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. Despite intensive research, the early identification of an approaching critical point from observations is still an open challenge. Many data analysis techniques have been proposed, but their performance depends on the system and on the characteristics of the observed data (the resolution, the level of noise, the existence of unobserved variables, etc.). Here, we propose an entropy-based approach to identify an upcoming transition in spatiotemporal data. We apply this approach to observational vegetation data and simulations from two models of vegetation dynamics to infer the arrival of an abrupt shift to an arid state. We show that the permutation entropy (PE) computed from the probabilities of two-dimensional ordinal patterns may provide an early warning indicator of an approaching tipping point, as it may display a maximum (or minimum) before decreasing (or increasing) as the transition approaches. Like other spatial early warning indicators, the spatial permutation entropy does not need a time series of the system dynamics, and it is suited for spatially extended systems evolving on long time scales, like vegetation plots. We quantify its performance and show that, depending on the system and data, the performance can be better, similar or worse than the spatial correlation. Hence, we propose the spatial PE as an additional indicator to try to anticipate regime shifts in vegetated ecosystems.Peer ReviewedPostprint (published version

Correlation lags give early warning signals of approaching bifurcations

Identifying approaching bifurcations and regime transitions from observations is an important challenge in time series analysis with practical applications in many fields of science. Well-known indicators are the increase in spatial and temporal correlations. However, the performance of these indicators depends on the system under study and on the type of approaching bifurcation, and no indicator provides a reliable warning for any system and bifurcation. Here we propose an indicator that simultaneously takes into account information about spatial and temporal correlations. By performing a bivariate correlation analysis of signals recorded in pairs of adjacent spatial points, and analyzing the distribution of lag times that maximize the cross-correlation, we find that the variance of the lag distribution displays an extreme value that is a consistent early warning indicator of the approaching bifurcation. We demonstrate the reliability of this indicator using different types of models that present different types of bifurcations, including local bifurcations (transcritical, saddle-node, supercritical and subcritical Hopf), and global bifurcations.This work was funded by the Spanish Ministerio de Ciencia, Innovación y Universidades (PGC2018-099443-B-I00 ) and the ICREA ACADEMIA program of Generalitat de Catalunya.Peer ReviewedPostprint (published version

A study of the air-sea interaction in the South Atlantic Convergence Zone through Granger causality

Air-sea interaction in the region of the South Atlantic Convergence Zone (SACZ) is studied using Granger causality (GC) as a measure of directional coupling. Calculation of the area weighted connectivity indicates that the SACZ region is the one with largest mutual air-sea connectivity in the south Atlantic basin during summertime. Focusing on the leading mode of daily coupled variability, GC allows distinguishing four regimes characterized by different coupling: there are years in which the forcing is mainly directed from the atmosphere to the ocean, years in which the ocean forces the atmosphere, years in which the influence is mutual and years in which the coupling is not significant. A composite analysis shows that ocean-driven events have atmospheric anomalies that develop first and are strongest over the ocean, while in events without coupling anomalies develop from the continent where they are strongest and have smaller oceanic extension.Peer ReviewedPostprint (author's final draft

Binary image classification using collective optical modes of an array of nanolasers

Recent advancements in nanolaser design and manufacturing open up unprecedented perspectives in terms of high integration densities and ultra-low power consumption, making these devices ideal for high-performance optical computing systems. In this work, we exploit the symmetry properties of the collective modes of a nanolaser array for a simple binary classification task of small digit images. The implementation is based on a 8 × 8 nanolaser array and relies on the activation of a collective optical mode of the array—the so-called “zero-mode”—under spatially modulated pump patterns.This work was supported by a public grant overseen by the French National Research Agency (ANR) as part of the “Investissements d’Avenir” program (Labex NanoSaclay, Reference No. ANR-10-LABX-0035) and by Grant No. ANR UNIQ DS078. G.T. and C.M. are supported, in part, by Ministerio de Ciencia, Innovación y Universidades (Grant No. PID2021-123994NA-C22); C.M. also acknowledges funding from Institució Catalana de Recerca i Estudis Avançats (Academia). K.J. acknowledges support from the China Scholarship Council (Grant No. 202006970015).Peer ReviewedPostprint (published version

Assessing causal dependencies in climatic indices

We evaluate causal dependencies between thirteen indices that represent large-scale climate patterns (El Nino/Southern Oscillation, the North Atlantic Oscillation, the Pacifc Decadal Oscillation, etc.) using a recently proposed approach based on a linear approximation of the transfer entropy. We demonstrate that this methodology identifes causal relations that are well-known, as well as it uncovers some relations which, to the best of our knowledge, have not yet been reported in the literature. We also identify signifcant changes in causal dependencies that have occurred in the last three decades.Open Access funding provided thanks to the CRUECSIC agreement with Springer Nature. This work received funding from the European Union’s Horizon 2020 research and innovation program under Grant Agreement No 813844. C.M. also acknowledges funding by the ICREA ACADEMIA program of Generalitat de Catalunya and Ministerio de Ciencia e Innovacion, Spain, project PID2021-123994NB-C21.Peer ReviewedPostprint (published version

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. We show that the connectivity can be inferred by considering only the observed dynamics of a single variable of the three that define the phase space of each oscillator. We also show that both the coupling strength and the network architecture can be inferred even when the oscillators are close to synchronization. Simulation results are provided to show the effectiveness and applicability of the proposed method.This work was supported in part by Spanish Ministerio de Ciencia, Innovación y Universidades (PGC2018- 099443-B-I00), AGAUR FI scholarship (E.F.) and ICREA ACADEMIA (C. M.), Generalitat de Catalunya.Peer ReviewedPostprint (published version

Inferring directed climatic interactions with renormalized partial directed coherence and directed partial correlation

ACKNOWLEDGMENTS This work was supported in part by Spanish MINECO/FEDER (FIS2015-66503-C3-2-P) and ITN LINC (FP7 289447). C.M. also acknowledges partial support from ICREA ACADEMIAPeer reviewedPublisher PD

Inferring the connectivity of coupled oscillators from time-series statistical similarity analysis

A system composed by interacting dynamical elements can be represented by a network, where the nodes represent the elements that constitute the system, and the links account for their interactions, which arise due to a variety of mechanisms, and which are often unknown. A popular method for inferring the system connectivity (i.e., the set of links among pairs of nodes) is by performing a statistical similarity analysis of the time-series collected from the dynamics of the nodes. Here, by considering two systems of coupled oscillators (Kuramoto phase oscillators and Rossler chaotic electronic oscillators) with known and controllable coupling conditions, we aim at testing the performance of this inference method, by using linear and non linear statistical similarity measures. We find that, under adequate conditions, the network links can be perfectly inferred, i.e., no mistakes are made regarding the presence or absence of links. These conditions for perfect inference require: i) an appropriated choice of the observed variable to be analysed, ii) an appropriated interaction strength, and iii) an adequate thresholding of the similarity matrix. For the dynamical units considered here we find that the linear statistical similarity measure performs, in general, better than the non-linear ones.Peer ReviewedPostprint (published version

Self-collimated axial jets seeds from thin accretion disks

We show how an appropriate stationary crystalline structure of the magnetic field can induce a partial fragmentation of the accretion disk, generating an axial jet seed composed of hot plasma twisted in a funnel-like structure due to the rotation of the system. The most important feature we outline is the high degree of collimation, naturally following from the basic assumptions underlying the crystalline structure. The presence of non-zero dissipative effects allows the plasma ejection throughout the axial jet seed and the predicted values of the accretion rate are in agreement with observations.Comment: 8 pages, 7 figure

Disentangling climatic interactions and detecting tipping points by means of complex networks

En una situación de grandes cambios climáticos, el conocimiento de el sistema Tierra ha devenido, en los últimos años, una de las tareas mas importantes para la comunidad científica. En los últimos diez años, el incremento de la potencia de cálculo de los superordenadores, así como un mejor entendimiento de los procesos físicos subyacentes la dinámica de la Tierra (como por ejemplo la formación de nubes o el intercambio de humedad entre el suelo y el atmósfera) han mejorado grandemente la cualidad de los modelos climáticos. Además, un incremento en la cobertura satelital, ha consentido la generación de bases de datos muy detalladas, llamadas "reanalysis data", que dan el estado de las variables mas importantes por la dinámica de la Tierra con una alta resolución espaciotemporal por lo menos en los últimos 40 años. La grande cantidad da datos ha sido utilizada por la comunidad científica de los climatólogos para investigar la naturaleza de los procesos de el sistema Tierra. El incremento de esas base de datos motiva el desarrollo de un nuevo análisis. En particular, dado que en primera aproximación el comportamiento climatológico de la atmósfera puede ser descrito por modelos lineales relativamente simples, el análisis no lineal ha sido muy subestimado hasta ahora. De todas maneras, muchos procesos climáticos de hecho tienen una fuerte componente no lineal. Un ejemplo emblemático es El Niño Southern Oscillation, un sistema donde el emparejamiento entre el océano y la atmósfera puede ser representado en primera aproximación como un oscilador con retroalimentación retrasada. Otro fenómeno de el sistema climático en lo cual las no linealidades juegan un papel es, sin duda alguna, la corriente a en chorro barotrópica, que está mantenida por los esfuerzos no lineales producidos por sus mismos "eddies" (remolinos). De esta forma, se establece un sistema de retroalimentaciones positivas y negativas, influenciando la variabilidad sinóptica a las altas latitudes. Dado esto, es muy importante estudiar estos fenómenos con herramientas propia de la teoría de los sistemas complejos. En particular, en esta tesis, presentaremos nuevas técnicas de análisis de datos basadas en la teoría de la información y en las redes complejas, que toman en cuenta las características no lineales de los procesos climáticos en análisis, y además aportan un nuevo punto de vista en el campo de la análisis de datos climatológicos. Las redes complejas aparecieron en los últimos años como una técnica potente para investigar una grande variedad de fenómenos donde sea posible identificar un cierto numero de componentes entre las cuales se puede establecer una relación. Siendo esto un concepto muy genérico, no es sorprendente que haya sido aplicado con éxito en muchos campos distintos, como la sociología, la biología, etcétera En particular, en esta tesis, nos enfocaremos en la construcción le redes climáticas, o sea redes donde los nodos describen áreas de la Tierra y los enlaces están dados por las relaciones entre ellas. Consideraremos enlaces computados a partir de las similitudes estadísticas de las dinámicas de una variable climatológica (como la temperatura de el aire a la superficie) en cada uno de los nodos. Este es una técnica muy general que, dependiendo de la definición de similitud estadística utilizada, permite de investigar distintas características de las variables en análisis. Definiremos la similitud estadística utilizando conceptos propios de la teoría de la información.In a scenario of major global climatic changes, the understanding of the Earth system has become in recent years an impelling task of the scientific community. In the last decade, an increased performance of supercomputers as well as a better understanding of the physical processes underlying Earth dynamics (such as cloud formation, moist exchange between soil and atmosphere, and so on) improved dramatically the quality of climate models. Moreover, an increasing satellite coverage allowed the generation of very detailed databases, called reanalysis data, that give with good precision the state of the most important dynamical variables at high spatio-temporal resolution for at least the past 40 years. This huge amount of data is being used by the climatological scientific community to investigate the nature of the ongoing physical processes in the Earth system. The increasing of such datasets motivates the development of new analysis. In particular, since in first approximation the climatological behaviour of the atmosphere can be described by relatively simply linear models, the non-linear data analysis has been largely overlooked so far. However, many relevant climatic processes have a strong non-linear component. A paradigmatic example is the so-called El Niño-Southern Oscillation, a coupled ocean-atmosphere process that can be sketched in first approximation as a non-linear oscillator with delayed feedback. Another phenomenon of the Earth system in which the non-linearities play a major role is doubtlessly the barotropic polar jet, that is maintained by the non-linear stress produced by its own eddies. In this way a complex system of positive and negative feedbacks is established, influencing the dynamics of the major actor in the synoptical variability in the high latitudes. Given these considerations, it is important to study such phenomena with tools coming from the field of complex systems. In particular, in this thesis we present new data analysis techniques based on information theory and complex networks that take into account the non-linear nature of the climate processes under examination, as well as give a new perspective to climatological data analysis. Complex networks have emerged in the recent years as a useful and powerful tool to investigate a large variety of phenomena in which it is possible to identify a discrete number of components among which relations can be established. Being this a very general concept, it is not surprising that it found successful application in very different field such as sociology, biology, epidemics, geophysics, and so on. In particular in this thesis we will focus in the construction of what are called climate networks, i. e. networks in which the nodes are composed by geographical locations on Earth and the links are given by relations among them. We will generally consider links computed from the statistical similarity of the dynamics of a climatological variable available at each geographical location, such as the surface air temperature (SAT). This is a quite general approach that, depending on the definition of the statistical similarity employed, allows to investigate different characteristics of the variable under examination. We will define the statistical similarity using concepts that are adopted from information theory.Postprint (published version