91 research outputs found
Unveiling the connectivity of complex networks using ordinal transition methods
Ordinal measures provide a valuable collection of tools for analyzing
correlated data series. However, using these methods to understand the
information interchange in networks of dynamical systems, and uncover the
interplay between dynamics and structure during the synchronization process,
remains relatively unexplored. Here, we compare the ordinal permutation
entropy, a standard complexity measure in the literature, and the permutation
entropy of the ordinal transition probability matrix that describes the
transitions between the ordinal patterns derived from a time series. We find
that the permutation entropy based on the ordinal transition matrix outperforms
the rest of the tested measures in discriminating the topological role of
networked chaotic R\"ossler systems. Since the method is based on permutation
entropy measures, it can be applied to arbitrary real-world time series
exhibiting correlations originating from an existing underlying unknown network
structure. In particular, we show the effectiveness of our method using
experimental datasets of networks of nonlinear oscillators.Comment: 9 pages, 5 figure
A symbolic network-based nonlinear theory for dynamical systems observability
EBM and MSB acknowledge the Engineering and Physical Sciences Research Council (EPSRC), grant Ref. EP/I032608/1. ISN acknowledges partial support from the Ministerio de Economía y Competitividad of Spain under project FIS2013-41057-P and from the Group of Research Excelence URJC-Banco de Santander.Peer reviewedPublisher PD
Cooperation transitions in social games induced by aspiration-driven players
Cooperation and defection are social traits whose evolutionary origin is
still unresolved. Recent behavioral experiments with humans suggested that
strategy changes are driven mainly by the individuals' expectations and not by
imitation. This work theoretically analyzes and numerically explores an
aspiration-driven strategy updating in a well-mixed population playing games.
The payoffs of the game matrix and the aspiration are condensed into just two
parameters that allow a comprehensive description of the dynamics. We find
continuous and abrupt transitions in the cooperation density with excellent
agreement between theory and the Gillespie simulations. Under strong selection,
the system can display several levels of steady cooperation or get trapped into
absorbing states. These states are still relevant for experiments even when
irrational choices are made due to their prolonged relaxation times. Finally,
we show that for the particular case of the Prisoner Dilemma, where defection
is the dominant strategy under imitation mechanisms, the self-evaluation update
instead favors cooperation nonlinearly with the level of aspiration. Thus, our
work provides insights into the distinct role between imitation and
self-evaluation with no learning dynamics.Comment: 11 pages, 9 figures; Correction of typos in the metadat
Nonlocal analysis of modular roles
We introduce a new methodology to characterize the role that a given node plays inside the community structure of a complex network. Our method relies on the ability of the links to reduce the number of steps between two nodes in the network, which is measured by the number of shortest paths crossing each link, and its impact on the node proximity. In this way, we use node closeness to quantify the importance of a node inside its community. At the same time, we define a participation coefficient that depends on the shortest paths contained in the links that connect two communities. The combination of both parameters allows to identify the role played by the nodes in the network, following the same guidelines introduced by Guimerà et al. [Guimerà & Amaral, 2005] but, in this case, considering global information about the network. Finally, we give some examples of the hub characterization in real networks and compare our results with the parameters most used in the literature
Synchronization waves in geometric networks
We report synchronization of networked excitable nodes embedded in a metric space, where the connectivity properties are mostly determined by the distance between units. Such a high clustered structure, combined with the lack of long-range connections, prevents full synchronization and yields instead the emergence of synchronization waves. We show that this regime is optimal for information transmission through the system, as it enhances the options of reconstructing the topology from the dynamics. Measurements of topological and functional centralities reveal that the wave-synchronization state allows detection of the most structurally relevant nodes from a single observation of the dynamics, without any a priori information on the model equations ruling the evolution of the ensembl
Integration versus segregation in functional brain networks
We propose a new methodology to evaluate the balance between segregation and integration in functional brain networks by using singular value decomposition techniques. By means of magnetoencephalography, we obtain the brain activity of a control group of 19 individuals during a memory task. Next, we project the node-to-node correlations into a complex network that is analyzed from the perspective of its modular structure encoded in the contribution matrix. In this way, we are able to study the role that nodes play I/O its community and to identify connector and local hubs. At the mesoscale level, the analysis of the contribution matrix allows us to measure the degree of overlapping between communities and quantify how far the functional networks are from the configuration that better balances the integrated and segregated activit
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