Isolated effective coherence (iCoh): causal information flow excluding indirect paths

A problem of great interest in real world systems, where multiple time series measurements are available, is the estimation of the intra-system causal relations. For instance, electric cortical signals are used for studying functional connectivity between brain areas, their directionality, the direct or indirect nature of the connections, and the spectral characteristics (e.g. which oscillations are preferentially transmitted). The earliest spectral measure of causality was Akaike's (1968) seminal work on the noise contribution ratio, reflecting direct and indirect connections. Later, a major breakthrough was the partial directed coherence of Baccala and Sameshima (2001) for direct connections. The simple aim of this study consists of two parts: (1) To expose a major problem with the partial directed coherence, where it is shown that it is affected by irrelevant connections to such an extent that it can misrepresent the frequency response, thus defeating the main purpose for which the measure was developed, and (2) To provide a solution to this problem, namely the "isolated effective coherence", which consists of estimating the partial coherence under a multivariate auto-regressive model, followed by setting all irrelevant associations to zero, other than the particular directional association of interest. Simple, realistic, toy examples illustrate the severity of the problem with the partial directed coherence, and the solution achieved by the isolated effective coherence. For the sake of reproducible research, the software code implementing the methods discussed here (using lazarus free-pascal "www.lazarus.freepascal.org"), including the test data as text files, are freely available at: https://sites.google.com/site/pascualmarqui/home/icoh-isolated-effective-coherenceComment: 2014-02-21 pre-print, technical report, KEY Institute for Brain-Mind Research, University of Zurich, et a

On the Similarity of Functional Connectivity between Neurons Estimated across Timescales

A central objective in neuroscience is to understand how neurons interact. Such functional interactions have been estimated using signals recorded with different techniques and, consequently, different temporal resolutions. For example, spike data often have sub-millisecond resolution while some imaging techniques may have a resolution of many seconds. Here we use multi-electrode spike recordings to ask how similar functional connectivity inferred from slower timescale signals is to the one inferred from fast timescale signals. We find that functional connectivity is relatively robust to low-pass filtering—dropping by about 10% when low pass filtering at 10 hz and about 50% when low pass filtering down to about 1 Hz—and that estimates are robust to high levels of additive noise. Moreover, there is a weak correlation for physiological filters such as hemodynamic or Ca2+ impulse responses and filters based on local field potentials. We address the origin of these correlations using simulation techniques and find evidence that the similarity between functional connectivity estimated across timescales is due to processes that do not depend on fast pair-wise interactions alone. Rather, it appears that connectivity on multiple timescales or common-input related to stimuli or movement drives the observed correlations. Despite this qualification, our results suggest that techniques with intermediate temporal resolution may yield good estimates of the functional connections between individual neurons

Dynamical complexity in the C.elegans neural network

We model the neuronal circuit of the C.elegans soil worm in terms of a Hindmarsh-Rose system of ordinary differential equa- tions, dividing its circuit into six communities which are determined via the Walktrap and Louvain methods. Using the numerical solution of these equations, we analyze important measures of dynamical com- plexity, namely synchronicity, the largest Lyapunov exponent, and the ?AR auto-regressive integrated information theory measure. We show that ?AR provides a useful measure of the information contained in the C.elegans brain dynamic network. Our analysis reveals that the C.elegans brain dynamic network generates more information than the sum of its constituent parts, and that attains higher levels of integrated information for couplings for which either all its communities are highly synchronized, or there is a mixed state of highly synchronized and de- synchronized communities

Forecasting inflation with thick models and neural networks

This paper applies linear and neural network-based “thick” models for forecasting inflation based on Phillips–curve formulations in the USA, Japan and the euro area. Thick models represent “trimmed mean” forecasts from several neural network models. They outperform the best performing linear models for “real-time” and “bootstrap” forecasts for service indices for the euro area, and do well, sometimes better, for the more general consumer and producer price indices across a variety of countries. JEL Classification: C12, E31bootstrap, Neural Networks, Phillips Curves, real-time forecasting, Thick Models

Asymptotically stable phase synchronization revealed by autoregressive circle maps

A new type of nonlinear time series analysis is introduced, based on phases, which are defined as polar angles in spaces spanned by a finite number of delayed coordinates. A canonical choice of the polar axis and a related implicit estimation scheme for the potentially underlying auto-regressive circle map (next phase map) guarantee the invertibility of reconstructed phase space trajectories to the original coordinates. The resulting Fourier approximated, Invertibility enforcing Phase Space map (FIPS map) is well suited to detect conditional asymptotic stability of coupled phases. This rather general synchronization criterion unites two existing generalisations of the old concept and can successfully be applied e.g. to phases obtained from ECG and airflow recordings characterizing cardio-respiratory interaction.Comment: PDF file, 232 KB, 24 pages, 3 figures; cheduled for Phys. Rev. E (Nov) 200

Étude de la propagation acoustique en milieu complexe par des réseaux de neurones profonds

Abstract : Predicting the propagation of aerocoustic noise is a challenging task in the presence of complex mean flows and geometry installation effects. The design of future quiet propul- sion systems requires tools that are able to perform many accurate evaluations with a low computational cost. Analytical models or hybrid numerical approaches have tradition- ally been employed for that purpose. However, such methods are typically constrained by simplifying hypotheses that are not easily relaxed. Thus, the main objective of this thesis is to develop and validate novel methods for the fast and accurate prediction of aeroacoustic propagation in complex mean flows and geometries. For that, data-driven deep convolutional neural networks acting as auto-regressive spatio-temporal predictors are considered. These surrogates are trained on high-fidelity data, generated by direct aeroacoustic numerical solvers. Such datasets are able to model complex flow phenomena, along with complex geometrical parameters. The neural network is designed to substitute the high-fidelity solver at a much lower computational cost once the training is finished, while predicting the time-domain acoustic propagation with sufficient accuracy. Three test cases of growing complexity are employed to test the approach, where the learned surrogate is compared to analytical and numerical solutions. The first one corresponds to the two-dimensional propagation of Gaussian pulses in closed domains, which allows understanding the fundamental behavior of the employed convolution neural networks. Second, the approach is extended in order to consider a variety of boundary conditions, from non-reflecting to curved reflecting obstacles, including the reflection and scattering of waves at obstacles. This allows the prediction of acoustic propagation in configurations closer to industrial problems. Finally, the effects of complex mean flows is investigated through a dataset of acoustic waves propagating inside sheared flows. These applications highlight the flexibility of the employed data-driven methods using convolutional neural networks. They allow a significant acceleration of the acoustic predictions, while keeping an adequate accuracy and being also able to correctly predict the acoustic propagation outside the range of the training data. For that, prior knowledge about the wave propa- gation physics is included during and after the neural network training phase, allowing an increased control over the error performed by the surrogate. Among this prior knowledge, the conservation of physics quantities and the correct treatment of boundary conditions are identified as key parameters that improve the surrogate predictions.Prédire la propagation du bruit aéroacoustique est une tâche difficile en présence d’écoulements moyens complexes et d’effets géométriques d’installation. La conception des futurs systèmes de propulsion silencieux appelle au développement d’outils capables d’effectuer de nombreuses évaluations avec une faible erreur et un faible coût de calcul. Traditionnellement, des modèles analytiques ou des approches numériques hybrides ont été utilisés à cette fin. Cependant, ces méthodes sont généralement contraintes par des hypothèses simplificatrices qui ne sont pas facilement assouplies. Ainsi, l’objectif principal de cette thèse est de développer et de valider de nouvelles méthodes pour la prédiction rapide et précise de la propagation aéroacoustique dans des écoulements moyens et des géométries complexes. Pour cela, des réseaux de neurones profonds à convolution, entraînés sur des données, et agissant comme prédicteurs spatio-temporels sont considérés. Ces modèles par substitution sont entraînés sur des données de haute fidélité, générées par des solveurs numériques aérocoustiques directs. De telles bases de données sont capables de modéliser des phénomènes d’écoulement, ainsi que des paramètres géométriques complexes. Le réseau de neurones est conçu pour remplacer le solveur haute fidélité à un coût de calcul beaucoup plus faible une fois la phase d’entraînement terminée, tout en prédisant la propagation acoustique dans le domaine temporel avec une précision suffisante. Trois cas de test, de complexité croissante, sont utilisés pour tester l’approche, où le substitut appris est comparé à des solutions analytiques et numériques. Le premier cas correspond à la propagation acoustique bidimensionnelle dans des domaines fermés, où des sources impulsionnelles Gaussiennes sont considérées. Ceci permet de comprendre le comportement fondamental des réseaux de neurones à convolution étudiés. Deuxièmement, l’approche est étendue afin de prendre en compte une variété de conditions aux limites, notamment des conditions aux limites non réfléchissantes et des obstacles réfléchissants de géométrie arbitraire, modélisant la réflexion et la diffusion des ondes acoustiques sur ces obstacles. Cela permet de prédire la propagation acoustique dans des configurations plus proches des problématiques industrielles. Enfin, les effets des écoulements moyens complexes sont étudiés à travers une base de données d’ondes acoustiques qui se propagent à l’intérieur d’écoulements cisaillés. Ces applications mettent en évidence la flexibilité des méthodes basées sur les données, utilisant des réseaux de neurones à convolution. Ils permettent une accélération significative des prédictions acoustiques, tout en gardant une précision adéquate et en étant également capables de prédire correctement la propagation acoustique en dehors de la gamme de paramètres des données d’apprentissage. Pour cela, des connaissances préalables sur la physique de propagation des ondes sont incluses pendant et après la phase d’apprentissage du réseau de neurones, permettant un contrôle accru sur l’erreur effectuée par le substitut. Parmi ces connaissances préalables, la conservation des grandeurs physiques et le traitement correct des conditions aux limites sont identifiés comme des paramètres clés qui améliorent les prédictions du modèle proposé

Optoelectronic Reservoir Computing

Reservoir computing is a recently introduced, highly efficient bio-inspired approach for processing time dependent data. The basic scheme of reservoir computing consists of a non linear recurrent dynamical system coupled to a single input layer and a single output layer. Within these constraints many implementations are possible. Here we report an opto-electronic implementation of reservoir computing based on a recently proposed architecture consisting of a single non linear node and a delay line. Our implementation is sufficiently fast for real time information processing. We illustrate its performance on tasks of practical importance such as nonlinear channel equalization and speech recognition, and obtain results comparable to state of the art digital implementations.Comment: Contains main paper and two Supplementary Material