# Publications sur H.A.L.

Retour Accueil / Recherche / Publications sur H.A.L.

### [hal-02445223] Inverse problem for a coupling model of reaction-diffusion and ordinary differential equations systems. Application to an epidemiological model

This paper investigates an identifiability method for a class of systems of reaction diffusion equations in the L^2 framework. This class is composed of a master system of ordinary differential equations coupled with a slave system of diffusion equations. It can model two populations, the second one being diffusive contrary to the first one. The identifiability method is based on an elimination procedure providing relations called input-output polynomials and linking the unknown parameters , the inputs and the outputs of the model. These polynomials can also be used to estimate the parameters as shown in this article. To our best knowledge, such an identifiability method and a parameter estimation procedure have not yet been explored for such a system in the L^2 framework. This work is applied on an epidemiological model describing the propagation of the chikungunya in a local population.

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdière), Nathalie Verdière

### [hal-01919067] A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints

In this work, we develop an a-posteriori-steered algorithm for a compositional two-phase flow with exchange of components between the phases in porous media. As a model problem, we choose the two-phase liquid-gas flow with appearance and disappearance of the gas phase formulated as a system of nonlinear evolutive partial differential equations with nonlinear complementarity constraints. The discretization of our model is based on the backward Euler scheme in time and the finite volume scheme in space. The resulting nonlinear system is solved via an inexact semismooth Newton method. The key ingredient for the a posteriori analysis are the discretization, linearization, and algebraic flux reconstructions allowing to devise estimators for each error component. These enable to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver whenever the corresponding error components do not affect significantly the overall error. Numerical experiments are performed using the Newton-min algorithm as well as the Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative linear solver to show the efficiency of the proposed adaptive method.

ano.nymous@ccsd.cnrs.fr.invalid (Ibtihel Ben Gharbia), Ibtihel Ben Gharbia

### [hal-01914536] Optimal initial state for fast parameter estimation in nonlinear dynamical systems

Background and Objective: This paper deals with the improvement of parameter estimation in terms of precision and computational time for dynamical models in a bounded error context. Methods: To improve parameter estimation, an optimal initial state design is proposed combined with a contractor. This contractor is based on a volumetric criterion and an original condition initializing this contractor is given. Based on a sensitivity analysis, our optimal initial state design methodology consists in searching the minimum value of a proposed criterion for the interested parameters. In our framework, the uncertainty (on measurement noise and parameters) is supposed unknown but belongs to known bounded intervals. Thus guaranteed state and sensitivity estimation have been considered. An elementary effect analysis on the number of sampling times is also implemented to achieve the fast and guaranteed parameter estimation. Results: The whole procedure is applied to a pharmacokinetics model and simulation results are given. Conclusions: The good improvement of parameter estimation in terms of computational time and precision for the case study highlights the potential of the proposed methodology.

ano.nymous@ccsd.cnrs.fr.invalid (Qiaochu Li), Qiaochu Li

### [hal-01919067] A posteriori error estimates and adaptive stopping criteria for a compositional two-phase flow with nonlinear complementarity constraints

In this work, we develop an a-posteriori-steered algorithm for a compositional two-phase flow with exchange of components between the phases in porous media. As a model problem, we choose the two-phase liquid-gas flow with appearance and disappearance of the gas phase formulated as a system of nonlinear evolutive partial differential equations with nonlinear complementarity constraints. The discretization of our model is based on the backward Euler scheme in time and the finite volume scheme in space. The resulting nonlinear system is solved via an inexact semismooth Newton method. The key ingredient for the a posteriori analysis are the discretization, linearization, and algebraic flux reconstructions allowing to devise estimators for each error component. These enable to formulate criteria for stopping the iterative algebraic solver and the iterative linearization solver whenever the corresponding error components do not affect significantly the overall error. Numerical experiments are performed using the Newton-min algorithm as well as the Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative linear solver to show the efficiency of the proposed adaptive method.

ano.nymous@ccsd.cnrs.fr.invalid (Ibtihel Ben Gharbia), Ibtihel Ben Gharbia

### [inria-00625293] Exact MLE and asymptotic properties for nonparametric semi-Markov models

This article concerns maximum-likelihood estimation for discrete time homogeneous nonparametric semi-Markov models with finite state space. In particular, we present the exact maximum-likelihood estimator of the semi-Markov kernel which governs the evolution of the semi-Markov chain (SMC). We study its asymptotic properties in the following cases: (i) for one observed trajectory, when the length of the observation tends to infinity, and (ii) for parallel observations of independent copies of an SMC censored at a fixed time, when the number of copies tends to infinity. In both cases, we obtain strong consistency, asymptotic normality, and asymptotic efficiency for every finite dimensional vector of this estimator. Finally, we obtain explicit forms for the covariance matrices of the asymptotic distributions.

ano.nymous@ccsd.cnrs.fr.invalid (Samis Trevezas), Samis Trevezas

### [cea-02360117] Estimating Stochastic Dynamical Systems Driven by a Continuous-Time Jump Markov Process

We discuss the use of a continuous-time jump Markov process as the driving process in stochastic differential systems. Results are given on the estimation of the infinitesimal generator of the jump Markov process, when considering sample paths on random time intervals. These results are then applied within the framework of stochastic dynamical systems modeling and estimation. Numerical examples are given to illustrate both consistency and asymptotic normality of the estimator of the infinitesimal generator of the driving process. We apply these results to fatigue crack growth modeling as an example of a complex dynamical system, with applications to reliability analysis.

ano.nymous@ccsd.cnrs.fr.invalid (Julien Chiquet), Julien Chiquet

### [hal-01666845] Adaptive inexact semismooth Newton methods for the contact problem between two membranes

We propose an adaptive inexact version of a class of semismooth Newton methods. As a model problem, we study the system of variational inequalities describing the contact between two membranes. This problem is discretized with conforming finite elements of order $p \geq 1$, yielding a nonlinear algebraic system of variational inequalities. We consider any iterative semismooth linearization algorithm like the Newton-min or the Newton--Fischer--Burmeister which we complement by any iterative linear algebraic solver. We then derive an a posteriori estimate on the error between the exact solution and the approximate solution which is valid at any step of the linearization and algebraic resolutions. Our estimate is based on flux reconstructions in discrete subspaces of $\mathbf{H}(\mathrm{div}, \Omega)$ and on potential reconstructions in discrete subspaces of $H^1(\Omega)$ satisfying the constraints. It distinguishes the discretization, linearization, and algebraic components of the error. Consequently, we can formulate adaptive stopping criteria for both solvers, giving rise to an adaptive version of the considered inexact semismooth Newton algorithm. Under these criteria, the efficiency of our estimates is also established, meaning that we prove them equivalent with the error up to a generic constant, except for a typically small contact term. Numerical experiments for the Newton-min algorithm in combination with the GMRES algebraic solver confirm the efficiency of the developed adaptive method.

### [hal-01939854] A New Algorithm of Proper Generalized Decomposition for Parametric Symmetric Elliptic Problems

We introduce a new algorithm of proper generalized decomposition (PGD) for parametric symmetric elliptic partial differential equations. For any given dimension, we prove the existence of an optimal subspace of at most that dimension which realizes the best approximation---in the mean parametric norm associated to the elliptic operator---of the error between the exact solution and the Galerkin solution calculated on the subspace. This is analogous to the best approximation property of the proper orthogonal decomposition (POD) subspaces, except that in our case the norm is parameter-dependent. We apply a deflation technique to build a series of approximating solutions on finite-dimensional optimal subspaces, directly in the online step, and we prove that the partial sums converge to the continuous solution in the mean parametric elliptic norm. We show that the standard PGD for the considered parametric problem is strongly related to the deflation algorithm introduced in this paper. This opens the possibility of computing the PGD expansion by directly solving the optimization problems that yield the optimal subspaces.

ano.nymous@ccsd.cnrs.fr.invalid (M. Azaïez), M. Azaïez

### [insu-00159752] EBSD investigation of SiC for HTR fuel particles

Electron back-scattering diffraction (EBSD) can be successfully performed on SiC coatings for HTR fuel particles. EBSD grain maps obtained from thick and thin unirradiated samples are presented, along with pole figures showing textures and a chart showing the distribution of grain aspect ratios. This information is of great interest, and contributes to improving the process parameters and ensuring the reproducibility of coatings

ano.nymous@ccsd.cnrs.fr.invalid (D. Helary), D. Helary

### [hal-01006087] Multidimensional Independent Component Analysis with Higher-order cumulant matrices for vector sources with possibly differing dimensions

The paper addresses the separation of multidimensional sources, with possibly different dimensions, by means of higher-order cumulant matrices. First, it is rigorously proved, in a general setting, that contracted cumulant matrices of any order are all block-diagonalizable in the same basis. Second, a family of joint block-diagonalization algorithms is proposed that separate multidimensional sources by combining contracted cumulant matrices of arbitrary orders. Third, a specific solution is given to determine the source dimensions when they are unknown but all different. The performances of the proposed algorithms are compared between them and with algorithms of the literature based on orders 3 and 6.

ano.nymous@ccsd.cnrs.fr.invalid (Hanany Ould-Baba), Hanany Ould-Baba

### [hal-01006074] Concise formulae for the cumulant matrices of a random vector

Concise formulae are given for the cumulant matrices of a random vector up to order 6. In addition to usual matrix operations, they involve only the Kronecker product, the vec operator, and the commutation matrix. Orders 5 and 6 are provided here for the first time; the same method as provided in the paper can be applied to compute higher orders. An immediate consequence of these formulae is to return 1) upper bounds on the rank of the cumulant matrices and 2) the expression of the sixth-order moment matrix of a Gaussian vector. Due to their conciseness, the proposed formulae also have a computational advantage as compared to the repeated use of Leonov and Shiryaev formula.

ano.nymous@ccsd.cnrs.fr.invalid (Hanany Ould-Baba), Hanany Ould-Baba

### [hal-01635222] Reliability and probability of first occurred failure for discrete-time semi-Markov systems

In this chapter, we present the empirical estimation of some reliability measures, such as the rate of occurrence of failures and the steady-state availability, for a discrete-time semi-Markov system. The probability of first occurred failure is introduced and estimated. A numerical application is given to illustrate the strong consistency of these estimators.

### [hal-02153384] Hypotheses testing and posterior concentration rates for semi-Markov processes

In this paper, we adopt a nonparametric Bayesian approach and investigate the asymptotic behavior of the posterior distribution in continuous time and general state space semi-Markov processes. In particular, we obtain posterior concentration rates for semi-Markov kernels. For the purposes of this study, we construct robust statistical tests between Hellinger balls around semi-Markov kernels and present some specifications to particular cases, including discrete-time semi-Markov processes and finite state space Markov processes. The objective of this paper is to provide sufficient conditions on priors and semi-Markov kernels that enable us to establish posterior concentration rates.

ano.nymous@ccsd.cnrs.fr.invalid (V Barbu), V Barbu

### [hal-01635178] Estimation of the Expected Number of Earthquake Occurrences Based on Semi-Markov Models

The present paper aims at the introduction of the semi-Markov model in continuous time as a candidate model for the description of seismicity patterns in time domain in the Northern Aegean Sea (Greece). Estimators of the semi-Markov kernels, Markov renewal functions and transition functions are calculated through a nonparametric method. Moreover , the hitting times for spatial occurrence of the strongest earthquakes as well as the confidence intervals of certain important indicators are estimated. Firstly, the classification of model states is based on earthquakes magnitude. The instantaneous earthquake occurrence rate between the states of the model as well as the total earthquake occurrence rate are calculated. In order to increase the consistency between the model and the process of earthquake generation, seismotectonic features have been incorporated as an important component in the model. Therefore, a new classification of states is proposed which combines both magnitude and fault orientation states. This model which takes into account seismotectonic features contributes significantly to the seismic hazard assessment in the region under study. The model is applied to earthquake catalogues for the Northern Aegean Sea, an area that accommodates high seismicity, being a key structure from the seismotec-tonic point of view.

ano.nymous@ccsd.cnrs.fr.invalid (Irene Votsi), Irene Votsi

### [hal-02025747] Optimal input design for parameter estimation in a bounded-error context for nonlinear dynamical systems

This paper deals with optimal input design for parameter estimation in a bounded-error context. Uncertain controlled nonlinear dynamical models, when the input can be parametrized by a finite number of parameters, are considered. The main contribution of this paper concerns criteria for obtaining optimal inputs in this context. Two input design criteria are proposed and analysed. They involve sensitivity functions. The first criterion requires the inversion of the Gram matrix of sensitivity functions. The second one does not require this inversion and is then applied for parameter estimation of a model taken from the aeronautical domain. The estimation results obtained using an optimal input are compared with those obtained with an input optimized in a more classical context (Gaussian measurement noise and parameters a priori known to belong to some boxes). These results highlight the potential of optimal input design in a bounded-error context.

ano.nymous@ccsd.cnrs.fr.invalid (Carine Jauberthie), Carine Jauberthie

### [hal-02315520] Identification of words in biological sequences under the semi-Markov hypothesis

Identifying a word (pattern) in a long sequence of letters is not an easy task. To achieve this objective several models have been proposed under the assumption that the sequence of letters is described by a Markov chain. The Markovian hypothesis imposes restrictions on the distribution of the sojourn time in a state, which has geometric distribution in a discrete process. This is the main drawback when applying Markov chains in real problems. By contrast, semi-Markov processes generalize semi-Markov processes. In semi-Markov processes the sojourn time in a state can be governed by any distribution function. The goal of this article is compute the first hitting time (position) of a word (pattern) in a semi-Markov sequence. To achieve this objective we use the auxiliary prefix and backward chain. To give an example of the applications of the proposed model, the model is tested in a bacteriophage DNA sequence where is looking the enzyme SmaI. We compute the probability that a word occurs for the first time after n nucleotides in a DNA sequence. The corresponding probability distribution, the mean waiting position, the variance and rate of the occurrence of the word are obtained.

ano.nymous@ccsd.cnrs.fr.invalid (Brenda Ivette Garcia-Maya), Brenda Ivette Garcia-Maya

### [hal-02307169] Genetic background and immunological status influence B cell repertoire diversity in mice

The relationship between the immune repertoire and the physiopathological status of individuals is essential to apprehend the genesis and the evolution of numerous pathologies. Nevertheless, the methodological approaches to understand these complex interactions are challenging. We performed a study evaluating the diversity harbored by different immune repertoires as a function of their physiopathological status. In this study, we base our analysis on a murine scFv library previously described and representing four different immune repertoires: i) healthy and naïve, ii) healthy and immunized, iii) autoimmune prone and naïve, and iv) autoimmune prone and immunized. This library, 2.6 × 10 9 in size, is submitted to high throughput sequencing (Next Generation Sequencing, NGS) in order to analyze the gene subgroups encoding for immunoglobulins. A comparative study of the distribution of immunoglobulin gene subgroups present in the four libraries has revealed shifts in the B cell repertoire originating from differences in genetic background and immunological status of mice. The adaptive immune system is capable of producing antibodies against a large number of immunogens. This vast diversity of immunoglobulin sequences is not provided by the limited number of genes present in the genome, but by rearrangements of the germline at specific loci. In the case of B cell receptors, rearrangement of variable (V), diversity (D), and joining (J) gene segments in V-Domain creates a combinatorial diversity for the immu-noglobulin heavy chain (IGH), whereas rearrangement of V and J gene segments provides a similar diversity for the lambda or kappa light chains (IGL/IGK) 1 (Fig. 1). Additionally, at the junctions of V-D and D-J segments, a process of random deletion and addition of nucleotides creates an immense junctional diversity. Finally, somatic hypermutations focused on Complementary Determining Regions (CDR) supplement the mechanisms of immu-noglobulin maturation, expanding still further the diversity and leading to affine and specific antibodies. Studies have shown that this vast diversity, as well as other characteristics of the immune repertoire, can be influenced by factors such as immunization 2,3 or pathology, notably autoimmune diseases 4-6. Generation of antibody libraries is a crucial step in the attempt to study in vivo immune repertoires 7,8. Care needs to be taken to ensure the coverage of a large antibody sequence diversity in order to mimic the natural B cell repertoire as close as possible. Recently, we have described an original strategy allowing to improve the library construction process and increase its diversity 9. This strategy is based on a technological optimization relying on Rolling Circle Amplification (RCA), combined with a newly designed set of oligonucleotide primers based on a thorough analysis of the IMGT/LIGM-DB database 10. In the present study, we have used this strategy to generate libraries form two murine inbred strains were used, namely Balb/C (healthy) and SJL/J (susceptible to autoimmune disease), together representing 4 different IgG immune repertoires: i) healthy and naïve (NB for naïve Balb/C), ii) healthy and immunized (IB for immunized Balb/C), iii) autoimmune prone and naïve (NS for naïve SJL/J), and iv) autoimmune prone and immunized (IS for immunized SJL/J) 11. We have decidedly chosen to

ano.nymous@ccsd.cnrs.fr.invalid (Nancy Chaaya), Nancy Chaaya

### [hal-01280269] Stationary Flow of Blood in a Rigid Vessel in the Presence of an External Magnetic Field : Considerations about the Forces and Wall Shear Stresses

The magnetohydrodynamics laws govern the motion of a conducting fluid, such as blood, in an externally applied static magnetic field B 0. When an artery is exposed to a magnetic field, the blood charged particles are deviated by the Lorentz force thus inducing electrical currents and voltages along the vessel walls and in the neighboring tissues. Such a situation may occur in several bio-medical applications: magnetic resonance imaging (MRI), magnetic drug transport and targeting, tissue engineering… In this paper, we consider the steady unidirectional blood flow in a straight circular rigid vessel with non-conducting walls, in the presence of an exterior static magnetic field. The exact solution of Gold (1962) (with the induced fields not neglected) is revisited. It is shown that the integration over a cross section of the vessel of the longitudinal projection of the Lorentz force is zero, and that this result is related to the existence of current return paths, whose contributions compensate each other over the section. It is also demonstrated that the classical definition of the shear stresses cannot apply in this situation of magnetohydrodynamic flow, because, due to the existence of the Lorentz force, the axisymmetry is broken.

ano.nymous@ccsd.cnrs.fr.invalid (Agnès Drochon), Agnès Drochon

### [hal-01993267] Identifiability and identification of a pollution source in a river by using a semi-discretized model

This paper is devoted to the identification of a pollution source in a river. A simple mathematical model of such a problem is given by a one-dimensional linear advection–dispersion–reaction equation with a right hand side spatially supported in a point (the source) and a time varying intensity, both unknown. There exist some identifiability results about this distributed system. But the numerical estimation of the unknown quantities require the introduction of an approximated model, whose identifiability properties are not analyzed usually. This paper has a double purpose: – to do the identifiability analysis of the differential system considered for estimating the parameters, – to propose a new numerical global search of these parameters, based on the previous analysis. Another consequence of this approach is to give the unknown pollution intensity directly as the solution of a differential equation. Lastly, the numerical algorithm is described in detail, completed with some applications.

ano.nymous@ccsd.cnrs.fr.invalid (Nathalie Verdière), Nathalie Verdière

### [hal-01391578] A Coq formal proof of the Lax–Milgram theorem

The Finite Element Method is a widely-used method to solve numerical problems coming for instance from physics or biology. To obtain the highest confidence on the correction of numerical simulation programs implementing the Finite Element Method, one has to formalize the mathematical notions and results that allow to establish the sound-ness of the method. The Lax–Milgram theorem may be seen as one of those theoretical cornerstones: under some completeness and coercivity assumptions, it states existence and uniqueness of the solution to the weak formulation of some boundary value problems. This article presents the full formal proof of the Lax–Milgram theorem in Coq. It requires many results from linear algebra, geometry, functional analysis , and Hilbert spaces.

ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo

### [hal-01581807] Preuve formelle du théorème de Lax–Milgram

Résumé du papier "A Coq formal proof of the Lax-Milgram Theorem", CPP 2017.

ano.nymous@ccsd.cnrs.fr.invalid (Sylvie Boldo), Sylvie Boldo

### [hal-01070701] Implementation of an adaptive energy-efficient MAC protocol in OMNeT++/MiXiM

In recent years, many MAC protocols for wireless sensor networks have been proposed and most of them are evaluated using Matlab simulator and/or network simulators (OMNeT++, NS2, etc). However, most of them have a static behavior and few network simulations are available for adaptive protocols. Specially, in OMNeT++/MiXiM, there are few energy efficient MAC protocols for WSNs (B-MAC & L-MAC) and no adaptive ones. To this end, the TAD-MAC (Traffic Aware Dynamic MAC) protocol has been simulated in OMNeT++ with the MiXiM framework and implementation details are given in this paper. The simulation results have been used to evaluate the performance of TAD-MAC through comparisons with B-MAC and L-MAC protocols.

ano.nymous@ccsd.cnrs.fr.invalid (Van-Thiep Nguyen), Van-Thiep Nguyen

### [hal-02181712] Diusion Approximation of Near Critical Branching Processes in Fixed and Random Environment

We consider Bienaymé-Galton-Watson and continuous-time Markov branching processes and prove diffusion approximation results in the near critical case, in fixed and random environment. In one hand, in the fixed environment case, we give new proofs and derive necessary and sufficient conditions for diffusion approximation to get hold of Feller-Jiřina and Jagers theorems. In the other hand, we propose a continuous-time Markov branching process with random environments and obtain diffusion approximation results. An averaging result is also presented. Proofs here are new, where weak convergence in the Skorohod space is proved via singular perturbation technique for convergence of generators and tightness of the distributions of the considered families of stochastic processes.

ano.nymous@ccsd.cnrs.fr.invalid (Nikolaos Limnios), Nikolaos Limnios

### [hal-02274493] A posteriori estimates distinguishing the error components and adaptive stopping criteria for numerical approximations of parabolic variational inequalities

We consider in this paper a model parabolic variational inequality. This problem is discretized with conforming Lagrange finite elements of order p ≥ 1 in space and with the backward Euler scheme in time. The nonlinearity coming from the complementarity constraints is treated with any semismooth Newton algorithm and we take into account in our analysis an arbitrary iterative algebraic solver. In the case p = 1, when the system of nonlinear algebraic equations is solved exactly, we derive an a posteriori error estimate on both the energy error norm and a norm approximating the time derivative error. When p ≥ 1, we provide a fully computable and guaranteed a posteriori estimate in the energy error norm which is valid at each step of the linearization and algebraic solvers. Our estimate, based on equilibrated flux reconstructions, also distinguishes the discretization, linearization, and algebraic error components. We build an adaptive inexact semismooth Newton algorithm based on stopping the iterations of both solvers when the estimators of the corresponding error components do not affect significantly the overall estimate. Numerical experiments are performed with the semismooth Newton-min algorithm and the semismooth Newton-Fischer-Burmeister algorithm in combination with the GMRES iterative algebraic solver to illustrate the strengths of our approach.

### [hal-02182974] Characterization of palladium species after γ-irradiation of a TBP–alkane–Pd(NO 3 ) 2 system

[...]

ano.nymous@ccsd.cnrs.fr.invalid (Bénédicte Simon), Bénédicte Simon

### [cea-02023046] Aerosols released during the laser cutting of a Fukushima Daiichi debris simulant

One of the important challenges for the decommissioning of the damaged reactors of the Fukushima Daiichi Nuclear Power Plant is the safe retrieval of the fuel debris or corium. It is especially primordial to investigate the cutting conditions for air configuration and for underwater configuration at different water levels. Concerning the cutting techniques, the laser technique is well adapted to the cutting of expected material such as corium that has an irregular shape and heterogeneous composition. A French consortium (ONET Technologies, CEA and IRSN) is being subsidized by the Japanese government to implement R&D related to the laser cutting of Fukushima Daiichi fuel debris and related to dust collection technology. Debris simulant have been manufactured in the PLINIUS platform to represent Molten Core Concrete Interaction as estimated from Fukushima Daiichi calculations. In this simulant, uranium is replaced by hafnium and the major fission products have been replaced by their natural isotopes. During laser cutting experiments in the DELIA facility, aerosols have been collected thanks to filters and impactors. The collected aerosols have been analyzed. Both chemical analysis (dissolution + ICP MS and ICP AES) and microscopic analyses (SEM EDS) will be presented and discussed. These data provide insights on the expected dust releases during cutting and can be converted to provide radioactivity estimates. They have also been successfully compared to thermodynamic calculations with the NUCLEA database.

ano.nymous@ccsd.cnrs.fr.invalid (Christophe Journeau), Christophe Journeau

### [inria-00576514] An EM and a stochastic version of the EM algorithm for nonparametric Hidden semi-Markov models

The Hidden semi-Markov models (HSMMs) have been introduced to overcome the constraint of a geometric sojourn time distribution for the different hidden states in the classical hidden Markov models. Several variations of HSMMs have been proposed that model the sojourn times by a parametric or a nonparametric family of distributions. In this article, we concentrate our interest on the nonparametric case where the duration distributions are attached to transitions and not to states as in most of the published papers in HSMMs. Therefore, it is worth noticing that here we treat the underlying hidden semi–Markov chain in its general probabilistic structure. In that case, Barbu and Limnios (2008) proposed an Expectation–Maximization (EM) algorithm in order to estimate the semi-Markov kernel and the emission probabilities that characterize the dynamics of the model. In this paper, we consider an improved version of Barbu and Limnios' EM algorithm which is faster than the original one. Moreover, we propose a stochastic version of the EM algorithm that achieves comparable estimates with the EM algorithm in less execution time. Some numerical examples are provided which illustrate the efficient performance of the proposed algorithms.

ano.nymous@ccsd.cnrs.fr.invalid (Sonia Malefaki), Sonia Malefaki

### [hal-00018493] A Stochastic EM algorithm for a semiparametric mixture model

Recently several authors considered finite mixture models with semi-/non-parametric component distributions. Identifiability of such model parameters is generally not obvious, and when it occurs, inference methods are rather specific to the mixture model under consideration. In this paper we propose a generalization of the EM algorithm to semiparametric mixture models. Our approach is methodological and can be applied to a wide class of semiparametric mixture models. The behavior of the EM type estimators we propose is studied numerically through several Monte Carlo experiments but also by comparison with alternative methods existing in the literature. In addition to these numerical experiments we provide applications to real data showing that our estimation methods behaves well, that it is fast and easy to be implemented.

ano.nymous@ccsd.cnrs.fr.invalid (Laurent Bordes), Laurent Bordes

### [hal-01083975] Pulsed magnetohydrodynamic blood flow in a rigid vessel under physiological pressure gradient

Blood flow in a steady magnetic field has been of great interest over the past years.Many researchers have examined the effects of magnetic fields on velocity profiles and arterial pressure, and major studies focused on steady or sinusoidal flows. In this paper we present a solution for pulsed magnetohydrodynamic blood flow with a somewhat realistic physiological pressure wave obtained using a windkessel lumped model. A pressure gradient is derived along a rigid vessel placed at the output of a compliant module which receives the ventricle outflow. Then, velocity profile and flow rate expressions are derived in the rigid vessel in the presence of a steady transverse magnetic field. As expected, results showed flow retardation and flattening. The adaptability of our solution approach allowed a comparison with previously addressed flow cases and calculations presented a good coherence with those well established solutions.

ano.nymous@ccsd.cnrs.fr.invalid (Dima Abi Abdallah), Dima Abi Abdallah

### [hal-02176154] Global representation and multi-scale expansion for the Dirichlet problem in a domain with a small hole close to the boundary

For each pair ε = (ε 1 , ε 2) of positive parameters, we define a perforated domain Ω ε by making a small hole of size ε 1 ε 2 in an open regular subset Ω of R n (n ≥ 3). The hole is situated at distance ε 1 from the outer boundary ∂Ω of the domain. Then, when ε → (0, 0) both the size of the hole and its distance from ∂Ω tend to zero, but the size shrinks faster than the distance. In such perforated domain Ω ε we consider a Dirichlet problem for the Laplace equation and we denote by u ε its solution. Our aim is to represent the map that takes ε to u ε in term of real analytic functions of ε defined in a neighborhood of (0, 0). In contrast with previous results valid only for restrictions of u ε to suitable subsets of Ω ε , we prove a global representation formula that holds on the whole of Ω ε. Such a formula allows to rigorously justify multi-scale expansions, which we subsequently construct.

ano.nymous@ccsd.cnrs.fr.invalid (Virginie Bonnaillie-Noël), Virginie Bonnaillie-Noël

### [hal-01263494] Résolution d’un Problème de Cauchy en EEG

Dans cet article, nous traitons un problème de Cauchy dans le cadre de la localisation des sources épileptiques en Electro-Encéphalo-Graphie (EEG). Plus particulièrement, il s'agit du problème de construction des données de Cauchy sur la surface du cerveau à partir des données du potentiel mesuré par l'EEG à la surface de la tête. Notre résolution est basée sur un algorithme itératif alternatif initialement proposé par Kozlov, Mazjya et Fomin. Nous présentons dans ce papier l'étude umérique de cette méthode que nous avons implémentée en trois dimensions. Nous donnons également des applications et des résultats numériques.

### [hal-01523020] Fast iterative boundary element methods for high-frequency scattering problems in 3D elastodynamics

The fast multipole method is an efficient technique to accelerate the solution of large scale 3D scattering problems with boundary integral equations. However, the fast multipole accelerated boundary element method (FM-BEM) is intrinsically based on an iterative solver. It has been shown that the number of iterations can significantly hinder the overall efficiency of the FM-BEM. The derivation of robust preconditioners for FM-BEM is now inevitable to increase the size of the problems that can be considered. The main constraint in the context of the FM-BEM is that the complete system is not assembled to reduce computational times and memory requirements. Analytic preconditioners offer a very interesting strategy by improving the spectral properties of the boundary integral equations ahead from the discretization. The main contribution of this paper is to combine an approximate adjoint Dirichlet to Neumann (DtN) map as an analytic preconditioner with a FM-BEM solver to treat Dirichlet exterior scattering problems in 3D elasticity. The approximations of the adjoint DtN map are derived using tools proposed in [40]. The resulting boundary integral equations are preconditioned Combined Field Integral Equations (CFIEs). We provide various numerical illustrations of the efficiency of the method for different smooth and non smooth geometries. In particular, the number of iterations is shown to be completely independent of the number of degrees of freedom and of the frequency for convex obstacles.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphanie Chaillat), Stéphanie Chaillat

### [hal-01187242] Approximate local Dirichlet-to-Neumann map for three-dimensional time-harmonic elastic waves

It has been proven that the knowledge of an accurate approximation of the Dirichlet-to-Neumann (DtN) map is useful for a large range of applications in wave scattering problems. We are concerned in this paper with the construction of an approximate local DtN operator for time-harmonic elastic waves. The main contributions are the following. First, we derive exact operators using Fourier analysis in the case of an elastic half-space. These results are then extended to a general three-dimensional smooth closed surface by using a local tangent plane approximation. Next, a regularization step improves the accuracy of the approximate DtN operators and a localization process is proposed. Finally, a first application is presented in the context of the On-Surface Radiation Conditions method. The efficiency of the approach is investigated for various obstacle geometries at high frequencies.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphanie Chaillat), Stéphanie Chaillat

### [hal-01788510] A comparative review of soil charcoal data : Spatiotemporal patterns of origin and long-term dynamics of Western European nutrient-poor grasslands

The nutrient-poor grasslands of Western Europe are of major conservation concern because land use changes threaten their high biodiversity. Studies assessing their characteristics show that their past and ongoing dynamics are strongly related to human activities. Yet, the initial development patterns of this specific ecosystem remain unclear. Here, we examine findings from previous paleoecological investigations performed at local level on European grassland areas ranging from several hundred square meters to several square kilometers. Comparing data from these locally relevant studies at a regional scale, we investigate these grasslands' spatiotemporal patterns of origin and long-term dynamics. The study is based on taxonomic identification and radiocarbon AMS dating of charcoal pieces from soil/soil sediment archives of nutrient-poor grasslands in Mediterranean and temperate Western Europe (La Crau plain, Mont Lozère, Grands Causses, Vosges Mountains, Franconian Alb, and Upper-Normandy region). We address the following questions: (1) What are the key determinants of the establishment of these nutrient-poor grasslands? (2) What temporal synchronicities might there be? and (3) What is the spatial scale of these grasslands' past dynamics? The nutrient-poor grasslands in temperate Western Europe are found to result from the first anthropogenic woodland clearings during the late Neolithic, revealed by fire events in mesophilious mature forests. In contrast, the sites with Mediterranean affinities appear to have developed at earlier plant successional stages (pine forest, matorral), established before the first human impacts in the same period. However, no general pattern of establishment and dynamics of the nutrient-poor grasslands could be identified. Local mechanisms appear to be the key determinants of the dynamics of these ecosystems. Nevertheless, this paleoecological synthesis provides insights into past climate or human impacts on present-day vegetation.

ano.nymous@ccsd.cnrs.fr.invalid (Vincent Robin), Vincent Robin

### [hal-00112170] The mortar spectral element method in domains of operators Part II : The curl operator and the vector potential problem

The mortar spectral element method is a domain decomposition technique that allows for discretizing second- or fourth-order elliptic equations when set in standard Sobolev spaces.he aim of this paper is to extend this method to problems formulated in the space of square-integrable vector fields with square-integrable curl.We consider the problem of computing the vector potential associated with a divergence- free function in dimension 3 and propose a discretization of it. The numerical analysis of the discrete problem is performed and numerical experiments are presented, they turn out to be in good coherency with the theoretical results.

ano.nymous@ccsd.cnrs.fr.invalid (Mjedi Azaïez), Mjedi Azaïez

### [hal-01958872] Solving coupled problems of lumped parameter models in a platform for severe accidents in nuclear reactors

This paper focuses on solving coupled problems of lumped parameter models. Such problems are of interest for the simulation of severe accidents in nuclear reactors: these coarse-grained models allow for fast calculations for statistical analysis used for risk assessment and solutions of large problems when considering the whole severe accident scenario. However, this modeling approach has several numerical flaws. Besides, in this industrial context, computational efficiency is of great importance leading to various numerical constraints. The objective of this research is to analyze the applicability of explicit coupling strategies to solve such coupled problems and to design implicit coupling schemes allowing stable and accurate computations. The proposed schemes are theoretically analyzed and tested within CEA's procor platform on a problem of heat conduction solved with coupled lumped parameter models and coupled 1D models. Numerical results are discussed and allow us to emphasize the benefits of using the designed coupling schemes instead of the usual explicit coupling schemes.

ano.nymous@ccsd.cnrs.fr.invalid (Louis Viot), Louis Viot

### [hal-02130362] Structure learning of Bayesian networks involving cyclic structures

Many biological networks include cyclic structures. In such cases, Bayesian networks (BNs), which must be acyclic, are not sound models for structure learning. Dynamic BNs can be used but require relatively large time series data. We discuss an alternative model that embeds cyclic structures within acyclic BNs, allowing us to still use the fac-torization property and informative priors on network structure. We present an implementation in the linear Gaussian case, where cyclic structures are treated as multivariate nodes. We use a Markov Chain Monte Carlo algorithm for inference, allowing us to work with posterior distribution on the space of graphs.

ano.nymous@ccsd.cnrs.fr.invalid (Witold Wiecek), Witold Wiecek

### [inria-00136971] Numerical simulation of blood flows through a porous interface

We propose a model for a medical device, called a stent, designed for the treatment of cerebral aneurysms. The stent consists of a grid, immersed in the blood flow and located at the inlet of the aneurysm. It aims at promoting a clot within the aneurysm. The blood flow is modelled by the incompressible Navier-Stokes equations and the stent by a dissipative surface term. We propose a stabilized finite element method for this model and we analyse its convergence in the case of the Stokes equations. We present numerical results for academical test cases, and on a realistic aneurysm obtained from medical imaging.

ano.nymous@ccsd.cnrs.fr.invalid (Miguel Angel Fernández), Miguel Angel Fernández

### [hal-01005515] Finite element methods for the temperature in composite media with contact resistance

Nous considérons une ́equation qui modélise la diffusion de la température dans une mousse de graphite contenant des capsules de sel. Les conditions de transition de la température entre le graphite et le sel doivent être traitées correctement. Nous effectuons l'analyse de ce modèle et prouvons qu'il est bien posé. Puis nous en proposons une discrétisation par éléments finis et effectuons l'analyse a priori du problème discret. Quelques expériences numériques confirment l'intérêt de cette approche.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

### [hal-00781238] Mixed finite element discretization of a model for organic pollution in waters Part I. The problem and its discretization

We consider a mixed reaction diffusion system describing the organic pollution in stream-waters. It may be viewed as the static version of Streeter-Phelps equations relating the Biochemical Oxygen Demand and Dissolved Oxygen to which dispersion terms are added. In this work, we propose a mixed variational formulation and prove its well-posedness. Next, we develop two finite element discretizations of this problem and establish optimal a priori error estimates for the second discrete problem.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

### [inria-00628032] MagnetoHemoDynamics in Aorta and Electrocardiograms

This paper addresses a complex multi-physical phenomemon involving cardiac electrophysiology and hemodynamics. The purpose is to model and simulate a phenomenon that has been observed in MRI machines: in the presence of a strong magnetic field, the T-wave of the electrocardiogram (ECG) gets bigger, which may perturb ECG-gated imaging. This is due a magnetohydrodynamic (MHD) eff ect occurring in the aorta. We reproduce this experimental observation through computer simulations on a realistic anatomy, and with a three-compartment model: inductionless magnetohydrodynamic equations in the aorta, bidomain equations in the heart and electrical di ffusion in the rest of the body. These compartments are strongly coupled and solved using fi nite elements. Several benchmark tests are proposed to assess the numerical solutions and the validity of some modeling assumptions. Then, ECGs are simulated for a wide range of magnetic field intensities (from 0 to 20 Tesla).

ano.nymous@ccsd.cnrs.fr.invalid (Vincent Martin), Vincent Martin

### [edutice-00000726] XMLlab1 : un outil générique de simulation basé sur XML et Scilab

Nous présentons un environnement de génération automatique de simulations entièrement basé sur les technologies XML. Le langage de description proposé permet de décrire des objets mathématiques tels que des systèmes d'équations différentielles, des systèmes d'équations non-linéaires, des équations aux dérivées partielles en dimension 2, ou bien de simples courbes et surfaces. Il permet aussi de décrire les paramètres dont dépendent ces objets. Ce langage est indépendant du logiciel et permet donc de garantir la pérennité du travail des auteurs ainsi que leur mutualisation et leur réutilisation. Nous décrivons aussi l'architecture d'une «chaîne de compilation» permettant de transformer ces fichiers XML sous forme de scripts et de les faire fonctionner dans le logiciel Scilab.

ano.nymous@ccsd.cnrs.fr.invalid (Stéphane Mottelet), Stéphane Mottelet

### [hal-00815297] Direct electrochemical reduction of solid uranium oxide in molten fluoride salts

The direct electrochemical reduction of UO2 solid pellets was carried out in LiF-CaF2 (+ 2 mass. % Li2O) at 850°C. An inert gold anode was used instead of the usual reactive sacrificial carbon anode. In this case, oxidation of oxide ions present in the melt yields O2 gas evolution on the anode. Electrochemical characterisations of UO2 pellets were performed by linear sweep voltammetry at 10mV/s and reduction waves associated to oxide direct reduction were observed at a potential 150mV more positive in comparison to the solvent reduction. Subsequent, galvanostatic electrolyses runs were carried out and products were characterised by SEM-EDX, EPMA/WDS and XRD. In one of the runs, uranium oxide was partially reduced and three phases were observed: non reduced UO2 in the centre, pure metallic uranium on the external layer and an intermediate phase representing the initial stage of reduction taking place at the grain boundaries. In another run, the UO2 sample was fully reduced. Due to oxygen removal, the U matrix had a typical coral-like structure which is characteristic of the pattern observed after the electroreduction of solid oxides.

ano.nymous@ccsd.cnrs.fr.invalid (Mathieu Gibilaro), Mathieu Gibilaro

### [hal-01279503] First-order indicators for the estimation of discrete fractures in porous media

Faults and geological barriers can drastically affect the flow patterns in porous media. Such fractures can be modeled as interfaces that interact with the surrounding matrix. We propose a new technique for the estimation of the location and hydrogeological properties of a small number of large fractures in a porous medium from given distributed pressure or flow data. At each iteration, the algorithm builds a short list of candidates by comparing fracture indicators. These indicators quantify at the first order the decrease of a data misfit function; they are cheap to compute. Then, the best candidate is picked up by minimization of the objective function for each candidate. Optimally driven by the fit to the data, the approach has the great advantage of not requiring remeshing, nor shape derivation. The stability of the algorithm is shown on a series of numerical examples representative of typical situations.

ano.nymous@ccsd.cnrs.fr.invalid (Hend Ben Ameur), Hend Ben Ameur

### [hal-00818370] Detection and Location of Moving Point Sources in Contaminant Transport Models. Uniqueness and Minimal Observations

We are interested in an inverse problem of recovering the position of a pollutant or contaminant source in a stream water. Advection, dispersive transport and the reaction of the solute is commonly modeled by a linear or non-linear parabolic equation. In former works, it is established that a point-wise source is fully identifiable from measurements recorded by a couple of sensors placed, one up-stream and the other down-stream of the pollution source. The observability question we try to solve here is related to the redundancy of sensors when additional information is available on the point-wise source. It may occur, in hydrological engineering, that the intensity of the pollutant is known in advance. In this case, we pursue an identifiability result of a moving source location using a single observation. The chief mathematical tools to prove identifiability are the unique continuation theorem together with an appropriate maximum principle for the parabolic equation under investigation.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

### [hal-01286821] A Preconditioned Richardson Regularization for the Data Completion Problem and the Kozlov-Maz’ya-Fomin Method

Using a preconditioned Richardson iterative method as a regularization to the data completion problem is the aim of the contribution. The problem is known to be exponentially ill posed that makes its numerical treatment a hard task. The approach we present relies on the Steklov-Poincaré variational framework introduced in [Inverse Problems, vol. 21, 2005]. The resulting algorithm turns out to be equivalent to the Kozlov-Maz’ya-Fomin method in [Comp. Math. Phys., vol. 31, 1991]. We conduct a comprehensive analysis on the suitable stopping rules that provides some optimal estimates under the General Source Condition on the exact solution. Some numerical examples are finally discussed to highlight the performances of the method.

ano.nymous@ccsd.cnrs.fr.invalid (Duc Thang Du), Duc Thang Du

### [hal-01761591] A stabilized Lagrange multiplier finite-element method for flow in porous media with fractures

In this work we introduce a stabilized, numerical method for a multi-dimensional, discrete-fracture model (DFM) for single-phase Darcy flow in fractured porous media. In the model, introduced in an earlier work, flow in the (n − 1)-dimensional fracture domain is coupled with that in the n-dimensional bulk or matrix domain by the use of Lagrange multipliers. Thus the model permits a finite element discretization in which the meshes in the fracture and matrix domains are independent so that irregular meshing and in particular the generation of small elements can be avoided. In this paper we introduce in the numerical formulation, which is a saddle-point problem based on a primal, variational formulation for flow in the matrix domain and in the fracture system, a consistent stabilizing term which penalizes discontinuities in the Lagrange multipliers. For this penalized scheme we show stability and prove convergence. With numerical experiments we analyze the performance of the method for various choices of the penalization parameter and compare with other numerical DFM's.

ano.nymous@ccsd.cnrs.fr.invalid (Markus Köppel), Markus Köppel

### [hal-01525249] Shape sensitivity analysis for elastic structures with generalized impedance boundary conditions of the Wentzell type -Application to compliance minimization

This paper focuses on Generalized Impedance Boundary Conditions (GIBC) with second order derivatives in the context of linear elasticity and general curved interfaces. A condition of the Wentzell type modeling thin layer coatings on some elastic structure is obtained through an asymptotic analysis of order one of the transmission problem at the thin layer interfaces with respect to the thickness parameter. We prove the well-posedness of the approximate problem and the theoretical quadratic accuracy of the boundary conditions. Then we perform a shape sensitivity analysis of the GIBC model in order to study a shape optimization/optimal design problem. We prove the existence and characterize the first shape derivative of this model. A comparison with the asymptotic expansion of the first shape derivative associated to the original thin layer transmission problem shows that we can interchange the asymptotic and shape derivative analysis. Finally we apply these results to the compliance minimization problem. We compute the shape derivative of the compliance in this context and present some numerical simulations.

ano.nymous@ccsd.cnrs.fr.invalid (Fabien Caubet), Fabien Caubet

### [hal-01394849] Strong approximations for the $p$-fold integrated empirical process with applications to statistical tests

The main purpose of this paper is to investigate the strong approximation of the $p$-fold integrated empirical process, $p$ being a fixed positive integer. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on results of Koml\'os, Major and Tusn\'ady (1975). Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of integrated empirical processes when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of integrated empirical processes.

### [hal-00222765] Inégalités de Calderon-Zygmund, Potentiels et Transformées de Riesz dans des Espaces avec Poids

[...]

ano.nymous@ccsd.cnrs.fr.invalid (Chérif Amrouche), Chérif Amrouche

### [hal-01157178] Some asymptotic results for the integrated empirical process with applications to statistical tests

The main purpose of this paper is to investigate the strong approximation of the integrated empirical process. More precisely, we obtain the exact rate of the approximations by a sequence of weighted Brownian bridges and a weighted Kiefer process. Our arguments are based in part on the Komlós et al. (1975)'s results. Applications include the two-sample testing procedures together with the change-point problems. We also consider the strong approximation of the integrated empirical process when the parameters are estimated. Finally, we study the behavior of the self-intersection local time of the partial sum process representation of the integrated empirical process.Reference: Koml\'os, J., Major, P. and Tusn\'ady, G. (1975). An approximation of partial sums of independent RV's and the sample DF. I. Z. Wahrscheinlichkeitstheorie und Verw. Gebiete, 32, 111-131.

### [hal-01023384] A Finite Element Method for the Boundary Data Recovery in an Oxygen-Balance Dispersion Model

The inverse problem under investigation consists of the boundary data completion in a deoxygenation-reaeration model in stream-waters. The unidimensional transport model we deal with is based on the one introduced by Streeter and Phelps, augmented by Taylor dispersion terms. The missing boundary condition is the load or/and the flux of the biochemical oxygen demand indicator at the outfall point. The counterpart is the availability of two boundary conditions on the dissolved oxygen tracer at the same point. The major consequences of these non-standard boundary conditions is that dispersive transport equations on both oxygen tracers are strongly coupled and the resulting system becomes ill-posed. The main purpose is a finite element space-discretization of the variational problem put under a non-symmetric mixed form. Combining analytical calculations, numerical computations and theoretical justifications, we try to elucidate the characteristics related to the ill-posedness of this data completion dynamical problem and understand its mathematical structure.

ano.nymous@ccsd.cnrs.fr.invalid (Faker Ben Belgacem), Faker Ben Belgacem

### [hal-01784139] Stein’s method for diffusive limit of Markov processes

The invariance principle for M/M/1 and M/M/∞ queues states that when properly renormalized (i.e. rescaled and centered), the Markov processes which describe these systems both converge to a diffusive limit when the driving parameters go to infinity: a killed Brownian motion in the former case and an Ornstein-Uhlenbeck process for the latter. The purpose of this paper is to assess the rate of convergence in these diffusion approximations. To this end, we extend to these contexts, the functional Stein's method introduced for the Brownian approximation of Poisson processes.

ano.nymous@ccsd.cnrs.fr.invalid (Eustache Besançon), Eustache Besançon

### [inria-00561601] Modeling fractures as interfaces with nonmatching grids

We consider a model for fluid flow in a porous medium with a fracture. In this model, the fracture is represented as an interface between subdomains, where specific equations have to be solved. In this article we analyse the discrete problem, assuming that the fracture mesh and the subdomain meshes are completely independent, but that the geometry of the fracture is respected. We show that despite this non-conformity, first order convergence is preserved with the lowest order Raviart-Thomas(-Nedelec) mixed finite elements. Numerical simulations confirm this result.

ano.nymous@ccsd.cnrs.fr.invalid (Najla Frih), Najla Frih

### [hal-01136619] Guaranteed State and Parameter Estimation for Nonlinear Dynamical Aerospace Models

This paper deals with parameter and state estimation in a bounded-error context for uncertain dynamical aerospace models when the input is considered optimized or not. In a bounded-error context, perturbations are assumed bounded but otherwise unknown. The parameters to be estimated are also considered bounded. The tools of the presented work are based on a guaranteed numerical set integration solver of ordinary differential equations combined with adapted set inversion computation. The main contribution of this work consists in developing procedures for parameter estimation whose performance is highly related with the input of system. In this paper, a comparison with a classical non-optimized input is proposed.

ano.nymous@ccsd.cnrs.fr.invalid (Qiaochu Li), Qiaochu Li