References of "Sepulchre, Rodolphe"
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See detailA spectral characterization of nonlinear normal modes
Cirillo, G. I.; Mauroy, A.; Renson, Luc ULiege et al

in Journal of Sound and Vibration (2016), 377

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we ... [more ▼]

This paper explores the relationship that exists between nonlinear normal modes (NNMs) defined as invariant manifolds in phase space and the spectral expansion of the Koopman operator. Specifically, we demonstrate that NNMs correspond to zero level sets of specific eigenfunctions of the Koopman operator. Thanks to this direct connection, a new, global parametrization of the invariant manifolds is established. Unlike the classical parametrization using a pair of state-space variables, this parametrization remains valid whenever the invariant manifold undergoes folding, which extends the computation of NNMs to regimes of greater energy. The proposed ideas are illustrated using a two-degree-of-freedom system with cubic nonlinearity. © 2016 Elsevier Ltd [less ▲]

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See detailCerebral functional connectivity periodically (de)synchronizes with anatomical constraints
Liegeois, Raphaël ULiege; Ziegler, Erik; Bahri, Mohamed Ali ULiege et al

in Brain Structure and Function (2015)

This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber ... [more ▼]

This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber tractography. Instead of a static analysis based on the correlation between SC and the FC averaged over the entire fMRI time series, we propose a dynamic analysis, based on the time evolution of the correlation between SC and a suitably windowed FC. Assessing the statistical significance of the time series against random phase permutations, our data show a pronounced peak of significance for time window widths around 20-30 TR (40-60 sec). Using the appropriate window width, we show that FC patterns oscillate between phases of high modularity, primarily shaped by anatomy, and phases of low modularity, primarily shaped by inter-network connectivity. Building upon recent results in dynamic FC, this emphasizes the potential role of SC as a transitory architecture between different highly connected resting state FC patterns. Finally, we show that networks implied in consciousness-related processes, such as the default mode network (DMN), contribute more to these brain-level fluctuations compared to other networks, such as the motor or somatosensory networks. This suggests that the fluctuations between FC and SC are capturing mind-wandering effects. [less ▲]

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See detailDynamic Input Conductances Shape Neuronal Spiking
Drion, Guillaume ULiege; Franci, Alessio ULiege; Dethier, Julie ULiege et al

in eNeuro (2015)

Assessing the role of biophysical parameter variations in neuronal activity is critical to the understanding of modulation, robustness and homeostasis of neuronal signaling. The paper proposes that this ... [more ▼]

Assessing the role of biophysical parameter variations in neuronal activity is critical to the understanding of modulation, robustness and homeostasis of neuronal signaling. The paper proposes that this question can be addressed through the analysis of dynamic input conductances. Those voltage-dependent curves aggregate the concomitant activity of all ion channels in distinct timescales. They are shown to shape the current-voltage dynamical relationships that determine neuronal spiking. We propose an experimental protocol to measure dynamic input conductances in neurons. In addition, we provide a computational method to extract dynamic input conductances from arbitrary conductance-based models and to analyze their sensitivity to arbitrary parameters. We illustrate the relevance of the proposed approach for modulation, compensation and robustness studies in a published neuron model based on data of the stomatogastric ganglion of the crab Cancer borealis. [less ▲]

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See detailSparse plus low-rank autoregressive identification in neuroimaging time series
Liegeois, Raphaël ULiege; Mishra, Bamdev ULiege; Zorzi, Mattia et al

in Proceedings of CDC 2015 (2015)

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See detailA positive feedback at the cellular level promotes robustness and modulation at the circuit level
Dethier, Julie; Drion, Guillaume ULiege; Franci et al

in Journal of Neurophysiology (2015)

This article highlights the role of a positive feedback gating mechanism at the cellular level in the robustness and modulation properties of rhythmic activities at the circuit level. The results are ... [more ▼]

This article highlights the role of a positive feedback gating mechanism at the cellular level in the robustness and modulation properties of rhythmic activities at the circuit level. The results are presented in the context of half-center oscillators, which are simple rhythmic circuits composed of two reciprocally connected inhibitory neuronal populations. Specifically, we focus on rhythms that rely on a particular excitability property, the postinhibitory rebound, an intrinsic cellular property that elicits tran- sient membrane depolarization when released from hyperpolarization. Two distinct ionic currents can evoke this transient depolarization: a hyperpolarization-activated cation current and a low-threshold T-type calcium current. The presence of a slow activation is specific to the T-type calcium current and provides a slow positive feedback at the cellular level that is absent in the cation current. We show that this slow positive feedback is required to endow the network rhythm with physiological modulation and robustness properties. This study thereby identifies an essential cellular property to be retained at the network level in modeling network robustness and modulation. [less ▲]

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See detailOn the projective geometry of Kalman filter
Carli, Francesca Paola ULiege; Sepulchre, Rodolphe ULiege

in Proc. of 54th IEEE Conference on Decision and Control (CDC), 2015 (2015)

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See detailTotal connectivity: a marker of dynamical functional connectivity applied to consciousness
Liegeois, Raphaël ULiege; Phillips, Christophe ULiege; Bahri, Mohamed Ali ULiege et al

Poster (2015)

In the last years functional connectivity (FC) has become one of the most popular tools to explore and characterize information contained in fMRI =me series. The classical hypothesis on FC consists of ... [more ▼]

In the last years functional connectivity (FC) has become one of the most popular tools to explore and characterize information contained in fMRI =me series. The classical hypothesis on FC consists of considering it as constant (or static) over the whole fMRI time series. However, it has been emphasized recently that FC should be treated as a dynamical quantity, for example by using sliding windows of the fMRI time courses in order to compute a dynamical FC. We propose a comprehensive marker of FC based on an auto-regressive (AR) model of fMRI time series capturing its static and dynamic properties. We call it total connectivity and we illustrate the benefits of our approach on data of patients undergoing four different states of consciousness. [less ▲]

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See detailCalcium-dependent potassium channels.
Drion, Guillaume ULiege; Philippart, Fabian ULiege; Sepulchre, Rodolphe ULiege et al

in Jaeger, Dieter; Jung, Ranu (Eds.) Encyclopedia of Computational Neuroscience (2015)

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See detailSensitivity analysis of oscillator models in the space of phase response curves: Oscillators as open systems
Sacré, Pierre ULiege; Sepulchre, Rodolphe ULiege

in IEEE Control Systems Magazine (2014), 34(2), 50-74

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See detailA differential Lyapunov framework for contraction analysis
Forni, Fulvio ULiege; Sepulchre, Rodolphe ULiege

in IEEE Transactions on Automatic Control (2014), 59(3), 614-628

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to ... [more ▼]

Lyapunov's second theorem is an essential tool for stability analysis of differential equations. The paper provides an analog theorem for incremental stability analysis by lifting the Lyapunov function to the tangent bundle. The Lyapunov function endows the state-space with a Finsler structure. Incremental stability is inferred from infinitesimal contraction of the Finsler metrics through integration along solutions curves. [less ▲]

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See detailAssessing dynamical correlations between functional and structural brain connectivity
Liegeois, Raphaël ULiege; Ziegler, Erik; Phillips, Christophe ULiege et al

Poster (2014)

The link between resting­‐state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC) has been repeatedly investigated recently ... [more ▼]

The link between resting­‐state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC) has been repeatedly investigated recently. Meanwhile, the importance of considering the dynamics of neuronal processes has also been highlighted. In this work we show how the classical static (i.e. considered as constant) relationship between SC and FC could be enriched when the FC dynamics are taken into account. We use a sliding window approach to explore these dynamics and show that the window width should be chosen in a particular range in order to unveil statistically significant (i.e. not due to noise) fluctuations of the FC-­‐SC correlation. [less ▲]

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See detailModeling the Modulation of Neuronal Bursting: A Singularity Theory Approach
Franci, Alessio ULiege; Drion, Guillaume ULiege; Sepulchre, Rodolphe ULiege

in SIAM Journal on Applied Dynamical Systems (2014), 13(2), 798-829

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory ... [more ▼]

Exploiting the specific structure of neuron conductance-based models, the paper investigates the mathematical modeling of neuronal bursting modulation. The proposed approach combines singularity theory and geometric singular perturbations to capture the geometry of multiple time-scale attractors in the neighborhood of high-codimension singularities. We detect a three–time-scale bursting attractor in the universal unfolding of the winged cusp singularity and discuss the physiological relevance of the bifurcation and unfolding parameters in determining a physiological modulation of bursting. The results suggest generality and simplicity in the organizing role of the winged cusp singularity for the global dynamics of conductance-based models. [less ▲]

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See detailCerebral functional connectivity periodically (de)synchronizes with anatomical constraints
Liegeois, Raphaël ULiege; Sepulchre, Rodolphe ULiege; LAUREYS, Steven ULiege

E-print/Working paper (2014)

This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber ... [more ▼]

This paper studies the link between resting-state functional connectivity (FC), measured by the correlations of the fMRI BOLD time courses, and structural connectivity (SC), estimated through fiber tractography. Instead of a static analysis based on the correlation between SC and the FC averaged over the entire fMRI time series, we propose a dynamic analysis, based on the time evolution of the correlation between SC and a suitably windowed FC. Assessing the statistical significance of the time series against random phase permutations, our data show a pronounced peak of significance for time window widths around 20-30 TR (40-60 sec). Using the appropriate window width, we show that FC patterns oscillate between phases of high modularity, primarily shaped by anatomy, and phases of low modularity, primarily shaped by inter-network connectivity. Building upon recent results in dynamic FC, this emphasizes the potential role of SC as a transitory architecture between different highly connected resting state FC patterns. Finally, we show that networks implied in consciousness-related processes, such as the default mode network (DMN), contribute more to these brain-level fluctuations compared to other networks, such as the motor or somatosensory networks. This suggests that the fluctuations between FC and SC are capturing mind-wandering effects. [less ▲]

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See detailSensitivity analysis of circadian entrainment in the space of phase response curves
Sacré, Pierre ULiege; Sepulchre, Rodolphe ULiege

in Kulkarni, Vishwesh V.; Stan, Guy-Bart; Raman, Karthik (Eds.) A Systems Theoretic Approach to Systems and Synthetic Biology II: Analysis and Design of Cellular Systems (2014)

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output ... [more ▼]

Sensitivity analysis is a classical and fundamental tool to evaluate the role of a given parameter in a given system characteristic. Because the phase response curve is a fundamental input–output characteristic of oscillators, we developed a sensitivity analysis for oscillator models in the space of phase response curves. The proposed tool can be applied to high-dimensional oscillator models without facing the curse of dimensionality obstacle associated with numerical exploration of the parameter space. Application of this tool to a state-of-the-art model of circadian rhythms suggests that it can be useful and instrumental to biological investigations. [less ▲]

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See detailHomeostatic principles are consistent with sensitivity analysis of neuronal rhythmicity
Franci, Alessio ULiege; O'Leary, Timothy; Drion, Guillaume ULiege et al

Poster (2013, November)

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See detailFirst spike latency sensitivity of spiking neuron models
Trotta, Laura ULiege; Franci, Alessio ULiege; Sepulchre, Rodolphe ULiege

Poster (2013, July 08)

First spike latency is the long-lasting period preceding the first spike of a neuron submitted to a super-threshold stimulus. It has been suggested that this latency could code for stimulus recognition in ... [more ▼]

First spike latency is the long-lasting period preceding the first spike of a neuron submitted to a super-threshold stimulus. It has been suggested that this latency could code for stimulus recognition in several sensory systems. To encode information reliably, first spike latency should be sensitive to sensory inputs but robust to external perturbations. This paper studies the robustness of the first spike latency in spiking neuron models. We show the interplay between bistability, first spike latency and a type of neuronal excitability called regenerative excitability. [less ▲]

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