Publications

2017

• Multipreconditioning for nonsymmetric problems: the case of orthomin and biCG
  
  • Bovet Christophe
  • Gosselet Pierre
  • Spillane Nicole
  Comptes rendus de l'Académie des sciences. Série I, Mathématique, Elsevier, 2017, 355 (3), pp.354-358. Preconditioned Krylov subspace methods are powerful tools for solving linear systems but sometimes they converge very slowly, and often after a long stagnation. A natural way to fix this is by enlarging the space in which the solution is computed at each iteration. Following this idea, we propose in this note two multipreconditioned algorithms: multipreconditioned orthomin and multipreconditioned biCG which aim at solving general nonsingular linear systems in a small number of iterations. After describing the algorithms, we illustrate their behaviour on systems arising from the FETI domain decomposition method, where in order to enlarge the search space, each local component in the usual preconditioner is kept as a separate preconditioner. (10.1016/j.crma.2017.01.010)
  DOI : 10.1016/j.crma.2017.01.010
• Incoherent Fermi-Pasta-Ulam Recurrences and Unconstrained Thermalization Mediated by Strong Phase Correlations
  
  • Guasoni M.
  • Garnier Josselin
  • Rumpf B.
  • Sugny D.
  • Fatome J.
  • Amrani F.
  • Millot G.
  • Picozzi A.
  Physical Review X, American Physical Society, 2017, 7 (1). (10.1103/PhysRevX.7.011025)
  DOI : 10.1103/PhysRevX.7.011025
• Small obstacle asymptotics for a 2D semi-linear convex problem
  
  • Chesnel Lucas
  • Claeys Xavier
  • Nazarov Sergei A
  Applicable Analysis, Taylor & Francis, 2017, pp.20. We study a 2D semi-linear equation in a domain with a small Dirichlet obstacle of size δ. Using the method of matched asymptotic expansions, we compute an asymptotic expansion of the solution as δ tends to zero. Its relevance is justified by proving a rigorous error estimate. Then we construct an approximate model, based on an equation set in the limit domain without the small obstacle, which provides a good approximation of the far field of the solution of the original problem. The interest of this approximate model lies in the fact that it leads to a variational formulation which is very simple to discretize. We present numerical experiments to illustrate the analysis. (10.1080/00036811.2017.1295449)
  DOI : 10.1080/00036811.2017.1295449
• Direct Numerical Simulation of bubbles with Adaptive Mesh Refinement with Distributed Algorithms
  
  • Talpaert Arthur
  , 2017. This PhD work presents the implementation of the simulation of two-phase flows in conditions of water-cooled nuclear reactors, at the scale of individual bubbles. To achieve that, we study several models for Thermal-Hydraulic flows and we focus on a technique for the capture of the thin interface between liquid and vapour phases. We thus review some possible techniques for Adaptive Mesh Refinement (AMR) and provide algorithmic and computational tools adapted to patch-based AMR, which aim is to locally improve the precision in regions of interest. More precisely, we introduce a patch-covering algorithm designed with balanced parallel computing in mind. This approach lets us finely capture changes located at the interface, as we show for advection test cases as well as for models with hyperbolic-elliptic coupling. The computations we present also include the simulation of the incompressible Navier-Stokes system, which models the shape changes of the interface between two non-miscible fluids.
• Ion transport through deformable porous media:derivation of the macroscopic equations using upscaling
  
  • Allaire Grégoire
  • Bernard Olivier
  • Dufrêche Jean-François
  • Mikelic Andro
  Computational & Applied Mathematics, Springer Verlag, 2017, 36, pp.1431-1462. We study the homogenization (or upscaling) of the transport of a multicomponentelectrolyte in a dilute Newtonian solvent through a deformable porous medium. The porescale interaction between the flow and the structure deformation (modeled by linearizedelasticity equations) is taken into account. After a careful adimensionalization process, we first consider so-called equilibrium solutions, in the absence of external forces, for which thevelocity and diffusive fluxes vanish and the electrostatic potential is the solution of a Poisson–Boltzmann equation. When the motion is governed by a small static electric field and smallhydrodynamic and elastic forces, we use O’Brien’s argument to deduce a linearized model.Then we perform the homogenization of these linearized equations for a suitable choice oftime scale. It turns out that the deformation of the porous medium is weakly coupled tothe electrokinetics system in the sense that it does not influence electrokinetics although thelatter one yields an osmotic pressure term in the mechanical equations. As a consequence,the effective tensor satisfies Onsager properties, namely is symmetric positive definite. (10.1007/s40314-016-0321-0)
  DOI : 10.1007/s40314-016-0321-0
• Une approche tropicale de la programmation bi-niveau
  
  • Akian Marianne
  • Bouhtou Mustapha
  • Eytard Jean Bernard
  • Gaubert Stephane
  , 2017.
• Integrals of spherical harmonics with Fourier exponents in multidimensions
  
  • Goncharov F O
  , 2017. We consider integrals of spherical harmonics with Fourier exponents on the sphere $S^n , n ≥ 1$. Such transforms arise in the framework of the theory of weighted Radon transforms and vector diffraction in electromagnetic fields theory. We give analytic formulas for these integrals, which are exact up to multiplicative constants. These constants depend on choice of basis on the sphere. In addition, we find these constants explicitly for the class of harmonics arising in the framework of the theory of weighted Radon transforms. We also suggest formulas for finding these constants for the general case.
• Robust domain decomposition methods in industrial context applied to large business cases
  
  • Parret-Fréaud Augustin
  • Rey Christian
  • Feyel Frédéric
  • Bovet Christophe
  • Gosselet Pierre
  • Marchand Basile
  • Spillane Nicole
  , 2017.
• MCMC design-based non-parametric regression for rare-event. Application to nested risk computations
  
  • Fort Gersende
  • Gobet Emmanuel
  • Moulines Éric
  Monte Carlo Methods and Applications, De Gruyter, 2017, 23 (1), pp.21--42. We design and analyze an algorithm for estimating the mean of a function of a conditional expectation, when the outer expectation is related to a rare-event. The outer expectation is evaluated through the average along the path of an ergodic Markov chain generated by a Markov chain Monte Carlo sampler. The inner conditional expectation is computed as a non-parametric regression, using a least-squares method with a general function basis and a design given by the sampled Markov chain. We establish non asymptotic bounds for the L2-empirical risks associated to this least-squares regression; this generalizes the error bounds usually obtained in the case of i.i.d. observations. Global error bounds are also derived for the nested expectation problem. Numerical results in the context of financial risk computations illustrate the performance of the algorithms.
• Simulation of reactive polydisperse sprays strongly coupled to unsteady flows in solid rocket motors: Efficient strategy using Eulerian Multi-Fluid methods
  
  • Sibra Alaric
  • Dupays Joel
  • Murrone Angelo
  • Laurent Frédérique
  • Massot Marc
  Journal of Computational Physics, Elsevier, 2017. In this paper, we tackle the issue of the accurate simulation of evaporating and reactive polydisperse sprays strongly coupled to unsteady gaseous flows. In solid propulsion, aluminum particles are included in the propellant to improve the global performances but the distributed combustion of these droplets in the chamber is suspected to be a driving mechanism of hydrodynamic and acoustic instabilities. The faithful prediction of two-phase interactions is a determining step for future solid rocket motor optimization. When looking at saving computational ressources as required for industrial applications, performing reliable simulations of two-phase flow instabilities appears as a challenge for both modeling and scientific computing. The size polydispersity, which conditions the droplet dynamics, is a key parameter that has to be accounted for. For moderately dense sprays, a kinetic approach based on a statistical point of view is particularly appropriate. The spray is described by a number density function and its evolution follows a Williams-Boltzmann transport equation. To solve it, we use Eulerian Multi-Fluid methods, based on a continuous discretization of the size phase space into sections, which offer an accurate treatment of the polydispersion. The objective of this paper is threefold: first to derive a new Two Size Moment Multi-Fluid model that is able to tackle evaporating polydisperse sprays at low cost while accurately describing the main driving mechanisms, second to develop a dedicated evaporation scheme to treat simultaneously mass, moment and energy exchanges with the gas and between the sections. Finally, to design a time splitting operator strategy respecting both reactive two-phase flow physics and cost/accuracy ratio required for industrial computations. Using a research code, we provide 0D validations of the new scheme before assessing the splitting technique's ability on a reference two-phase flow acoustic case. Implemented in the industrial oriented CEDRE code, all developments allow to simulate realistic solid rocket motor configurations featuring the first polydisperse reactive computations with a fully Eulerian method. (10.1016/j.jcp.2017.02.003)
  DOI : 10.1016/j.jcp.2017.02.003
• Online EM for Functional Data
  
  • Maire Florian
  • Moulines Éric
  • Lefebvre Sidonie
  Computational Statistics and Data Analysis, Elsevier, 2017, 111, pp.27-47. A novel approach to perform unsupervised sequential learning for functional data is proposed. The goal is to extract reference shapes (referred to as templates) from noisy, deformed and censored realizations of curves and images. The proposed model generalizes the Bayesian dense deformable template model, a hierarchical model in which the template is the function to be estimated and the deformation is a nuisance, assumed to be random with a known prior distribution. The templates are estimated using a Monte Carlo version of the online Expectation–Maximization (EM) algorithm. The designed sequential inference framework is significantly more computationally efficient than equivalent batch learning algorithms, especially when the missing data is high-dimensional. Some numerical illustrations on curve registration problem and templates extraction from images are provided to support the methodology.</br> Highlights <ul> <li>A mixture of deformable models for functional data (curves and shapes).</li> <li>Inference is conducted using a novel approach, the Monte Carlo online EM algorithm.</li> <li>Templates from data with high time/geometric dispersion.</li> <li>Processing observations on the fly, MCoEM is more efficient than batch EM algorithms.</li> </ul> (10.1016/j.csda.2017.01.006)
  DOI : 10.1016/j.csda.2017.01.006
• Checking the strict positivity of Kraus maps is NP-hard
  
  • Gaubert Stéphane
  • Qu Zheng
  Information Processing Letters, Elsevier, 2017, 118, pp.35--43. Basic properties in Perron-Frobenius theory are positivity, primitivity, and irreducibility. Whereas these properties can be checked in polynomial time for stochastic matrices, we show that for Kraus maps - the noncommutative generalization of stochastic matrices - checking positivity is NP-hard. This is in contrast with irreducibility and primitivity, which we show to be checkable in strongly polynomial time for completely positive maps - the noncommutative generalization of nonpositive matrices. As an intermediate result, we get that the bilinear feasibility problem over $\mathbb{Q}$ is NP-hard. (10.1016/j.ipl.2016.09.008)
  DOI : 10.1016/j.ipl.2016.09.008
• A Positive and Entropy-Satisfying Finite Volume Scheme for the Baer-Nunziato Model
  
  • Coquel Frédéric
  • Hérard Jean-Marc
  • Saleh Khaled
  Journal of Computational Physics, Elsevier, 2017, 330, pp.401-435. We present a relaxation scheme for approximating the entropy dissipating weak solutions of the Baer-Nunziato two-phase flow model. This relaxation scheme is straightforwardly obtained as an extension of the relaxation scheme designed in [16] for the isentropic Baer-Nunziato model and consequently inherits its main properties. To our knowledge, this is the only existing scheme for which the approximated phase fractions, phase densities and phase internal energies are proven to remain positive without any restrictive condition other than a classical fully computable CFL condition. For ideal gas and stiffened gas equations of state, real values of the phasic speeds of sound are also proven to be maintained by the numerical scheme. It is also the only scheme for which a discrete entropy inequality is proven, under a CFL condition derived from the natural sub-characteristic condition associated with the relaxation approximation. This last property, which ensures the non-linear stability of the numerical method, is satisfied for any admissible equation of state. We provide a numerical study for the convergence of the approximate solutions towards some exact Riemann solutions. The numerical simulations show that the relaxation scheme compares well with two of the most popular existing schemes available for the Baer-Nunziato model, namely Schwendeman-Wahle-Kapila's Godunov-type scheme [39] and Toro-Tokareva's HLLC scheme [42]. The relaxation scheme also shows a higher precision and a lower computational cost (for comparable accuracy) than a standard numerical scheme used in the nuclear industry, namely Rusanov's scheme. Finally, we assess the good behavior of the scheme when approximating vanishing phase solutions. (10.1016/j.jcp.2016.11.017)
  DOI : 10.1016/j.jcp.2016.11.017
• From Hard Sphere Dynamics to the Stokes–Fourier Equations: An Analysis of the Boltzmann–Grad Limit
  
  • Bodineau Thierry
  • Gallagher Isabelle
  • Saint-Raymond Laure
  Annals of PDE, Springer, 2017, 3 (1). We derive the linear acoustic and Stokes-Fourier equations as the limiting dynamics of a system of N hard spheres of diameter $\epsilon$ in two space dimensions, when N $\rightarrow$ $\infty$, $\epsilon$ $\rightarrow$ 0, N $\epsilon$ = $\alpha$ $\rightarrow$ $\infty$, using the linearized Boltzmann equation as an intermediate step. Our proof is based on Lanford's strategy [18], and on the pruning procedure developed in [5] to improve the convergence time to all kinetic times with a quantitative control which allows us to reach also hydrodynamic time scales. The main novelty here is that uniform L 2 a pri-ori estimates combined with a subtle symmetry argument provide a weak version of chaos, in the form of a cumulant expansion describing the asymptotic decorrelation between the particles. A refined geometric analysis of recollisions is also required in order to discard the possibility of multiple recollisions. (10.1007/s40818-016-0018-0)
  DOI : 10.1007/s40818-016-0018-0
• Methods and algorithms to learn spatio-temporal changes from longitudinal manifold-valued observations
  
  • Schiratti Jean-Baptiste
  , 2017. We propose a generic Bayesian mixed-effects model to estimate the temporal progression of a biological phenomenon from manifold-valued observations obtained at multiple time points for an individual or group of individuals. The progression is modeled by continuous trajectories in the space of measurements, which is assumed to be a Riemannian manifold. The group-average trajectory is defined by the fixed effects of the model. To define the individual trajectories, we introduced the notion of « parallel variations » of a curve on a Riemannian manifold. For each individual, the individual trajectory is constructed by considering a parallel variation of the average trajectory and reparametrizing this parallel in time. The subject specific spatiotemporal transformations, namely parallel variation and time reparametrization, are defined by the individual random effects and allow to quantify the changes in direction and pace at which the trajectories are followed. The framework of Riemannian geometry allows the model to be used with any kind of measurements with smooth constraints. A stochastic version of the Expectation-Maximization algorithm, the Monte Carlo Markov Chains Stochastic Approximation EM algorithm (MCMC-SAEM), is used to produce produce maximum a posteriori estimates of the parameters. The use of the MCMC-SAEM together with a numerical scheme for the approximation of parallel transport is discussed. In addition to this, the method is validated on synthetic data and in high-dimensional settings. We also provide experimental results obtained on health data.
• Volumetric expressions of the shape gradient of the compliance in structural shape optimization
  
  • Giacomini Matteo
  • Pantz Olivier
  • Trabelsi Karim
  , 2017. In this article, we consider the problem of optimal design of a compliant structure under a volume constraint, within the framework of linear elasticity. We introduce the pure displacement and the dual mixed formulations of the linear elasticity problem and we compute the volumetric expressions of the shape gradient of the compliance by means of the velocity method. A preliminary qualitative comparison of the two expressions of the shape gradient is performed through some numerical simulations using the Boundary Variation Algorithm.
• Acceleration of saddle-point methods in smooth cases
  
  • Tan Pauline
  , 2017. In the present paper we propose a novel convergence analysis of the Alternating Direction Methods of Multipliers (ADMM), based on its equivalence with the overrelaxed Primal-Dual Hybrid Gradient (oPDHG) algorithm. We consider the smooth case, which correspond to the cas where the objective function can be decomposed into one differentiable with Lipschitz continuous gradient part and one strongly convex part. An accelerated variant of the ADMM is also proposed, which is shown to converge linearly with same rate as the oPDHG.
• Linearly Convergent Evolution Strategies via Augmented Lagrangian Constraint Handling
  
  • Atamna Asma
  • Auger Anne
  • Hansen Nikolaus
  , 2017, pp.149 - 161. We analyze linear convergence of an evolution strategy for constrained optimization with an augmented Lagrangian constraint handling approach. We study the case of multiple active linear constraints and use a Markov chain approach—used to analyze ran-domized optimization algorithms in the unconstrained case—to establish linear convergence under sufficient conditions. More specifically , we exhibit a class of functions on which a homogeneous Markov chain (defined from the state variables of the algorithm) exists and whose stability implies linear convergence. This class of functions is defined such that the augmented Lagrangian, centered in its value at the optimum and the associated Lagrange multipliers, is positive homogeneous of degree 2, and includes convex quadratic functions. Simulations of the Markov chain are conducted on linearly constrained sphere and ellipsoid functions to validate numerically the stability of the constructed Markov chain. (10.1145/3040718.3040732)
  DOI : 10.1145/3040718.3040732
• Quality Gain Analysis of the Weighted Recombination Evolution Strategy on General Convex Quadratic Functions
  
  • Akimoto Youhei
  • Auger Anne
  • Hansen Nikolaus
  , 2017, pp.111-126. We investigate evolution strategies with weighted recombi-nation on general convex quadratic functions. We derive the asymptotic quality gain in the limit of the dimension to infinity, and derive the optimal recombination weights and the optimal step-size. This work is an extension of previous works where the asymptotic quality gain of evolution strategies with weighted recombination was derived on the infinite dimensional sphere function. Moreover, for a finite dimensional search space, we derive rigorous bounds for the quality gain on a general quadratic function. They reveal the dependency of the quality gain both in the eigenvalue distribution of the Hessian matrix and on the recombina-tion weights. Taking the search space dimension to infinity , it turns out that the optimal recombination weights are independent of the Hessian matrix, i.e., the recombination weights optimal for the sphere function are optimal for convex quadratic functions. (10.1145/3040718.3040720)
  DOI : 10.1145/3040718.3040720
• Direct and inverse solvers for scattering problems from locally perturbed infinite periodic layers
  
  • Nguyen Thi Phong
  , 2017. We are interested in this thesis by the analysis of scattering and inverse scattering problems for locally perturbed periodic infinite layers at a fixed frequency. This problem has connexions with non destructive testings of periodic media like photonics structures, optical fibers, gratings, etc. We first analyze the forward scattering problem and establish some conditions under which there exist no guided modes. This type of conditions is important as it shows that measurements can be done on a layer above the structure without loosing substantial informations in the propagative part of the wave. We then propose a numerical method that solves the direct scattering problem based on Floquet-Bloch transform in the periodicity directions of the background media. We discretize the problem uniformly in the Floquet-Bloch variable and use a spectral method in the space variable. The discretization in space exploits a volumetric reformulation of the problem in a cell (Lippmann-Schwinger integral equation) and a periodization of the kernel in the direction orthogonal to the periodicity. The latter allows the use of FFT techniques to speed up Matrix-Vector product in an iterative to solve the linear system. One ends up with a system of coupled integral equations that can be solved using a Jacobi decomposition. The convergence analysis is done for the case with absorption and numerical validating results are conducted in 2D. For the inverse problem we extend the use of three sampling methods to solve the problem of retrieving the defect from the knowledge of mutistatic data associated with incident near field plane waves. We analyze these methods for the semi-discretized problem in the Floquet-Bloch variable. We then propose a new method capable of retrieving directly the defect without knowing either the background material properties nor the defect properties. This so-called differential-imaging functional that we propose is based on the analysis of sampling methods for a single Floquet-Bloch mode and the relation with solutions toso-called interior transmission problems. The theoretical investigations are corroborated with numerical experiments on synthetic data. Our analysis is done first for the scalar wave equation where the contrast is the lower order term of the Helmholtz operator. We then sketch the extension to the cases where the contrast is also present in the main operator. We complement our thesis with two results on the analysis of the scattering problem for periodic materials with negative indices. Weestablish the well posedness of the problem in 2D in the case of a contrast equals -1. We also show the Fredholm properties of the volume potential formulation of the problem using the T-coercivity approach in the case of a contrast different from -1.
• Branching diffusion representation of semilinear PDEs and Monte Carlo approximation *
  
  • Henry-Labordère Pierre
  • Oudjane Nadia
  • Tan Xiaolu
  • Touzi Nizar
  • Warin Xavier
  , 2017. We provide a representation result of parabolic semi-linear PD-Es, with polynomial nonlinearity, by branching diffusion processes. We extend the classical representation for KPP equations, introduced by Skorokhod [23], Watanabe [27] and McKean [18], by allowing for polynomial nonlinearity in the pair (u, Du), where u is the solution of the PDE with space gradient Du. Similar to the previous literature, our result requires a non-explosion condition which restrict to " small maturity " or " small nonlinearity " of the PDE. Our main ingredient is the automatic differentiation technique as in [15], based on the Malliavin integration by parts, which allows to account for the nonlin-earities in the gradient. As a consequence, the particles of our branching diffusion are marked by the nature of the nonlinearity. This new representation has very important numerical implications as it is suitable for Monte Carlo simulation. Indeed, this provides the first numerical method for high dimensional nonlinear PDEs with error estimate induced by the dimension-free Central limit theorem. The complexity is also easily seen to be of the order of the squared dimension. The final section of this paper illustrates the efficiency of the algorithm by some high dimensional numerical experiments.
• Unbiased simulation of stochastic differential equations *
  
  • Henry-Labordère Pierre
  • Tan Xiaolu
  • Touzi Nizar
  , 2017. We propose an unbiased Monte-Carlo estimator for E[g(X t 1 , · · · , X tn)], where X is a diffusion process defined by a multi-dimensional stochastic differential equation (SDE). The main idea is to start instead from a well-chosen simulatable SDE whose coefficients are updated at independent exponential times. Such a simulatable process can be viewed as a regime-switching SDE, or as a branching diffusion process with one single living particle at all times. In order to compensate for the change of the coefficients of the SDE, our main representation result relies on the automatic differentiation technique induced by Bismu-Elworthy-Li formula from Malliavin calculus, as exploited by Fournié et al. [14] for the simulation of the Greeks in financial applications. In particular, this algorithm can be considered as a variation of the (infinite variance) estimator obtained in Bally and Kohatsu-Higa [3, Section 6.1] as an application of the parametrix method. MSC2010. Primary 65C05, 60J60; secondary 60J85, 35K10.
• Analyse des liens entre un modèle d'endommagement et un modèle de fracture
  
  • Azem Leila
  , 2017. Cette thèse est consacrée à la dérivation des modèles de fracture comme limite de modèles d'endommagement.L'étude est justifiée essentiellement à travers des simulations numériques.On s'intéresse à étudier un modèle d'endommagement initié par Allaire, Jouve et Vangoethem.Nous apportons des améliorations significatives à ce modèle justifiant la cohérence physique de cette approche.D'abord, on ajoute une contrainte sur l'épaisseur minimale de la zone endommagée, puis on ajoute la condition d'irréversibilité forte.Nous considérons en outre un modèle de fracture avec pénalisation de saut obtenu comme limite asymptotique d'un modèle d'endommagement.Nous justifions ce modèle par une étude numérique et asymptotique formelle unidimensionnelle.Ensuite, la généralisation dans le cas 2D est illustrée par des exemples numériques.
• A new accurate residual-based a posteriori error indicator for the BEM in 2D-acoustics
  
  • Bakry Marc
  • Pernet Sebastien
  • Collino Francis
  Computers & Mathematics with Applications, Elsevier, 2017, 73 (12), pp.2501 - 2514. In this work we construct a new reliable, efficient and local a posteriori error estimate for the single layer and hyper-singular boundary integral equations associated to the Helmholtz equation in two dimensions. It uses a localization technique based on a generic operator Λ which is used to transport the residual into L2. Under appropriate conditions on the construction of Λ, we show that it is asymptotically exact with respect to the energy norm of the error. The single layer equation and the hyper-singular equation are treated separately. While the current analysis requires the boundary to be smooth, numerical experiments show that the new error estimators also perform well for non-smooth boundaries. (10.1016/j.camwa.2017.03.016)
  DOI : 10.1016/j.camwa.2017.03.016
• Couplings, gradient estimates and logarithmic Sobolev inequalitiy for Langevin bridges
  
  • Conforti Giovanni
  • von Renesse Max-K.
  Probability Theory and Related Fields, Springer Verlag, 2017. In this paper we establish quantitative results about the bridges of the Langevin dynamics and the associated reciprocal processes. They include an equivalence between gradient estimates for bridge semigroups and couplings, comparison principles, bounds of the distance between bridges of different Langevin dynamics, and a logarithmic Sobolev inequality for bridge measures. The existence of an invariant measure for the bridges is also discussed and quantitative bounds for the convergence to the invariant measure are proven. All results are based on a seemingly new expression of the drift of a bridge in terms of the reciprocal characteristic, which, roughly speaking, quantifies the “mean acceleration” of a bridge. (10.1007/s00440-017-0814-9)
  DOI : 10.1007/s00440-017-0814-9