Spatial immunization to abate disease spreading in transportation hubs.

Proximity social interactions are crucial for infectious diseases transmission. Crowded agglomerations pose serious risk of triggering superspreading events. Locations like transportation hubs (airports and stations) are designed to optimize logistic efficiency, not to reduce crowding, and are characterized by a constant in and out flow of people. Here, we analyze the paradigmatic example of London Heathrow, one of the busiest European airports. Thanks to a dataset of anonymized individuals' trajectories, we can model the spreading of different diseases to localize the contagion hotspots and to propose a spatial immunization policy targeting them to reduce disease spreading risk. We also detect the most vulnerable destinations to contagions produced at the airport and quantify the benefits of the spatial immunization technique to prevent regional and global disease diffusion. This method is immediately generalizable to train, metro and bus stations and to other facilities such as commercial or convention centers.

Effects of demand control on the complex dynamics of electric power system blackouts.

The propagation of failures and blackouts in electric networks is a complex problem. Typical models, such as the ORNL-PSerc-Alaska (OPA), are based on a combination of fast and slow dynamics. The first describes the cascading failures while the second describes the grid evolution through line and generation upgrades as well as demand growth, all taking place in time scales from days to years. The growing integration of renewable energy sources, whose power fluctuates in time scales from seconds to hours, together with the increase in demand, which also presents fast fluctuations, requires the incorporation of distributed methods of control in the demand side to avoid the high cost of ordinary control in conventional power plants. In this work, we extend the OPA model to include fluctuations in the demand at time scales of the order of minutes, intraday demand variations, and the effect of demand control. We find that demand control effectively reduces the number of blackouts without increasing the probability of large-scale events.

Fluctuations and correlations in Kerr optical frequency combs with additive Gaussian noise.

We investigate the effects of environmental stochastic fluctuations on Kerr optical frequency combs. This spatially extended dynamical system can be accurately studied using the Lugiato-Lefever equation, and we show that when additive noise is accounted for, the correlations of the modal field fluctuations can be determined theoretically. We propose a general theory for the computation of these field fluctuations and correlations, which is successfully compared to numerical simulations.

Migrant mobility flows characterized with digital data.

Monitoring migration flows is crucial to respond to humanitarian crisis and to design efficient policies. This information usually comes from surveys and border controls, but timely accessibility and methodological concerns reduce its usefulness. Here, we propose a method to detect migration flows worldwide using geolocated Twitter data. We focus on the migration crisis in Venezuela and show that the calculated flows are consistent with official statistics at country level. Our method is versatile and far-reaching, as it can be used to study different features of migration as preferred routes, settlement areas, mobility through several countries, spatial integration in cities, etc. It provides finer geographical and temporal resolutions, allowing the exploration of issues not contemplated in official records. It is our hope that these new sources of information can complement official ones, helping authorities and humanitarian organizations to better assess when and where to intervene on the ground.

Field theory for recurrent mobility.

Understanding human mobility is crucial for applications such as forecasting epidemic spreading, planning transport infrastructure and urbanism in general. While, traditionally, mobility information has been collected via surveys, the pervasive adoption of mobile technologies has brought a wealth of (real time) data. The easy access to this information opens the door to study theoretical questions so far unexplored. In this work, we show for a series of worldwide cities that commuting daily flows can be mapped into a well behaved vector field, fulfilling the divergence theorem and which is, besides, irrotational. This property allows us to define a potential for the field that can become a major instrument to determine separate mobility basins and discern contiguous urban areas. We also show that empirical fluxes and potentials can be well reproduced and analytically characterized using the so-called gravity model, while other models based on intervening opportunities have serious difficulties.

In-phase, out-of-phase and T/4 synchronization of square waves in delay-coupled non-identical optoelectronic oscillators.

We model two non-identical delay-line optoelectronic oscillators mutually coupled through delayed cross-feedback. The system can generate multi-stable nanosecond periodic square-wave solutions which arise through a Hopf instability. We show that for suitable ratios between self and cross delay times, the two oscillators generate square waves with different amplitude but synchronized in phase, out of phase or with a dephasing of a quarter of the period. We also show that the synchronization is robust to small mismatches in the delay times.

Dynamical properties induced by state-dependent delays in photonic systems.

In many dynamical systems and complex networks time delays appear naturally in feedback loops or coupling connections of individual elements. Moreover, in a whole class of systems, these delay times can depend on the state of the system. Nevertheless, so far the understanding of the impact of such state-dependent delays remains poor with a particular lack of systematic experimental studies. Here we fill this gap by introducing a conceptually simple photonic system that exhibits dynamics of self-organised switching between two loops with two different delay times, depending on the state of the system. On the basis of experiments and modelling on semiconductor lasers with frequency-selective feedback mirrors, we characterize the switching between the states defined by the individual delays. Our approach opens new perspectives for the study of this class of dynamical systems and enables applications in which the self-organized switching can be exploited.

Synchronization of tunable asymmetric square-wave pulses in delay-coupled optoelectronic oscillators.

We consider a model for two delay-coupled optoelectronic oscillators under positive delayed feedback as prototypical to study the conditions for synchronization of asymmetric square-wave oscillations, for which the duty cycle is not half of the period. We show that the scenario arising for positive feedback is much richer than with negative feedback. First, it allows for the coexistence of multiple in- and out-of-phase asymmetric periodic square waves for the same parameter values. Second, it is tunable: The period of all the square-wave periodic pulses can be tuned with the ratio of the delays, and the duty cycle of the asymmetric square waves can be changed with the offset phase while the total period remains constant. Finally, in addition to the multiple in- and out-of-phase periodic square waves, low-frequency periodic asymmetric solutions oscillating in phase may coexist for the same values of the parameters. Our analytical results are in agreement with numerical simulations and bifurcation diagrams obtained by using continuation techniques.

Theory for the spatiotemporal dynamics of domain walls close to a nonequilibrium Ising-Bloch transition.

We derive a generic model for the interaction of domain walls close to a nonequilibrium-Bloch transition. The universal scenario predicted by the model includes stationary Ising and Bloch localized structures (dissipative solitons), as well as drifting and oscillating Bloch structures. Our theory also explains the behavior of Bloch walls during a collision. The results are confirmed by numerical simulations of the Ginzburg-Landau equation forced at twice its natural frequency and are in agreement with previous observations in several physical systems.

Tweets on the road.

The pervasiveness of mobile devices, which is increasing daily, is generating a vast amount of geo-located data allowing us to gain further insights into human behaviors. In particular, this new technology enables users to communicate through mobile social media applications, such as Twitter, anytime and anywhere. Thus, geo-located tweets offer the possibility to carry out in-depth studies on human mobility. In this paper, we study the use of Twitter in transportation by identifying tweets posted from roads and rails in Europe between September 2012 and November 2013. We compute the percentage of highway and railway segments covered by tweets in 39 countries. The coverages are very different from country to country and their variability can be partially explained by differences in Twitter penetration rates. Still, some of these differences might be related to cultural factors regarding mobility habits and interacting socially online. Analyzing particular road sectors, our results show a positive correlation between the number of tweets on the road and the Average Annual Daily Traffic on highways in France and in the UK. Transport modality can be studied with these data as well, for which we discover very heterogeneous usage patterns across the continent.

Tuning the period of square-wave oscillations for delay-coupled optoelectronic systems.

We analyze the response of two delay-coupled optoelectronic oscillators. Each oscillator operates under its own delayed feedback. We show that the system can display square-wave periodic solutions that can be synchronized in phase or out of phase depending on the ratio between self- and cross-delay times. Furthermore, we show that multiple periodic synchronized solutions can coexist for the same values of the fixed parameters. As a consequence, it is possible to generate square-wave oscillations with different periods by just changing the initial conditions.

Formation of localized structures in bistable systems through nonlocal spatial coupling. I. General framework.

The present work studies the influence of nonlocal spatial coupling on the existence of localized structures in one-dimensional extended systems. We consider systems described by a real field with a nonlocal coupling that has a linear dependence on the field. Leveraging spatial dynamics we provide a general framework to understand the effect of the nonlocality on the shape of the fronts connecting two stable states. In particular we show that nonlocal terms can induce spatial oscillations in the front tails, allowing for the creation of localized structures, that emerge from pinning between two fronts. In parameter space the region where fronts are oscillatory is limited by three transitions: the modulational instability of the homogeneous state, the Belyakov-Devaney transition in which monotonic fronts acquire spatial oscillations with infinite wavelength, and a crossover in which monotonically decaying fronts develop spatial oscillations with a finite wavelength. We show how these transitions are organized by codimension 2 and 3 points and illustrate how by changing the parameters of the nonlocal coupling it is possible to bring the system into the region where localized structures can be formed.

Formation of localized structures in bistable systems through nonlocal spatial coupling. II. The nonlocal Ginzburg-Landau equation.

We study the influence of a linear nonlocal spatial coupling on the interaction of fronts connecting two equivalent stable states in the prototypical 1-dimensional real Ginzburg-Landau equation. While for local coupling the fronts are always monotonic and therefore the dynamical behavior leads to coarsening and the annihilation of pairs of fronts, nonlocal terms can induce spatial oscillations in the front, allowing for the creation of localized structures, emerging from pinning between two fronts. We show this for three different nonlocal influence kernels. The first two, mod-exponential and Gaussian, are positive definite and decay exponentially or faster, while the third one, a Mexican-hat kernel, is not positive definite.

Electro-optic phase chaos systems with an internal variable and a digital key.

We consider an electro-optic phase chaos system with two feedback loops organized in a parallel configuration such that the dynamics of one of the loops remains internal. We show that this configuration intrinsically conceals in the transmitted variable the internal delay times, which are critical for decoding. The scheme also allows for the inclusion, in a very efficient way, of a digital key generated as a long pseudorandom binary sequence. A single digital key can operate both in the internal and transmitted variables leading to a large sensitivity of the synchronization to a key-mismatch. The combination of intrinsic delay time concealment and digital key selectivity provides the basis for a large enhancement of the confidentiality in chaos-based communications.

Role of the phase in the identification of delay time in semiconductor lasers with optical feedback.

We consider a semiconductor laser with external optical feedback operating at a regime for which the delay time signature is extremely difficult to identify from the analysis of the intensity time series, using standard techniques. We show that such a delay signature can be successfully retrieved by computing the same quantifiers from the phase, the real or the imaginary part of the field, even in the presence of noise. Therefore, the choice of the observable is the determinant for parameter identification.

Digital key for chaos communication performing time delay concealment.

We introduce a scheme that integrates a digital key in a phase-chaos electro-optical delay system for optical chaos communications. A pseudorandom binary sequence (PRBS) is mixed within the chaotic dynamics in a way that a mutual concealment is performed; e.g., the time delay is hidden by the binary sequence, and the PRBS is also masked by the chaos. In addition to bridging the gap between algorithmic symmetric key cryptography and chaos-based analog encoding, the proposed approach is intended to benefit from the complex algebra mixing between a (pseudorandom) Boolean variable, and another continuous time (chaotic) variable. The scheme also provides a large flexibility allowing for easy reconfigurations to communicate securely at a high bit rate between different systems.

Nonuniversal results induced by diversity distribution in coupled excitable systems.

We consider a system of globally coupled active rotators near the excitable regime. The system displays a transition to a state of collective firing induced by disorder. We show that this transition is found generically for any diversity distribution with well-defined moments. Singularly, for the Lorentzian distribution (widely used in Kuramoto-like systems) the transition is not present. This warns about the use of Lorentzian distributions to understand the generic properties of coupled oscillators.

Controlling the unstable emission of a semiconductor laser subject to conventional optical feedback with a filtered feedback branch.

We show the advantages of controlling the unstable dynamics of a semiconductor laser subject to conventional optical feedback by means of a second filtered feedback branch. We give an overview of the analytical solutions of the double cavity feedback and show numerically that the region of stabilization is much larger when using a second branch with filtered feedback than when using a conventional feedback one.

Synchronization properties of coupled semiconductor lasers subject to filtered optical feedback.

We study numerically the synchronization properties of two unidirectionally coupled semiconductor lasers subject to filtered optical feedback. By adding a perturbation (a message) to the output of the master laser, we show that mutual information allows distinguishing between chaotic synchronization (at low to moderate coupling strengths) and injection locking (at large coupling strength). We find that a receiver subject to a feedback similar to that of the emitter (closed-loop receiver) shows better synchronization with the master laser when compared with a receiver without feedback (open-loop receiver). Closed-loop receivers also show better capability to recover weak messages. The filter in the feedback loop allows reducing the bandwidth of the chaotic carrier, improves the synchronization with respect to the conventional feedback case, and requires less coupling strength with a minor loss in complexity.

Effects of gain and bandwidth on the multimode behavior of optoelectronic microwave oscillators.

We show that when subjected to high gain, delay-line optoelectronic oscillators can display a strongly multimode behavior depending on the feedback bandwidth. We found that this dynamical regime may arise when the bandwidth of the feedback loop spans over several hundreds of ring cavity-modes, and also when the oscillator is switched on abruptly. Such a persistent multimode regime is detrimental to the performances of this system which is normally intended to provide ultra-pure and single-mode microwaves. We experimentally evidence this multimode dynamics and we propose a theory to explain this undesirable feature.