CNRS Jean Kuntzmann Laboratory

Grenoble, France

CNRS Jean Kuntzmann Laboratory

Grenoble, France
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Ditlevsen S.,Copenhagen University | Samson A.A.,University of Paris Descartes | Samson A.A.,CNRS Jean Kuntzmann Laboratory
Annals of Applied Statistics | Year: 2014

Parameter estimation in multidimensional diffusion models with only one coordinate observed is highly relevant in many biological applications, but a statistically difficult problem. In neuroscience, the membrane potential evolution in single neurons can be measured at high frequency, but biophysical realistic models have to include the unobserved dynamics of ion channels. One such model is the stochastic Morris-Lecar model, defined by a nonlinear two-dimensional stochastic differential equation. The coordinates are coupled, that is, the unobserved coordinate is nonautonomous, the model exhibits oscillations to mimic the spiking behavior, which means it is not of gradient-type, and the measurement noise from intracellular recordings is typically negligible. Therefore, the hidden Markov model framework is degenerate, and available methods break down. The main contributions of this paper are an approach to estimate in this ill-posed situation and nonasymptotic convergence results for the method. Specifically, we propose a sequential Monte Carlo particle filter algorithm to impute the unobserved coordinate, and then estimate parameters maximizing a pseudo-likelihood through a stochastic version of the Expectation-Maximization algorithm. It turns out that even the rate scaling parameter governing the opening and closing of ion channels of the unobserved coordinate can be reasonably estimated. An experimental data set of intracellular recordings of the membrane potential of a spinal motoneuron of a red-eared turtle is analyzed, and the performance is further evaluated in a simulation study. © Institute of Mathematical Statistics, 2014.

Laadhari A.,CNRS Jean Kuntzmann Laboratory | Saramito P.,CNRS Jean Kuntzmann Laboratory | Misbah C.,French National Center for Scientific Research
Physics of Fluids | Year: 2012

Vesicles under flow constitute a model system for the study of red blood cells (RBCs) dynamics and blood rheology. In the blood circulatory system the Reynolds number (at the scale of the RBC) is not always small enough for the Stokes limit to be valid. We develop a numerical method in two dimensions based on the level set approach and solve the fluid/membrane coupling by using an adaptive finite element technique. We find that a Reynolds number of order one can destroy completely the vesicle tumbling motion obtained in the Stokes regime. We analyze in details this phenomenon and discuss some of the far reaching consequences. We suggest experimental tests on vesicles. © 2012 American Institute of Physics.

Cheddadi I.,CNRS Jean Kuntzmann Laboratory
The European physical journal. E, Soft matter | Year: 2011

Foams, gels, emulsions, polymer solutions, pastes and even cell assemblies display both liquid and solid mechanical properties. On a local scale, such "soft glassy" systems are disordered assemblies of deformable rearranging units, the complexity of which gives rise to their striking flow behaviour. On a global scale, experiments show that their mechanical behaviour depends on the orientation of their elastic deformation with respect to the flow direction, thus requiring a description by tensorial equations for continuous materials. However, due to their strong non-linearities, the numerous candidate models have not yet been solved in a general multi-dimensional geometry to provide stringent tests of their validity. We compute the first solutions of a continuous model for a discriminant benchmark, namely the flow around an obstacle. We compare it with experiments of a foam flow and find an excellent agreement with the spatial distribution of all important features: we accurately predict the experimental fields of velocity, elastic deformation, and plastic deformation rate in terms of magnitude, direction, and anisotropy. We analyse the role of each parameter, and demonstrate that the yield strain is the main dimensionless parameter required to characterize the materials. We evidence the dominant effect of elasticity, which explains why the stress does not depend simply on the shear rate. Our results demonstrate that the behaviour of soft glassy materials cannot be reduced to an intermediate between that of a solid and that of a liquid: the viscous, the elastic and the plastic contributions to the flow, as well as their couplings, must be treated simultaneously. Our approach opens the way to the realistic multi-dimensional prediction of complex flows encountered in geophysical, industrial and biological applications, and to the understanding of the link between structure and rheology of soft glassy systems.

Carbou G.,University of Bordeaux 1 | Labbe S.,CNRS Jean Kuntzmann Laboratory
ESAIM - Control, Optimisation and Calculus of Variations | Year: 2012

In this paper we study a one dimensional model of ferromagnetic nano-wires of finite length. First we justify the model by Γ-convergence arguments. Furthermore we prove the existence of wall profiles. These walls being unstable, we stabilize them by the mean of an applied magnetic field. © 2010 EDP Sciences, SMAI.

Bidegaray-Fesquet B.,CNRS Jean Kuntzmann Laboratory
Annals of Physics | Year: 2010

The aim of this paper is to derive a raw Bloch model for the interaction of light with quantum boxes in the framework of a two-electron-species (conduction and valence) description. This requires a good understanding of the one-species case and of the treatment of level degeneracy. In contrast with some existing literature, we obtain a Liouville equation which induces the positiveness and the boundedness of solutions, that are necessary for future mathematical studies involving higher order phenomena. © 2010 Elsevier Inc.

Cheddadi I.,French Institute for Research in Computer Science and Automation | Saramito P.,CNRS Jean Kuntzmann Laboratory | Graner F.,French Institute of Health and Medical Research | Graner F.,University Paris Diderot
Journal of Rheology | Year: 2012

The Herschel-Bulkley rheological fluid model includes terms representing viscosity and plasticity. In this classical model, below the yield stress the material is strictly rigid. Complementing this model by including elastic behavior below the yield stress leads to a description of an elastoviscoplastic (EVP) material such as an emulsion or a liquid foam. We include this modification in a completely tensorial description of cylindrical Couette shear flows. Both the EVP model parameters, at the scale of a representative volume element, and the predictions (velocity, strain and stress fields) can be readily compared with experiments. We perform a detailed study of the effect of the main parameters, especially the yield strain. We discuss the role of the curvature of the cylindrical Couette geometry in the appearance of localization; we determine the value of the localization length and provide an approximate analytical expression. We then show that, in this tensorial EVP model of cylindrical Couette shear flow, the normal stress difference strongly influences the velocity profiles, which can be smooth or nonsmooth according to the initial conditions on the stress. This feature could explain several open questions regarding experimental measurements on Couette flows for various EVP materials such as emulsions or liquid foams, including the nonreproducibility that has been reported in flows of foams. We then discuss the suitability of Couette flows as a way to measure rheological properties of EVP materials. © 2012 The Society of Rheology.

Ycart B.,CNRS Jean Kuntzmann Laboratory
PLoS ONE | Year: 2013

The estimation of mutation rates and relative fitnesses in fluctuation analysis is based on the unrealistic hypothesis that the single-cell times to division are exponentially distributed. Using the classical Luria-Delbrück distribution outside its modelling hypotheses induces an important bias on the estimation of the relative fitness. The model is extended here to any division time distribution. Mutant counts follow a generalization of the Luria-Delbrück distribution, which depends on the mean number of mutations, the relative fitness of normal cells compared to mutants, and the division time distribution of mutant cells. Empirical probability generating function techniques yield precise estimates both of the mean number of mutations and the relative fitness of normal cells compared to mutants. In the case where no information is available on the division time distribution, it is shown that the estimation procedure using constant division times yields more reliable results. Numerical results both on observed and simulated data are reported. © 2013 Bernard Ycart.

Mazure M.-L.,CNRS Jean Kuntzmann Laboratory
Computer Aided Geometric Design | Year: 2016

A Quasi Extended Chebyshev (QEC) space is a space of sufficiently differentiable functions in which any Hermite interpolation problem which is not a Taylor problem is unisolvent. On a given interval the class of all spaces which contains constants and for which the space obtained by differentiation is a QEC-space has been identified as the largest class of spaces (under ordinary differentiability assumptions) which can be used for design. As a first step towards determining the largest class of splines for design, we consider a sequence of QEC-spaces on adjacent intervals, all of the same dimension, we join them via connection matrices, so as to maintain both the dimension and the unisolvence. The resulting space is called a Quasi Extended Chebyshev Piecewise (QECP) space. We show that all QECP-spaces are inverse images of two-dimensional Chebyshev spaces under piecewise generalised derivatives associated with systems of piecewise weight functions. We show illustrations proving that QECP-spaces can produce interesting shape effects. © 2016 Elsevier B.V.

Malick J.,CNRS Jean Kuntzmann Laboratory | Roupin F.,University of Paris 13
Mathematical Programming | Year: 2012

This paper deals with the computation of exact solutions of a classical NP-hard problem in combinatorial optimization, the k-cluster problem. This problem consists in finding a heaviest subgraph with k nodes in an edge weighted graph. We present a branch-and-bound algorithm that applies a novel bounding procedure, based on recent semidefinite programming techniques. We use new semidefinite bounds that are less tight than the standard semidefinite bounds, but cheaper to get. The experiments show that this approach is competitive with the best existing ones. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

Malick J.,CNRS Jean Kuntzmann Laboratory | Roupin F.,University of Paris 13
Mathematical Programming | Year: 2013

This article presents a family of semidefinite programming bounds, obtained by Lagrangian duality, for 0-1 quadratic optimization problems with linear or quadratic constraints. These bounds have useful computational properties: they have a good ratio of tightness to computing time, they can be optimized by a quasi-Newton method, and their final tightness level is controlled by a real parameter. These properties are illustrated on three standard combinatorial optimization problems: unconstrained 0-1 quadratic optimization, heaviest k -subgraph, and graph bisection. © 2012 Springer-Verlag Berlin Heidelberg and Mathematical Optimization Society.

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