Raul Vicente

Transfer entropy--a model-free measure of effective connectivity for the neurosciences

Understanding causal relationships, or effective connectivity, between parts of the brain is of utmost importance because a large part of the brain’s activity is thought to be internally generated and, hence, quantifying stimulus response relationships alone does not fully describe brain dynamics. Past efforts to determine effective connectivity mostly relied on model based approaches such as Granger causality or dynamic causal modeling. Transfer entropy (TE) is an alternative measure of effective connectivity based on information theory. TE does not require a model of the interaction and is inherently non-linear. We investigated the applicability of TE as a metric in a test for effective connectivity to electrophysiological data based on simulations and magnetoencephalography (MEG) recordings in a simple motor task. In particular, we demonstrate that TE improved the detectability of effective connectivity for non-linear interactions, and for sensor level MEG signals where linear methods are hampered by signal-cross-talk due to volume conduction.

Untangling cross-frequency coupling in neuroscience.

Cross-frequency coupling (CFC) has been proposed to coordinate neural dynamics across spatial and temporal scales. Despite its potential relevance for understanding healthy and pathological brain function, the standard CFC analysis and physiological interpretation come with fundamental problems. For example, apparent CFC can appear because of spectral correlations due to common non-stationarities that may arise in the total absence of interactions between neural frequency components. To provide a road map towards an improved mechanistic understanding of CFC, we organize the available and potential novel statistical/modeling approaches according to their biophysical interpretability. While we do not provide solutions for all the problems described, we provide a list of practical recommendations to avoid common errors and to enhance the interpretability of CFC analysis.

Analysis and characterization of the hyperchaos generated by a semiconductor laser subject to a delayed feedback loop

We characterize the chaotic dynamics of semiconductor lasers subject to either optical or electrooptical feedback modeled by Lang-Kobayashi and Ikeda equations, respectively. This characterization is relevant for secure optical communications based on chaos encryption. In particular, for each system we compute as a function of tunable parameters the Lyapunov spectrum, Kaplan-Yorke dimension and Kolmogorov-Sinai entropy.

Transfer entropy in magnetoencephalographic data: Quantifying information flow in cortical and cerebellar networks

The analysis of cortical and subcortical networks requires the identification of their nodes, and of the topology and dynamics of their interactions. Exploratory tools for the identification of nodes are available, e.g. magnetoencephalography (MEG) in combination with beamformer source analysis. Competing network topologies and interaction models can be investigated using dynamic causal modelling. However, we lack a method for the exploratory investigation of network topologies to choose from the very large number of possible network graphs. Ideally, this method should not require a pre-specified model of the interaction. Transfer entropy--an information theoretic implementation of Wiener-type causality--is a method for the investigation of causal interactions (or information flow) that is independent of a pre-specified interaction model. We analysed MEG data from an auditory short-term memory experiment to assess whether the reconfiguration of networks implied in this task can be detected using transfer entropy. Transfer entropy analysis of MEG source-level signals detected changes in the network between the different task types. These changes prominently involved the left temporal pole and cerebellum--structures that have previously been implied in auditory short-term or working memory. Thus, the analysis of information flow with transfer entropy at the source-level may be used to derive hypotheses for further model-based testing.

TRENTOOL: A Matlab open source toolbox to analyse information flow in time series data with transfer entropy

BackgroundTransfer entropy (TE) is a measure for the detection of directed interactions. Transfer entropy is an information theoretic implementation of Wieners principle of observational causality. It offers an approach to the detection of neuronal interactions that is free of an explicit model of the interactions. Hence, it offers the power to analyze linear and nonlinear interactions alike. This allows for example the comprehensive analysis of directed interactions in neural networks at various levels of description. Here we present the open-source MATLAB toolbox TRENTOOL that allows the user to handle the considerable complexity of this measure and to validate the obtained results using non-parametrical statistical testing. We demonstrate the use of the toolbox and the performance of the algorithm on simulated data with nonlinear (quadratic) coupling and on local field potentials (LFP) recorded from the retina and the optic tectum of the turtle (Pseudemys scripta elegans) where a neuronal one-way connection is likely present.ResultsIn simulated data TE detected information flow in the simulated direction reliably with false positives not exceeding the rates expected under the null hypothesis. In the LFP data we found directed interactions from the retina to the tectum, despite the complicated signal transformations between these stages. No false positive interactions in the reverse directions were detected.ConclusionsTRENTOOL is an implementation of transfer entropy and mutual information analysis that aims to support the user in the application of this information theoretic measure. TRENTOOL is implemented as a MATLAB toolbox and available under an open source license (GPL v3). For the use with neural data TRENTOOL seamlessly integrates with the popular FieldTrip toolbox.

Measuring Information-Transfer Delays

In complex networks such as gene networks, traffic systems or brain circuits it is important to understand how long it takes for the different parts of the network to effectively influence one another. In the brain, for example, axonal delays between brain areas can amount to several tens of milliseconds, adding an intrinsic component to any timing-based processing of information. Inferring neural interaction delays is thus needed to interpret the information transfer revealed by any analysis of directed interactions across brain structures. However, a robust estimation of interaction delays from neural activity faces several challenges if modeling assumptions on interaction mechanisms are wrong or cannot be made. Here, we propose a robust estimator for neuronal interaction delays rooted in an information-theoretic framework, which allows a model-free exploration of interactions. In particular, we extend transfer entropy to account for delayed source-target interactions, while crucially retaining the conditioning on the embedded target state at the immediately previous time step. We prove that this particular extension is indeed guaranteed to identify interaction delays between two coupled systems and is the only relevant option in keeping with Wiener’s principle of causality. We demonstrate the performance of our approach in detecting interaction delays on finite data by numerical simulations of stochastic and deterministic processes, as well as on local field potential recordings. We also show the ability of the extended transfer entropy to detect the presence of multiple delays, as well as feedback loops. While evaluated on neuroscience data, we expect the estimator to be useful in other fields dealing with network dynamics.

Open-versus closed-loop performance of synchronized chaotic external-cavity semiconductor lasers

We numerically study the synchronization or entrainment of two unidirectional coupled single-mode semiconductor lasers in a master-slave configuration. The emitter laser is an external-cavity laser subject to optical feedback that operates in a chaotic regime. The receiver can either operate at a chaotic regime similar to the emitter (closed-loop configuration) or without optical feedback and consequently under continuous-wave conditions when it is uncoupled (open-loop configuration). We compute the degree of synchronization of the two lasers as a function of the emitter-receiver coupling constant, the feedback rate of the receiver, and the detuning. We find that the closed-loop scheme has, in general, a larger region of synchronization when compared with the open loop. We also study the possibility of message encoding and decoding in both open and closed loops and their robustness against parameter mismatch. Finally, we compute the time it takes the system to recover the synchronization or entrainment state when the coupling between the two subsystems is lost. We find that this time is much larger in the closed loop than in the open one.

Simultaneous bidirectional message transmission in a chaos-based communication scheme

We introduce a chaos-based communication scheme allowing for bidirectional exchange of information. Coupling [corrected] two semiconductor lasers through a partially transparent optical mirror, placed in the pathway connecting the lasers [corrected] delay dynamics is induced in both lasers. We numerically demonstrate that this dynamics can be identically synchronized, and moreover, information introduced on both ends of the link can be simultaneously transmitted. This scheme allows one to negotiate a key through a public channel.

Synchronization properties of network motifs : Influence of coupling delay and symmetry

We investigate the effect of coupling delays on the synchronization properties of several network motifs. In particular, we analyze the synchronization patterns of unidirectionally coupled rings, bidirectionally coupled rings, and open chains of Kuramoto oscillators. Our approach includes an analytical and semianalytical study of the existence and stability of different in-phase and out-of-phase periodic solutions, complemented by numerical simulations. The delay is found to act differently on networks possessing different symmetries. While for the unidirectionally coupled ring the coupling delay is mainly observed to induce multistability, its effect on bidirectionally coupled rings is to enhance the most symmetric solution. We also study the influence of feedback and conclude that it also promotes the in-phase solution of the coupled oscillators. We finally discuss the relation between our theoretical results on delay-coupled Kuramoto oscillators and the synchronization properties of networks consisting of real-world delay-coupled oscillators, such as semiconductor laser arrays and neuronal circuits.

Neutralization of Nogo-A Enhances Synaptic Plasticity in the Rodent Motor Cortex and Improves Motor Learning in Vivo

The membrane protein Nogo-A is known as an inhibitor of axonal outgrowth and regeneration in the CNS. However, its physiological functions in the normal adult CNS remain incompletely understood. Here, we investigated the role of Nogo-A in cortical synaptic plasticity and motor learning in the uninjured adult rodent motor cortex. Nogo-A and its receptor NgR1 are present at cortical synapses. Acute treatment of slices with function-blocking antibodies (Abs) against Nogo-A or against NgR1 increased long-term potentiation (LTP) induced by stimulation of layer 2/3 horizontal fibers. Furthermore, anti-Nogo-A Ab treatment increased LTP saturation levels, whereas long-term depression remained unchanged, thus leading to an enlarged synaptic modification range. In vivo, intrathecal application of Nogo-A-blocking Abs resulted in a higher dendritic spine density at cortical pyramidal neurons due to an increase in spine formation as revealed by in vivo two-photon microscopy. To investigate whether these changes in synaptic plasticity correlate with motor learning, we trained rats to learn a skilled forelimb-reaching task while receiving anti-Nogo-A Abs. Learning of this cortically controlled precision movement was improved upon anti-Nogo-A Ab treatment. Our results identify Nogo-A as an influential molecular modulator of synaptic plasticity and as a regulator for learning of skilled movements in the motor cortex.