References of "Sepulchre, Rodolphe"
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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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See detailA Novel Phase Portrait to Understand Neuronal Excitability
Drion, Guillaume ULg; Franci, Alessio ULg; Seutin, Vincent ULg et al

Conference (2012, March)

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

Conference (2012, March)

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See detailDecision making in noisy bistable switches A local analysis for non local predictions
Trotta, Laura ULg; Bullinger, Eric ULg; Sepulchre, Rodolphe ULg

Conference (2012, March)

In this paper, we try to estimate some statistics about the decision making process in a bistable model submitted to noise by studying the local properties of the system around an hyperbolic saddle point ... [more ▼]

In this paper, we try to estimate some statistics about the decision making process in a bistable model submitted to noise by studying the local properties of the system around an hyperbolic saddle point. Despite the fact that the saddle is not an equilibrium point of the stochastic system, we show that a local approach is still instructive. Under appropriate assumptions, the system can be reduced to an Orsntein-Uhlenbeck process whose dynamics depend on the properties of the saddle point. Yet, Orstein-Uhlenbeck processes have been used to study decision making under uncertainty in a broad variety of fields including statistics and cognitive neurosciences . [less ▲]

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See detailMetrics for oscillator models: an input-to-phase approach
Sacré, Pierre ULg; Sepulchre, Rodolphe ULg

Conference (2012, March)

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See detailAn Organizing Center in a Planar Model of Neuronal Excitability
Franci, Alessio ULg; Drion, Guillaume ULg; Sepulchre, Rodolphe ULg

in SIAM Journal on Applied Dynamical Systems (2012), 11(4), 1698-1722

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative ... [more ▼]

The paper studies the excitability properties of a generalized FitzHugh-Nagumo model. The model differs from the purely competitive FitzHugh-Nagumo model in that it accounts for the effect of cooperative gating variables such as activation of calcium currents. Excitability is explored by unfolding a pitchfork bifurcation that is shown to organize five different types of excitability. In addition to the three classical types of neuronal excitability, two novel types are described and distinctly associated to the presence of cooperative variables. [less ▲]

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See detailMitochondrion- and endoplasmic reticulum-induced SK channel dysregulation as a potential origin of the selective neurodegeneration in Parkinson’s disease
Drion, Guillaume ULg; Sepulchre, Rodolphe ULg; Seutin, Vincent ULg

in Wellstead, Peter; Cloutier, Mathieu (Eds.) The Systems Biology of Parkinson's Disease (2012)

Mitochondrial dysfunction and metabolic issues are known to have strong implications in the pathogenesis of Parkinson’s disease (PD). But it is also known that the neuronal loss leading to PD symptoms is ... [more ▼]

Mitochondrial dysfunction and metabolic issues are known to have strong implications in the pathogenesis of Parkinson’s disease (PD). But it is also known that the neuronal loss leading to PD symptoms is selective for particular areas of the brain. In particular, the characteristic motor symptoms of PD are mainly due to abnormal neuronal activity in the basal ganglia, through the degeneration of substantia nigra pars compacta (SNc), but not ventral tegmental area (VTA), dopaminergic (DA) neurons. How a metabolic dysfunction triggers such a selective loss is considered from a range of perspectives in several contributions to this volume. The aim of this chapter is to investigate the potential role of small conductance calcium-activated potassium (SK) channels in this selective degeneration. Based on a recently proposed model and experimental data, we underline the fundamental role of SK channels in regulating the excitability of SNc DA neurons. The fact that SK channels do not play this regulating role in VTA DA neurons suggests the hypothesis that one reason for the preferential vulnerability of SNc DA neurons in Parkinson’s disease is that SK channels, which have a profound influence on their firing physiologically, are dysregulated by a dysfunction of mitochondria and/or endoplasmic reticulum. [less ▲]

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See detailLow-rank optimization with trace norm penalty
Mishra, Bamdev ULg; Meyer, Gilles ULg; Bach, Francis et al

E-print/Working paper (2012)

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is ... [more ▼]

The paper addresses the problem of low-rank trace norm minimization. We propose an algorithm that alternates between fixed-rank optimization and rank-one updates. The fixed-rank optimization is characterized by an efficient factorization that makes the trace norm differentiable in the search space and the computation of duality gap numerically tractable. The search space is nonlinear but is equipped with a particular Riemannian structure that leads to efficient computations. We present a second-order trust-region algorithm with a guaranteed quadratic rate of convergence. Overall, the proposed optimization scheme converges super-linearly to the global solution while still maintaining complexity that is linear in the number of rows of the matrix. To compute a set of solutions efficiently for a grid of regularization parameters we propose a predictor-corrector approach on the quotient manifold that outperforms the naive warm-restart approach. The performance of the proposed algorithm is illustrated on problems of low-rank matrix completion and multivariate linear regression. [less ▲]

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See detailContraction of monotone phase-coupled oscillators
Mauroy, Alexandre ULg; Sepulchre, Rodolphe ULg

in Systems & Control Letters (2012), 61(11), 1097-1102

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The ... [more ▼]

This paper establishes a global contraction property for networks of phase-coupled oscillators characterized by a monotone coupling function. The contraction measure is a total variation distance. The contraction property determines the asymptotic behavior of the network, which is either finite-time synchronization or asymptotic convergence to a splay state. © 2012 Elsevier B.V. All rights reserved. [less ▲]

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See detailFixed-rank matrix factorizations and Riemannian low-rank optimization
Mishra, Bamdev ULg; Meyer, Gilles ULg; Bonnabel, Silvere et al

E-print/Working paper (2012)

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of ... [more ▼]

Motivated by the problem of learning a linear regression model whose parameter is a large fixed-rank non-symmetric matrix, we consider the optimization of a smooth cost function defined on the set of fixed-rank matrices. We adopt the geometric optimization framework of optimization on Riemannian matrix manifolds. We study the underlying geometries of several well-known fixed-rank matrix factorizations and then exploit the Riemannian geometry of the search space in the design of a class of gradient descent and trust-region algorithms. The proposed algorithms generalize our previous results on fixed-rank symmetric positive semidefinite matrices, apply to a broad range of applications, scale to high-dimensional problems and confer a geometric basis to recent contributions on the learning of fixed-rank non-symmetric matrices. We make connections with existing algorithms in the context of low-rank matrix completion and discuss relative usefulness of the proposed framework. Numerical experiments suggest that the proposed algorithms compete with the state-of-the-art and that manifold optimization offers an effective and versatile framework for the design of machine learning algorithms that learn a fixed-rank matrix. [less ▲]

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See detailA Riemannian geometry for low-rank matrix completion
Mishra, Bamdev ULg; Karavadi, Adithya Apuroop; Sepulchre, Rodolphe ULg

E-print/Working paper (2012)

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the ... [more ▼]

We propose a new Riemannian geometry for fixed-rank matrices that is specifically tailored to the low-rank matrix completion problem. Exploiting the degree of freedom of a quotient space, we tune the metric on our search space to the particular least square cost function. At one level, it illustrates in a novel way how to exploit the versatile framework of optimization on quotient manifold. At another level, our algorithm can be considered as an improved version of LMaFit, the state-of-the-art Gauss-Seidel algorithm. We develop necessary tools needed to perform both first-order and second-order optimization. In particular, we propose gradient descent schemes (steepest descent and conjugate gradient) and trust-region algorithms. We also show that, thanks to the simplicity of the cost function, it is numerically cheap to perform an exact linesearch given a search direction, which makes our algorithms competitive with the state-of-the-art on standard low-rank matrix completion instances. [less ▲]

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See detailMatching an oscillator model to a phase response curve
Sacré, Pierre ULg; Sepulchre, Rodolphe ULg

in Proceedings of the Joint 50th IEEE Conference on Decision and Control and European Control Conference (2011, December)

The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a ... [more ▼]

The Phase Response Curve (PRC) has proven a useful tool for the reduction of complex oscillator models. It is also an information often experimentally available to the biologist. This paper introduces a numerical tool based on the sensitivity analysis of the PRC to adapt initial model parameters in order to match a particular PRC shape. We illustrate the approach on a simple biochemical model of circadian oscillator. [less ▲]

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See detailLow-rank optimization for distance matrix completion
Mishra, Bamdev ULg; Meyer, Gilles ULg; Sepulchre, Rodolphe ULg

in Proceedings of the 50th IEEE Conference on Decision and Control (2011, December)

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly ... [more ▼]

This paper addresses the problem of low-rank distance matrix completion. This problem amounts to recover the missing entries of a distance matrix when the dimension of the data embedding space is possibly unknown but small compared to the number of considered data points. The focus is on high-dimensional problems. We recast the considered problem into an optimization problem over the set of low-rank positive semidefinite matrices and propose two efficient algorithms for low-rank distance matrix completion. In addition, we propose a strategy to determine the dimension of the embedding space. The resulting algorithms scale to high-dimensional problems and monotonically converge to a global solution of the problem. Finally, numerical experiments illustrate the good performance of the proposed algorithms on benchmarks. [less ▲]

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