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Note on how cerebral functional connectivity encodes structural constraints of the human brain Liegeois, Raphaël ; Soddu, Andrea ; Sepulchre, Rodolphe Conference (2013) Detailed reference viewed: 10 (2 ULg)Rank-preserving geometric means of positive semi-definite matrices ; Collard, Anne ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 44 (9 ULg)A Balance Equation Determines a Switch in Neuronal Excitability Franci, Alessio ; Drion, Guillaume ; Seutin, Vincent 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 ▲] Detailed reference viewed: 104 (14 ULg)Global analysis of a continuum model for monotone pulse-coupled oscillators Mauroy, Alexandre ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 32 (1 ULg)On differential passivity of physical systems Forni, Fulvio ; Sepulchre, Rodolphe ; 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 ▲] Detailed reference viewed: 41 (4 ULg)On differentially dissipative dynamical systems Forni, Fulvio ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 71 (9 ULg)Kick synchronization versus diffusive synchronization Mauroy, Alexandre ; Sacré, Pierre ; Sepulchre, Rodolphe in Proceedings of the 51st IEEE Conference on Decision and Control (invited tutorial session) (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 ▲] Detailed reference viewed: 36 (5 ULg)Antiwindup regulation of saturated linear systems Forni, Fulvio ; ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 89 (21 ULg)A balance between competitive and cooperative ion channels regulates neuronal excitability Franci, Alessio ; Drion, Guillaume ; Massotte, Laurent et al Poster (2012, October) Detailed reference viewed: 12 (4 ULg)A novel phase portrait for neuronal excitability Drion, Guillaume ; Franci, Alessio ; Seutin, Vincent 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 ▲] Detailed reference viewed: 66 (12 ULg)Anisotropy preserving interpolation of diffusion tensors Collard, Anne ; ; Phillips, Christophe et al Poster (2012, June) Detailed reference viewed: 16 (10 ULg)Decision-making in noisy bistable models : a local analysis for non local predictions Trotta, Laura ; Bullinger, Eric ; Sepulchre, Rodolphe Poster (2012, May) Detailed reference viewed: 31 (8 ULg)Global analysis of dynamical decision-making models through local computation around the hidden saddle Trotta, Laura ; Bullinger, Eric ; Sepulchre, Rodolphe in PLoS ONE (2012), 7(3), Detailed reference viewed: 62 (21 ULg)A Novel Phase Portrait to Understand Neuronal Excitability Drion, Guillaume ; Franci, Alessio ; Seutin, Vincent et al Conference (2012, March) Detailed reference viewed: 10 (0 ULg)Anisotropy preserving interpolation of diffusion tensors Collard, Anne ; ; Phillips, Christophe et al Conference (2012, March) Detailed reference viewed: 25 (5 ULg)Decision making in noisy bistable switches A local analysis for non local predictions Trotta, Laura ; Bullinger, Eric ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 41 (3 ULg)Metrics for oscillator models: an input-to-phase approach Sacré, Pierre ; Sepulchre, Rodolphe Conference (2012, March) Detailed reference viewed: 90 (26 ULg)Large-scale optimization for component analysis of fMRI resting brain data Liegeois, Raphaël ; Soddu, Andrea ; Sepulchre, Rodolphe Conference (2012) Detailed reference viewed: 15 (2 ULg)An Organizing Center in a Planar Model of Neuronal Excitability Franci, Alessio ; Drion, Guillaume ; Sepulchre, Rodolphe 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 ▲] Detailed reference viewed: 29 (8 ULg)Mitochondrion- and endoplasmic reticulum-induced SK channel dysregulation as a potential origin of the selective neurodegeneration in Parkinson’s disease Drion, Guillaume ; Sepulchre, Rodolphe ; Seutin, Vincent 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 ▲] Detailed reference viewed: 18 (0 ULg) |
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