Impact of lag information on network inference

Extracting useful information from data is a fundamental challenge across disciplines as diverse as climate, neuroscience, genetics, and ecology. In the era of ``big data'', data is ubiquitous, but appropriated methods are needed for gaining reliable information from the data. In this work we consider a complex system, composed by interacting units, and aim at inferring which elements influence each other, directly from the observed data. The only assumption about the structure of the system is that it can be modeled by a network composed by a set of $N$ units connected with $L$ un-weighted and un-directed links, however, the structure of the connections is not known. In this situation the inference of the underlying network is usually done by using interdependency measures, computed from the output signals of the units. We show, using experimental data recorded from randomly coupled electronic R{\"o}ssler chaotic oscillators, that the information of the lag times obtained from bivariate cross-correlation analysis can be useful to gain information about the real connectivity of the system

Interpreting Physical Flows in Networks as a Communication System

ACKNOWLEDGEMENTS NR acknowledges the support of PEDECIBA, Uruguay. CG and MSB thank the Scottish University Physics Alliance (SUPA) support. MSB also acknowledges the support of EPSRC grant Ref. EP/I032606/1.Peer reviewedPublisher PD

Electronically--implemented coupled logistic maps

The logistic map is a paradigmatic dynamical system originally conceived to model the discrete-time demographic growth of a population, which shockingly, shows that discrete chaos can emerge from trivial low-dimensional non-linear dynamics. In this work, we design and characterize a simple, low-cost, easy-to-handle, electronic implementation of the logistic map. In particular, our implementation allows for straightforward circuit-modifications to behave as different one-dimensional discrete-time systems. Also, we design a coupling block in order to address the behavior of two coupled maps, although, our design is unrestricted to the discrete-time system implementation and it can be generalized to handle coupling between many dynamical systems, as in a complex system. Our findings show that the isolated and coupled maps' behavior has a remarkable agreement between the experiments and the simulations, even when fine-tuning the parameters with a resolution of $\sim 10^{-3}$. We support these conclusions by comparing the Lyapunov exponents, periodicity of the orbits, and phase portraits of the numerical and experimental data for a wide range of coupling strengths and map's parameters.Comment: 8 pages, 10 figure

Approximate solution for frequency synchronization in a finite-size Kuramoto model

Peer reviewedPublisher PD

Exact detection of direct links in networks of interacting dynamical units

Authors NR, EB-M, CG, and MSB acknowledge the Scottish Universities Physics Alliance (SUPA). EB-M and MSB also acknowledge the Engineering and Physical Science Research Council (EPSRC) project Ref. EP/I032 606/1. ACM and CM acknowledge the LINC project (FP7-PEOPLE-2011-ITN, grant no. 289447). ACM also aknowledges PEDECIBA and CSIC(Uruguay). CM also acknowledges grant FIS2012–37655-C02–01 from the Spanish MCI, grant 2009 SGR 1168, and the ICREA Academia programme from the Generalitat de Catalunya.Peer reviewedPublisher PD

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation.Comment: Submitted to EPJ-ST Power Grids, May 201

Low frequency oscillations drive EEG’s complexity changes during wakefulness and sleep

ACKNOWLEDGEMENT J.G. acknowledges the support of Comisio´n Acade´mica de Posgrado (CAP), CSIC Iniciacio´n and PEDECIBA. P. T. and N.R. also acknowledges the support of PEDECIBAPeer reviewedPublisher PD

Exact detection of direct links in networks of interacting dynamical units

The inference of an underlying network topology from local observations of a complex system composed of interacting units is usually attempted by using statistical similarity measures, such as cross-correlation (CC) and mutual information (MI). The possible existence of a direct link between different units is, however, hindered within the time-series measurements. Here we show that, for the class of systems studied, when an abrupt change in the ordered set of CC or MI values exists, it is possible to infer, without errors, the underlying network topology from the time-series measurements, even in the presence of observational noise, non-identical units, and coupling heterogeneity. We find that a necessary condition for the discontinuity to occur is that the dynamics of the coupled units is partially coherent, i.e., neither complete disorder nor globally synchronous patterns are present. We critically compare the inference methods based on CC and MI, in terms of how effective, robust, and reliable they are, and conclude that, in general, MI outperforms CC in robustness and reliability. Our findings could be relevant for the construction and interpretation of functional networks, such as those constructed from brain or climate data.Peer Reviewe

Models for the modern power grid

This article reviews different kinds of models for the electric power grid that can be used to understand the modern power system, the smart grid. From the physical network to abstract energy markets, we identify in the literature different aspects that co-determine the spatio-temporal multilayer dynamics of power system. We start our review by showing how the generation, transmission and distribution characteristics of the traditional power grids are already subject to complex behaviour appearing as a result of the the interplay between dynamics of the nodes and topology, namely synchronisation and cascade effects. When dealing with smart grids, the system complexity increases even more: on top of the physical network of power lines and controllable sources of electricity, the modernisation brings information networks, renewable intermittent generation, market liberalisation, prosumers, among other aspects. In this case, we forecast a dynamical co-evolution of the smart grid and other kind of networked systems that cannot be understood isolated. This review compiles recent results that model electric power grids as complex systems, going beyond pure technological aspects. From this perspective, we then indicate possible ways to incorporate the diverse co-evolving systems into the smart grid model using, for example, network theory and multi-agent simulation22324232437CONSELHO NACIONAL DE DESENVOLVIMENTO CIENTÍFICO E TECNOLÓGICO - CNPQCOORDENAÇÃO DE APERFEIÇOAMENTO DE PESSOAL DE NÍVEL SUPERIOR - CAPES490235/2012-3; 312146/2012-4076/2012This work was partly supported by the Science without Boarders Special Visiting Researcher fellowship CAPES/Brazil 076/2012, SUSTAIN Finnish Academy and CNPq/Brazil 490235/2012-3 jointly funded project, CNPq/Brazil 312146/2012-4. MSB acknowledges EPSRC grant EP/I032606/