On a comparative study between dependence scales determined by linear and non-linear measures

In this manuscript we present a comparative study about the determination of the relaxation (\textit{i.e.}, independence) time scales obtained from the correlation function, the mutual information, and a criterion based on the evaluation of a nonextensive generalisation of mutual entropy. Our results show that, for systems with a small degree of complexity, standard mutual information and the criterion based on its nonextensive generalisation provide the same scale, whereas for systems with a higher complex dynamics the standard mutual information presents a time scale consistently smaller.Comment: 14 pages. To appear in Physica

Abrupt Convergence and Escape Behavior for Birth and Death Chains

We link two phenomena concerning the asymptotical behavior of stochastic processes: (i) abrupt convergence or cut-off phenomenon, and (ii) the escape behavior usually associated to exit from metastability. The former is characterized by convergence at asymptotically deterministic times, while the convergence times for the latter are exponentially distributed. We compare and study both phenomena for discrete-time birth-and-death chains on Z with drift towards zero. In particular, this includes energy-driven evolutions with energy functions in the form of a single well. Under suitable drift hypotheses, we show that there is both an abrupt convergence towards zero and escape behavior in the other direction. Furthermore, as the evolutions are reversible, the law of the final escape trajectory coincides with the time reverse of the law of cut-off paths. Thus, for evolutions defined by one-dimensional energy wells with sufficiently steep walls, cut-off and escape behavior are related by time inversion.Comment: 2 figure

The impact of regional heterogeneity in whole-brain dynamics in the presence of oscillations

Large variability exists across brain regions in health and disease, considering their cellular and molecular composition, connectivity and function. Large-scale whole-brain models comprising coupled brain regions provide insights into the underlying dynamics that shape complex patterns of spontaneous brain activity. In particular, biophysically grounded mean-field whole-brain models in the asynchronous regime were used to demonstrate the dynamical consequences of including regional variability. Nevertheless, the role of heterogeneities when brain dynamics are supporting by synchronous oscillating state, which is a ubiquitous phenomenon in brain, remains poorly understood. Here, we implemented two models capable of presenting oscillatory behaviour with different levels of abstraction: a phenomenological Stuart Landau model and an exact mean-field model. The fit of these models informed by structural-to-functional–weighted MRI signal (T1w/T2w) allowed to explore the implication of the inclusion of heterogeneities for modelling resting-state fMRI recordings from healthy participants. We found that disease-specific regional functional heterogeneity imposed dynamical consequences within the oscillatory regime in fMRI recordings from neurodegeneration with specific impacts in brain atrophy/structure (Alzheimer patients). Overall, we found that models with oscillations perform better when structural and functional regional heterogeneities are considered showing that phenomenological and biophysical models behave similarly at the brink of the Hopf bifurcation.Fil: Sanz Perl Hernandez, Yonatan. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Universidad de San Andrés; Argentina. Universitat Pompeu Fabra; EspañaFil: Zamora Lopez, Gorka. Universitat Pompeu Fabra; EspañaFil: Montbrió, Ernest. Universitat Pompeu Fabra; EspañaFil: Monge Asensio, Martí. Universitat Pompeu Fabra; EspañaFil: Vohryzek, Jakub. Universitat Pompeu Fabra; España. University of Oxford; Reino UnidoFil: Fittipaldi, María Sol. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentina. University of California; Estados Unidos. Trinity College; IrlandaFil: Gonzalez Campo, Cecilia. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; ArgentinaFil: Moguilner, Sebastian Gabriel. University of California; Estados Unidos. Trinity College; Irlanda. Universidad Adolfo Ibañez; ChileFil: Ibañez, Agustin Mariano. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de San Andrés; Argentina. University of California; Estados Unidos. Trinity College; Irlanda. Universidad Adolfo Ibañez; ChileFil: Tagliazucchi, Enzo Rodolfo. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentina. Universidad de Buenos Aires; Argentina. Universidad de San Andrés; Argentina. Universidad Adolfo Ibañez; ChileFil: Yeo, B. T. Thomas. National University of Singapore; SingapurFil: Kringelbach, Morten L.. University of Oxford; Reino Unido. University Aarhus; Dinamarca. Universidade do Minho; PortugalFil: Deco, Gustavo. Universitat Pompeu Fabra; España. Max Planck Institute for Human Cognitive and Brain Sciences; Alemania. Monash University; Australi

Onset of negative interspike interval correlations in adapting neurons

Negative serial correlations in single spike trains are an effective method to reduce the variability of spike counts. One of the factors contributing to the development of negative correlations between successive interspike intervals is the presence of adaptation currents. In this work, based on a hidden Markov model and a proper statistical description of conditional responses, we obtain analytically these correlations in an adequate dynamical neuron model resembling adaptation. We derive the serial correlation coefficients for arbitrary lags, under a small adaptation scenario. In this case, the behavior of correlations is universal and depends on the first-order statistical description of an exponentially driven time-inhomogeneous stochastic process.Comment: 12 pages (10 pages in the journal version), 6 figures, published in Phys. Rev. E; http://link.aps.org/doi/10.1103/PhysRevE.84.04190

A toolbox for the fast information analysis of multiple-site LFP, EEG and spike train recordings

<p>Abstract</p> <p>Background</p> <p>Information theory is an increasingly popular framework for studying how the brain encodes sensory information. Despite its widespread use for the analysis of spike trains of single neurons and of small neural populations, its application to the analysis of other types of neurophysiological signals (EEGs, LFPs, BOLD) has remained relatively limited so far. This is due to the limited-sampling bias which affects calculation of information, to the complexity of the techniques to eliminate the bias, and to the lack of publicly available fast routines for the information analysis of multi-dimensional responses.</p> <p>Results</p> <p>Here we introduce a new C- and Matlab-based information theoretic toolbox, specifically developed for neuroscience data. This toolbox implements a novel computationally-optimized algorithm for estimating many of the main information theoretic quantities and bias correction techniques used in neuroscience applications. We illustrate and test the toolbox in several ways. First, we verify that these algorithms provide accurate and unbiased estimates of the information carried by analog brain signals (i.e. LFPs, EEGs, or BOLD) even when using limited amounts of experimental data. This test is important since existing algorithms were so far tested primarily on spike trains. Second, we apply the toolbox to the analysis of EEGs recorded from a subject watching natural movies, and we characterize the electrodes locations, frequencies and signal features carrying the most visual information. Third, we explain how the toolbox can be used to break down the information carried by different features of the neural signal into distinct components reflecting different ways in which correlations between parts of the neural signal contribute to coding. We illustrate this breakdown by analyzing LFPs recorded from primary visual cortex during presentation of naturalistic movies.</p> <p>Conclusion</p> <p>The new toolbox presented here implements fast and data-robust computations of the most relevant quantities used in information theoretic analysis of neural data. The toolbox can be easily used within Matlab, the environment used by most neuroscience laboratories for the acquisition, preprocessing and plotting of neural data. It can therefore significantly enlarge the domain of application of information theory to neuroscience, and lead to new discoveries about the neural code.</p

Community detection for correlation matrices

A challenging problem in the study of complex systems is that of resolving, without prior information, the emergent, mesoscopic organization determined by groups of units whose dynamical activity is more strongly correlated internally than with the rest of the system. The existing techniques to filter correlations are not explicitly oriented towards identifying such modules and can suffer from an unavoidable information loss. A promising alternative is that of employing community detection techniques developed in network theory. Unfortunately, this approach has focused predominantly on replacing network data with correlation matrices, a procedure that tends to be intrinsically biased due to its inconsistency with the null hypotheses underlying the existing algorithms. Here we introduce, via a consistent redefinition of null models based on random matrix theory, the appropriate correlation-based counterparts of the most popular community detection techniques. Our methods can filter out both unit-specific noise and system-wide dependencies, and the resulting communities are internally correlated and mutually anti-correlated. We also implement multiresolution and multifrequency approaches revealing hierarchically nested sub-communities with `hard' cores and `soft' peripheries. We apply our techniques to several financial time series and identify mesoscopic groups of stocks which are irreducible to a standard, sectorial taxonomy, detect `soft stocks' that alternate between communities, and discuss implications for portfolio optimization and risk management.Comment: Final version, accepted for publication on PR