Balears), Universidad de Burgos, Universidad Carlos III de Madrid, Universitat Rovira i Virgili, Universitat de València y Universidad de Zaragoza - Instituto de Biocomputación y FÃsica de los Sistemas Complejos.Este libro blanco analiza por primera vez las principales fuerzas de la investigación española en ciencias de la complejidad en el contexto de los sistemas socio-tecnológicos.El Libro Blanco de los Sistemas Complejos Socio-tecnológicos forma parte del conjunto de acciones realizadas por la red temática SocioComplex FIS2015-71795-REDT financiada por parte del Ministerio de EconomÃa, Industria y Competitividad – Agencia Estatal de Investigación y del Fondo Europeo de Desarrollo Regional (FEDER)
The structure and dynamics of multilayer networks
In the past years, network theory has successfully characterized the
interaction among the constituents of a variety of complex systems, ranging
from biological to technological, and social systems. However, up until
recently, attention was almost exclusively given to networks in which all
components were treated on equivalent footing, while neglecting all the extra
information about the temporal- or context-related properties of the
interactions under study. Only in the last years, taking advantage of the
enhanced resolution in real data sets, network scientists have directed their
interest to the multiplex character of real-world systems, and explicitly
considered the time-varying and multilayer nature of networks. We offer here a
comprehensive review on both structural and dynamical organization of graphs
made of diverse relationships (layers) between its constituents, and cover
several relevant issues, from a full redefinition of the basic structural
measures, to understanding how the multilayer nature of the network affects
processes and dynamics.Comment: In Press, Accepted Manuscript, Physics Reports 201