arXiv subjects

Rodolphe Sepulchre

Publications and source records attributed to Rodolphe Sepulchre.

At least 109 records · Page 6Linked to original sources

arXiv2014

A positive feedback at the cellular level promotes robustness and modulation at the circuit level

The paper highlights the role of a positive feedback gating mechanism at the cellular level in the robust- ness 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 particu- lar excitability property, the post-inhibitory rebound, an intrinsic cellular property that elicits transient 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 necessary and sufficient 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.

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arXiv2014

AR Identification of Latent-variable Graphical Models

The paper proposes an identification procedure for autoregressive gaussian stationary stochastic processes wherein the manifest (or observed) variables are mostly related through a limited number of latent (or hidden) variables. The method exploits the sparse plus low-rank decomposition of the inverse of the manifest spectral density and the efficient convex relaxations recently proposed for such decomposition.

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arXiv2014

Differentially positive systems

The paper introduces and studies differentially positive systems, that is, systems whose linearization along an arbitrary trajectory is positive. A generalization of Perron Frobenius theory is developed in this differential framework to show that the property induces a (conal) order that strongly constrains the asymptotic behavior of solutions. The results illustrate that behaviors constrained by local order properties extend beyond the well-studied class of linear positive systems and monotone systems, which both require a constant cone field and a linear state space.

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arXiv2014

Realization of nonlinear behaviors from organizing centers

Borrowing the concept of organizing center from singularity theory, the paper proposes a methodology to realize nonlinear behaviors such as switches, relaxation oscillators, or bursters from core circuits that reveal the fundamental role of monotonicity and feedback in their robustness and modulation.

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arXiv2014

Cerebral functional connectivity periodically (de)synchronizes with anatomical constraints

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.

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arXiv2014

Differential analysis of nonlinear systems: revisiting the pendulum example

Differential analysis aims at inferring global properties of nonlinear behaviors from the local analysis of the linearized dynamics. The paper motivates and illustrates the use of differential analysis on the nonlinear pendulum model, an archetype example of nonlinear behavior. Special emphasis is put on recent work by the authors in this area, which includes a differential Lyapunov framework for contraction analysis and the concept of differential positivity.

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arXiv2014

Sensitivity analysis of oscillator models in the space of phase-response curves: Oscillators as open systems

Oscillator models are central to the study of system properties such as entrainment or synchronization. Due to their nonlinear nature, few system-theoretic tools exist to analyze those models. The paper develops a sensitivity analysis for phase-response curves, a fundamental one-dimensional phase reduction of oscillator models. The proposed theoretical and numerical analysis tools are illustrated on several system-theoretic questions and models arising in the biology of cellular rhythms.

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arXiv2013

Modeling the modulation of neuronal bursting: a singularity theory approach

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-scales 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.

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arXiv2013

Modulation of beta oscillations during movement initiation: modeling the ionic basis of a functional switch

We use a computational model to propose a physiological mechanism by which transient control of beta oscillations in the indirect pathway of the basal ganglia is orchestrated at the cellular level. Our model includes a simple and robust mechanism by which a cellular switch (from bursting to tonic) almost instantaneously translates into a functional gating switch (from blocking to conducive) in an excitatory-inhibitory network. Applied to the control of beta oscillations in the basal ganglia, the model shows the modulation of beta activity under the action of a transient depolarization, for instance a dopamine signal. The model predicts, by analogy to the thalamocortical circuit, a novel gating function by which the transfer of cortical spikes through the indirect pathway is blocked under the inhibitory drive preceding movement but briefly released at the onset of movement execution.

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arXiv2013

Modulation and Robustness of Endogenous Neuronal Spiking

Neuronal spiking exhibits an exquisite combination of modulation and robustness properties, rarely matched in artificial systems. We exploit the particular interconnection structure of conductance based models to investigate this remarkable property. We find that much of neuronal modulation and robustness can be explained by separating the total transmembrane current into three different components corresponding to the three time scales of neuronal bursting. Each equivalent current aggregates many ionic contributions into an equivalent voltage-dependent conductance, which defines a key modulation parameter. Plugging those equivalent feedback gains in a minimal abstract model recovers many experimental modulation scenarii as modulatory paths in elementary two-parameter charts. Likewise, robustness owes to the many possible physiological realizations of a same equivalent conductance, highlighting the role of equivalent conductances as prominent targets for neuromodulation and intrinsic homeostasis.

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arXiv2013

A differential Lyapunov framework for contraction analysis

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.

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arXiv2013

Control limitations from distributed sensing: theory and Extremely Large Telescope application

We investigate performance bounds for feedback control of distributed plants where the controller can be centralized (i.e. it has access to measurements from the whole plant), but sensors only measure differences between neighboring subsystem outputs. Such "distributed sensing" can be a technological necessity in applications where system size exceeds accuracy requirements by many orders of magnitude. We formulate how distributed sensing generally limits feedback performance robust to measurement noise and to model uncertainty, without assuming any controller restrictions (among others, no "distributed control" restriction). A major practical consequence is the necessity to cut down integral action on some modes. We particularize the results to spatially invariant systems and finally illustrate implications of our developments for stabilizing the segmented primary mirror of the European Extremely Large Telescope.

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arXiv2013

On differential passivity of physical systems

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.

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arXiv2013

Manopt, a Matlab toolbox for optimization on manifolds

Optimization on manifolds is a rapidly developing branch of nonlinear optimization. Its focus is on problems where the smooth geometry of the search space can be leveraged to design efficient numerical algorithms. In particular, optimization on manifolds is well-suited to deal with rank and orthogonality constraints. Such structured constraints appear pervasively in machine learning applications, including low-rank matrix completion, sensor network localization, camera network registration, independent component analysis, metric learning, dimensionality reduction and so on. The Manopt toolbox, available at www.manopt.org, is a user-friendly, documented piece of software dedicated to simplify experimenting with state of the art Riemannian optimization algorithms. We aim particularly at reaching practitioners outside our field.

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arXiv2013

The geometry of low-rank Kalman filters

An important property of the Kalman filter is that the underlying Riccati flow is a contraction for the natural metric of the cone of symmetric positive definite matrices. The present paper studies the geometry of a low-rank version of the Kalman filter. The underlying Riccati flow evolves on the manifold of fixed rank symmetric positive semidefinite matrices. Contraction properties of the low-rank flow are studied by means of a suitable metric recently introduced by the authors.

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arXiv2013

On differentially dissipative dynamical systems

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.

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arXiv2013

Statistical tests for group comparison of manifold-valued data

Motivated by population studies of Diffusion Tensor Imaging, the paper investigates the use of mean-based and dispersion-based permutation tests to define and compute the significance of a statistical test for data taking values on nonlinear manifolds. The paper proposes statistical tests that are computationally tractable and geometrically sound for Diffusion Tensor Imaging.

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arXiv2013

A Balance Equation Determines a Switch in Neuronal Excitability

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 different published conductance based models always finds the transcritical bifurcation and the associated switch in excitability, which suggests that the mathematical predictions have a physiological relevance and that a same regulatory mechanism is potentially involved in the excitability and signaling of many neurons.

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