Publications sur HAL

[hal-02459246] 13C-Metabolic Flux Analysis in Developing Flax (Linum usitatissinum L.) Embryos to Understand Storage Lipid Biosynthesis

Flax (Linum usitatissinum L.) oil is an important source of α-linolenic (C18:3 ω-3). This polyunsaturated fatty acid is well known for its nutritional role in human and animal diets. Understanding storage lipid biosynthesis in developing flax embryos can lead to an increase in seed yield via marker-assisted selection. While a tremendous amount of work has been done on different plant species to highlight their metabolism during embryo development, a comprehensive analysis of metabolic flux in flax is still lacking. In this context, we have utilized in vitro cultured developing embryos of flax and determined net fluxes by performing three complementary parallel labeling experiments with 13C-labeled glucose and glutamine. Metabolic fluxes were estimated by computer-aided modeling of the central metabolic network including 11 cofactors of 118 reactions of the central metabolism and 12 pseudo-fluxes. A focus on lipid storage biosynthesis and the associated pathways was done in comparison with rapeseed, arabidopsis, maize and sunflower embryos. In our hands, glucose was determined to be the main source of carbon in flax embryos, leading to the conversion of phosphoenolpyruvate to pyruvate. The oxidative pentose phosphate pathway (OPPP) was identified as the producer of NADPH for fatty acid biosynthesis. Overall, the use of 13C-metabolic flux analysis provided new insights into the flax embryo metabolic processes involved in storage lipid biosynthesis. The elucidation of the metabolic network of this important crop plant reinforces the relevance of the application of this technique to the analysis of complex plant metabolic systems.

ano.nymous@ccsd.cnrs.fr.invalid (Sébastien Acket), Sébastien Acket

[hal-05659943] Semilinear Elliptic Problems with NonLinear Contact Resistance in Composite Domains

In heat diffusion, Kapitza contact resistance impedes heat transfer across the interfaces between different media and generates a temperature jump. In many applications, this resistance depends on the temperature field, making the problem nonlinear. Models with temperature-dependent contact resistance are increasingly relevant. At low temperatures, particularly in cooling processes, this dependence is often governed by a power law. This work extends the results of [E. Bejaoui et al., MATCOM, 2026] by incorporating a volume heat source. The primary objective is to derive an L ∞ -estimate for the (a priori) solutions, thereby providing a rigorous mathematical meaning to the variational formulation. De Giorgi’s method is successfully applied to obtain the desired a priori bounds. The existence of solutions is then established using the Schauder fixed-point theorem. Finally, the non-uniqueness is investigated, and the presence of multiple solutions is illustrated for a one-dimensional setting.

ano.nymous@ccsd.cnrs.fr.invalid (E Bejaoui), E Bejaoui

[hal-05647342] Does Normalization Choice Matter for Causal Large Time-Series Models ?

Large models for time-series forecasting have been emerged as a promising paradigm for training models on heterogeneous collections of signals. These models typically rely on causal autoregressive architectures, where each observation is sequentially predicted from past. In practice, real-world time-series exhibit non-stationarities, which significantly influence predictive performance. To mitigate this, normalization is commonly employed. However, in efficient causal settings it might induce information leakage from future observations during training. Recent alternatives, including causal normalization and statistics computed from initial observations, have been proposed to address this issue, but their practical implications remain insufficiently understood. In this work, we evaluate normalization strategies for transformer-based large time-series models trained with patching and efficient causal strategy. We showcase that normalization choice significantly influences both training convergence and forecasting performance.

ano.nymous@ccsd.cnrs.fr.invalid (Samy-Melwan Vilhes), Samy-Melwan Vilhes

[hal-05396759] Monomial and Graded Orders in Rocq

Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the finite element method. This article provides definitions, operators, and proofs of properties about relations and orders with a focus on monomial orders, that are total orders compatible with the monoid operation. More than its definition and proved properties, we define several of them, among them the lexicographic and grevlex orders. For the sake of genericity, we formalize the grading of an order, a high-level operator that transforms a binary relation into another one, and we prove that grading an order preserves many of its properties, such as the monomial order property. This leads us to the definition and properties of four different graded orders, with very factorized proofs. We therefore provide a comprehensive and user-friendly Rocq library about orders, including monomial and graded orders, that contains more than 700 lemmas.

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

[hal-05396788] Monomial and Graded Orders in Rocq

Even if binary relations and orders are a common formalization topic, we need to formalize specific orders (namely monomial and graded) in the process of formalizing in Rocq the finite element method. This article provides definitions, operators, and proofs of properties about relations and orders with a focus on monomial orders, that are total orders compatible with the monoid operation. More than its definition and proved properties, we define several of them, among them the lexicographic and grevlex orders. For the sake of genericity, we formalize the grading of an order, a high-level operator that transforms a binary relation into another one, and we prove that grading an order preserves many of its properties, such as the monomial order property. This leads us to the definition and properties of four different graded orders, with very factorized proofs. We therefore provide a comprehensive and user-friendly Rocq library about orders, including monomial and graded orders, that contains more than 700 lemmas.

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

[hal-04702353] Full Frequency-Domain Inference for Weak FARIMA Models via Whittle Estimation

This paper studies frequency-domain inference for weak FARIMA models based on the classical Whittle estimator. Although consistency and asymptotic normality of the Whittle estimator are by now well understood under weak dependence conditions, feasible estimation of its asymptotic covariance matrix remains a challenging issue in non-Gaussian and dependent settings. In weak FARIMA models, the limiting covariance matrix is not determined solely by the spectral density, but also depends on the fourth-order dependence structure of the innovation process through its trispectrum. The main contribution of this paper is to construct a consistent estimator of this asymptotic covariance matrix, thereby making feasible asymptotic inference possible for the Whittle estimator. In doing so, we address, within the FARIMA framework, the issue left open by Shao (2010) concerning the practical estimation of the limiting covariance matrix in weak time series models. The proposed approach adapts and extends earlier trispectrum-based methods, originally developed for observable short-memory processes, to the more delicate setting where the relevant fourth-order structure is associated with unobservable innovations and must therefore be recovered through residuals. We establish the consistency of the resulting covariance estimator and illustrate its finite-sample performance by Monte Carlo experiments.

ano.nymous@ccsd.cnrs.fr.invalid (Samir Ben-Hariz), Samir Ben-Hariz

[hal-05128905] A Rocq Formalization of Simplicial Lagrange Finite Elements

Formalization of mathematics is a major topic, that includes in particular numerical analysis, towards proofs of scientific computing programs. The present study is about the finite element method, a popular method to numerically solve partial differential equations. In the long-term goal of proving its correctness, we focus here on the formal definition of what is a finite element. Mathematically, a finite element describes what happens in a cell of a mesh. It notably includes the geometry of the cell, the polynomial approximation space, and a finite set of linear forms that computationally characterizes the polynomials. Formally, we design a finite element as a record in the Rocq proof assistant with both values (such as the vertices of the cell) and proofs of validity (such as the dimension of the approximation space). The decisive validity proof is unisolvence, that makes the previous characterization unique. We then instantiate this record with the most popular and useful, the simplicial Lagrange finite elements for evenly distributed nodes, for any dimension and any polynomial degree, including the difficult unisolvence proof. These proofs require many results (definitions, lemmas, canonical structures) about finite families, affine spaces, multivariate polynomials, in the context of finite or infinite-dimensional spaces.

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

[hal-05128954] A Rocq Formalization of Simplicial Lagrange Finite Elements

Formalization of mathematics is a major topic, that includes in particular numerical analysis, towards proofs of scientific computing programs. The present study is about the finite element method, a popular method to numerically solve partial differential equations. In the long-term goal of proving its correctness, we focus here on the formal definition of what is a finite element. Mathematically, a finite element describes what happens in a cell of a mesh. It notably includes the geometry of the cell, the polynomial approximation space, and a finite set of linear forms that computationally characterizes the polynomials. Formally, we design a finite element as a record in the Rocq proof assistant with both values (such as the vertices of the cell) and proofs of validity (such as the dimension of the approximation space). The decisive validity proof is unisolvence, that makes the previous characterization unique. We then instantiate this record with the most popular and useful, the simplicial Lagrange finite elements for evenly distributed nodes, for any dimension and any polynomial degree, including the difficult unisolvence proof. These proofs require many results (definitions, lemmas, canonical structures) about finite families, affine spaces, multivariate polynomials, in the context of finite or infinite-dimensional spaces.

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

[hal-05448476] Virtual Element methods for non-Newtonian shear-thickening fluid flow problems

In this work, we present a comprehensive theoretical analysis for Virtual Element discretizations of incompressible non-Newtonian flows governed by the Carreau-Yasuda constitutive law, in the shear-thickening regime ( r > 2) including both degenerate (delta = 0) and non-degenerate (delta > 0) cases. The proposed Virtual Element method features two distinguishing advantages: the construction of an exactly divergence-free discrete velocity field and compatibility with general polygonal meshes. The analysis presented in this work extends a previous work, where only shear-thinning behavior (1 < r < 2) was considered. Indeed, the theoretical analysis of the shear-thickening setting requires several novel analytical tools, including: an inf-sup stability analysis of the discrete velocity-pressure coupling in non-Hilbertian norms, a stabilization term specifically designed to address the nonlinear structure as the exponent r > 2; and the introduction of a suitable discrete norm tailored to the underlying nonlinear constitutive relation. Numerical results demonstrate the practical performance of the proposed formulation.

ano.nymous@ccsd.cnrs.fr.invalid (Paola F. Antonietti), Paola F. Antonietti

[hal-04844328] A finite volume scheme for the local sensing chemotaxis model

In this paper we design, analyze and simulate a finite volume scheme for a cross-diffusion system which models chemotaxis with local sensing. This system has the same Lyapunov function (or entropy) as the celebrated minimal Keller-Segel system, but unlike the latter, its solutions are known to exist globally in 2D. The long-time behavior of solutions is only partially understood which motivates numerical exploration with a reliable numerical method. We propose a linearly implicit, two-point flux finite volume approximation of the system. We show that the scheme preserves, at the discrete level, the main features of the continuous system, namely mass conservation, non-negativity of solution, entropy dissipation, and duality estimates. These properties allow us to prove the well-posedness, unconditional stability and convergence of the scheme. We also show rigorously that the scheme possesses an asymptotic preserving (AP) property in the quasi-stationary limit. We complement our analysis with thorough numerical experiments investigating convergence and AP properties of the scheme as well as its reliability with respect to stability properties of steady solutions.

ano.nymous@ccsd.cnrs.fr.invalid (Maxime Herda), Maxime Herda

[hal-05027791] PatchTrAD : A Patch-Based Transformer focusing on Patch-Wise Reconstruction Error for Time Series Anomaly Detection

Time series anomaly detection (TSAD) focuses on identifying whether observations in streaming data deviate significantly from normal patterns. With the prevalence of connected devices, anomaly detection on time series has become paramount, as it enables real-time monitoring and early detection of irregular behaviors across various application domains. In this work, we introduce PatchTrAD, a Patch-based Transformer model for time series anomaly detection. Our approach leverages a Transformer encoder along with the use of patches under a reconstructionbased framework for anomaly detection. Empirical evaluations on multiple benchmark datasets show that PatchTrAD is on par, in terms of detection performance, with state-of-the-art deep learning models for anomaly detection while being time efficient during inference.

ano.nymous@ccsd.cnrs.fr.invalid (Samy-Melwan Vilhes), Samy-Melwan Vilhes

[hal-04053732] Non-parametric Observation Driven HMM

The hidden Markov models (HMM) are used in many different fields, to study the dynamics of a process that cannot be directly observed. However, in some cases, the structure of dependencies of a HMM is too simple to describe the dynamics of the hidden process. In particular, in some applications in finance or in ecology, the transition probabilities of the hidden Markov chain can also depend on the current observation. In this work we are interested in extending the classical HMM to this situation. We define a new model, referred to as the Observation Driven-Hidden Markov Model (OD-HMM). We present a complete study of the general non-parametric OD-HMM with discrete and finite state spaces (hidden and observed variables). We study its identifiability. Then we study the consistency of the maximum likelihood estimators. We derive the associated forward-backward equations for the E-step of the EM algorithm. The quality of the procedure is tested on simulated data sets. Finally, we illustrate the use of the model on an application on the study of annual plants dynamics. This works sets theoretical and practical foundations for a new framework that could be further extended, on one hand to the non-parametric context to simplify estimation, and on the other hand to the hidden semi-Markov models for more realism.

ano.nymous@ccsd.cnrs.fr.invalid (Hanna Bacave), Hanna Bacave

[hal-04282819] Gaussian-Smoothed Sliced Probability Divergences

Gaussian smoothed sliced Wasserstein distance has been recently introduced for comparing probability distributions, while preserving privacy on the data. It has been shown that it provides performances similar to its non-smoothed (non-private) counterpart. However, the computational and statistical properties of such a metric have not yet been well-established. This work investigates the theoretical properties of this distance as well as those of generalized versions denoted as Gaussian-smoothed sliced divergences. We first show that smoothing and slicing preserve the metric property and the weak topology. To study the sample complexity of such divergences, we then introduce $\hat{\hat\mu}_{n}$ the double empirical distribution for the smoothed-projected $\mu$. The distribution $\hat{\hat\mu}_{n}$ is a result of a double sampling process: one from sampling according to the origin distribution $\mu$ and the second according to the convolution of the projection of $\mu$ on the unit sphere and the Gaussian smoothing. We particularly focus on the Gaussian smoothed sliced Wasserstein distance and prove that it converges with a rate $O(n^{-1/2})$. We also derive other properties, including continuity, of different divergences with respect to the smoothing parameter. We support our theoretical findings with empirical studies in the context of privacy-preserving domain adaptation.

ano.nymous@ccsd.cnrs.fr.invalid (Mokhtar Z. Alaya), Mokhtar Z. Alaya

[hal-04479672] Evolution of Bladder Cancer Estimated by Using a State-Space Model with a Semi-Markov Process and Censored Data : A Case Study

We consider a Semi-Markov Process (SMP) to model the evolution of bladder cancer, which takes different states over time. A multi-state model has been constructed and applied to data collected from 847 patients during a period of fifteen years. Biomedicine databases usually contain censored data and this study shows that, despite this, a good fit of the main survival measures is achieved by using our specific model. This paper aims to present estimators for the semi-Markov kernel, the survival function and the mean time to disease progression. The strong consistency properties of the estimators are proved.

ano.nymous@ccsd.cnrs.fr.invalid (Alicia Perez A. P. das Neves Yedig), Alicia Perez A. P. das Neves Yedig

[hal-02459255] Metabolic Flux Analysis in Isotope Labeling Experiments Using the Adjoint Approach

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

[hal-04180133] Non parametric observation driven HMM

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ano.nymous@ccsd.cnrs.fr.invalid (Hanna Bacave), Hanna Bacave

[hal-04000700] A convergent finite-volume scheme for nonlocal cross-diffusion systems for multi-species populations

An implicit Euler finite-volume scheme for a nonlocal cross-diffusion system on the one-dimensional torus, arising in population dynamics, is proposed and analyzed. The kernels are assumed to be in detailed balance and satisfy a weak cross-diffusion condition. The latter condition allows for negative off-diagonal coefficients and for kernels defined by an indicator function. The scheme preserves the nonnegativity of the densities, conservation of mass, and production of the Boltzmann and Rao entropies. The key idea is to « translate » the entropy calculations for the continuous equations to the finite-volume scheme, in particular to design discretizations of the mobilities, which guarantee a discrete chain rule even in the presence of nonlocal terms. Based on this idea, the existence of finite-volume solutions and the convergence of the scheme are proven. As a by-product, we deduce the existence of weak solutions to the continuous cross-diffusion system. Finally, we present some numerical experiments illustrating the behavior of the solutions to the nonlocal and associated local models.

ano.nymous@ccsd.cnrs.fr.invalid (Ansgar Jüngel), Ansgar Jüngel

[hal-03564379] Lebesgue Induction and Tonelli’s Theorem in Coq

Lebesgue integration is a well-known mathematical tool, used for instance in probability theory, real analysis, and numerical mathematics. Thus, its formalization in a proof assistant is to be designed to fit different goals and projects. Once the Lebesgue integral is formally defined and the first lemmas are proved, the question of the convenience of the formalization naturally arises. To check it, a useful extension is Tonelli’s theorem, stating that the (double) integral of a nonnegative measurable function of two variables can be computed by iterated integrals, and allowing to switch the order of integration. This article describes the formal definition and proof in Coq of product sigma-algebras, product measures and their uniqueness, the construction of iterated integrals, up to Tonelli’s theorem. We also advertise the Lebesgue induction principle provided by an inductive type for nonnegative measurable functions.

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

[hal-03889276] A Coq Formalization of Lebesgue Induction Principle and Tonelli’s Theorem

Lebesgue integration is a well-known mathematical tool, used for instance in probability theory, real analysis, and numerical mathematics. Thus, its formalization in a proof assistant is to be designed to fit different goals and projects. Once the Lebesgue integral is formally defined and the first lemmas are proved, the question of the convenience of the formalization naturally arises. To check it, a useful extension is Tonelli’s theorem, stating that the (double) integral of a nonnegative measurable function of two variables can be computed by iterated integrals, and allowing to switch the order of integration. This article describes the formal definition and proof in Coq of product sigma-algebras, product measures and their uniqueness, the construction of iterated integrals, up to Tonelli’s theorem. We also advertise the Lebesgue induction principle provided by an inductive type for nonnegative measurable functions.

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

[hal-03700112] Fast calibration of weak FARIMA models

In this paper, we investigate the asymptotic properties of Le Cam’s one-step estimator for weak Fractionally AutoRegressive Integrated Moving-Average (FARIMA) models. For these models, noises are uncorrelated but neither necessarily independent nor martingale differences errors. We show under some regularity assumptions that the onestep estimator is strongly consistent and asymptotically normal with the same asymptotic variance as the least squares estimator. We show through simulations that the proposed estimator reduces computational time compared with the least squares estimator. An application for providing remotely computed indicators for time series is proposed.

ano.nymous@ccsd.cnrs.fr.invalid (Samir Ben Hariz), Samir Ben Hariz

[hal-03471095] A Coq Formalization of Lebesgue Integration of Nonnegative Functions

Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains. Formalizing the mathematical concept of integration and the associated results in a formal proof assistant helps in providing the highest confidence on the correctness of numerical programs involving the use of integration, directly or indirectly. By its capability to extend the (Riemann) integral to a wide class of irregular functions, and to functions defined on more general spaces than the real line, the Lebesgue integral is perfectly suited for use in mathematical fields such as probability theory, numerical mathematics, and real analysis. In this article, we present the Coq formalization of $\sigma$-algebras, measures, simple functions, and integration of nonnegative measurable functions, up to the full formal proofs of the Beppo Levi (monotone convergence) theorem and Fatou’s lemma. More than a plain formalization of the known literature, we present several design choices made to balance the harmony between mathematical readability and usability of Coq theorems. These results are a first milestone toward the formalization of $L^p$~spaces such as Banach spaces.

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

[hal-03194113] A Coq Formalization of Lebesgue Integration of Nonnegative Functions

Integration, just as much as differentiation, is a fundamental calculus tool that is widely used in many scientific domains. Formalizing the mathematical concept of integration and the associated results in a formal proof assistant helps in providing the highest confidence on the correctness of numerical programs involving the use of integration, directly or indirectly. By its capability to extend the (Riemann) integral to a wide class of irregular functions, and to functions defined on more general spaces than the real line, the Lebesgue integral is perfectly suited for use in mathematical fields such as probability theory, numerical mathematics, and real analysis. In this article, we present the Coq formalization of $\sigma$-algebras, measures, simple functions, and integration of nonnegative measurable functions, up to the full formal proofs of the Beppo Levi (monotone convergence) theorem and Fatou’s lemma. More than a plain formalization of the known literature, we present several design choices made to balance the harmony between mathematical readability and usability of Coq theorems. These results are a first milestone toward the formalization of $L^p$~spaces such as Banach spaces.

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

[hal-03339115] A Data-Driven Space-Time-Parameter Reduced-Order Model with Manifold Learning for Coupled Problems : Application to Deformable Capsules Flowing in Microchannels

An innovative data-driven model-order reduction technique is proposed to model dilute micrometric or nanometric suspensions of microcapsules, i.e., microdrops protected in a thin hyperelastic membrane, which are used in Healthcare as innovative drug vehicles. We consider a microcapsule flowing in a similar-size microfluidic channel and vary systematically the governing parameter, namely the capillary number, ratio of the viscous to elastic forces, and the confinement ratio, ratio of the capsule to tube size. The resulting space-time-parameter problem is solved using two global POD reduced bases, determined in the offline stage for the space and parameter variables, respectively. A suitable low-order spatial reduced basis is then computed in the online stage for any new parameter instance. The time evolution of the capsule dynamics is achieved by identifying the nonlinear low-order manifold of the reduced variables; for that, a point cloud of reduced data is computed and a diffuse approximation method is used. Numerical comparisons between the full-order fluid-structure interaction model and the reduced-order one confirm both accuracy and stability of the reduction technique over the whole admissible parameter domain. We believe that such an approach can be applied to a broad range of coupled problems especially involving quasistatic models of structural mechanics.

ano.nymous@ccsd.cnrs.fr.invalid (Toufik Boubehziz), Toufik Boubehziz

[hal-03003563] A priori identifiability : An overview on definitions and approaches

For a system, a priori identifiability is a theoretical property depending only on the model and guarantees that its parameters can be uniquely determined from observations. This paper provides a survey of the various and numerous definitions of a priori identifiability given in the literature, for both deterministic continuous and discrete-time models. A classification is done by distinguishing analytical and algebraic definitions as well as local and global ones. Moreover, this paper provides an overview on the distinct methods to test the parameter identifiability. They are classified into the so-called output equality approaches, local state isomorphism approaches and differential algebra approaches. A few examples are detailed to illustrate the methods and complete this survey.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

[hal-03228076] Cuban history of CRF19 recombinant subtype of HIV-1

CRF19 is a recombinant form of HIV-1 subtypes D, A1 and G, which was first sampled in Cuba in 1999, but was already present there in 1980s. CRF19 was reported almost uniquely in Cuba, where it accounts for ∼25% of new HIV-positive patients and causes rapid progression to AIDS (∼3 years). We analyzed a large data set comprising ∼350 pol and env sequences sampled in Cuba over the last 15 years and ∼350 from Los Alamos database. This data set contained both CRF19 (∼315), and A1, D and G sequences. We performed and combined analyses for the three A1, G and D regions, using fast maximum likelihood approaches, including: (1) phylogeny reconstruction, (2) spatio-temporal analysis of the virus spread, and ancestral character reconstruction for (3) transmission mode and (4) drug resistance mutations (DRMs). We verified these results with a Bayesian approach. This allowed us to acquire new insights on the CRF19 origin and transmission patterns. We showed that CRF19 recombined between 1966 and 1977, most likely in Cuban community stationed in Congo region. We further investigated CRF19 spread on the Cuban province level, and discovered that the epidemic started in 1970s, most probably in Villa Clara, that it was at first carried by heterosexual transmissions, and then quickly spread in the 1980s within the “men having sex with men” (MSM) community, with multiple transmissions back to heterosexuals. The analysis of the transmission patterns of common DRMs found very few resistance transmission clusters. Our results show a very early introduction of CRF19 in Cuba, which could explain its local epidemiological success. Ignited by a major founder event, the epidemic then followed a similar pattern as other subtypes and CRFs in Cuba. The reason for the short time to AIDS remains to be understood and requires specific surveillance, in Cuba and elsewhere.

ano.nymous@ccsd.cnrs.fr.invalid (Anna Zhukova), Anna Zhukova

[hal-03112758] 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 (I. Votsi), I. Votsi

[hal-02635638] Caracterisation de la composition chimique des aerosols issus de la decoupe laser de simulants du corium

Dans le contexte du démantèlement des réacteurs de Fukushima Daiichi, plusieurs projets ont été subventionnés par le gouvernement japonais pour préparer les opérations de retrait du corium. Dans ce cadre, une étude conjointe menée entre ONET Technologies et les laboratoires du CEA et de l’IRSN a permis de démontrer la faisabilité de l’utilisation de la technique de découpe par laser et d’estimer le terme source aérosol ainsi généré. Deux simulants du corium synthétisés et caractérisés par le CEA-Cadarache ont fait l’objet d’essais de tirs laser sous air et sous eau au sein de l’installation DELIA du CEA Saclay, et les aérosols émis ont été caractérisés par l’IRSN. La caractérisation des particules émises en termes de concentration et de distribution granulométrique a permis d’apporter des informations pour prédire notamment le transport et le dépôt des particules, mais la connaissance de la composition chimique par classe de taille est une information nécessaire pour une meilleure gestion des risques professionnels et environnementaux. Cet article présente les résultats concernant la caractérisation de la composition chimique de l’aérosol d’un simulant du corium, en condition de découpe laser sous air, et la distribution granulométrique associée

ano.nymous@ccsd.cnrs.fr.invalid (Emmanuel Porcheron), Emmanuel Porcheron

[hal-02307512] Generic properties of the spectrum of the Stokes system with Dirichlet boundary condition in R-3

Let (S D-Omega) be the Stokes operator defined in a bounded domain Omega of R-3 with Dirichlet boundary conditions. We prove that, generically with respect to the domain Omega with C-5 boundary, the spectrum of (S D-Omega) satisfies a non-resonant property introduced by C. Foias and J.C. Saut in [17] to linearize the Navier-Stokes system in a bounded domain Omega of R-3 with Dirichlet boundary conditions. For that purpose, we first prove that, generically with respect to the domain Omega with C-5 boundary, all the eigenvalues of (SD Omega) are simple. That answers positively a question raised by J.H. Ortega and E. Zuazua in [27, Section 6]. The proofs of these results follow a standard strategy based on a contradiction argument requiring shape differentiation. One needs to shape differentiate at least twice the initial problem in the direction of carefully chosen domain variations. The main step of the contradiction argument amounts to study the evaluation of Dirichlet-to-Neumann operators associated to these domain variations. (C) 2014 Elsevier Masson SAS. All rights reserved.

ano.nymous@ccsd.cnrs.fr.invalid (Yacine Chitour), Yacine Chitour

[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-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-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 S Barbu), V S Barbu

[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-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-01412768] Modeling spatial spread of an epidemiologic model in a spatially continuous domain

In this paper, we study a Chikungunya epidemic transmission model which describes an epidemic disease transmitted by Aedes mosquitoes. This model includes the spatial mobility of humans which is probably a factor that has influenced the re-emergence of several diseases. Assuming that the spatial mobility of humans is random described as Brownian random motion, an original model including a reaction-diffusion system is proposed. Since the displacement of mosquitoes is limited to a few meters, compared with humans, one can ignore mosquitoes mobility. Therefore, the complete model is composed of a reaction-diffusion system coupled with ordinary differential equations (ODEs). In this paper, we prove the existence and uniqueness, the positivity and boundedness of the global solution for the model and give some numerical simulations.

ano.nymous@ccsd.cnrs.fr.invalid (Shousheng Zhu), Shousheng Zhu

[hal-01361082] Dynamic sensitivity analysis of a suspension model

A sensitivity analysis of a suspension model has been performed in order to highlight the most influential parameters on the sprung mass displacement. To analyse this dynamical model, a new global and bounded dynamic method is investigated. This method, based on the interval analysis, consists in determining lower and upper bounds including the dynamic sensitivity indices. It requires only the knowledge of the parameter variation ranges and not the joint probability density function of the parameters which is hard to estimate. The advantage of the proposed approach is that it takes into account the recursive behavior of the system dynamics.

ano.nymous@ccsd.cnrs.fr.invalid (Sabra Hamza), Sabra Hamza

[hal-01294471] SENSITIVITY ANALYSIS FOR THE EEG MODEL IN NEONATES WITH RESPECT TO VARIATIONS OF THE CONDUCTIVITY

A mathematical model for the forward problem in electroencephalographic (EEG) source localization in neonates is proposed. The model is able to take into account the presence and ossification process of fontanels which are characterized by a variable conductivity. A subtraction approach is used to deal with the singularity in the source term, and existence and uniqueness results are proved for the continuous problem. Discretization is performed with 3D Finite Elements of type P1 and error estimates are proved in the energy (H 1-)norm. Numerical simulations for a three-layer spherical model as well as for a realistic neonatal head model have been obtained and corroborate the theoretical results. A mathematical tool related to the concept of Gâteau derivatives is introduced which is able to measure the sensitivity of the electric potential with respect to small variations in the fontanel conductivity. Numerical simulations attest that the presence of fontanels in neonates does have an impact on EEG measurements. The present work is an essential preamble to the numerical analysis of the corresponding EEG source reconstruction.

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

[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-01166654] IDENTIFIABILITY STUDY IN A MODEL DESCRIBING THE PROPAGATION OF THE CHIKUNGUNYA TO THE HUMAN POPULATION.

In different fields of research, modeling has become a major issue for studying and predicting the possible evolution of a system, in particular in epidemiology. Indeed, according to the globalization of our societies and the genetic mutation of certain diseases or transmission vectors, several epidemics have appeared in the last years in regions not yet concerned by such a catastrophe. One can name, for example, the chikungunya epidemic on the Réunion Island in 2005-2006. In this paper, a model describing the propagation of the chikungunya to the human population is taken again from \cite{Moulay2010}. In such models, some parameters are not directly accessible from experiments and have to be estimated numerically from an iterative algorithm. However, before searching for their values, it is essential to verify the identifiability of model parameters to assess whether the set of unknown parameters can be uniquely determined from the data. Indeed, this study insures that numerical procedures can be successful and if the identifiability is not ensured, some supplementary data have to be added or the set of admissible data has to be reduced. A first identifiability study had been done in \cite{Moulay2012} in considering that the number of eggs can be easily counted. However, after discussing with epidemiologist searchers, it appears that it is the number of larvae who can be estimated weeks by weeks. Thus, this paper proposes to do an identifiability study with this assumption and thanks to an integration of one of the model equations, some easier equations linking the inputs, outputs and parameters are obtained permitting a simpler identifiability study.

ano.nymous@ccsd.cnrs.fr.invalid (Zhu Shousheng), Zhu Shousheng

[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

[hal-01088077] Sensitivity analysis for models with dynamic inputs : a case study to control the heat consumption of a real passive house

In this communication, we perform the sensitivity analysis of a building energy model. The aim is to assess the impact of the weather data on the performance of a model of a passive house, in order to better control it. The weather data are uncertain dynamic inputs to the model. To evaluate their impact, the problem of generating coherent weather data arises. To solve it, we carry out the Karhunen-Loève decomposition of the uncertain dynamic inputs. We then propose an approach for the sensitivity analysis of this kind of models. The originality for sensitivity analysis purpose is to separate the random variable of the dynamic inputs, propagated to the model response, from the deterministic spatio/temporal function. This analysis highlights the role of the solar gain on a high-insulated passive building, during winter time.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

[hal-01084362] REMOVING THE MHD ARTIFACTS FROM THE ECG SIGNAL FOR CARDIAC MRI SYNCHRONIZATION

Blood flow in high static magnetic fields induces elevated voltages that disrupt the ECG signal recorded simultaneously during MRI scans for synchronization purposes. This is known as the magnetohydrodynamic (MHD) effect, it increases the amplitude of the T wave, thus hindering correct R peak detection. In this paper, we present an algorithm for extracting an efficient reference signal from an ECG contaminated by the Nuclear Magnetic Resonance (NMR) environment, that performs a good separation of the R-wave and the MHD artifacts. The proposed signal processing method is based on sub-band decomposition using the wavelet transform, and has been tested on human and small rodents ECG signals acquired during MRI scans in various magnetic field intensities. The results showed an almost flawless trigger generation in fields up to 4.7 Tesla during the three tested imaging sequences (GE, FSE and IRSE)

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

[hal-00937113] An extremal eigenvalue problem for the Wentzell-Laplace operator

We consider the question of giving an upper bound for the first nontrivial eigenvalue of the Wentzell-Laplace operator of a domain $\Omega$, involving only geometrical informations. We provide such an upper bound, by generalizing Brock’s inequality concerning Steklov eigenvalues, and we conjecture that balls maximize the Wentzell eigenvalue, in a suitable class of domains, which would improve our bound. To support this conjecture, we prove that balls are critical domains for the Wentzell eigenvalue, in any dimension, and that they are local maximizers in dimension 2 and 3, using an order two sensitivity analysis. We also provide some numerical evidence.

ano.nymous@ccsd.cnrs.fr.invalid (Marc Dambrine), Marc Dambrine

[hal-01063795] Sensitivity analysis of complex models : coping with dynamic and static inputs

In this paper, we address the issue of performing sensitivity analysis of complex models presenting uncertain static and dynamic inputs. The dynamic inputs are viewed as random processes which can be represented by a linear combination of the deterministic functions depending on time whose coefficients are uncorrelated random variables. To achieve this, the Karhunen-Loève decomposition of the dynamic inputs is performed. For sensitivity analysis purposes, the influence of the dynamic inputs onto the model response is then given by the one of the uncorrelated random coefficients of the Karhunen-Loève decomposition, which is the originality here. The approach is applied to a building energy model, in order to assess the impact of the uncertainties of the material properties and the weather data on the energy performance of a real low energy consumption house.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

[hal-00926454] UASA of complex models : Coping with dynamic and static inputs

Uncertainty Analysis and Sensitivity Analysis of complex models: Coping with dynamic and static inputs

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett-Collin), Floriane Anstett-Collin

[hal-00728680] Identifiablility of parameters in an epidemiologic model modeling the transmission of the Chikungunya

[…]

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

[hal-00699172] Identifiablility of parameters in an epidemiologic model modeling the transmission of the Chikungunya

In the last years, several epidemics have been reported in particular the chikungunya epidemic on the R eunion Island. For predicting its possible evolution, new models describing the transmission of the chikungunya to the human population have been proposed and studied in the literature. In such models, some parameters are not directely accessible from experiments and for estimating them, iterative algorithms can be used. However, before searching for their values, it is essential to verify the identi ability of models parameters to assess wether the set of unknown parameters can be uniquely determined from the data. Thus, identi ability is particularly important in modeling. Indeed, if the model is not identi able, numerical procedures can fail and in that case, some supplementary data have to be added or the set of admissible data has to be reduced. Thus, this paper proposes to study the identi ability of the proposed models by (Moulay, Aziz-Alaoui & Cadivel 2011).

ano.nymous@ccsd.cnrs.fr.invalid (Djamila Moulay), Djamila Moulay

[hal-00699171] Modeling Pollutant Emissions of Diesel Engine based on Kriging Models : a Comparison between Geostatistic and Gaussian Process Approach

In order to optimize the performance of a diesel engine subject to legislative constraints on pollutant emissions, it is necessary to improve their design, and to identify how design parameters a ect engine behaviours. One speci city of this work is that it does not exist a physical model of engine behaviour under all possible operational conditions. A powerful strategy for engine modeling is to build a fast emulator based on carefully chosen observations, made according to an experimental design. In this paper, two Kriging models are considered. One is based on a geostatistical approach and the other corresponds to a Gaussian process metamodel approach. Our aim is to show that the use of each of these methods does not lead to the same results, particularly when « atypical » points are present in our database. In a more precise way, the statistical approach allows us to obtain a good quality modeling even if atypical data are present, while this situation leads to a bad quality of the modeling by the geostatistical approach. This behaviour takes a fundamental importance for the problem of the pollutant emissions, because the analysis of these atypical data, which are rarely erroneous data, can supply precious information for the engine tuning in the design stage.

ano.nymous@ccsd.cnrs.fr.invalid (Sébastien Castric), Sébastien Castric

[hal-00696683] Identifiability and identification of a pollution source in a river by using a semi-discretized model

The aim of this paper is to identify the localization and the flow rate of a pollution source in a river by measuring the concentration of a substrate giving significant information. This concentration is assumed to be measured in two points of the river. The simplest model of such a problem consists in a parabolic partial derivative equation. We propose to discretize this P.D.E. in space, which leads to a system of differential equations in time. Then, the analysis of identifiability is carried out using an approach based on differential algebra. A numerical parameter estimation is inferred from this procedure, which gives a first parameter estimate without a priori knowledge about unknown parameters.

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

[hal-00696660] An efficient algorithm for testing nonlinear dynamical model identifiability

This paper is concerned by the analysis of nonlinear controlled or uncontrolled dynamical model identifiability. The proposed approach is based on the construction of an input-output ideal. The aim is to develop an algorithm which gives identifiability results from this approach. Differential algebra theory allows realization of such a project. In order to state the algorithm, new results of differential algebra must be proved. Then the implementation is done in a symbolic computing language

ano.nymous@ccsd.cnrs.fr.invalid (Lilianne Denis-Vidal), Lilianne Denis-Vidal

[hal-00696659] Two approaches for testing identifiability and corresponding algorithms

This paper considers two different methods in the analysis of nonlinear controlled dynamical system identifiability. The corresponding identifiability definitions are not equivalent. Moreover one is based on the construction of an input-output ideal and the other on the similarity transformation theorem. Our aim is to develop algorithms which give identifiability results from both approaches. Differential algebra theory allows realization of such a project. In order to state these algorithms, new results of differential algebra must be proved. Then the implementation of these algorithms is done in a symbolic computation language.

ano.nymous@ccsd.cnrs.fr.invalid (Lilianne Denis-Vidal), Lilianne Denis-Vidal

[hal-00696672] A new method for estimating derivatives based on a distribution approach

In many applications, the estimation of derivatives has to be done from noisy measured signal. In this paper, an original method based on a distribution approach is presented. Its interest is to report the derivatives on infinitely differentiable functions. Thus, the estimation of the derivatives is done only from the signal. Besides, this method gives some explicit formulae leading to fast calculus. For all these reasons, it is an efficient method in the case of noisy signals as it will be confirmed in several examples.

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

[hal-00565512] Two stage approaches for modeling pollutant emission of diesel engine based on Kriging model

Nowdays, one of the greatest problems that earth has to face up is pollution, and that is what leads European Union to make stricter laws about pollution constraints. Moreover, the European laws lead to the increase of emission constraints. In order to take into account these constraints, automotive constructors are obliged to create more and more complex systems. The use of model to predict systems behavior in order to make technical choices or to understand its functioning, has become very important during the last decade. This paper presents two stage approaches for the prediction of NOx (nitrogen oxide) emissions, which are based on an ordinary Kriging method. In the first stage, a reduction of data will take place by selecting signals with correlations studies and by using a fast Fourier transformation. In the second stage, the Kriging method is used to solve the problem of the estimation of NOx emissions under given conditions. Numerical results are presented and compared to highlight the effectiveness of the proposed methods

ano.nymous@ccsd.cnrs.fr.invalid (El Hassane Brahmi), El Hassane Brahmi

[hal-00267626] Identifiability of discrete-time nonlinear systems : the local state isomorphism approach

A new theorem is provided to test the identifiability of discrete-time systems with polynomial nonlinearities. That extends to discrete-time systems the local state isomorphism approach for continuous-time systems. Two examples are provided to illustrate the approach.

ano.nymous@ccsd.cnrs.fr.invalid (Floriane Anstett), Floriane Anstett