Laura C. Carpi

Causality and the entropy–complexity plane: Robustness and missing ordinal patterns

We deal here with the issue of determinism versus randomness in time series. One wishes to identify their relative weights in a given time series. Two different tools have been advanced in the literature to such effect, namely, (i) the “causal” entropy–complexity plane [O.A. Rosso, H.A. Larrondo, M.T. Martin, A. Plastino, M.A. Fuentes, Distinguishing noise from chaos, Phys. Rev. Lett. 99 (2007) 154102] and (ii) the estimation of the decay rate of missing ordinal patterns [J.M. Amigo, S. Zambrano, M.A.F. Sanjuan, True and false forbidden patterns in deterministic and random dynamics, Europhys. Lett. 79 (2007) 50001; L.C. Carpi, P.M. Saco, O.A. Rosso, Missing ordinal patterns in correlated noises. Physica A 389 (2010) 2020–2029]. In this work we extend the use of these techniques to address the analysis of deterministic finite time series contaminated with additive noises of different degree of correlation. The chaotic series studied here was via the logistic map (r=4) to which we added correlated noise (colored noise with f−k Power Spectrum, 0≤k≤2) of varying amplitudes. In such a fashion important insights pertaining to the deterministic component of the original time series can be gained. We find that in the entropy–complexity plane this goal can be achieved without additional computations.

Distinguishing Noise from Chaos: Objective versus Subjective Criteria Using Horizontal Visibility Graph

A recently proposed methodology called the Horizontal Visibility Graph (HVG) [Luque et al., Phys. Rev. E., 80, 046103 (2009)] that constitutes a geometrical simplification of the well known Visibility Graph algorithm [Lacasa et al., Proc. Natl. Sci. U.S.A. 105, 4972 (2008)], has been used to study the distinction between deterministic and stochastic components in time series [L. Lacasa and R. Toral, Phys. Rev. E., 82, 036120 (2010)]. Specifically, the authors propose that the node degree distribution of these processes follows an exponential functional of the form , in which is the node degree and is a positive parameter able to distinguish between deterministic (chaotic) and stochastic (uncorrelated and correlated) dynamics. In this work, we investigate the characteristics of the node degree distributions constructed by using HVG, for time series corresponding to chaotic maps, 2 chaotic flows and different stochastic processes. We thoroughly study the methodology proposed by Lacasa and Toral finding several cases for which their hypothesis is not valid. We propose a methodology that uses the HVG together with Information Theory quantifiers. An extensive and careful analysis of the node degree distributions obtained by applying HVG allow us to conclude that the Fisher-Shannon information plane is a remarkable tool able to graphically represent the different nature, deterministic or stochastic, of the systems under study.

Quantification of network structural dissimilarities

Identifying and quantifying dissimilarities among graphs is a fundamental and challenging problem of practical importance in many fields of science. Current methods of network comparison are limited to extract only partial information or are computationally very demanding. Here we propose an efficient and precise measure for network comparison, which is based on quantifying differences among distance probability distributions extracted from the networks. Extensive experiments on synthetic and real-world networks show that this measure returns non-zero values only when the graphs are non-isomorphic. Most importantly, the measure proposed here can identify and quantify structural topological differences that have a practical impact on the information flow through the network, such as the presence or absence of critical links that connect or disconnect connected components.

Information theory perspective on network robustness

Abstract A crucial challenge in network theory is the study of the robustness of a network when facing a sequence of failures. In this work, we propose a dynamical definition of network robustness based on Information Theory, that considers measurements of the structural changes caused by failures of the networks components. Failures are defined here as a temporal process defined in a sequence. Robustness is then evaluated by measuring dissimilarities between topologies after each time step of the sequence, providing a dynamical information about the topological damage. We thoroughly analyze the efficiency of the method in capturing small perturbations by considering different probability distributions on networks. In particular, we find that distributions based on distances are more consistent in capturing network structural deviations, as better reflect the consequences of the failures. Theoretical examples and real networks are used to study the performance of this methodology.

Evaluation of the Copycat Model for Predicting Complex Network Growth

We deal here with the issue of complex network evolution. In particular, we propose the use of the Copycat Model as a framework to predict the dynamic behavior of networks. This model has the ability to dynamically adjust the topological properties step by step during the network’s growth. We test the methodology with three networks, an artificial net called popularity vs. similarity and two real ones Manufacturing Emails Network and Slashdot threads Network. The results show that the methodology is able to correctly predict network’s evolution reproducing several network properties.

Characterisation of emergent properties during the transition to optical turbulence in a fibre laser

Fibre lasers display complex dynamical regimes which involve nonlinear interactions of millions of cavity modes. Recently, the transition to “optical turbulence” [1] (in analogy with the laminar-turbulence transition in hydrodynamic) was experimentally studied and was shown to be a phase transition which is accompanied by the occurrence of temporal correlations in the laser intensity with specific time-scales [2].

Dynamics of Climate Networks

A methodology to analyze dynamical changes in dynamic climate systems based on complex networks and Information Theory quantifiers is discussed. In particular, the square root of the Jensen–Shannon divergence, a measure of dissimilarity between two probability distributions, is used to quantify states in the network evolution process by means of their degree distribution. We explore the evolution of the surface air temperature (SAT) climate network on the Tropical Pacific region. We find that the proposed quantifier is able not only to capture changes in the dynamics of the studied process but also to quantify and compare states in its evolution. The dynamic network topology is investigated for temporal windows of one-year duration over the 1948–2009 period. The use of this novel methodology, allows us to consistently compare the evolving networks topologies and to capture a cyclic behavior consistent with that of El Nino/Southern Oscillation. This cyclic behavior involves alternating states of less/more efficient information transfer during El Nino/La Nina years, respectively, reflecting a higher climatic stability for La Nina years which is in agreement with current observations. The study also detects a change in the dynamics of the network structure, which coincides with the 76/77 climate shift, after which, conditions of less-efficient information transfer are more frequent and intense.