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

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

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

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

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 ULg; Sepulchre, Rodolphe ULg

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

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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See detailSingularly perturbed phase response curves
Sacré, Pierre ULg; Franci, Alessio ULg; Sepulchre, Rodolphe ULg

Conference (2013, March 26)

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See detailA Balance Equation Determines a Switch in Neuronal Excitability
Franci, Alessio ULg; Drion, Guillaume ULg; Seutin, Vincent ULg et al

in PLoS Computational Biology (2013)

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a ... [more ▼]

We use the qualitative insight of a planar neuronal phase portrait to detect an excitability switch in arbitrary conductance-based models from a simple mathematical condition. The condition expresses a balance between ion channels that provide a negative feedback at resting potential (restorative channels) and those that provide a positive feedback at resting potential (regenerative channels). Geometrically, the condition imposes a transcritical bifurcation that rules the switch of excitability through the variation of a single physiological parameter. Our analysis of six di erent published conductance based models always nds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological rel- evance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons. [less ▲]

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See detailGlobal analysis of a continuum model for monotone pulse-coupled oscillators
Mauroy, Alexandre ULg; Sepulchre, Rodolphe ULg

in IEEE Transactions on Automatic Control (2013), 58(5), 1154-1166

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupledmodels, the stability results ... [more ▼]

We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupledmodels, the stability results obtained in the continuum limit are global. For the nonlinear transport equation governing the evolution of the oscillators, we propose (under technical assumptions) a global Lyapunov function which is induced by a total variation distance between quantile densities. The monotone time evolution of the Lyapunov function completely characterizes the dichotomic behavior of the oscillators: either the oscillators converge in finite time to a synchronous state or they asymptotically converge to an asynchronous state uniformly spread on the circle. The results of the present paper apply to popular phase oscillators models (e.g., the well-known leaky integrate-and-fire model) and show a strong parallel between the analysis of finite and infinite populations. In addition, they provide a novel approach for the (global) analysis of pulse-coupled oscillators. © 2012 IEEE. [less ▲]

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See detailOn differential passivity of physical systems
Forni, Fulvio ULg; Sepulchre, Rodolphe ULg; van der Schaft, Arjan

in 52nd IEEE Conference on Decision and Control (2013)

Differential passivity is a property that allows to check with a pointwise criterion that a system is incrementally passive, a property that is relevant to study interconnected systems in the context of ... [more ▼]

Differential passivity is a property that allows to check with a pointwise criterion that a system is incrementally passive, a property that is relevant to study interconnected systems in the context of regulation, synchronization, and estimation. The paper investigates how restrictive is the property, focusing on a class of open gradient systems encountered in the coenergy modeling framework of physical systems, in particular the Brayton-Moser formalism for nonlinear electrical circuits. [less ▲]

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See detailRank-preserving geometric means of positive semi-definite matrices
Bonnabel, Silvère; Collard, Anne ULg; Sepulchre, Rodolphe ULg

in Linear Algebra & its Applications (2013), 438(8), 3202-3216

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of ... [more ▼]

The generalization of the geometric mean of positive scalars to positive definite matrices has attracted considerable attention since the seminal work of Ando. The paper generalizes this framework of matrix means by proposing the definition of a rank-preserving mean for two or an arbitrary number of positive semi-definite matrices of fixed rank. The proposed mean is shown to be geometric in that it satisfies all the expected properties of a rank-preserving geometric mean. The work is motivated by operations on low-rank approximations of positive definite matrices in high-dimensional spaces. [less ▲]

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See detailOn differentially dissipative dynamical systems
Forni, Fulvio ULg; Sepulchre, Rodolphe ULg

in IFAC-PapersOnLine website. (2013)

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent ... [more ▼]

Dissipativity is an essential concept of systems theory. The paper provides an extension of dissipativity, named differential dissipativity, by lifting storage functions and supply rates to the tangent bundle. Differential dissipativity is connected to incremental stability in the same way as dissipativity is connected to stability. It leads to a natural formulation of differential passivity when restricting to quadratic supply rates. The paper also shows that the interconnection of differentially passive systems is differentially passive, and provides preliminary examples of differentially passive electrical systems. [less ▲]

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See detailKick synchronization versus diffusive synchronization
Mauroy, Alexandre ULg; Sacré, Pierre ULg; Sepulchre, Rodolphe ULg

in Proceedings of the 51st IEEE Conference on Decision and Control (2012, December)

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on ... [more ▼]

The paper provides an introductory discussion about two fundamental models of oscillator synchronization: the (continuous-time) diffusive model, that dominates the mathematical literature on synchronization, and the (hybrid) kick model, that accounts for most popular examples of synchronization, but for which only few theoretical results exist. The paper stresses fundamental differences between the two models, such as the different contraction measures underlying the analysis, as well as important analogies that can be drawn in the limit of weak coupling. [less ▲]

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See detailAntiwindup regulation of saturated linear systems
Forni, Fulvio ULg; Zaccarian, Luca; Sepulchre, Rodolphe ULg

in 51st IEEE Conference on Decision and Control (2012, December)

We consider the output regulation problem for linear systems subject to actuators saturation. A state-feedback unconstrained regulator is transformed into an error-feedback bounded regulator by ... [more ▼]

We consider the output regulation problem for linear systems subject to actuators saturation. A state-feedback unconstrained regulator is transformed into an error-feedback bounded regulator by introducing an observer which is then decomposed into the sum of "unconstrained" and "antiwindup" dynamics. The unconstrained dynamics are regulated towards a predefined reference trajectory, by a control signal u which may violate the saturation bounds during transients. The antiwindup dynamics transiently store the mismatch between unconstrained and constrained dynamics. The antiwindup design also applies to a predefined error-feedback dynamic regulator for the unconstrained system, as in standard antiwindup setting. As a particular case of distinct interest, the design provides a new global asymptotic stabilizer for saturated null-controllable systems. [less ▲]

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See detailA novel phase portrait for neuronal excitability
Drion, Guillaume ULg; Franci, Alessio ULg; Seutin, Vincent ULg et al

in PLoS ONE (2012), 7(8),

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power ... [more ▼]

Fifty years ago, FitzHugh introduced a phase portrait that became famous for a twofold reason: it captured in a physiological way the qualitative behavior of Hodgkin-Huxley model and it revealed the power of simple dynamical models to unfold complex firing patterns. To date, in spite of the enormous progresses in qualitative and quantitative neural modeling, this phase portrait has remained a core picture of neuronal excitability. Yet, a major difference between the neurophysiology of 1961 and of 2011 is the recognition of the prominent role of calcium channels in firing mechanisms. We show that including this extra current in Hodgkin-Huxley dynamics leads to a revision of FitzHugh-Nagumo phase portrait that affects in a fundamental way the reduced modeling of neural excitability. The revisited model considerably enlarges the modeling power of the original one. In particular, it captures essential electrophysiological signatures that otherwise require non-physiological alteration or considerable complexification of the classical model. As a basic illustration, the new model is shown to highlight a core dynamical mechanism by which calcium channels control the two distinct firing modes of thalamocortical neurons. [less ▲]

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See detailAnisotropy preserving interpolation of diffusion tensors
Collard, Anne ULg; Bonnabel, Silvère; Phillips, Christophe ULg et al

Poster (2012, June)

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