Statistical Complexity and Nontrivial Collective Behavior in Electroencephalografic Signals

We calculate a measure of statistical complexity from the global dynamics of electroencephalographic (EEG) signals from healthy subjects and epileptic patients, and are able to stablish a criterion to characterize the collective behavior in both groups of individuals. It is found that the collective dynamics of EEG signals possess relative higher values of complexity for healthy subjects in comparison to that for epileptic patients. To interpret these results, we propose a model of a network of coupled chaotic maps where we calculate the complexity as a function of a parameter and relate this measure with the emergence of nontrivial collective behavior in the system. Our results show that the presence of nontrivial collective behavior is associated to high values of complexity; thus suggesting that similar dynamical collective process may take place in the human brain. Our findings also suggest that epilepsy is a degenerative illness related to the loss of complexity in the brain.Comment: 13 pages, 3 figure

Minimal approach to neuro-inspired information processing

© 2015 Soriano, Brunner, Escalona-Morán, Mirasso and Fischer. To learn and mimic how the brain processes information has been a major research challenge for decades. Despite the efforts, little is known on how we encode, maintain and retrieve information. One of the hypothesis assumes that transient states are generated in our intricate network of neurons when the brain is stimulated by a sensory input. Based on this idea, powerful computational schemes have been developed. These schemes, known as machine-learning techniques, include artificial neural networks, support vector machine and reservoir computing, among others. In this paper, we concentrate on the reservoir computing (RC) technique using delay-coupled systems. Unlike traditional RC, where the information is processed in large recurrent networks of interconnected artificial neurons, we choose a minimal design, implemented via a simple nonlinear dynamical system subject to a self-feedback loop with delay. This design is not intended to represent an actual brain circuit, but aims at finding the minimum ingredients that allow developing an efficient information processor. This simple scheme not only allows us to address fundamental questions but also permits simple hardware implementations. By reducing the neuro-inspired reservoir computing approach to its bare essentials, we find that nonlinear transient responses of the simple dynamical system enable the processing of information with excellent performance and at unprecedented speed. We specifically explore different hardware implementations and, by that, we learn about the role of nonlinearity, noise, system responses, connectivity structure, and the quality of projection onto the required high-dimensional state space. Besides the relevance for the understanding of basic mechanisms, this scheme opens direct technological opportunities that could not be addressed with previous approaches.The authors acknowledge support by MINECO (Spain) under Projects TEC2012-36335 (TRIPHOP) and FIS2012-30634 (Intense@cosyp), FEDER and Govern de les Illes Balears via the program Grups Competitius. The work of MS was supported by the Conselleria d'Educació, Cultura i Universitats del Govern de les Illes Balears and the European Social Fund.Peer Reviewe

Computational Properties of Delay-Coupled Systems

Tesis Doctoral presentada por Miguel Angel Escalona Morán para optar al título de Doctor, en el Programa de Física del Departamento de Física de la Universitat de les Illes Balears, realizada en el IFISC bajo la dirección de Claudio Mirasso, catedrático de universidad y Miguel Cornelles Soriano, contratado postdoctoral CAIB.In this research work we study the computational properties of delay-coupled systems. In particular, we use a machine learning technique known as reservoir computing. In machine learning, a computer learns to solve different tasks using examples and without knowing explicitly their solution. For the study of the computational properties, a numerical toolbox, written in Python, was developed. This toolbox allows a fast implementation of the different scenarios described in this thesis. Using a reservoir computer, we studied several computational properties, focusing on its kernel quality, its ability to separate different input samples and the intrinsic memory capacity. This intrinsic memory is related to the delayed- feedback of the reservoir. We used a delay-coupled system as reservoir to study its computational ability in three different kinds of tasks: system’s modeling, time-series prediction and classification tasks. The system’s modeling task was performed using the Nonlinear Autoregressive Moving Average (of ten steps), NARMA10. The NARMA10 model creates autoregressive time series from a set of normally distributed random sequences. The reservoir computer learns how to emulate the system using only the sequence of random numbers and the autoregressive time series, but without knowing the equations of the NARMA10. The results of our approach are equivalent to those published by other authors and show the computational power of our method. For the time-series prediction tasks, we used three kinds of time series: a model that gives the variations in temperature of the sea surface that provoke El Niño phenomenon, the Lorenz system and the dynamics of a chaotic laser. Different scenarios were explored depending on the nature of the time series. For the prediction of the variation in temperature of the sea surface, we perform estimations of one, three and six months in advance. The error was measured as the Normalized Root Mean Square Error (NRMSE). For the different prediction horizons, we obtained errors of 2%, 8% and 24%, respectively. The classification tasks were carried out for a Spoken Digit Recognition (SDR) task and a real-world biomedical task. The SDR was used to illustrate different scenarios of a machine learning problem. The biomedical task consists on the automatic classification of heartbeats with cardiac arrhythmias. We use the MIT-BIH Arrhythmia database, a widely used database in cardiology. For comparison purposes, we followed the guidelines of the Association for the Advancement of Medical Instrumentation for the evaluation of arrhythmia-detector algorithms. We used a biostatistical learning process named logistic regression that allowed to compute the probability that a heartbeat belongs to a particular class.This is in contrast to the commonly used linear regression. The results obtained in this work show the versatility and efficiency of our implemented reservoir computer. Our results are equivalent and show improvement over other reported results on this problem under similar conditions and using the same database. To enhance the computational ability of our delay-coupled system, we included a multivariate scheme that allows the consideration of different variables of a system. We evaluated the influence of this multivariate scenario using a time- series prediction and the classification of heartbeat tasks. The results show improvement in the performance of the reservoir computer in comparison with the same tasks in the univariate case.Peer reviewe

Information Processing Using Transient Dynamics of Semiconductor Lasers Subject to Delayed Feedback

The increasing amount of data being generated in different areas of science and technology require novel and efficient techniques of processing, going beyond traditional concepts. In this paper, we numerically study the information processing capabilities of semiconductor lasers subject to delayed optical feedback. Based on the recent concept of reservoir computing, we show that certain tasks, which are inherently hard for traditional computers, can be efficiently tackled by such systems. Major advantages of this approach comprise the possibility of simple and low-cost hardware implementation of the reservoir and ultrafast processing speed. Experimental results corroborate the numerical predictions. © 1995-2012 IEEE.Peer Reviewe

Electrocardiogram Classification Using Reservoir Computing With Logistic Regression

An adapted state-of-the-art method of processing information known as Reservoir Computing is used to show its utility on the open and time-consuming problem of heartbeat classification. The MIT-BIH arrhythmia database is used following the guidelines of the Association for the Advancement of Medical Instrumentation. Our approach requires a computationally inexpensive preprocessing of the electrocardiographic signal leading to a fast algorithm and approaching a real-time classification solution. Our multiclass classification results indicate an average specificity of 97.75% with an average accuracy of 98.43%. Sensitivity and positive predicted value show an average of 84.83% and 88.75%, respectively, what makes our approach significant for its use in a clinical context.This work was supported by the grant FIS2012-30634 (Intense@cosyp) from MINECO (Spain) and FEDER and Grups Competitius, Comunitat Autonoma de les Illes Balears, Spain.Peer Reviewe

Multivariate nonlinear time-series estimation using delay-based reservoir computing

Multivariate nonlinear time-series analysis represents a major challenge in complex systems science, specially when the full underlying dynamics is unknown. Often, time-series forecast relies on the information contained in a single measured variable. However, in many cases one might benefit from other available measures of the system to improve the prediction of its dynamical evolution. Here, we utilize Reservoir Computing techniques to process sequential multivariate information. As reservoir, we employ a Mackey-Glass delay system. We discuss the approximation of a three-dimensional theoretical model (the Lorenz model) by comparing prediction performance for one variable using either one or two variables as input. Finally, we apply these insights to improve the performance of a relevant biomedical task, namely multi-electrode heartbeat classification

Multivariate nonlinear time-series estimation using delay-based reservoir computing

Multivariate nonlinear time-series analysis represents a major challenge in complex systems science, specially when the full underlying dynamics is unknown. Often, time-series forecast relies on the information contained in a single measured variable. However, in many cases one might benefit from other available measures of the system to improve the prediction of its dynamical evolution. Here, we utilize Reservoir Computing techniques to process sequential multivariate information. As reservoir, we employ a Mackey-Glass delay system. We discuss the approximation of a three-dimensional theoretical model (the Lorenz model) by comparing prediction performance for one variable using either one or two variables as input. Finally, we apply these insights to improve the performance of a relevant biomedical task, namely multi-electrode heartbeat classification. © 2014, EDP Sciences and Springer.Peer Reviewe

Digital Implementation of a Single Dynamical Node Reservoir Computer

© 2015 IEEE. Minimal hardware implementations of machine-learning techniques have been attracting increasing interest over the last decades. In particular, field-programmable gate array (FPGA) implementations of neural networks (NNs) are among the most appealing ones, given the match between system requirements and FPGA properties, namely, parallelism and adaptation. Here, we present an FPGA implementation of a conceptually simplified version of a recurrent NN based on a single dynamical node subject to delayed feedback. We show that this configuration is capable of successfully performing simple real-time temporal pattern classification and chaotic time-series prediction.This work was supported in part by the Spanish Ministry of Economy and Competitiveness (MINECO), the Regional European Development Funds (FEDER), and the Comunitat Autònoma de les Illes Balears under Grant contracts TEC2011-23113, TEC2012-36335, and TEC2014-56244-R, Grups Competitius and a fellowship (FPI/1513/2012) financed by thThis brief was recommended by Associate Editor G. Masera.Peer Reviewe