Time-delay identification using multiscale ordinal quantifiers

Time-delayed interactions naturally appear in a multitude of real-world systems due to the finite propagation speed of physical quantities. Often, the time scales of the interactions are unknown to an external observer and need to be inferred from time series of observed data. We explore, in this work, the properties of several ordinal-based quantifiers for the identification of time-delays from time series. To that end, we generate artificial time series of stochastic and deterministic time-delay models. We find that the presence of a nonlinearity in the generating model has consequences for the distribution of ordinal patterns and, consequently, on the delay-identification qualities of the quantifiers. Here, we put forward a novel ordinal-based quantifier that is particularly sensitive to nonlinearities in the generating model and compare it with previously-defined quantifiers. We conclude from our analysis on artificially generated data that the proper identification of the presence of a time-delay and its precise value from time series benefits from the complementary use of ordinal-based quantifiers and the standard autocorrelation function. We further validate these tools with a practical example on real-world data originating from the North Atlantic Oscillation weather phenomenon.Fil: Soriano, Miguel C.. Consejo Superior de Investigaciones Científicas. Instituto de Física Interdisciplinar y Sistemas Complejos; EspañaFil: Zunino, Luciano José. Provincia de Buenos Aires. Gobernación. Comisión de Investigaciones Científicas; Argentina. Universidad Nacional de La Plata. Facultad de Ingeniería; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas. Centro Científico Tecnológico Conicet - La Plata; Argentin

Determining the sub-Lyapunov exponent of delay systems from time series

© 2015 American Physical Society. For delay systems the sign of the sub-Lyapunov exponent (sub-LE) determines key dynamical properties. This includes the properties of strong and weak chaos and of consistency. Here we present a robust algorithm based on reconstruction of the local linearized equations of motion, which allows for calculating the sub-LE from time series. The algorithm is inspired by a method introduced by Pyragas for a nondelayed drive-response scheme [K. Pyragas, Phys. Rev. E 56, 5183 (1997)1063-651X10.1103/PhysRevE.56.5183]. In the presented extension to delay systems, the delayed feedback takes over the role of the drive, whereas the response of the low-dimensional node leads to the sub-Lyapunov exponent. Our method is based on a low-dimensional representation of the delay system. We introduce the basic algorithm for a discrete scalar map, extend the concept to scalar continuous delay systems, and give an outlook to the case of a full vector-state system, from which only a scalar observable is recorded.This work was supported by a fellowship within the Postdoc-Programme of the German Academic Exchange Service (DAAD), FEDER and MINECO (Spain) under Project No. TEC2012-36335 (TRIPHOP) and Comunitat Autonoma de les Illes Balears via Grups Competitius.Peer Reviewe

La información litológica mejora los modelos de distribución de especies de plantas basados en datos de baja resolución espacial

The aim of this study was to assess the improvement of plant species distribution models based on coarse-grained occurrence data when adding lithologic data to climatic models. The distributions of 40 woody plant species from continental Spain were modelled. A logistic regression model with climatic predictors was fitted for each species and compared to a second model with climatic and lithologic predictors. Improvements on model likelihood and prediction accuracy on validation subsamples were assessed, as well as the effect of calcicole–calcifuge habit on model improvemenClimatic models had reasonable mean prediction accuracy, but adding lithologic data improved model likelihood in most cases and increased mean prediction accuracy. Therefore, we recommend utilizing lithologic data for species distribution models based on coarse-grained occurrence data. Our data did not support the hypothesis that calcicole–calcifuge habit may explain model improvement when adding lithologic data to climatic models, but further research is needed.El objetivo de este estudio es evaluar la mejora que supone la incorporación de la litología a modelos climáticos de distribución de especies basados en datos de baja resolución espacial. La zona de estudio es la España peninsular. Se ha ajustado un modelo de regresión logística con variables climáticas para cada una de las 40 especies vegetales consideradas y se ha comparado a un segundo modelo con variables climáticas y litológicas. Se ha evaluado la mejora en la verosimilitud y la capacidad predictiva en submuestras de validación, así como el efecto del grado de preferencia de las especies por suelos calcáreos o silíceos en dicha mejora. Los modelos climáticos ofrecen una capacidad predictiva media razonablemente buena, pero la adición de la litología aumenta la verosimilitud del modelo en la mayoría de los casos y la precisión media de las predicciones aumentan significativamente. Se recomienda utilizar información litológica para los modelos de distribución de especies de plantas basados en datos de baja resolución espacial. Con los datos usados no se puede aceptar la hipótesis de que el grado de preferencia de las especies por suelos calcáreos o silíceos explica las diferencias entre especies en la mejora de los modelos debido a la incorporación de información litológica, pero este aspecto debe ser estudiado con más profundidad en futuras investigaciones

Characterizing the Hyperchaotic Dynamics of a Semiconductor Laser Subject to Optical Feedback Via Permutation Entropy

The time evolution of the output of a semiconductor laser subject to delayed optical feedback can exhibit highdimensional chaotic fluctuations. In this contribution, our aim is to quantify the degree of unpredictability of this hyperchaotic time evolution. To that end, we estimate permutation entropy, a novel information-theory-derived quantifier particularly robust in a noisy environment. The permutation entropy is defined as a functional of a symbolic probability distribution, evaluated using the Bandt-Pompe recipe to assign a probability distribution function to the time series generated by the chaotic system. This measure quantifies the diversity of orderings present in the associated time series. In order to evaluate the performance of this novel quantifier, we compare with the results obtained by using a more standard chaos quantifier, namely the KolmogorovSinai entropy. Here, we present numerical results showing that the permutation entropy, evaluated at specific time-scales involved in the chaotic regime of the semiconductor laser subject to optical feedback, give valuable information about the degree of unpredictability of the chaotic laser dynamics. The influence of additive observational noise on the proposed tool is also investigated.L.Z. and O.A.R. were supported by Consejo Nacional de Investigaciones Cient´ıficas y T´ecnicas (CONICET), Argentina. O.A.R. is PVE fellowship, CAPES, Brazil. Part of this work was funded by MEC (Spain), MICINN (Spain) and FEDER under Projects TEC2009-14101 (DeCoDicA) and FIS2007-60327 (FISICOS), and by the EC Project PHOCUS Grant 240763.Peer reviewe

Experimental Phase-Space Tomography of Semiconductor Laser Dynamics

© 2015 American Physical Society. We perform phase-space tomography of semiconductor laser dynamics by simultaneous experimental determination of optical intensity, frequency, and population inversion with high temporal resolution. We apply this technique to a laser with delayed feedback, serving as prominent example for high-dimensional chaotic dynamics and as model system for fundamental investigations of complex systems. Our approach allows us to explore so far unidentified trajectories in phase space and identify the underlying physical mechanism.This work was supported by Comunitat Autònoma de les Illes Balears via program Grups Competitius, FEDER and MINECO via project TRIPHOP (TEC2012-36335).Peer Reviewe

Chaos-Based Optical Communications: Encryption Versus Nonlinear Filtering

7 pages, 8 figures.Several chaos encoding schemes codify the message in such a way that the mean value of the transmitted signal (carrier with the message) is different for bits “0” and “1”. We present a nonlinear filtering method that is able to detect very small changes in the mean value of a signal and therefore recover this kind of messages if its amplitude is larger than the chaotic fluctuations in the mean over the length of a bit.We also introduce a new codification method in which the mean value of the transmitted signal, over the length of each bit, is preserved and we show how it is able to beat the decryption scheme.This work was supported by MEC (Spain) and Feder under Projects TEC2006-1009/MIC (PhoDECC), TEC-2006-28105-E, and FIS2007-60327 (FISICOS); from EC Project PICASSO Grant IST-2005- 34551. The work of M. C. Soriano was supported by the MEC under a “Juan de la Cierva” contract.Peer reviewe

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 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 presence of noise. Therefore the choice of the observable is determinant for parameter identification.Financial support from the Ministerio de Ciencia e Innovacion (MICINN), Spain, and the Fondo Europeo de Desarrollo Regional under projects FIS2007-60327 [Física Interdisciplinar de Sistemas Complejos (FISICOS)] and TEC2009-14101 [Delay-Coupled Diode Lasers for Photonic Applications (DeCoDicA)] and by the European Commission (EC) Project PHOCUS (FP7-ICT-2009-C- 240763) is acknowledged. R. M. Nguimdo also acknowledges fellowship BES-2007-14627 under the FPI program of MICINN.Peer reviewe

'Anomalous' magnetic fabrics of dikes in the stable single domain/superparamagnetic threshold

'Anomalous' magnetic fabrics in dikes that appear to indicate flowinto thewall confound many workers. Here, we present extensivemagnetic data on five dikes from Tenerife, Canary Islands, and use these to interpret the causes of the anomalous fabrics. Comparison of the anisotropy of magnetic susceptibility (AMS) and anhysteretic magnetization (AARM) results show that, in some cases, the anomalous fabrics are caused by single-domain grains, which produce AMS fabrics perpendicular to the grain elongation, whereas AARM fabrics are parallel. To check this, hysteresis experiments were used to characterize the domain state. These show most are mixtures of pseudo-single-domain or single-domain plus multi-domain particles, but many have wasp-waisted hysteresis loops, likely indicating mixed populations of stable single domain and superparamagnetic grains. First-order reversal curves were used to better characterize this and show mixtures of stable single-domain and superparamagnetic grains dominate the magnetic signal. Magnetic particles at the stable single-domain/superparamagnetic threshold are unstable at timespans relevant to the analytical techniques, so they produce complicated results. This suggests that anomalous AMS fabrics in dikes cannot simply be attributed to elongated stable single-domain particles and that mixtures of the different grain types can produce hybrid fabrics, in which the fabrics are neither perpendicular or parallel to the dike plane, that are difficult to interpret without extensive magnetic analysis

Photonic delay systems as machine learning implementations

Nonlinear photonic delay systems present interesting implementation platforms for machine learning models. They can be extremely fast, offer great degrees of parallelism and potentially consume far less power than digital processors. So far they have been successfully employed for signal processing using the Reservoir Computing paradigm. In this paper we show that their range of applicability can be greatly extended if we use gradient descent with backpropagation through time on a model of the system to optimize the input encoding of such systems. We perform physical experiments that demonstrate that the obtained input encodings work well in reality, and we show that optimized systems perform significantly better than the common Reservoir Computing approach. The results presented here demonstrate that common gradient descent techniques from machine learning may well be applicable on physical neuro-inspired analog computers.P.B., M.H. and J.D. acknowledge support by the interuniversity attraction pole (IAP) Photonics@be of the Belgian Science Policy Office, the ERC NaResCo Starting grant and the European Union Seventh Framework Programme under grant agreement no. 604102 (Human Brain Project). M.C.S. and I.F. acknowledge support by MINECO (Spain), Comunitat Autónoma de les Illes Balears, FEDER, and the European Commission under Projects TEC2012-36335 (TRIPHOP), and Grups Competitius. M.H. and I.F. acknowledge support from the Universitat de les Illes Balears for an Invited Young Researcher Grant.Peer Reviewe

Scalable photonic platform for real-time quantum reservoir computing

Quantum Reservoir Computing (QRC) exploits the information processing capabilities of quantum systems to solve non-trivial temporal tasks, improving over their classical counterparts. Recent progress has shown the potential of QRC exploiting the enlarged Hilbert space, but real-time processing and the achievement of a quantum advantage with efficient use of resources are prominent challenges towards viable experimental realizations. In this work, we propose a photonic platform suitable for real-time QRC based on a physical ensemble of reservoirs in the form of identical optical pulses recirculating through a closed loop. While ideal operation achieves maximum capacities, statistical noise is shown to undermine a quantum advantage. We propose a strategy to overcome this limitation and sustain the QRC performance when the size of the system is scaled up. The platform is conceived for experimental implementations to be viable with current technology