Hachmi Ben Dhia
email: hachmi.ben-dhia@ecp.fr

Nadia Elkhodja
email: nadia.elkhodja@ecp.fr

François-Xavier Roux
email: francois-xavier.roux@onera.fr

Multimodeling of multi-alterated structures in the Arlequin framework. Solution with a Domain-Decomposition solver

Keywords: multi-alteration, multi-patch, multimodel, Arlequin framework, substructuring, parallel computing, FETI method MOTS-CLÉS : multi-altération, multi-patch, multi-modèle, cadre Arlequin, parallélisme, méthode

The goal of this work is the development of a numerical methodology for flexible and low-cost computation and/ or design of complex structures that might have been obtained by a multialteration of a sound simple structure. The multimodel Arlequin framework is herein used to meet the flexibility and low-costs requirements. A preconditioned FETI-like solver is adapted to the solution of the discrete mixed Arlequin problems obtained by using the Finite Element Method. Enlightening numerical results are given.

RÉSUMÉ. L'objectif de ce travail est le développement d'une stratégie numérique pour le calcul et/ou la conception flexible et "low-cost" de structures complexes pouvant résulter de la multi-altération d'une structure simple de base. Le cadre multi-modèle Arlequin est utilisépour les besoins de la flexibilité et la réduction des côuts. Pour améliorer les performances numériques, un solveur multi-domaine de type FETI préconditionné est adapté à la résolution des problèmes Arlequin mixtes discrétisés par la Méthode des Eléments Finis. Des résultats numériques éclairent la démarche globale.

Introduction

The design of mechanical structures such as the multiperforated turbine blade (see Figure 1) submitted to thermomechanical loads is rather complex. For the latter and from a numerical point of view, the main difficulty relies on the discrepancy between involved scales.

Figure 1. Multiperforated turbine blade

Mono-modeling domain decomposition-like methodologies, qualified as micromacro approaches were developed to tackle this complexity (see e.g. [START_REF] Ladevèze | A new micro-macro computational strategy for structural analysis[END_REF], [START_REF] Feyel | FE 2 multiscale approach for modelling the elastoviscoplastic behaviour of long fiber SiC-Ti composite material[END_REF]). Mono-model local-global and enrichement methods were also developed for the same purpose (see e.g. [START_REF] Fish | The s-version of the finite element method[END_REF][START_REF] Strouboulis | The design and analysis of the Generalized Finite Element Method[END_REF]). In this paper, we suggest to use the multi-model Arlequin framework [START_REF] Dhia | Problèmes mécaniques multi-échelles : la méthode Arlequin[END_REF][START_REF] Dhia | Numerical modelling of multiscale problems : the Arlequin method[END_REF] and particularly its mixed version that has been analyzed theoretically ( [START_REF] Dhia | Mathematical analysis of the mixed Arlequin method[END_REF][START_REF] Dhia | Simulation de la propagation fragile des fissures dans le cadre Arlequin[END_REF] and assessed practically (e.g. [START_REF] Dhia | Application of the Arlequin method to some structures with defects[END_REF][START_REF] Dhia | The Arlequin method as a flexible engineering design tool[END_REF]) as a tool able to introduce with an enhanced flexibilty merely any kind of alteration in a given sound model. This is basically achieved by superposing and gluing a local patch containing the alteration to the global sound model, while partitioning the energies in the superposition zone and stressing the appropriate model. Formally, the Arlequin framework can be used in a straightforward manner to take into account by several patches several alterations of a structure. However, one has to address the discrete (here in the finite element sense) alterations separation issue. This issue is herein studied numerically for a very simple 1D model: a parametric study is carried out to show that when the alterations can be separated by patches whose free part size contains the alterated coarse elements, then accurate Arlequin results are obtained. As a matter of fact, this methodology, when combined to the finite element or any other discretization method leads to a mixed algebraic system. For an efficient solution of this system, a preconditioned and parallel multi-domain solver of FETI-type (see the paper by Farhat and Roux [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF]) is adapted to this mixed system, implemented and tested. Our first numerical results show the effectiveness of the global methodology.

An outline of the paper is the following. We first recall the continuous mixed mono-patch Arlequin formulation for a model elasticity problem. In Section 3, this formulation is used to calculate an elastic bar whose uniform Young's modulus is alterated first in one localised zone, second in two localised zones. The precondioned iterative solver used to solve the discrete Arlequin problems is given in Section 4. Its parallel implementation is detailed in Section 5 and assessed in Section 6 through a 3D numerical test.

Arlequin formulations

For the sake of simplicity, we consider a static linearized elasticity problem defined in a polyhedral domain Ω 0 . We let Γ, f , ε(v) and σ(v) respectively denote the clamped part of the boundary ∂Ω 0 , the applied density of body forces, the linearized strain and stress tensors associated to the displacement field v by the Hooke's law.

To alterate the structure occupying Ω 0 according to the Arlequin framework, we consider a local polyhedral domain Ω 1 whose intersection S 01 with Ω 0 is not empty. To clarify and simplify the notations, it will be assumed that Ω 1 is a subdomain of Ω 0 and that the clamped part Γ is in ∂Ω 0 . We let S 01 g denote the gluing zone supposed to be a non zero measured subset of the superposition zone S 01 such that ∂Ω 0 is included in ∂S 01 g . The complementary free zone is denoted by S 01 f . To model the gluing forces, we can use the "natural" energy scalar product analyzed in [START_REF] Dhia | Mathematical analysis of the mixed Arlequin method[END_REF], for which there are established nice mathematical and numerical properties. As a matter of fact, as mentioned in [START_REF] Dhia | The Arlequin method as a flexible engineering design tool[END_REF] (see also [START_REF] Dhia | Simulation de la propagation fragile des fissures dans le cadre Arlequin[END_REF] for a further insight), any equivalent scalar-product generates both a well-posed mathematical problem and an easy-to-implement numerical gluing operator. In order to perform the Arlequin method, we use here the most physical one of them ( a kind of volume rigidity of glue). This operator, defined below, is a pure elastic energy-based scalar product.

With these elements, the Arlequin mono-patch problem can be written as follows.

Find (u 0 , u 1 , λ 01 ) ∈ W 0 × W 1 × W 01 g ; ∀v 0 ∈ W 0 , Ω0 α 0 σ(u 0 ) : ε(v 0 ) + C(λ 01 , v 0 ) = Ω0 β 0 f .v 0 [1] ∀v 1 ∈ W 1 , Ω1 α 1 σ(u 1 ) : ε(v 1 ) -C(λ 01 , v 1 ) = Ω1 β 1 f .v 1 [2] ∀µ ∈ W 01 g , C(µ, u 0 -u 1 ) = 0 [3]
where α i and β i , for i = 0, 1, respectively denote two positive weight parameter functions whose sum is equal to 1 and where:

W 0 = {v 0 ∈ H 1 (Ω 0 ) ; v 0 = 0 on Γ} [4] W 1 = H 1 (Ω 1 ) [5] W 01 g = H 1 (S 01 g ) [6] C(λ 01 , v) = S 01 g σ(λ 01 ) : ε(v) [7]
Notice here that rigid body motions for λ 01 have to be handled for stability reasons (see [START_REF] Dhia | Mathematical analysis of the mixed Arlequin method[END_REF]) Now, by using the finite element method while following the recommandations for the choice of compatible spaces given in ( [START_REF] Dhia | Mathematical analysis of the mixed Arlequin method[END_REF]), one can derive and solve mixed discrete finite element Arlequin problems.

In the continuous framework, the generalization to a finite number of patches is straightforward, as far as these patches are geometrically separate. Indeed, one has basically to couple each local model defined in each patch to the underlying global model exactly in the manner described above. This procedure can for instance be used to formulate an Arlequin problem for the multi-perforated blade shown in Figure 1. Finite element discretisations of the obtained problem can also be formally derived and solved. However, in the discrete finite element framework, the accuracy of the numerical results becomes dependent not only of the separation of patches hypothesis, but also of the link between the diameter (say d f ) of S 01 f of a patch and the global mesh size (say H). In a previous work [START_REF] Dhia | Simulation de la propagation fragile des fissures dans le cadre Arlequin[END_REF], stress intensity factors were calculated for an Arlequin 2D problem in which one cracked patch was super-imposed to a sound plate. It has been numerically observed that accurate stress intensity factors are obtained when d f is of the order of H.

In the following section, we investigate further this geometrical aspect of the Arlequin method and examine numerically the case of a multi-patched simple structure.

Analysis of an elastic bar with one and two inclusions

In a first step, we consider a linear elastic bar whose length l 0 = 18 and Young's modulus is E1 = 1 except in a localised zone (x 1a = 6.4 and l 1a = 0.2) where a much more low young's modulus E2 = 10 -3 is considered to simulate a 1D inclusion. The bar is submitted to a uniform "volume" load f = 1. The problem is solved in a standard manner and a reference solution is derived. Then, by using the Arlequin framework, a local patch whose free zone contains and is centered on the inclusion, is superposed to a global bar model with a homogeneous young modulus E1 = 1. Finite element Arlequin problems are then derived with a coarse global mesh not fitting the interface heterogeneity and a local fine mesh, fitting the interface heterogeneity. The discrete Arlequin solutions are calculated by choosing the weight parameters α 1 and β 1 associated to the patch quite near from 1.

In a second step, the same procedure is followed for the computation of the solutions of a bi-alterated elastic bar. The two problems are represented in Figure 2.

¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¡ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ ¢ ¡¢ ¡¢ ¡¢ £ ¡£ £ ¡£ ¤ ¡¤ ¤ ¡¤ ¥ ¡¥ ¥ ¡¥ ¦ ¡¦ ¦ ¡¦ Ω 1 Ω 0 01 f E1 E2 E1 f S l 0 l1 l1f 1a x l1a § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § § ¡ § ¡ § ¡¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¡ ¡¨© © © © Ω 1 01 f E2 f S Ω S f 02 2 E2 E1 E1 E1 Ω 0 x 1a l 1a l 0 1 l 1f l l2f 2 l 2a l x 2a ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! !

A bar with a single alteration

The displacement fields are represented in Figure 3a and the relative discrete L 2 error with respect to the free zone size is ploted in Figure 3b for different sizes of the coarse mesh H. We denote h the size of the patch mesh. A noticable numerical result here is the following: to achieve a good accuracy for the Arlequin solution, the free zone has at least to include the alterated coarse elements (of course as far as the coarse mesh is sufficiently fine to give a good solution for the non alterated bar).

A bar with two inclusions

The case of a bi-alterated bar is considered now. Two scenarii are investigated here. In the first scenario, the two alterations are taken into account by a unique refined patch. Many numerical simulations not reported here show exactly the same tendancy for the numerical solutions than in the previous sub-section: the Arlequin solutions are accurate, by comparison with the reference classical solution, when the free domain of the patch includes all the alterated coarse elements. A representative result is shown in Figure 4. For the second scenarii, two refined patches have been considered, each of them containing a single alterated zone (see Figure 2b). The same conclusion holds for this second scenarii: the Arlequin solution is accurate as far as the two patches are seperate and each free zone of them contains the coarse elements containing the associated alterated zone (see Figure 5). Moreover, the size of the discrete mixed Arlequin problem is smaller in this second scenario than in the former. Observe however that when the two alterations are near from each other, by comparison with the coarse mesh size, the use a single patch containing the two alterations of two patches may lead to a non accurate solution. Two practical possibilities can be used in this case. Either define a single refined patch containing the two alterations leading us to the first scenario or refine locally the coarse mesh (a solution that misses flexibility !). A transition patch could also be introduced.

Figure 5. Arlequin/reference solutions for a bi-alterated bar with

H = 1, h = 10 -2 , l 1 = l 2 = 1.6, l 1f = l 2f = 1.2, l 1a = l 2a = 0.2
To optimize the Arlequin methodology performances as a computational tool of multi-alterated structures, an efficient iterative solver adapted to the solution of the linear mixed Arlequin problems by parallel machines is developed. This solver is obtained by a straightforward adaptation of the FETI method [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF].

Iterative computational strategy

We here focus on solving [1]-[3] by means of the FEM. To this end, we let (ϕ i 0 ), (ϕ j 1 ) and (ϕ k g ) denote the finite element basis functions of W h0 , W h1 and W 01 hg which are finite element subspaces of W 0 , W 1 and W g . The vectors U 0 , U 1 and Λ respectively stand for the coordinates of u h0 , u h1 and λ 01 hg in these bases. The FE discrete Arlequin problem derived from [1]-[3] is equivalent to the following linear system:

  K 0 0 C T 0 0 K 1 -C T 1 C 0 -C 1 0     U 0 U 1 Λ   =   F 0 F 1 0   [8]
where K i , F i and C i are the rigidity matrices, the force vectors and the coupling matrices.

Techniques for solving linear systems can be broadly divided into direct and iterative. Direct methods are robust and reliable with a predictable CPU time. However they require a global data struture that grows rapidly with the problem size. Further, direct solvers are not scable to massively parallel systems with thousands of processors. Iterative methods, on the other hand, usually scale well with increasing numbers of processors. Thus, we propose here an iterative strategy in order to treat linear multipach Arlequin problem with optimal efficiency. In the simplest case, when both K 0 and K 1 are non-singular we can write:

U 0 = K -1 0 (F 0 -C T 0 Λ) [9] U 1 = K -1 1 (F 1 + C T 1 Λ) [10]
Substituting these in (C 0 U 0 -C 1 U 1 ) = 0, we obtain a condensed problem on the gluing zone which is written

(C 0 K -1 0 C T 0 + C 1 K -1 1 C T 1 )Λ = (C 0 K -1 0 F 0 -C 1 K -1 1 F 1 ) [11]
or with obvious notations for A and d

A Λ = d [12]
The system [12] can be solved for Λ. Once Λ is obtained, the displacements U 0 and U 1 can be obtained by substituting for Λ in Equations [9] and [10]. The objective of iterative strategy is to solve by a Krylov algorithm the condensed problem, defined in our case on the gluing zone instead of the original problem [8]. As a matter of fact, the convergence of the condensed problem, based on a Conjugate Gradient (Krylov) method can be improved through the use of preconditioning techniques. As the matrice A of our condensed problem is homogeneous to a stiffness, the natural preconditioner has to be homogeneous to an inverse of a stiffness matrice. The mechanically driven preconditioner we suggest for A is defined as an inverse of the coupling operator, namely K -1 c . This preconditioner is mecanically consistent and is referred to as a flexibility matrice.

Planing step:

At each iteration k, Λ k is fixed, we -solve U 0 and U 1 , -compute the residual A Λ k -d (ie: C 0 U 0 -C 1 U 1 ),
-choose the descent direction by the residual vector.

In most problems however, not all the stiffness matrices associated to the patches will be non-singular, that is, the Arlequin methodology will likely produce some "floating" patches. In these cases, the solution process described above will break down, and a special adaptation of the computational strategy is required to handle the local singularities. Several solutions can be used. We detail two of them:

(i) The penalty method consists in regularizing the system [8] by adding a penalty coupling term to prevent the infinitesimal rigid movements of floating patches. (ii) According to FETI vision [START_REF] Farhat | A method of finite element tearing and interconnecting and its parallel solution algorithm[END_REF], a general solution can be written. For the simplified case considered here, it reads:

U 1 = K + 1 (F 1 + C T 1 Λ) + R (1) α [13] R (1) T (F 1 + C T 1 Λ) = 0 [14]
where 1) represents the rigid body modes of Ω 1 and R (1) α indicates a linear combination of these modes. Combining the equations [10],[13], [14] we obtain the condensed problem as follows:

K + 1 is a pseudo-inverse of K 1 , R (
A I C 1 R (1) R (1) T C T 1 0 Λ α = C 0 K -1 0 F 0 -C 1 K + 1 F 1 -R (1) T F 1 [15]
where

A I = C 0 K -1 0 C T 0 + C 1 K + 1 C T 1 .
Till now, many implementations of the Arlequin method have been designed for sequential codes. To lower down the solution costs we are herein interested on parallel implementations. Several levels of parallelism can be designed: between domains (here patches and global domain) and inside each domain. We focus on the first level of parallelism.

Parallel programming paradigm

In this section, we present a parallel programming paradigm. Knowing that hg . In this case, the coupling operators can be written as

W 01 hg ⊂ W h0
C 0 = K c P 0→c and C 1 = K c R 1→c .
Parallel programming paradigm can be summarized as in Table1.

K 0 U 0 = F 0 -P T 0→c K T c Λ K 1 U 1 = F 1 + R T 1→c K T c Λ computing P 0→c U 0 sending (P 0→c U 0 ) -→ -→ receiving (P 0→c U 0 ) computing the residual g = K c P 0→c U 0 -K c R 1→c U 1 receiving the residual g ←- ←-sending the residual g REMARK.
-All the processors carry out in parallel similar tasks. An additional task is realized in the processor which is assigned for the computation of the coupling operator K c . This computational strategy can be generelized for the solution of problems with a large number of patches ("subdomains") by a large number of parallel processors. In order to demonstrate the possibilities of the iterative and parallel strategy with and without preconditioning, some numerical results are given in the following section.

Numerical experimentations

We consider a linear elastic homogeneous and isotropic cube on which we superimpose, in the Arlequin framework, a 3D patch containing an heterogeneity. The latter is machanically labeled inclusion. The cube is clamped on one face and submitted to a non axial density of loads on the opposite face. The Young's modulus is taken equal to 2000M P a and the poisson's ratio is equal to 0, 3. The Young's modulus of the inclusion is equal to 20M P a which corresponds to heterogeneity ratio of 10 2 and its Poisson coefficient is equal to 0, 3. The discrete finite element solution of this problem is calculated by using the meshes shown in Figure 6a, with trilinear finite element spaces. The global cube model contains 3000 d.o.f. and the patch model contains 18000 d.o.f. The computations are carried out in a parallel machine by following the strategy described by Table 1. The deformed meshes are represented in Figure 6b. The convergence of the residual norm to 0 is clearly related to the thickness of S 01 g . The larger this parameter is , the faster is the convergence. Observe however that the size of the interface problem increases with the thickness of the gluing zone. In our case, the optimal choice seems to be 2h.

In a second step, the same computations are carried out by using a pre-conditioner. The results are shown in Figure 8, by which one can conclude that, the smaller the gluing zone thickness is, the more efficient is the preconditioner : by comparison with the results shown in Figure 7, the number of iterations is divided by a factor 7 when the thikness of S 01 g is equal to h and by factors ranging between 3 and 4 for the other cases. Moreover the additional preconditioner costs are lower for the small thiknesses than for the large ones.

Conclusion and perspectives

In this paper, we have numerically designed a practical Arlequin strategy that allow us to handle multi-alterated structures with enhanced flexibility. A noticable numerical result obtained for a model 1D elastic bar with one or two alterations is that to achieve a good accuracy for the Arlequin solution, the free zone of a patch has at least to include the alterated coarse elements (as far as the coarse mesh is sufficiently fine to transmit a good solution for the non alteratd bar). Moreover, a very significant improvement of the global solution strategy is realized by i) considering a pure energybased coupling operator and ii) adapting a preconditioned FETI-like solver to solve the mixed Arlequin linear systems.

Figure 2a .

 2a Figure 2a. A single alterationFigure2b. A double alteration

Figure 3a .

 3a Figure 3a. The displacement solutionsFigure3b. Relative discrete L2 errors with H = 1, h = 0.01, l 1 = 3, l 1f = 2.9 versus the the size of S 01 f

Figure 4 .

 4 Figure 4. Arlequin/reference solutions for a bi-alterated bar with H = 2, h = 10 -2 , l 1 = 4, l 1f = 3.8, x 1a = 8.4, x 2a = 9.4, l 1a = l 2a = 0.2

Figure 6a .

 6a Figure 6a. Cube and heterogeneous Figure 6b. Displacement solution patch meshes We first study the influence of the gluing zone thickness (respecting the Arlequin methodology requirements) on solver convergence. The results are shown in Figure 7 where several thicknesses, related to the patch mesh size h are considered.

Figure 7 .

 7 Figure 7. Evolution of the logarithmic residual for several size of gluing zone

Figure 8 .

 8 Figure 8. Residual for several size of gluing zone with preconditioner

Table 1 .

 1 Parallel programming paradigmInput data : K 0 , F 0 and P 0→cInput data : K 1 , K c , F 1 , Λ 0 and R 1→c

	Global model Ω 0 -Processor 1	Local model (patch) Ω 1 -Processor 2
	output data: U 0 receiving (K T c Λ) term ←-solving concurrently the equilib-rium equation	output data: Λ and U 1 computing coupling term K T c Λ ←-sending (K T c Λ) term solving concurrently the equilibrium equa-tion


Christian Salim

Nathalie Mitton

Image Similarity based Data Reduction Technique in Wireless Video Sensor Networks for Smart Agriculture

Keywords: Wireless video sensor networks, Data Reduction, Geometric Correlation, Inter-Nodes Similarity

Nowadays, to improve animal well being in livestock farming or beekeeping application, a wireless video sensor network (WVSN) can be deployed to early detect injury or Asiatic hornets attacks. WVSN represents a low-cost monitoring solution compared to other technologies such as the closed circuit television technology (CCTV). WVSNs are composed of low-power resource-constrained video sensor nodes (motes). These nodes capture frames from videos at a given frequency (frame rate) and wirelessly send them to the sink. The big amount of data transferred from the nodes to the sink consumes a lot of energy on the sensor node, which represents a major challenge for energy-limited nodes. In this paper, we introduce two complementary mechanisms to reduce the overall number of frames sent to the sink. First, the Transmission Data Reduction algorithm (TDR) run on the sensor node leverages the similarity degree of consecutive images. Second, the Inter-Nodes Similarity algorithm (INS) exploits the spatio-temporal correlation between neighbouring nodes in order reduce the number of captured frames. The results show a 95% data reduction, surpassing other techniques in the literature by 30% at least.

Introduction

In recent years, the need for smart agriculture has increased [START_REF] Salim | Machine learning based data reduction in wsn for smart agriculture[END_REF]. Surveillance systems are deployed to support it, especially in remote sites in order for instance to monitor the animals behaviour, understand and protect the livestock and vegetables farming. To achieve it, a wireless video sensor network (WVSN) can serve as an Christian Salim and Nathalie Mitton Inria, France, e-mail: firstname.lastname@inria.fr 1 energy-efficient and low cost solution. In WVSN, the system normally operates periodically, sending all the captured frames to the sink [START_REF] Salim | Combining frame rate adaptation and similarity detection for video sensor nodes in wireless multimedia sensor networks[END_REF]. However, the system can be an event driven system sending only the frames that show a change in the area of interest. The wireless video sensor nodes are energy-limited nodes that monitor an area of interest according to their Field of Views (FOVs) and send the videos/frames to the sink. Shooting a video and capturing its frames consume a lot of energy but sending this great number of frames to the sink is even worse. In order to cover all the area of interest and prevent black holes, in general, WVSN are such that several FoVs overlap with each other. To reduce the energy consumption at the sensor node level, we aim to reduce the amount of data sent to the sink leveraging the overlap between FoVs and by applying a node embedded lightweight algorithm in order to cope with the nodes limited processing and energy resources.

In this paper, we propose a two-level data reduction approach. The first one, Transmission Data Reduction algorithm (TDR), runs on each node and selects only the critical frames to be sent to the sink. The second one, the Inter-Nodes Similarity algorithm (INS), leverages the spatio-temporal correlation between neighbour nodes to reduce the number of sent and captured frames. The TDR algorithm compares consecutive captured frames on the node based on a norm simple euclidean distance similarity method [START_REF] Salim | Energy-efficient secured data reduction technique using image difference function in wireless video sensor networks[END_REF]. According to the degree of similarity with the last frame sent to the sink, the node decides whether to send this frame or not [START_REF] Salim | Combining frame rate adaptation and similarity detection for video sensor nodes in wireless multimedia sensor networks[END_REF]. If the decision is to send the image, the node creates a new image img dif f that only includes the difference between the two compared images. img dif f is sent to the sink instead of the whole image. In this case, data reduction is attained when several consecutive frames represent a high similarity percentage (stable situation). To furthermore increase the data reduction, the INS algorithm computes the correlated degree of neighbouring nodes and compares their frames using the same norm simple euclidean distance metric. If the result detects a similarity for n consecutive frames, the node with the highest energy level sends the frames to the sink, the other one goes to idle mode and its frame rate is set to the minimum F R = 1. We compare this new method to another algorithm from the literature based on the colour and edge similarities and on the number of consecutive frames sent per period [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF]. The results show that our approach reduces the amount of energy by 95% outperforming the other approach, while capturing all the events. The remainder of this paper is organised as follows. Section 1.2, browses the related work. Section 1.3 describes the transmission data reduction algorithm while Section 1.4 details the INS algorithm The experimental results and the comparison with other methods are given in Section 1.5. Finally, Section 1.6 concludes and provides perspectives and future work.

Related work

In this section, we discuss some previous works regarding data reduction in WSN and in WVSN in particular. A lot of techniques based on scheduling [START_REF] Jiang | Probability-based prediction and sleep scheduling for energy-efficient target tracking in sensor networks[END_REF], [START_REF] Feng | Energy-balanced multisensory scheduling for target tracking in wireless sensor networks[END_REF], in-trusion location and clustering [START_REF] Salim | Kinematics based approach for data reduction in wireless video sensor networks[END_REF][START_REF] Ghosal | A survey on energy efficient intrusion detection in wireless sensor networks[END_REF], compressive sensing [START_REF] Veeraputhiran | Feature based fall detection system for elders using compressed sensing in wvsn[END_REF], data similarity [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF], [START_REF] Salim | Energy-efficient secured data reduction technique using image difference function in wireless video sensor networks[END_REF], and frame rate adaptation [START_REF] Tayeh | A new autonomous data transmission reduction method for wireless sensors networks[END_REF][START_REF] Monika | Energy efficient surveillance system using wvsn with reweighted sampling in modified fast haar wavelet transform domain[END_REF] exist for data reduction and for energyefficiency. The authors in [START_REF] Salim | Kinematics based approach for data reduction in wireless video sensor networks[END_REF] used the kinematics functions to predict the next location of the intrusion in the area of interest in order to increase the frame rate adaptation of the targeted nodes. This approach reduced the energy dissipation of the overall network, since only the targeted nodes are capturing and not all the nodes in the zone of interest. This approach can come as a complementary solution to our method which focuses on the nodes detecting the intrusion and not on the projected positions of the intrusion. In [START_REF] Salim | Energy-efficient secured data reduction technique using image difference function in wireless video sensor networks[END_REF] and [START_REF] Tayeh | A new autonomous data transmission reduction method for wireless sensors networks[END_REF], the authors worked on data reduction by adapting the frame rate of the nodes. This type of approaches is helpful and could be studied later on as a complementary work of the approach presented in this paper. The geometric correlation between several sensor nodes has been exploited by several authors such as [START_REF] Nu | Power-efficient video uploading for crowdsourced multiview video streaming[END_REF][START_REF] Dai | A spatial correlation model for visual information in wireless multimedia sensor networks[END_REF][START_REF] Mowafi | A novel approach for extracting spatial correlation of visual information in heterogeneous wireless multimedia sensor networks[END_REF]. In [START_REF] Dai | A spatial correlation model for visual information in wireless multimedia sensor networks[END_REF], the authors transform the coordinates of every point from 3D to a 2D coordinate system according to some reference points. Computing the disparity and the lengths of the reference vectors can determine whether for example two cameras are geometrically correlated according to a predefined threshold. In [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF], the authors proposed a similarity function to detect the percentage of similarity between consecutive frames to attain data reduction by sending the critical frames to the sink. They merge it with a correlation overlapping technique at the coordinator level. The proposed colour-edge similarity function is time and energy consuming especially in the colour part where every channel is taken into consideration. They compared the frames on the coordinator level to further reduce the amount of frames. In this paper, the proposed method reduces the number of frames sent from each node to the coordinator by using the L2-norm distance to measure the similarity. It is a way less heavy to be implemented at the sensor node unlike other techniques that use the colour-edge and pixel similarities as in [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF], [START_REF] Tayeh | A new autonomous data transmission reduction method for wireless sensors networks[END_REF], [START_REF] Monika | Energy efficient surveillance system using wvsn with reweighted sampling in modified fast haar wavelet transform domain[END_REF]. As explained in section 1.3 it is a less complex technique regarding the execution time comparison with other approaches for the same purpose of data reduction. Unlike other approaches that use a 3D to 2D transformation to implement a similarity algorithm as in [START_REF] Dai | A spatial correlation model for visual information in wireless multimedia sensor networks[END_REF], we complement the approach by proposing a 2-D spatial correlation between neighbour nodes based on some geometrical conditions using simple equations. If 2 nodes are said "correlated", the Inter-Nodes Similarity algorithm (INS) runs on both nodes, the one with the most residual energy sends the data, the other goes into idle transmission mode and lowers its frame rate to its minimum F R = 1.

Data Reduction

In WSN, sensor-nodes operate periodically, and send a huge amount of data to the coordinator simultaneously. This scenario consumes a lot of energy on each sensor node representing the most important challenge in WSN in general. In WVSN, packets sent are multimedia, which emphasises even more the challenge of energy consumption. To overcome this challenge and to lower its importance on the fea-sibility of the network deployment, we proposed a data reduction method at the sensor node to reduce the number of raw images sent from each node to the sink. This technique combines two mechanisms presented by the Transmission Data Reduction algorithm (TDR) and the Inter-Nodes Similarity algorithm (INS).

Transmission Data Reduction

The Transmission Data Reduction algorithm (TDR) is described in Algo. 1. TDR algorithm leverages the consecutive frames similarity as in [START_REF] Salim | Energy-efficient secured data reduction technique using image difference function in wireless video sensor networks[END_REF], using the norm simple euclidean distance similarity method to compare images. If two consecutive sensed frames are estimated as similar (no new information is represented in the second frame), the node does not send the second frame to the coordinator. The node counts the number of consecutive similar frames, if it surpasses nb (the required number of consecutive similar frames), the state of the area of interest monitored by the node is considered as stable (situation=1). This technique uses the norm L2 relative error function tested in C++ in OpenCV and compared to other techniques in [START_REF] Salim | Energy-efficient secured data reduction technique using image difference function in wireless video sensor networks[END_REF] where the time to execute this technique is way less important than other techniques (edge, colour, ...) for the same purpose of data reduction. To apply this function, each image is transformed into a matrix. If the similarity norm sim = dist(f r i , f r last ) between those images does not surpass a certain threshold of similarity (norm sim < th sim ), it means the images are not similar. In this case, the sensor-node creates and sends to the sink a new image called img dif f by adopting the absolute images difference function as shown in the equation below:

img dif f = absdif f (M AT A, M AT B) (1.1)
This function computes the absolute value of the difference for each pixel, for each channel of the two matrices. The img dif f is an image that represents the difference between both images using less bits. In this case, the size in Bytes of the transmitted packets decreases because only the difference between images is sent rather than the full new image. An example of the img dif f is shown in Figure 1.2c representing the difference image img dif f of the frames presented in Figures 1.2a and 1.2b taken from the dataset in [START_REF] Goyette | changedetection.net: A new change detection benchmark dataset[END_REF] 1 . As we can see, the shadow of the moving person and the person are the only differences taken into account. The last sent image to the coordinator is stored on the sensor node. Every new frame is compared to this last frame sent to the sink, it can replace this last frame if it represents a critical event or a change in the monitored zone as shown in Algo 1. In the remainder of this paper, the sent image img dif f is called critical frame. We called it critical, because the node sends only an image to the coordinator if an event or a change is happening in the area of interest. This whole process is explained in Fig. 1.1. Note that, the reconstruction algorithm at the sink level is out of the scope of this paper. Set nb sim = 0 the number of consecutive similar frames 4: while Energy > 0 do for each frame i do 6:

if norm sim < th sim then nb sim = 0; f r last = f r i

8:

Sends img dif f to the sink else 10:

nb sim = nb sim + 1 if nb sim > nb then 12: Situationu = 1 # Stable Situation end if 14:
end if end for 16: end while

Inter-Nodes Correlation: The Overlapping Method

In the above sections, we were interested in reducing the amount of sent frames from each node to the sink by applying a similarity function at the sensor node itself. To

Video Sensing Model

We consider a 2-D model of a video sensor node where z = 0 (XOY plane) and all the captured frames are compared as 2-D images not taking account of the third dimension. A video sensor node S is represented by the Field of View (FoV) of its camera. Unlike a wireless sensor which range is omnidirectional, a FoV covers only a part of the surrounding area of a video sensor as shown in Fig. 1.3a. A FoV is a vector of 4-tuple S(P, R s , -→ V , α) where P is the position of S, R s is its sensing range, -→ V is the vector representing the line of sight of the camera's FoV e.g. its sensing direction, and α is the offset angle of the FoV.

In [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF] the authors presented the FoV with 4 points a,b,c and the gravity centre g as shown in Fig. 1.3b. The overlapping area is detected based on those points as explained in the upcoming subsections. A point P 1 is said to lay in the FoV of a video sensor node S at position P if and only if the two following conditions are satisfied:

1. d(P, P 1 ) ≤ R s , where d(P, P 1 ) is the Euclidean distance between P and P 1 :

--→ P P 1 ≤ R s 2. The angle between --→ P P 1 and

- → V is within [-α, +α] : --→ P P 1 . - → V ≥ --→ P P 1 × - → V × cos(α).
In the remainder of this paper, we consider that all video nodes are identical, with the same sensing range R s and the same offset angle α. In the next section, we discuss the spatial correlation of overlapping neighbour nodes based on some geometrical conditions, and how we use it in order to increase the data reduction at the sensor node level.

Overlapping Sensor Nodes

In this part, we describe the geometric condition which determines if two neighbours are overlapping nodes. This condition is a combination of the angle condition between the FoV's of the nodes and the ratio of the overlapping area between them.

The Angle Condition

The angle between two neighbouring sensor nodes is defined as the angle between the vectors of their FoVs. If the angle between the FoVs of two neighbouring nodes is wide, these two nodes can not take part in the similarity comparison function to decide which one among them sends the data to the sink. Indeed, that means that they are not sensing the same area of interest. A frame from two different perspectives can be widely different. To be able to define two neighbour sensor nodes as overlapping sensor nodes, the angle between their FoVs must not surpass a certain angle threshold. In order to determine the angle between vectors ( V and V ) of the sensor nodes S and S respectively as shown in Figure 1.3c, we use the scalar product between those sensor nodes. Since all sensor nodes are identical, both vectors V and V have the same length l. The scalar product can be calculated in two formats. The first one according to their coordinates (x and y) where

V = (X V ,Y V ) and V = (X V ,Y V ) : V . V = X V × X V + Y V × Y V (1.2)
The second format is given according to the length of each vector and to the angle between both, as follows:

V . V = l 2 × cos( V , V ) (1.3) Where l = -→ V = - → V .
The below equation defines and computes the angle θ between the two vectors according to both formats of the scalar product:

θ = arccos((X V × X V + Y V × Y V )/l 2 ) (1.4)
If an angle threshold th angle is defined as 30 degrees, the angle between V and V must remain less than 30 degrees so the two sensor nodes S and S can proceed to the next step (the two points strategy), to be able at the end to take part in the similarity function process.

The two Points Condition

Inspired from [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF] we present below the two points condition as the second part of the geometric condition. A node S satisfies the two points condition with another node S if g (the gravity centre of abc) belongs to the FOV of S alongside other point between a, b and c from S s FOV as shown in Figure 1.3b. In this figure, S 1 , S 2 and S 3 satisfy this condition separately with S. In this scenario, each sensor node can be a candidate alongside S to apply the learning process and the similarity function between them on the one having the most residual energy. However, only S 1 and S 2 satisfy at the same time the angle and the two points conditions. For this purpose, S 1 and S 2 will be the nodes selected as two overlapping sensor nodes to test the inter nodes similarity algorithm IN S as explained in the next section.

Inter-Nodes Similarity

As mentioned earlier, the comparison between the frames captured by overlapping sensor nodes is done at the start of each stable situation in the zone of interest. We used the same norm simple euclidean distance function to measure the similarity. If the similarity computed ratio IN sim is greater than a predefined threshold IN th for the first frame as shown in Algo. 2, it means that the two correlated nodes present the same information when shooting the zone of interest. In this case, only one

Algorithm 2 IN S run on S u

Set n sim = 0 the number of similar frames Get situationv and f rv 0 from Sv 3:

if situationu = 1 AND situationv = 1 AND IN sim > IN th then if RN Su > RN Sv then
Su continues sending the frames running TDR 6:

else F Ru = 1 (and stop sending) end if 9: end if out of the two sensor nodes is selected to send the data, depending on the residual energy RN of both nodes. If S u has more energy left than S v (RN Su > RN Sv ), S u continues to send the data while S v goes to transmission idle mode and its frame rate is reduced to F R = 1 frame per second on S v . Once an event occurs in the FoV of S v the frame rate is back to its maximum of 30 frames per second.

Experimental Results

Several simulations have been conducted to validate our approach at the sensor node, aiming to minimise the number of frames sent from the node to the sink. We compare our approach to MASRA and SSA algorithms in [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF] and PPSS algorithm in [START_REF] Elson | Fine-grained network time synchronization using reference broadcasts[END_REF]. We have used a Matlab simulator. A scenario is introduced in Figure 1.3c where 2 video-sensor nodes S1,S2 are deployed as overlapped neighbour nodes to monitor the same area of interest from different perspectives as shown in Figure 1.3c. The angle threshold is set to 15 degrees, however in this case α = 10 and S 1 covers the gravity centre and one other point of the FoV of S 2 , which makes them two overlapping neighbour nodes in order to apply the INS algorithm on both. The main purpose in our work is to send to the sink the frames that represent the critical situations while maintaining the information by applying TDR and INS algorithms. We have used 2 Microsoft LifeCam VX-800 cameras to shoot a short video of 120s (3600 frames captured per node), each camera is connected to a laptop to do the processing via a Matlab simulator. Each camera captures 30 frames/s. In our scenario, an intrusion is detected at the following time-intervals: S1: 40s from 15 to 55 ; S2: 40s from 20 to 60. In the rest of the time, both sensor nodes had a stable situation. After conducting several simulations, the number of high similarities needed to detect a stable situation is set to n = 60 which means 2 seconds of stability. The similarity threshold th sim is set to 85% in TDR algorithm and 75% in INS algorithm. Note that a full compressed image size is equal to 30KB and the difference image img dif f size is 20KB. The thresholds and all the parameters can be adapted according to the application and the QoS required.

Transmission data reduction

Table 1.1 shows the number of frames sent by each node to the sink over 120 seconds using the TDR algorithm. This algorithm allows the reduction of the number and size of frames transmitted by the sensor-node as shown in Tables 1.1 and 1.2.

A transmission data reduction of more than 90% is reached by sending only the critical frames. However the size reduction reached 95% due to the image difference img dif f applied on every selected/critical frame. Once in a stable situation, the first frame is sent and due to similarity all the other frames are not transmitted to the sink.

Inter-Nodes Similarity

The INS algorithm runs on both nodes at the same time with TDR algorithm. In this section we consider that S 1 has more residual energy than S 2 , which puts S 2 into the idle mode and reduces its frame rate to F R 2 = 1 frame per second. In this case the data reduction is emphasised also on the sensing process for S 2 as shown in Table 1.3. In this case, the number of frames sent to the sink remains the same as in TDR alone, but the number of captured frames reduces by more than 50% on S 2 and 33% overall.

Comparison

We compare to the scheduling algorithm P P SS [START_REF] Elson | Fine-grained network time synchronization using reference broadcasts[END_REF] and to the M ASRA algorithm [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF] where the colour and edge similarities were both present to detect the difference between images. The difference between those approaches in terms of data reduction is shown in Table 1.4. As we can notice from Table 1.4, TDR and INS algorithms outperform MASRA algorithm [START_REF] Salim | Similarity based image selection with frame rate adaptation and local event detection in wireless video sensor networks[END_REF] and PPSS algorithm [START_REF] Elson | Fine-grained network time synchronization using reference broadcasts[END_REF] in terms of transmission data reduction by 70% and 90% respectively and in terms of the size of the data transmitted. This technique reduced the transmitted data by 95% and the sensed data by 33% of the overall data captured and transmitted. However, the sensing data reduction is better on MASRA algorithm by 45% which implements the frame rate adaptation of each node according to the scene but computes the geometric correlation on the sink not on the node, in this purpose they transmit 3 times more than our current approach. The overall gain remains positive by more than 30%.

Conclusion

In this paper, we introduced a distributed data reduction approach for wireless video sensor network. This approach is composed of two complementary algorithms, the transmission reduction algorithm (TDR) and the inter-nodes similarity (INS) algorithm. TDR detects the similarities between consecutive captured frames and decides to send only the difference image of each critical frame to the sink. The results show that the proposed algorithms did not miss any event in the recorded video sequence. The second part of the approach consists in a geometrical condition computed by neighbour nodes to detect whether they overlap and reduce accordingly their frame rate or transmission rate. Comparing our approach with MASRA and PPSS algorithms in terms of data reduction shows that our algorithm outperforms both algorithms by 30% and 90% respectively. As future works, first of all we aim to compare the relevance of our mathematical model by comparing it to other approaches. In order to increase the data reduction, the frame rate adaptation technique at the sensor node level can be taken into account.

Fig. 1 . 1 :Fig. 1 . 2 :

 1112 Fig. 1.1: Video sensor node and sink behaviours

  Fig. 1.3: Overlapping Model

Fig 1. 4 showsFig. 1 . 4 :

 414 Fig. 1.4: Two overlapping sensor nodes behaviour running INS

Table 1 .

 1 2: Overall data and size reduction

	Node Situation Captured Frames Sent Frames
	S 1	Stable	2300	2	Total Frames Type Frames Size Frames
	S 1	Event	1200	240	7200	Captured all 216000 KB
	S 2	Stable	2300	2	504	Critical all 15120 KB
	S 2	Event	1200	260	504	img dif f	10080 KB
	ALL	All	7200	504
	Table 1.1: TDR algorithm over 120s

http://changedetection.net 1 Image Similarity based Data Reduction in WVSN for SA

Acknowledgements

This work was partially supported by a grant from CPER DATA, by LIRIMA Agrinet project and the Inria/CEFIPRA Associate team DC4SCM.


Amandine Michelas
email: michelas@lpl-aix.fr

Sophie Dufour

Running Head: Accentual contrast discrimination When native contrasts are perceived as non-native: the role of the ear of presentation in the discrimination of accentual contrasts

Keywords: Speech perception, right hemisphere advantage, ear of presentation, accentual variation, French prosody

In two ABX experiments using natural and synthetic stimuli, we examined the ability of French listeners to perceive accentual variation by manipulating the ear of presentation. A native (/balɔ /-/baˈlɔ /) and a non-native (/ˈbalɔ /-/baˈlɔ /) contrasts were tested. The stimuli A and B varied either in accent (/ˈbalɔ /-/baˈlɔ /), in one phoneme (/baˈlo/-/baˈlɔ / "bundle-ball") or in both types of information (/ˈbalo/-/baˈlɔ /). For the non-native contrast, persistent difficulty was found regardless of the ear of presentation. For the native contrast, better performance was observed when the stimuli were presented to the left ear, and thus when the processing was pushed into the right hemisphere. Our findings also showed that the native contrast was processed as a non-native contrast when the processing was pushed into the left hemisphere.

More generally, our study indicates that accentual variation at the word level in French is processed as non-linguistic variation.

In lexical stress languages and in tone languages, prosodic information is linguistically contrastive at the word level. As a result, in these languages, prosodic information can change the meaning of a word as in the case of BEbe /ˈbebe/ "s/he drinks" and beBE /beˈbe/ "baby" in Spanish. Consequently, speakers of these languages show no difficulty in discriminating two items differing in prosodic information (e.g., [START_REF] Dupoux | A destressing "deafness" in French?[END_REF][START_REF] Dupoux | A robust method to study stress "deafness[END_REF][START_REF] Dupoux | Persistent stress 'deafness': The case of French learners of Spanish[END_REF]. Moreover, neuropsychological studies conducted on tone languages have shown that the left hemisphere is recruited to process contrastive prosodic information at the word level for speakers of these languages (e.g., [START_REF] Gandour | Pitch processing in the human brain is influenced by language experience[END_REF][START_REF] Gandour | A crosslinguistic PET study of tone perception[END_REF][START_REF] Gandour | A cross-linguistic FMRI study of spectral and temporal cues underlying phonological processing[END_REF][START_REF] Gandour | Hemispheric roles in the perception of speech prosody[END_REF][START_REF] Klein | A cross-linguistic PET study of tone perception in Mandarin Chinese and English speakers[END_REF]. But what happens for languages such as French in which prosodic information does not create meaning distinctions at the word level?

One of the most striking characteristics of French prosody is that accent 1 , the acoustic prominence given to a syllable, is determined post-lexically. As a result, a same word receives accent or not depending on its location within the phrase. For instance, the word ballon "ball" receives accent in ([un petit ba'LLON]) "a little ball" because it is in final position within the phrase while it is unaccented in ([un baLLON 'bleu]) "a blue ball" because it is not in final position. Hence the word ballon conserves the same meaning whether it is accented on its final syllable or not 2 . Because accent is not lexically contrastive in French, it has been repeatedly

shown that French listeners have difficulty discriminating between two items differing in lexical stress (e.g., BEbe /ˈbebe/ and beBE /beˈbe/; [START_REF] Dupoux | A destressing "deafness" in French?[END_REF][START_REF] Dupoux | A robust method to study stress "deafness[END_REF][START_REF] Dupoux | Persistent stress 'deafness': The case of French learners of Spanish[END_REF]. The term "stress deafness" has been widely used to qualify the low sensitivity of French listeners to accentual variation affecting the word level. However, recent studies conducted in our laboratory [START_REF] Michelas | How deaf are French speakers to stress?[END_REF][START_REF] Michelas | On French listeners' ability to use stress during spoken word processing[END_REF] have shown that this low sensitivity to accentual variation does not extend to all accentual contrasts. In fact, we showed that French listeners are fully able to discriminate between an unaccented (e.g., ballon /balɔ / "ball") and an accented word (baLLON /baˈlɔ / "ball"), namely between accentual differences that exist in their native language. Based on past studies showing that other sources of speech variation (i.e., talker variation) are processed by the right hemisphere when they are not linguistically relevant [START_REF] Van Lancker | Impairment of voice and face recognition in patients with hemispheric damage[END_REF][START_REF] Von Kriegstein | Modulation of neural responses to speech by directing attention to voices or verbal content[END_REF]Gonzalez & McLennan, 2007), we hypothesized that accentual variation at the word level in French would be primarily processed by the right hemisphere. In particular, using dichotic presentation, we examined the role of the ear of presentation and we predicted better performance in the discrimination of both native and non-native accentual contrasts when words are presented to the left ear, and thus, due to contralateral projections, when the processing was pushed into the right hemisphere.

What do we already know about French listeners' ability to discriminate accentual contrasts? In a seminal study, Dupoux and collaborators [START_REF] Dupoux | A destressing "deafness" in French?[END_REF] compared French and Spanish listeners' ability to discriminate lexical stress contrasts that exist in Spanish but not in French. In an ABX task, in which A, B and X were spoken by three different speakers, and in which participants judged whether X was identical to A or to B, they showed that, compared to Spanish speakers, French speakers had more difficulty discriminating between two nonsense words that differed only in stress (FIdape, fiDApe). In addition, unlike Spanish listeners, French listeners performed worse when the stimuli differed in stress (FIdape, fiDApe) than in phonemic identity (FIdape, LIdape). Together, these findings suggest that French listeners process an accentual and a phonemic contrast differently. However, their difficulties could be due to the fact that [START_REF] Dupoux | A destressing "deafness" in French?[END_REF] used stress location contrasts (BOpelo/boPElo and boPElo/bopeLO) that do not exist in French. [START_REF] Dupoux | A destressing "deafness" in French?[END_REF], recent studies [START_REF] Michelas | How deaf are French speakers to stress?[END_REF][START_REF] Michelas | On French listeners' ability to use stress during spoken word processing[END_REF] have examined the ability of French listeners to discriminate accentual contrasts that are frequently encountered in their native language. Using the same paradigm, the authors replicated [START_REF] Dupoux | A destressing "deafness" in French?[END_REF] 's results showing that French listeners had more difficulty discriminating two French words that differed in accent location (JUry-juRY "jury-jury") compared to words that differed in one phoneme (juRON-juRY "swearword-jury"). However, and crucially, no difficulty was observed when the stimuli differed in the presence or absence of accent (jury-juRY), namely on the accentual contrast that exists their native language. Such observation suggests that French listeners have difficulty discriminating non-native accentual contrasts, but that their difficulty with accent disappear as soon as they have to discriminate accentual contrasts that do exist in their native language.

Contrary to

Because French listeners have been shown to be able to differentiate an accented word from its unaccented version [START_REF] Michelas | How deaf are French speakers to stress?[END_REF][START_REF] Michelas | On French listeners' ability to use stress during spoken word processing[END_REF], in a recent study [START_REF] Michelas | Are Prosodic Variants Stored in the French Mental Lexicon?[END_REF], we have examined whether this accentual variation could be stored in the mental lexicon. In that study, participants heard a first block of stimuli (the priming block) followed by a second block (the target block) in which some of the words from the first block were repeated either with the same accentuation (banDEAU-banDEAU "headband-headband") or with a different accentuation (bandeau-banDEAU "headband-headband"). In comparison to a control condition in which primes and targets were unrelated (marron-banDEAU "chestnutheadband"), a repetition priming effect of similar magnitude was observed in the same and different accentuation conditions. Such a result suggests that accentual variation is not stored in the mental lexicon even though French native listeners are fully able to distinguish an accented and an unaccented word. This observation mirrors results for segmental contrasts in a second language showing that good performance in discrimination or categorization tasks does not necessarily extend to tasks involving lexical processing [START_REF] Darcy | Asymmetric lexical access and fuzzy lexical representations in second language learners[END_REF][START_REF] Díaz | Individual differences in late bilinguals' L2 phonological processes: From acoustic-phonetic analysis to lexical access[END_REF].

All the studies conducted on the French language so far could therefore suggest that accentual variation at the word level is processed as non-linguistic variation by French listeners.

In the current study, we examined this hypothesis following the approach of Gonzalez & McLennan (2007)'s study which showed that non-linguistic variation is primarily processed by the right hemisphere 3 . In particular, these authors showed that variation due to talker identity influenced spoken word processing only when stimuli were presented to the left ear, and thus primarily processed by the right hemisphere. Consequently, we wondered here whether French native listeners better succeed in discriminating accentual contrasts when stimuli were presented to the left ear. To do so, we used the [START_REF] Dupoux | A destressing "deafness" in French?[END_REF]'s ABX task again in which participants heard three words produced by three different speakers and had to decide whether X was similar to A or to B. A and B were produced by two different female speakers and X was always produced by a male speaker. Two types of accentual contrasts were tested: 1) the accentual contrast that exists in French, namely the difference between an unaccented word and the same word bearing primary accent on its last syllable: /balɔ / and /baˈlɔ / ballon "ball" (the 'native accentual pattern'), and 2) an accentual contrast that does not exist in French, namely the difference between a word bearing primary accent on its first syllable and a word bearing primary accent on its last syllable: /ˈbalɔ / and /baˈlɔ /, (the 'non-native accentual pattern'). Note that whatever the accentual contrast tested, accentual variation never creates meaning distinctions (i.e., ballon always means 'ball' whether it receives accent on its first syllable, on its second syllable or no accent) and thus the crucial manipulation concerns whether the accentual contrast exists or not in the French language. We expected participants to process an accentual mismatch with the same ability as a phonemic mismatch when stimuli were presented to the left ear and thus primarily processed in the right hemisphere. Within each accentual contrast, the accentual mismatch was always compared to a phonemic mismatch. In accordance with the growing body of evidence showing that phonemic representations are bilateral (e.g., [START_REF] Hickok | Towards a functional neuroanatomy of speech perception[END_REF], phonemic mismatch is expected to be processed with the same level of performance whatever the ear of presentation. In addition, as in Dupoux et al.'s study, a redundant condition was also used in which stimuli differed both in the accentual and phonemic information. The experimental conditions are illustrated in Table 1.

Table 1. Experimental conditions.

Accentual mismatch

Phonemic mismatch

Accentual and phonemic mismatch Native accentual pattern

/balɔ /-/baˈlɔ / /baˈlo/-/baˈlɔ / /balo/-/baˈlɔ / ballon -ballon ballot -ballon ballot -ballon "ball" -"ball" "bundle" -"ball" "bundle" -"ball" Non-native accentual pattern /ˈbalɔ /-/baˈlɔ / /ˈbalo/-/ˈbalɔ / /ˈbalo/-/baˈlɔ / ballon -ballon ballot -ballon ballot -ballon "ball" -"ball" "bundle" -"ball" "bundle" -"ball"

Experiment 1

In this experiment, native and non-native stimuli were obtained using natural speech.

Method

Participants: Fifty right-handed French native speakers between 18 and 37 years old participated in the experiment. All were students from Aix-Marseille University and reported having no neurological, hearing or language impairment. Each participant gave informed consent prior to experiment and was remunerated for their time. Half the participants heard stimuli in the right ear while the other half heard stimuli in the opposite ear. ). Because words bearing primary accent on the first syllable are not found in French, speakers were asked to produce accent on the first syllable of the target word by making the target syllable prominent. To avoid coarticulation effects due to contextualized speech, each word was extracted from its carrier sentence. The three speakers heard their own production of the 8 target words in their accented (both first accented syllable and second accented syllable)

and unaccented versions in isolation, and were instructed to reproduce the different versions.

The sentences and the 8 target words presented in isolation were recorded at a sampling rate of 44 100 Hz. Acoustic analyses using Praat software [START_REF] Boersma | Praat. Doing phonetics by computer (Version 6.1.09[END_REF] were then conducted to ensure that the repeated words were produced with the expected accentual patterns. To do so, for the three versions of each word (unaccented, with a primary accent on the second syllable and with a primary accent on the first syllable), we measured the length of both syllables as well as the f0 movement associated with these two syllables. The acoustic properties of the stimuli are shown in Table 2.

Table 2. Acoustic properties of the words in their unaccented and accented versions (1 st and 2 nd syllable with accent) for the three speakers (averaged on the eight target words). ) amplitude level for all the target words was equated to 70 dB. Figure 1 illustrates the acoustic properties of the word ballon /balɔ / "ball" produced by our male speaker in its unaccented version, with a primary accent on its second syllable and with a primary accent on its first syllable.

Accentual patterns

Figure 1. Phonemic and prosodic profile for the word /balɔ / "ball" produced by the male voice in its unaccented version (a), with primary accent on its second syllable (b) and with primary accent on its first syllable (c).

To minimize the involvement, via ipsilateral projections, of the same hemisphere as the ear receiving the stimuli, an audio file containing pink noise was presented to participants in the ear opposite to the one in which the stimuli were presented (see Gonzalez & McLennan, 2007). Pink noise was chosen because as for speech, its spectral level decreases with increasing frequency. Our file containing pink noise was 612 ms long, corresponding to the duration of the longest target word. RMS amplitude of the signal containing pink noise was equated to 50 dB.

Each trial consisted of three stimuli: A, B and X, with the first two spoken by the two females and the third one by the male. Within each accentual pattern ("native accentual contrast", "non-native accentual contrast"), A and B varied either in accent, in one phoneme or in both accent and one phoneme, thus leading to 6 experimental conditions (Table 1). The four pairs of words were used in each experimental condition. For each pair of words and within each experimental condition, 16 combinations were used. These combinations resulted from the crossing between accentual pattern (2 possible versions each time: e.g., ballon and baLLON "ball"), segmental content (2 possible words each time: e.g., ballon "ball" and ballot "bundle"), response type (2 possible responses: A and B) and type of voice (2 possible voices: female 1 and female 2). 384 trials were thus obtained (6 experimental conditions x 4 pairs of words x 16 combinations).

Procedure: Participants were tested in a sound attenuated booth, and the stimuli were presented over headphones at the same comfortable sound level (60dBA) for all participants. For half the participants, the stimuli were presented to the left ear, while pink noise was presented to the opposite ear. The contrary was true for the other half. Each experimental trial consisted of three stimuli (A, B and X) separated by an interval of 500ms. The participants were told that they would hear stimuli in one ear while hearing pink noise in the opposite ear. They were also told that the first two stimuli would be different, and that the third one would be similar to either the first one or the second one. They were required to press a button on their left or on their right to indicate whether X was identical to respectively A or B. Each participant heard the 384 trials and the experiment lasted approximatively 30 minutes. The trials were presented randomly, and the order of presentation was different for each participant. An inter-trial interval of 1000 ms elapsed between each participant's response and the beginning of the next trial. The participants began the experiment with a block of 12 practice trials.

Results and discussion

Data are available at the Open Resources and Tools for Language (ORTOLANG) repository (https://hdl.handle.net/11403/accentdiscrimination). The percentage of correct responses for the right and the left ear of presentation under each mismatch condition is presented in Figure 2a for the native accentual pattern and in Figure 2b for the non-native accentual pattern. We analyzed accuracy data (1=correct response, 0= incorrect response) using a mixedeffect regression model (lme4 package in R-studio statistics Version 1.1.456) with a logistic linking function [START_REF] Baayen | Mixed-effects modeling with crossed random effects for subjects and items[END_REF]. The model included mismatch (phonemic, accentual, phonemic and accentual), accentual pattern (native vs. non-native), ear of presentation (right vs. left) and their interactions as fixed effects. The model also included participants and items as random intercepts, plus random participant slopes for the withinparticipant factors mismatch and accentual pattern, and item slopes for the within-item factors ear of presentation and mismatch (see [START_REF] Barr | Random effects structure for confirmatory hypothesis testing: Keep it maximal[END_REF]. Since our data set was too large for the default fitting methods in glmer.nb, it was necessary to implement the function option nAGQ=0 for the model-fitting process to converge [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF]. Significance of variables was assessed using the Anova function from the car package [START_REF] Fox | Applied Regression Analysis and Generalized Linear Models[END_REF]. The model revealed a significant mismatch x accentual contrast x ear of presentation interaction (X 2 = 23. 02, p < .0001). This three-way interaction was examined in two mixed-effect models on native and non-native patterns respectively. The two models included both mismatch and ear of presentation as fixed factors, random intercepts by participant and by item, random participant slopes for the within-participant factor mismatch, and item slopes for the within-item factors ear of presentation and mismatch [START_REF] Barr | Random effects structure for confirmatory hypothesis testing: Keep it maximal[END_REF].

The nAGQ=0 function option was implemented for both models [START_REF] Bates | Fitting Linear Mixed-Effects Models Using lme4[END_REF].

Significance of variables was assessed using the Anova function from the car package and multiple comparisons were obtained using the glht function from the multcomp package with a Bonferonni correction.

For the native pattern, the model revealed a significant main effect of the ear of presentation (X 2 = 6.87, p < .01) with more correct responses when stimuli were presented to the left ear than to the right ear. The effect of mismatch was also significant (X 2 = 31.46, p <

.0001) with more correct responses in the phonemic mismatch condition than in the accentual mismatch condition (z=3.29, p < .01), and more correct responses in the accentual and phonemic mismatch condition than in the accentual mismatch condition (z=4.87, p < .0001).

There was no significant difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition (z=1.53, p > .20). Crucially, the interaction between the ear of presentation and the mismatch was significant (X 2 = 10.14, p < .01). When stimuli were presented to the left ear, no significant difference was found between the mismatch conditions (all p.values > .20). On the contrary, when stimuli were presented to the right ear, the model revealed more correct responses in the phonemic mismatch condition compared to the accentual mismatch condition (z=4.61, p < .0001). There were also more correct responses in the accentual and phonemic mismatch condition compared to the accentual mismatch condition (z=7.20, p < .0001). The difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition was not significant (z=0.98, p >.20).

For the non-native pattern, the model also revealed a significant main effect of mismatch (X 2 = 109.26, p < .0001) with more correct responses in the phonemic mismatch condition than in the accentual mismatch condition (z=8.49, p < .0001), and more correct responses in the accentual and phonemic mismatch condition than in the accentual mismatch condition (z=10.27, p < .0001). There was no significant difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition (z=0.10, p > .20). The effect of ear of presentation was not significant (X 2 = 0.81, p > .20). Crucially the interaction between the ear of presentation and the mismatch was not significant (X 2 = 0.10, p >.20).

To sum up, Experiment 1 showed an effect of the ear of presentation only for the native accentual contrast, with phoneme-like performance when stimuli were presented in the left ear, and thus when processing is constrained to the right hemisphere. In contrast, no effect of the ear of presentation was found for the non-native accentual contrast, and thus whatever the ear of presentation, French participants were still worse at processing accentual differences than phonemic differences. Before discussing more fully the implications of present results, we conducted another experiment with more controlled stimuli, especially in terms of pitch rise.

Indeed, a closer look at the acoustic characteristics of the stimuli used in Experiment 1 revealed that the pitch rise for the stimuli accented on the second syllable was 172% whereas it was of only 41% for the stimuli accented on the first syllable. Thus, the difficulties of French participants with the non-native contrast, especially when stimuli were presented in the left ear, could merely result from the fact that the accentuation on the first syllable was not sufficiently acoustically salient to be perceived. We thus re-ran Experiment 1 with more controlled stimuli on f0.

Experiment 2

Experiment 2 consisted of a replication of Experiment 1 using resynthesized stimuli so that the pitch rise reached that of the stimuli accented on the second syllable. Also, the duration parameter was controlled so that it was the same for the native and non-native accentual contrasts.

Method

Participants: Fifty right-handed French native speakers form the same pool as in Experiment 1 participated in the experiment. Each participant gave informed consent prior to experiment and was remunerated for their time. As in Experiment 1, half the participants heard stimuli in the right ear while the other half heard stimuli in the opposite ear.

Materials: The materials used in Experiment 2 was derived from natural versions of accented

(1 st syllable with accent and 2 nd syllable with accent) and unaccented words used in Experiment 1. First, the f0 curve was flattened for all unaccented syllables by adjusting the endpoint of the f0 plateau to the same value of the starting point of the f0 plateau. Second, for each word accented on its first syllable, the f0 maximal value was increased so that the f0 rise was equal to the f0 rise of the word accented on its second syllable. For example, before resynthesis, the f0 maximal value of the word ballon accented on its first syllable and produced by the male speaker was 152 Hz, and the pitch rise was 18% (f0 minimal value: 129Hz). In contrast, the f0 maximal value of the word ballon accented on its second syllable and produced by the male speaker was 305 Hz, and the pitch rise was 190% (f0 minimal value: 105Hz). As a result, for Experiment 2, the f0 maximal value of the word ballon accented on its first syllable and produced by the male speaker was increased to 374 Hz so that the f0 rise was now 190% (f0 minimal value: 129Hz). For the duration parameter, the duration of all unaccented syllables (first and second syllables of unaccented word, second syllable of words accented on their first syllable, first syllable of words accented on their second syllable) were considered and we selected the shortest duration. The duration of all unaccented syllables was then adjusted to this shortest duration. Among the accented syllables (first syllable of words accented on their first syllable and second syllable of words accented on their second syllable), the longest duration was selected, and then the duration of all accented syllables was adjusted to this longest duration. For example, before resynthesis, the duration of the first syllable of the word ballon accented on its first syllable and produced by the first female speaker was 356ms while the duration of the second syllable of the word ballon accented on its second syllable was 269ms.

For Experiment 2, the duration of the word ballon accented on its second syllable was thus increased to 356ms. Hence, the difference in duration between the accented and the unaccented syllable was 224ms for both ballon accented on its second syllable and ballon accented on its first syllable (i.e., duration of the unaccented syllables: 132ms). All acoustic manipulations were done using the Pitch Synchronous Overlap and Add method (PSOLA, Moulines & Charpentier 1990), which is known for the high degree of naturalness achieved. The acoustic properties of the re-synthesized stimuli are shown in Table 3.

Procedure: It was the same as in Experiment 1.

Results and discussion

Data are available at the Open Resources and Tools for Language (ORTOLANG) repository (https://hdl.handle.net/11403/accentdiscrimination). The percentage of correct responses for the right and the left ear of presentation under each mismatch condition is presented in Figure 3a for the native accentual pattern and in Figure 3b for the non-native accentual pattern. Exactly the same analyses as Experiment 1 were performed. A significant mismatch x accentual contrast

x ear of presentation interaction was again observed (X 2 = 12.46, p < .01). As in Experiment 1, separate analyses on native and non-native patterns were thus performed. For the native pattern, the model revealed a significant main effect of the ear of presentation (X 2 = 11.13, p < 0.001) with more correct responses when stimuli were presented to the left ear than to the right ear. The effect of mismatch was also significant (X 2 = 38.66, p <

.0001) with more correct responses in the phonemic mismatch condition than in the accentual mismatch condition (z=3.87, p < .001), and more correct responses in the accentual and phonemic mismatch condition than in the accentual mismatch condition (z=7.11, p < .0001).

The difference between the accentual and phonemic mismatch condition and the phonemic mismatch was also significant (z=4.63, p < .0001). Crucially, the interaction between the ear of presentation and the mismatch was significant (X 2 = 8.77, p < .05). When stimuli were presented to the left ear, no significant difference was found between the phonemic mismatch condition compared to the accentual mismatch condition (z=1.90, p > .20). The difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition was

Non-native accentual contrast

Phonemic mismatch Accentual mismatch Phonemic and accentual mismatch significant (z=3.98, p < .01). Also, the difference between the accentual and phonemic mismatch condition and the accentual condition was significant (z=4.45, p < .001). On the contrary, when stimuli were presented to the right ear, the model revealed more correct responses in the phonemic mismatch condition compared to the accentual mismatch condition (z=3.70, p < .01). There were also more correct responses in the accentual and phonemic mismatch condition compared to the accentual mismatch condition (z=5.44, p < .0001). The difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition was not significant (z=1.37, p >.20)

For the non-native pattern, the model also revealed a significant main effect of mismatch (X 2 = 137.94, p < .0001) with more correct responses in the phonemic mismatch condition than in the accentual mismatch condition (z=4.41, p < .0001), and more correct responses in the accentual and phonemic mismatch condition than in the accentual mismatch condition (z=12.58, p < .0001). Also, the difference between the accentual and phonemic mismatch condition and the phonemic mismatch condition was significant (z=5.41, p < .0001).

The effect of ear of presentation was not significant (X 2 = 0.58, p > .20). Crucially the interaction between the ear of presentation and the mismatch was not significant (X 2 = 2.34, p >.20).

To sum-up, as in Experiment 1, French participants were worse at processing non-native accentual differences than phonemic differences, and this was the case regardless of whether the stimuli were presented to the right or the left ear. Hence, the difficulties of French listeners with the non-native contrast cannot be merely explained by a lower acoustic salience, especially for pitch rise, for this contrast, in comparison to the native contrast. Note however, that contrary to Experiment, 1 a benefit in the discrimination ability was observed when the difference between words was carried out by accentual difference in addition to phonemic difference for native language. The situation was different for the native accentual contrast. In accordance with our prediction, French listeners performed equally well in the accentual and in the phonemic condition provided that the stimuli were presented to the left ear. Hence, when processing is constrained to the right hemisphere, French listeners are equally good at processing accentual and phonemic differences. In contrast, and perhaps more crucially, French listeners experienced difficulty processing their native accentual contrast when words were presented to the right ear, and thus when processing was constrained to the left hemisphere.

Consequently, despite the fact that French listeners routinely produce and perceive words in both their accented an unaccented versions, this native contrast is processed as a non-native contrast when it is managed by the cerebral hemisphere which is dominant for language processing. Finally, the processing of phonemic contrast was not influenced by the ear of presentation, and similar performance was observed when the processing was pushed into the right hemisphere and when it was pushed into the left hemisphere. Such a result thus adds to the growing body of evidence showing that phonemic information is bilaterally represented [START_REF] Hickok | Towards a functional neuroanatomy of speech perception[END_REF].

Together, our results strengthen all the studies showing that the phonological system of the native language, and especially here, its prosodic system, influences the way listeners perceive speech sounds (see [START_REF] Best | Discrimination of non-native consonant contrasts varying in perceptual assimilation to the listener's native phonological system[END_REF], for a review). Because in French, words cannot receive primary accent anywhere else than on their last syllable, French listeners encounter difficulty discriminating words that differ in stress location. Therefore, as soon as an accentual contrast does not exist in the native language, it is rather hard to overcome the perception difficulty induced by this contrast. In contrast, due to the specific characteristics of French prosody, French listeners are rather good at managing accentual variation due to the presence vs. absence of an accent, namely the variation that corresponds to the accentual patterns present in their native language (also see [START_REF] Michelas | On French listeners' ability to use stress during spoken word processing[END_REF].

Similarly to the right hemisphere advantage found by Gonzalez & McLennan (2007) for the processing of talker-specific variation, we showed a right hemisphere advantage for the processing of accentual variation that exists in French. This right hemisphere advantage could be explained by the fact that accentual information is not linguistically contrastive at the word level for French listeners. Concerning the non-native accentual contrast, the lack of a right hemisphere advantage is likely due to the fact French listeners are not used to process this nonlinguistic information. Hence, a training on this type of contrast could be useful to boost the performance especially when the processing is constrained to this right hemisphere. Our claim that accentual variation at the word level is processed as non-linguistic variation by French listeners is in accordance with a previous study focusing on the perception of lexical tones [START_REF] Hallé | Identification and discrimination of Mandarin Chinese tones by Mandarin Chinese vs. French listeners[END_REF]. In this study, the authors compared the way French and Taiwanese listeners perceived the tonal continua created by manipulating both f0 and the intensity of Mandarin Chinese tones. Participants performed an ABX task in which they had to decide whether X was identical to either A or B. A and B represented the continuum endpoints and X varied from one endpoint to the other through eight steps. The results showed that Taiwanese listeners had better performance when X was near the two extremities of the continuum than when X was located in the middle of the continuum. In contrast, French listeners had similar performance regardless of the location of X on the continuum. Together, these results showed that French and Taiwanese listeners process tonal information differently. Because tonal information creates meaning distinctions in Mandarin Chinese, it is linguistically relevant for Taiwanese listeners. Consequently, they perceive this information categorically. In contrast, because tonal information is not used to distinguish words in French, it is not linguistically relevant for French listeners. Consequently, they do not create abstract categories based on this information. Again, these observations mirror those observed for some segmental contrasts that have been shown to be processed at an acoustic level of processing when they do not exist in the native language [START_REF] Llompart | Imitation in a second language relies on phonological categories but does not reflect the productive usage of difficult sound contrasts[END_REF].

To conclude, our results are in line with Van Lancker (1980)'s hypothesis claiming that prosodic information is differently lateralized in the brain depending on the linguistic functions of prosody in the language. Because accentual information in French is not relevant at the word level, we showed that this information is primarily processed by the right hemisphere.

Consequently, our study revealed that a native contrast is processed as a non-native contrast when the processing is constrained to the cerebral hemisphere which is dominant for language processing. Finally, our study also showed that, for French native listeners, a non-native accentual contrast never reaches the performance of a native contrast, and this regardless of the cerebral hemisphere that primarily manages this information.

Footnotes

1 Because in French, the acoustic prominence given to a syllable is determined post-lexically and not lexically, the term 'accent' rather than 'stress' is usually used.

2 Even though an initial (or secondary) accent can optionally affect the first syllable of French words, this accent does not have the same acoustic properties than the primary accent which is the accent of interest in this study (see [START_REF] Welby | French intonational structure: Evidence from tonal alignment[END_REF].

Materials:

  Four pairs of 4-phoneme-long bisyllabic French words differing in one phoneme (e.g. ballon /balɔ / "ball" vs. ballot /balo/ "bundle") were selected. Three French speakers (two women, one man) produced the 8 target words (in bold in the following examples) within carrier sentences. Within these carrier sentences, target words either bore accent on their last syllable or were unaccented depending on their place within the phrase (e.g. [On m'avait parLÉ] [d'un ballon maGIQUE] [qui ne se creVAIT] [presque jaMAIS] "I was told about a magic ball that hardly ever burst" vs. [On m'avait parLÉ] [d'un petit baLLON] [qui ne se creVAIT] [presque jaMAIS] "I was told about a little ball that hardly ever burst"). The same carrier sentences as for the unaccented condition were used to obtain 8 target words that bore accent on their first syllable (e.g. [On m'avait parLÉ] [d'un BAllon maGIQUE] [qui ne se creVAIT] [presque jaMAIS]

Figure 2 .

 2 Figure 2. Percentage of correct responses as a function of the ear of presentation (right/left) and

Figure 3 .

 3 Figure 3. Percentage of correct responses as a function of the ear of presentation (right/left) and

Speaker Acoustic properties of the first syllable Acoustic properties of the second syllable

  < .0001; f0 rise: t(23)=13.14; p < .0001]. Finally, for the words that bore accent on their second syllable, the second syllables were longer and associated with a stronger f0 rise than the

	first syllables [syllable duration: t(23) = 8.05, p < .0001; f0 rise: t(23) = 30.19; p < .0001]. The
	root-mean-squared (RMS
		Syllable	f0	f0	f0	Syllable	f0	f0	f0
		duration	min*	max*	rise	duration	min*	max*	rise
		(ms)		(Hz)	(Hz)	(%)	(ms)	(Hz)	(Hz)	(%)
		Male	126 106 104	-2	128 102	96	-6
	Unaccented word	Female 1	135 195 191	-2	133 191 181	-5
	(e.g. ballon)	Female 2	141 219 210	-4	138 207 197	-5
		Mean	134 173 168	-3	133 167 158	-5
	Accented on the first syllable (e.g. BAllon)	Male Female 1 Female 2	261 125 162 30 257 210 301 44 321 224 329 48	178 183 182 173 99 94 187 214 205	-4 -5 -4
		Mean	280 186 264 41	183 165 157	-4
	Accented on the second syllable (e.g. baLLON)	Male Female 1 Female 2	174 105 201 193 173 -10 95 -9 196 206 191 -7	246 259 172 442 157 95 255 169 277 190 549 189
		Mean	190 168 153	-9	261 152 415 172
	Statistical analyses performed on the 8 target words produced by the three speakers were
	then performed on the two acoustic parameters. These analyses showed that for the unaccented
	words, the length and the f0 rise associated with the first syllables were not different from those
	of the second syllables [syllable duration: t(23)=0.77, p > .20; f0 rise: t(23)= 1.31; p > .20]. On

* For unstressed syllables, the minimum and maximum f0 values correspond to the values associated with the beginning and the end of the f0 plateau. the contrary, for the words that bore accent on their first syllable, the first syllables were longer and associated with a stronger f0 rise than the second syllables [syllable duration: t(23) = 7.75, p

Even if the activation dissipates from one cerebral hemisphere to the other via the interhemispherical connections and the corpus callosum, manipulating hemifield presentation proved to be effective to assess the respective role of each hemisphere in the processing of variation for both visual (e.g.,[START_REF] Marsolek | Abstractionist versus exemplar-based theories of visual word priming: A subsystems resolution[END_REF] and auditory words (seeGonzalez & McLennan, 2007).

 4 Note that the same level of performance was observed in the two experiments. Hence, the fact that we did not observe a significant difference between the phonemic condition and the accentual and phonemic condition in Experiment 1 is likely not due to a ceiling effect.

both the native and the non-native accentual contrasts 4 . It should also be noted that even if French participants showed difficulty in the non-native contrast, their performance was above the chance level (see also [START_REF] Dupoux | A destressing "deafness" in French?[END_REF][START_REF] Michelas | On French listeners' ability to use stress during spoken word processing[END_REF]. This boost in the performance in the case of redundant information both for the native and the non-native contrast could be explained by the fact that syllable lengthening was larger for resynthesized stimuli than for natural stimuli.

General discussion

The aim of this study was to examine how the ear of presentation affects the way French listeners use accentual variation to discriminate between words. Because accentual variation at the word level has not a contrastive role in French, our study was built on the strong assumption that this type of variation would be processed as non-linguistic variation by French listeners.

Based on McLennan & Gonzalez (2007)'s study showing that non-linguistic information is

mainly processed by the right hemisphere, we predicted that French listeners would process an accentual mismatch with the same ability as a phonemic mismatch when processing was pushed into the right hemisphere, and thus when stimuli were presented to the left ear. Contrary to our predictions, no effect of the ear of presentation was observed for the non-native contrast. Hence, whatever the ear of presentation, French listeners were worse at processing accentual differences than phonemic differences. Such a result replicates Dupoux et al.' studies [START_REF] Dupoux | A destressing "deafness" in French?[END_REF][START_REF] Dupoux | A robust method to study stress "deafness[END_REF][START_REF] Dupoux | Persistent stress 'deafness': The case of French learners of Spanish[END_REF] in showing that French listeners have persistent difficulty with accentual variation, which does not exist in their