Point process analysis of geographical diffusion of news in Argentina.

The diffusion of information plays a crucial role in a society, affecting its economy and the well-being of the population. Characterizing the diffusion process is challenging because it is highly non-stationary and varies with the media type. To understand the spreading of newspaper news in Argentina, we collected data from more than 27 000 articles published in six main provinces during 4 months.

Basin entropy as an indicator of a bifurcation in a time-delayed system.

The basin entropy is a measure that quantifies, in a system that has two or more attractors, the predictability of a final state, as a function of the initial conditions. While the basin entropy has been demonstrated on a variety of multistable dynamical systems, to the best of our knowledge, it has not yet been tested in systems with a time delay, whose phase space is infinite dimensional because the initial conditions are functions defined in a time interval [-τ,0], where τ is the delay time. Here, we consider a simple time-delayed system consisting of a bistable system with a linear delayed feedback term.

Permutation entropy analysis of EEG signals for distinguishing eyes-open and eyes-closed brain states: Comparison of different approaches.

Developing reliable methodologies to decode brain state information from electroencephalogram (EEG) signals is an open challenge, crucial to implementing EEG-based brain-computer interfaces (BCIs). For example, signal processing methods that identify brain states could allow motor-impaired patients to communicate via non-invasive, EEG-based BCIs. In this work, we focus on the problem of distinguishing between the states of eyes closed (EC) and eyes open (EO), employing quantities based on permutation entropy (PE).

Characterizing the spike timing of a chaotic laser by using ordinal analysis and machine learning.

Semiconductor lasers with optical feedback are well-known nonlinear dynamical systems. Under appropriate feedback conditions, these lasers emit optical pulses that resemble neural spikes. Influenced by feedback delay and various noise sources, including quantum spontaneous emission noise, the dynamics are highly stochastic.

Topological data analysis of the synchronization of a network of Rössler chaotic electronic oscillators.

Synchronization study allows a better understanding of the exchange of information among systems. In this work, we study experimental data recorded from a set of Rössler-like chaotic electronic oscillators arranged in a complex network, where the interactions between the oscillators are given in terms of a connectivity matrix, and their intensity is controlled by a global coupling parameter. We use the zero and one persistent homology groups to characterize the point clouds obtained from the signals recorded in pairs of oscillators.

Timing jitter reduction in semiconductor lasers induced by optical injection.

We present an experimental study of the effect of continuous-wave optical injection (OI) from a vertical-cavity surface-emitting laser (VCSEL) on the timing jitter of a gain-switched discrete-mode semiconductor laser (DML). Timing jitter was analyzed over a wide range of temperatures of the DML, which allowed tuning the detuning between the lasers emissions, and it was compared with the inter-pulse timing jitter. We have found that there is a range of detunings in which OI diminishes the jitter by 70% with respect to the jitter of the solitary DML.

Quantifying the synchronization of the spikes emitted by coupled lasers.

Synchronization phenomena is ubiquitous in nature, and in spite of having been studied for decades, it still attracts a lot of attention as is still challenging to detect and quantify, directly from the analysis of noisy signals. Semiconductor lasers are ideal for performing experiments because they are stochastic, nonlinear, and inexpensive and display different synchronization regimes that can be controlled by tuning the lasers' parameters. Here, we analyze experiments done with two mutually optically coupled lasers.

Experimental study of spatial and temporal coherence in a laser diode with optical feedback.

Optical feedback can reduce the linewidth of a semiconductor laser by several orders of magnitude, but it can also cause line broadening. Although these effects on the temporal coherence of the laser are well known, a good understanding of the effects of feedback on the spatial coherence is still lacking. Here we present an experimental technique that allows discriminating the effects of feedback on temporal and spatial coherence of the laser beam.

Parameter and coupling estimation in small networks of Izhikevich's neurons.

Nowadays, experimental techniques allow scientists to have access to large amounts of data. In order to obtain reliable information from the complex systems that produce these data, appropriate analysis tools are needed. The Kalman filter is a frequently used technique to infer, assuming a model of the system, the parameters of the model from uncertain observations.

Diffusion capacity of single and interconnected networks.

Understanding diffusive processes in networks is a significant challenge in complexity science. Networks possess a diffusive potential that depends on their topological configuration, but diffusion also relies on the process and initial conditions. This article presents Diffusion Capacity, a concept that measures a node's potential to diffuse information based on a distance distribution that considers both geodesic and weighted shortest paths and dynamical features of the diffusion process.

What Models and Tools can Contribute to a Better Understanding of Brain Activity?

Despite impressive scientific advances in understanding the structure and function of the human brain, big challenges remain. A deep understanding of healthy and aberrant brain activity at a wide range of temporal and spatial scales is needed. Here we discuss, from an interdisciplinary network perspective, the advancements in physical and mathematical modeling as well as in data analysis techniques that, in our opinion, have potential to further advance our understanding of brain structure and function.

Abrupt transition from low-coherence to high-coherence radiation in a semiconductor laser with optical feedback.

Semiconductor lasers are very sensitive to optical feedback. Although it is well known that coherent feedback lowers the threshold of the laser, the characteristics of the transition from low-coherence radiation-dominated by spontaneous emission-below threshold to high-coherence radiation-dominated by stimulated emission-above threshold have not yet been investigated. Here we show experimentally that, in contrast to the transition that occurs in the solitary laser, in the laser with feedback the transition to high-coherence emission can occur abruptly.

Entropy-based early detection of critical transitions in spatial vegetation fields.

In semiarid regions, vegetated ecosystems can display abrupt and unexpected changes, i.e., transitions to different states, due to drifting or time-varying parameters, with severe consequences for the ecosystem and the communities depending on it.

Perspectives on the importance of complex systems in understanding our climate and climate change-The Nobel Prize in Physics 2021.

The Nobel Prize in Physics 2021 was awarded to Syukuro Manabe, Klaus Hasselmann, and Giorgio Parisi for their "groundbreaking contributions to our understanding of complex systems," including major advances in the understanding of our climate and climate change. In this Perspective article, we review their key contributions and discuss their relevance in relation to the present understanding of our climate. We conclude by outlining some promising research directions and open questions in climate science.

Time crystal dynamics in a weakly modulated stochastic time delayed system.

Time crystal oscillations in interacting, periodically driven many-particle systems are highly regular oscillations that persist for long periods of time, are robust to perturbations, and whose frequency differs from the frequency of the driving signal. Making use of underlying similarities of spatially-extended systems and time-delayed systems (TDSs), we present an experimental demonstration of time-crystal-like behavior in a stochastic, weakly modulated TDS. We consider a semiconductor laser near threshold with delayed feedback, whose output intensity shows abrupt spikes at irregular times.

Dynamics of a semiconductor laser with feedback and modulation: experiments and model comparison.

We study experimentally and numerically the dynamics of a semiconductor laser near threshold, subject to optical feedback and sinusoidal current modulation. The laser operates in the low frequency fluctuation (LFF) regime where, without modulation, the intensity shows sudden spikes at irregular times. Under particular modulation conditions the spikes lock to the modulation and their timing becomes highly regular.

Inferring the connectivity of coupled chaotic oscillators using Kalman filtering.

Inferring the interactions between coupled oscillators is a significant open problem in complexity science, with multiple interdisciplinary applications. While the Kalman filter (KF) technique is a well-known tool, widely used for data assimilation and parameter estimation, to the best of our knowledge, it has not yet been used for inferring the connectivity of coupled chaotic oscillators. Here we demonstrate that KF allows reconstructing the interaction topology and the coupling strength of a network of mutually coupled Rössler-like chaotic oscillators.

Permutation entropy analysis of the output of a laser diode under stimulated Brillouin scattering optical feedback.

The chaotic output emitted by a diode laser with optical feedback has fascinated the community for decades. The external cavity delay time imparts a weak level of periodicity to the laser output (the so-called "time delay signature", TDS) that is a drawback for applications that require random optical signals. A lot of efforts have focused in suppressing the TDS either by post-processing the signal or by using alternative ways to generate random optical signals.

Evaluating Temporal Correlations in Time Series Using Permutation Entropy, Ordinal Probabilities and Machine Learning.

Time series analysis comprises a wide repertoire of methods for extracting information from data sets. Despite great advances in time series analysis, identifying and quantifying the strength of nonlinear temporal correlations remain a challenge. We have recently proposed a new method based on training a machine learning algorithm to predict the temporal correlation parameter, α, of flicker noise (FN) time series.

Discriminating chaotic and stochastic time series using permutation entropy and artificial neural networks.

Extracting relevant properties of empirical signals generated by nonlinear, stochastic, and high-dimensional systems is a challenge of complex systems research. Open questions are how to differentiate chaotic signals from stochastic ones, and how to quantify nonlinear and/or high-order temporal correlations. Here we propose a new technique to reliably address both problems.

Fast and effective pseudo transfer entropy for bivariate data-driven causal inference.

Identifying, from time series analysis, reliable indicators of causal relationships is essential for many disciplines. Main challenges are distinguishing correlation from causality and discriminating between direct and indirect interactions. Over the years many methods for data-driven causal inference have been proposed; however, their success largely depends on the characteristics of the system under investigation.

Neuronal Transmission of Subthreshold Periodic Stimuli Via Symbolic Spike Patterns.

We study how sensory neurons detect and transmit a weak external stimulus. We use the FitzHugh-Nagumo model to simulate the neuronal activity. We consider a sub-threshold stimulus, i.

Testing Critical Slowing Down as a Bifurcation Indicator in a Low-Dissipation Dynamical System.

We study a two-dimensional low-dissipation nonautonomous dynamical system, with a control parameter that is swept linearly in time across a transcritical bifurcation. We investigate the relaxation time of a perturbation applied to a variable of the system and we show that critical slowing down may occur at a parameter value well above the bifurcation point. We test experimentally the occurrence of critical slowing down by applying a perturbation to the accessible control parameter and we find that this perturbation leaves the system behavior unaltered, thus providing no useful information on the occurrence of critical slowing down.

Success rate analysis of the response of an excitable laser to periodic perturbations.

We use statistical tools to characterize the response of an excitable system to periodic perturbations. The system is an optically injected semiconductor laser under pulsed perturbations of the phase of the injected field. We characterize the laser response by counting the number of pulses emitted by the laser, within a time interval, ΔT, that starts when a perturbation is applied.