Mathieu Groussin
email: mathieu.groussin@univ-lyon1.fr

Bastien Boussau

Sandrine Charles

Samuel Blanquart

Manolo Gouy

The molecular signal

Keywords: Nonhomogeneous substitution model, Ancestral Sequence Reconstruction, Optimal Growth Temperature, Last Universal Common Ancestor

Introduction

Several lines of evidence support the hypothesis that, during early stages of the evolution, life was adapted to high temperatures that may have prevailed on the surface of the early earth. For instance, early studies discovered that the deepest branching lineages within the bacterial and archaeal domains are thermophilic [START_REF] Stetter | Hyperthermophiles in the history of life[END_REF]. This scenario was also supported by the resurrection of ancestral elongation factor Tu sequences that appear more and more thermostable when going back in time [START_REF] Gaucher | Palaeotemperature trend for Precambrian life inferred from resurrected proteins[END_REF], and by an estimation of the amino acid composition of ancestral proteomes that appear more similar to the composition of extant thermophiles than of mesophiles [START_REF] Brooks | A novel method for estimating ancestral amino acid composition and its application to proteins of the last universal ancestor[END_REF]. Boussau et al. [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] concluded that molecular sequence data confirm the hypothesis of high temperature adaptation during early stages of life, namely for the ancestors of the bacterial and archaeal domains. However, these authors reported strong evidence for a scenario in which the Last Universal Common Ancestor (LUCA) itself, living at a still earlier stage of the history of life, was a mesophilic organism. This non parsimonious scenario was obtained exploiting the tight relation that exists between either the G+C content in ribosomal RNAs or the amino-acid contents in proteins and the Optimal Growth Temperature (OGT) of Bacteria and Archaea. Such correlations between molecular compositions and temperature may be explained by structural adaptation to increase RNA and protein thermostability [START_REF] Galtier | Relationships between genomic G+C content, RNA secondary structures, and optimal growth temperature in prokaryotes[END_REF][START_REF] Zeldovich | Protein and DNA Sequence Determinants of Thermophilic Adaptation[END_REF] and are likely to remain constant over evolutionary time. They allow the construction of molecular thermometers [START_REF] Groussin | Adaptation to Environmental Temperature Is a Major Determinant of Molecular Evolutionary Rates in Archaea[END_REF] that can provide estimates of ancestral environmental temperatures if one obtains ancestral base and amino acid compositions through ancestral sequence reconstruction.

Through a number of control experiments, Boussau et al. [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] have shown that the use of nonhomogeneous models, which are capable of capturing the variation of composition among lineages, are key to accurately estimate ancestral base and amino acid compositions, and therefore, ancestral temperatures. But these authors have not identified the nature of the signal present in extant molecular sequences that informs evolutionary models to support such a non parsimonious scenario. In this letter, we aim at solving this issue.

Figure 1 Evolution

 1 Figure 1

Figure 2 The

 2 Figure 2

Acknowledgements

The authors thank Nicolas Lartillot, Vincent Daubin and the members of the Bioinformatics and Evolutionary Genomics team for suggestions and fruitful discussions. This work was supported by the French Agence Nationale de la Recherche (ANR) and is a contribution to the Ancestrome project (ANR-10-BINF-01-01).

Material and Methods

Data sets and nonhomogeneous models

Boussau et al. [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] built a concatenate of small-and large-subunit rRNAs from 456 organisms (2,239 sites) and used the sites restricted to stem regions (1,043 sites) to infer the ancestral G+C contents over the tree of life. From these alignments, we selected 125 species covering a broad taxonomic diversity without redundancy in the taxonomic sampling. Regarding the concatenation of proteins, the 56 gene families and 30 species considered in Boussau et al. [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] were used here, completed up to 38 species, especially with Archaea species, which were poorly represented in the first set of species. We reconstructed ML phylogenetic trees for rRNAs (on the 2,239 sites dataset) and proteins with PhyML [START_REF] Guindon | New algorithms and methods to estimate maximum-likelihood phylogenies: assessing the performance of PhyML 3.0[END_REF]. A three-domain tree was obtained and the root was placed on the bacterial branch. As in [START_REF] Galtier | A Nonhyperthermophilic Common Ancestor to Extant Life Forms[END_REF] and [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF], the branch-wise equilibrium frequencies were estimated along these universal phylogenetic trees. The stem dataset was analyzed with the BppML program [START_REF] Dutheil | Non-homogeneous models of sequence evolution in the Bio++ suite of libraries and programs[END_REF] assuming a discrete Gamma distribution with 8 categories to model rate variation among sites and the nonhomogeneous Galtier and Gouy (GG) substitution model [START_REF] Galtier | Inferring Pattern and Process: Maximum-Likelihood Implementation of a Nonhomogeneous Model of DNA Sequence Evolution for Phylogenetic Analysis[END_REF]. The GG model specifies branch-wise equilibrium G+C contents, as well as an independent G+C content on the root. For proteins, we used a new branch-wise nonhomogeneous model implemented in the Maximum Likelihood (ML) framework, named COaLA [START_REF] Groussin | A Branch-Heterogeneous Model of Protein Evolution for Efficient Inference of Ancestral Sequences[END_REF] that we recently designed. See supplementary Material for a description of the COaLA model and an evaluation of the fit to data of the nonhomogeneous models in comparison with homogeneous models.

Molecular thermometers

OGT highly correlates with the G+C content of the stem regions of rRNAs (ρ=0.76, p-value<0.001, Supplementary Figure 2) and with the second axis of the COA computed on aminoacid compositions of the protein dataset restricted to prokaryotic species (ρ=0.88, p-value<0.001, Supplementary Figure 3). We controled for phylogenetic inertia with the phylogenetic independent contrast approach [START_REF] Felsenstein | Phylogenies and the comparative method[END_REF] using the R package ape [START_REF] Paradis | APE: analyses of phylogenetics and evolution in R language[END_REF] and observed that these correlations are still strongly significant. Linear regressions between OGTs and compositions were then computed to obtain the molecular thermometers.

Inference of ancestral compositions and OGTs

The ancestral sequences were inferred with BppAncestor [START_REF] Dutheil | Non-homogeneous models of sequence evolution in the Bio++ suite of libraries and programs[END_REF] using the evolutionary parameters estimated by BppML. For each node of the tree, 100 ancestral sequences were generated by drawing amino-acids from the posterior distributions of probabilities. The average composition of these ancestral sequences was calculated and the corresponding ancestral temperatures were deduced from the molecular thermometers (See Supplementary Material for the confidence intervals computation).

Results and Discussion

We first confirm results obtained in [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] with the present rRNA and protein datasets and the nonhomogeneous GG [START_REF] Galtier | Inferring Pattern and Process: Maximum-Likelihood Implementation of a Nonhomogeneous Model of DNA Sequence Evolution for Phylogenetic Analysis[END_REF] and COaLA [START_REF] Groussin | A Branch-Heterogeneous Model of Protein Evolution for Efficient Inference of Ancestral Sequences[END_REF] substitution models in Maximum Likelihood (ML).

Figures 1 and2 show that LUCA is estimated to have lived in colder environments than the ancestors of Bacteria and Archaea (wilcoxon test, p-value<0.001), which were hyperthermophiles. Supp. Fig. 1 shows that this pattern is also recovered when an alternative tree topology is used, in which Eukaryotes branch within Archaea (Eocyte hypothesis [START_REF] Cox | The archaebacterial origin of eukaryotes[END_REF]) but is less pronounced with the homogeneous LG model, which infers a thermophilic LUCA.

The phylogenetic signal that informs a non-hyperthermophilic LUCA and yet two hyperthermophilic descendants is currently unknown. However, several points suggest that the variation in evolutionary rate among sites plays a role. First, Fournier and Gogarten [START_REF] Fournier | Signature of a Primitive Genetic Code in Ancient Protein Lineages[END_REF] highlighted that amino acids that are found in higher proportions in hyperthermophilic species are rarer at slow-evolving sites. Such amino-acids notably include charged residues [START_REF] Groussin | Adaptation to Environmental Temperature Is a Major Determinant of Molecular Evolutionary Rates in Archaea[END_REF]. Second, the signal for a parallel adaptation to high temperatures is partially lost when COaLA is employed without a Gamma distribution to model the variation in rate among sites (Supp Fig 1).

To highlight the influence of rate variation among sites in the differential recording of ancestral compositions, we partitioned the rRNA and protein datasets according to the site evolutionary rates. Figure 2a and2b show that with slow-evolving sites, all ancestors are inferred to be mesophilic organisms, LUCA being adapted to lower temperatures than its two descendants. The ancestral compositions of fast-evolving sites tend to favor hotter ancestral environments, even for LUCA with proteins. But LUCA is still inferred to live at lower temperatures than the ancestors of Bacteria and Archaea. As expected, the quantitative estimates of past temperatures inferred by both slow-and fast-evolving sites are different from those obtained with the complete dataset. Indeed, although slow-evolving sites conserved reliable signals for ancestral compositions, they carry less phylogenetic information for the early parallel adaptation to high temperature, which explains why this pattern is less pronounced than with the complete dataset. However, both the G+C content (rRNAs) and the third axis of a correspondence analysis (proteins) computed from the slowevolving sites of extant sequences correlate with OGT (ρ=0.72, p-value<0.001 and ρ=0.43, p-value<0.05, respectively), adding support to the idea that slow-evolving sites can respond to temperature and can represent accurate fossils of ancestral adaptation to temperature. Fast-evolving sites contain a stronger signal for this parallel adaptation but necessarily less reliable information for ancestral compositions and so, ancestral temperatures.

All these results suggest the presence of a genuine signal in molecular sequences indicating a mesophilic LUCA. This signal was recorded thanks to a combination of compositional variation in time and rate variation in site, such that slow-evolving sites more accurately reflect older temperatures, while fast evolving sites partially erased this oldest signal in favor of subsequent adaptations to higher temperatures.

Gowri-Shankar and Rattray [START_REF] Gowri-Shankar | On the correlation between composition and sitespecific evolutionary rate: implications for phylogenetic inference[END_REF] showed that there is an intrinsic correlation between evolutionary rates across sites and base composition in rRNAs. Therefore nucleotide composition varies across the sites of a rRNA alignment. These authors showed that branch-wise nonhomogeneous models, which account for the variation of composition in time but assume acrosssite homogeneity, may infer biased ancestral sequence compositions for sequences generated by a time-homogeneous process in which evolutionary rate and base compositions are correlated. The inference bias is directed towards the composition of slow-evolving sites which are, in the case of full-length rRNAs including both stem and loop regions, GC-poor. One could therefore wonder whether such an inference bias would be responsible for the low G+C content inferred for LUCA compared to the higher G+C contents of its first descendants. We reject this bias with two points.

First, as in the present study, Boussau et al. [START_REF] Boussau | Parallel Adaptation to High Temperature in the Archaean Eon[END_REF] applied the molecular thermometers on rRNAs to only the stem regions of the molecule. Supp Fig 4 shows that, for these regions, the correlation found by Gowri-Shankar and Rattray [START_REF] Gowri-Shankar | On the correlation between composition and sitespecific evolutionary rate: implications for phylogenetic inference[END_REF] is in the opposite direction, although non-significant, with G+C-enriched slow-evolving sites. Second, we simulated data in a context where the bias would apply, assuming only heterogeneity among sites and no heterogeneity among branches and verified if the correlation between site evolutionary rates and site compositions incorrectly informs the nonhomogeneous model to estimate a lower G+C content of LUCA than for its descendants. We partitioned rRNA alignment sites in 8 categories according to their evolutionary rate. For each ratespecific category, we simulated DNA sequences with a homogeneous Tamura92 model and the G+C equilibrium frequency fixed to the observed G+C frequency of the category and then concatenated the 8 simulated sets. We repeated this procedure 100 times and reconstructed ancestral G+C contents with the non-homogeneous GG model on each concatenated simulated alignment. Supp Fig 5 shows that the pattern of parallel increase in G+C content since LUCA found on real data is not recovered. Instead, LUCA has a higher G+C content than its two descendants. As slow-evolving sites of stem regions have globally higher G+C contents than fast-evolving ones (Supp Fig 4), this simulation result is in agreement with the bias of Gowri-Shankar and Rattray [START_REF] Gowri-Shankar | On the correlation between composition and sitespecific evolutionary rate: implications for phylogenetic inference[END_REF]. It further suggests that, if the non-homogeneous model applied on real data is affected by the bias as it is when applied to simulations, the true G+C content of LUCA may so far have been overestimated. All these results indicates that non-homogeneous models can capture a genuine time-wise variation in composition and that the pattern of parallel increase to high temperatures does not result from a bias due to a correlation between site-specific rates and site-specific compositions [START_REF] Gowri-Shankar | On the correlation between composition and sitespecific evolutionary rate: implications for phylogenetic inference[END_REF], but emerges in spite of this bias.


F Lecellier

S Jehan-Besson

J Fadili

Statistical region-based active contours for segmentation: an overview

In this paper we propose a brief survey on geometric variational approaches and more precisely on statistical region-based active contours for medical image segmentation. In these approaches, image features are considered as random variables whose distribution may be either parametric, and belongs to the exponential family, or non-parametric estimated with a kernel density method.

Statistical region-based terms are listed and reviewed showing that these terms can depict a wide spectrum of segmentation problems. A shape prior can also be incorporated to the previous statistical terms. A discussion of some optimization schemes available to solve the variational problem is also provided. Examples on real medical images are given to illustrate some of the given criteria.

Introduction

). Indeed, the computation of a given shape (i.e. segmentation) can be advantageously modeled as the optimum

of a wisely chosen continuous energy functional. Continuous energy functionals allow the use of photometric image properties such as texture [START_REF] Paragios | Geodesic active regions and level set methods for supervised texture segmentation[END_REF][START_REF] Aujol | Wavelet-based level set evolution for classification of textured images[END_REF][START_REF] Cremers | A review of statistical approaches to level set segmentation: integrating color, texture, motion and shape[END_REF][START_REF] Karoui | Region-based image segmentation using texture statistics and level-set methods[END_REF][START_REF] Fadili | Multiscale transforms for region-based texture segmentation[END_REF] and noise [START_REF] Martin | Influence of the noise model on level set active contour segmentation[END_REF][START_REF] Lecellier | Statistical regionbased active contours with exponential family observations[END_REF][START_REF] Galland | Multi-component image segmentation in homogeneous regions based on description length minimization: Application to speckle, Poisson and Bernoulli noise[END_REF][START_REF] Lecellier | Regionbased active contours with exponential family observations[END_REF], as well as geometric properties such as the prior shape of the object to be segmented [START_REF] Leventon | Statistical models for medical image analysis[END_REF][START_REF] Tsai | A shape-based approach to the segmentation of medical imagery using level sets[END_REF][START_REF] Gastaud | Combining shape prior and statistical features for active contour segmentation[END_REF][START_REF] Foulonneau | Affine-invariant geometric shape priors for region-based active contours[END_REF][START_REF] Lecellier | Regionbased active contours with noise and shape priors[END_REF][START_REF] Wojak | Introducing shape constraint via Legendre moments in a variational framework for cardiac segmentation on non-contrast CT images[END_REF], see also [START_REF] Paragios | Biomedical Image Analysis: Methodologies and Applications[END_REF] and more recently [START_REF] Bernard | Analyse d'images cardiaques et thoraciques, IC2-Information et Science du Vivant Hermes-Lavoisier[END_REF] for some reviews on deformable models and active contours in medical image segmentation.

In this paper, we propose to focus on region-based terms that take benefit of the probability density function of a given image feature inside the region of interest [1, [START_REF] Martin | Influence of the noise model on level set active contour segmentation[END_REF][START_REF] Paragios | Geodesic active regions: A new paradigm to deal with frame partition problems in computer vision[END_REF]. We more particularly review the optimization of divergences between pdfs which represent a general setting for both segmentation and tracking in medical images. When considering a segmentation framework, we aim at maximizing the distance between the pdf of the inside region and the pdf of the outside region. When considering a tracking application, we aim at minimizing the distance between the pdf of the region of interest and a reference one. The pdf can be considered as parametric (e.g. Gaussian, Rayleigh ...) or non parametric (no assumption is made on the law). In the literature, region tracking using non parametric probability density functions has been first proposed in [START_REF] Aubert | Image segmentation using active contours : Calculus of variations or shape gradients[END_REF] for video and then developed for cardiac structures tracking in perfusion MRI (p-MRI) sequences in [START_REF] Rougon | A non-rigid registration approach for quantifying myocardial contraction in tagged MRI using generalized information measures[END_REF]. On the other hand, some authors [START_REF] Michailovich | Image segmentation using active contours driven by the Bhattacharyya gradient flow[END_REF] have also proposed to take benefit of the maximization of the Bhattacharya distance of non parametric pdfs for segmentation. Concerning parametric pdfs, we restrict our study to the exponential family as first proposed in [START_REF] Martin | Influence of the noise model on level set active contour segmentation[END_REF]. The rationale behind using the exponential family is that it includes, among others, Gaussian, Rayleigh, Poisson and Bernoulli distributions that have proven to be useful to model the noise structure in many real image acquisition devices (e.g.

Poisson for photon counting devices such as X-ray or CCD cameras, Rayleigh for ultrasound images, etc). To cope with the occlusion and missing data and to alleviate initialization issues in medical image segmentation, a shape prior on the structure to be isolated can also prove necessary. For space reasons, we restrict our review to the use of the Legendre moments in a variational approach first proposed in [START_REF] Foulonneau | Affine-invariant geometric shape priors for region-based active contours[END_REF] and applied to echocardiography in [START_REF] Lecellier | Les contours actifs basés région avec a priori de bruit, de texture et de forme : Application à l'échocardiographie[END_REF] and in cardiac segmentation on non-contrast CT images in [START_REF] Wojak | Introducing shape constraint via Legendre moments in a variational framework for cardiac segmentation on non-contrast CT images[END_REF]. One of the difficult point concerning variational approaches remains the associated resolution schemes. We propose here to review two main schemes. The first one is based on advanced and efficient optimization tools (e.g. originating from shape derivation tools [START_REF] Delfour | Shape and geometries[END_REF] and the second one relies on efficient non-smooth convex optimization tools as proposed in [START_REF] Bresson | Fast global minimization of the active contour/snake model[END_REF]). Some segmentation examples of medical structures are taken (brain and cardiac MRI, echocardiography, MRI perfusion) to show the adaptability of such statistical segmentation methods.

Statistical region-based terms for segmentation

A region-based segmentation problem aims at finding a partition of the image domain Ω into n regions {Ω 1 , .., Ω n } of respective boundaries {∂Ω 1 , .., ∂Ω n } that minimizes the following criterion:

E(Ω 1 , .., Ω n , Γ) = n i=1 E ri (Ω i ) + λE b (Γ) , (1)
where E ri is the region-based term related to the domain Ω i , and Γ = n i=1 ∂Ω i . The regularization term E b is balanced with a positive parameter λ.

We focus here on statistical region-based term E ri that takes advantage of the pdf of some image features y whose realizations take values in χ ⊂ R p within each region Ω i (e.g. when considering the intensity in grey level images y(x) = I(x) with x the pixel location, p = 1 and χ = [0, 255]). This framework is then also adapted to the use of vectorial image features such as the coefficients of the wavelet transform or optical flow vectors. At this stage, we consider two main classes of region descriptors detailed in the two sections below. We also provide a comparison for brain MRI segmentation in section 6.2.

Statistical descriptors based on regions integrals

For the first kind of region descriptors, we consider the minimization of region integrals of some well chosen functions of the pdf of the feature y within the region Ω i , namely p(y(x), Ω i ). We then consider as a region-based term:

E ri (Ω i ) = Ωi Φ(p(y(x), Ω i )dx , (2)
with Φ at least C 1 and Lebesgue integrable function. Let us note that when Φ(t) = -log(t) the function ( 2) is known as the log-likelihood score function, used to describe the homogeneity of a region. It has been introduced in [1] using Gaussian pdfs and in [START_REF] Martin | Influence of the noise model on level set active contour segmentation[END_REF] using parametric pdfs from the exponential family. In [START_REF] Lecellier | Regionbased active contours with exponential family observations[END_REF], we consider a general setting replacing the -log by any proper function Φ within the exponential family. We also elucidate the impact of the estimation method of the hyper-parameters on the shape derivatives of the criterion.

Such a criterion has been also investigated using non parametric pdfs and some functions Φ related to mutual information and entropy as developed in [START_REF] Kim | Nonparametric methods for image segmentation using information theory and curve evolution[END_REF][START_REF] Herbulot | Shape gradient for multimodal image segmentation using mutual information[END_REF].

Statistical descriptors based on features integrals

Another class of statistical region descriptors may be interesting since it can depicts both supervised and unsupervised segmentation. In this class of statistical descriptors, we consider integrals over the feature domain χ and so we do not make any assumption on the independence of the random variable y(x) on the contrary to the region descriptors described using [START_REF] Chan | Active contours without edges[END_REF]. Let us then introduce the following functional which represents the distance, or more generally the divergence, between the current pdf estimate p(•, Ω i ) and another one q(•) for some appropriate function Ψ comparing pdfs:

E ri (Ω i ) = χ Ψ (p(y, Ω i ), q(y)) dy . (3)
We can introduce for example the Hellinger distance or the commonly used Kullback-Leibler divergence. Some other distances or divergences can be introduced to improve the accuracy and robustness of the segmentation such as the Wasserstein distance [START_REF] Peyré | Wasserstein active contours[END_REF] or alpha-divergences [START_REF] Meziou | Alpha-divergence maximization for statistical region-based active contour segmentation with non-parametric pdf estimations[END_REF]. Segmentation of complex regions can also take benefit of local estimation of the pdfs on small patches as proposed in [START_REF] Kangyu | Local histogram based segmentation using the wasserstein distance[END_REF].

Such divergences represent a general setting for both segmentation and tracking in medical images. Indeed, we may cast the segmentation problem as the maximization of the distance between the pdfs of the feature in the inside and outside regions. In order to fix ideas, let us consider a partition of an image in two regions Ω 1 and Ω 2 . The segmentation may be formulated as the maximization of the following criterion:

E r (Ω 1 , Ω 2 ) = χ Ψ (p(y, Ω 1 ), q(y, Ω 2 )) dy . (4)
In the tracking problem, one aims at finding a consistent region Ω i through a series of images. We can assume statistical similarity between the pdfs of the region in two consecutive images. We then search for the domain that minimizes the functional (3) where q(•) is a reference pdf that has been learned from the region of interest:

E ri (Ω i ) = χ Ψ (p(y, Ω i ), q ref (y)) dy . (5)
This framework may also be applied to supervised segmentation where a reference pdf is learned on the region of interest.

Statistical features description

For all the above criteria, the pdf can be either parametric or non-parametric.

Parametric pdfs are useful for the segmentation and tracking of homogeneous regions. The pdf can then be chosen according to the noise model as detailed thereafter. However parametric models may be subject to bias when the pdf model is only an approximation of the true noise model. In this case non parametric pdfs may be useful as well as in the case of segmentation or tracking of non homogeneous regions.

Parametric pdfs within the exponential family

In this case, image features are considered as random variables whose distribution belongs to some parametric family which is chosen according to the noise model. The exponential family is a flexible class of distributions that includes, among others, Gaussian, Rayleigh and Poisson distributions that have proven useful to model the noise structures in medical imaging systems. More formally, the current pdf estimate p(•, Ω i ) is now parametrized by a vector θ i ∈ Θ ⊂ R κ (e.g. we have κ = 2 and θ i = (µ i , σ i ) T where µ i is the mean and σ i the variance for Gaussian law), or equivalently, by the natural parameter vector η i in the terminology of the canonical exponential family [START_REF] Bickel | Mathematical statistics: basic ideas and selected topics[END_REF]. The estimate of θ i (or η i ) (performed using the maximum likelihood method for example) explicitly depends on the corresponding region, and this dependence must be taken into account when computing the derivatives of the functional. In [START_REF] Lecellier | Regionbased active contours with exponential family observations[END_REF], the expressions of the associated evolution equations were computed and detailed.

Non-parametric pdfs

Here we consider non-parametric density estimates using kernel-based methods. Given a region Ω i , we can estimate the pdf of the feature y through the use of the Parzen method [START_REF] Duda | Pattern Classification and Scene Analysis[END_REF]. Let K h : χ → R + be the Parzen window in general chosen as a Gaussian kernel of 0-mean and variance h (scale parameter):

q(y, Ω i ) = 1 | Ω i | Ω K h (y(x) -y) dx,
where y(x) is the value of the feature of interest at the point x of Ω i .

Such non parametric pdfs may be helpful for tracking non homogeneous regions (an example is given in section 6.3 for perfusion MRI) but also for the statistical description of more complex features such as the coefficients of linear texture transforms (e.g. wavelet, waveatoms). Some results are given in [START_REF] Fadili | Multiscale transforms for region-based texture segmentation[END_REF][START_REF] Lecellier | Les contours actifs basés région avec a priori de bruit, de texture et de forme : Application à l'échocardiographie[END_REF].

4 Segmentation with a shape prior Medical structures are often really complex and sometimes not very contrasted. The addition of a shape prior in the energy functional can then be crucial for many applications. Different approaches were considered that can be categorized as follows : minimization of a boundary-based functional [START_REF] Gastaud | Combining shape prior and statistical features for active contour segmentation[END_REF]; shape prior through a signed distance function [START_REF] Leventon | Statistical models for medical image analysis[END_REF]; scale and translation invariant shape moments, e.g. Legendre as in [START_REF] Foulonneau | Affine-invariant geometric shape priors for region-based active contours[END_REF].

In [START_REF] Lecellier | Regionbased active contours with noise and shape priors[END_REF], we propose to combine statistical data term with a shape prior computed using its Legendre Moments. Indeed, moments [START_REF] The | On image analysis by the methods of moments[END_REF] give a region-based compact representation of shapes through the projection of their characteristic functions on an orthogonal basis such as Legendre polynomials. Scale and translation invariance can be advantageously added as in [START_REF] Foulonneau | Affine-invariant geometric shape priors for region-based active contours[END_REF]. When combining statistical region-based terms and shape prior term, the criterion becomes:

E(Ω in , Ω out , Γ) = E in (x, Ω in ) + E out (x, Ω out ) + αD(Ω in , Ω ref ) + βE b (Γ) , (6)
where D(Ω in , Ω ref ) is defined as the Euclidian distance between the moments of the evolving region and the ones of the reference shape:

D(Ω in , Ω ref ) = λ(Ω in ) -λ(Ω ref ) 2 2 , (7)
where λ(Ω i ) are the moments of the region Ω i .

To drive this functional towards its minimum, the obtained evolution equation is iteratively run without the shape prior, then the shape prior term is updated, and the active contour evolves again by running the PDE with the shape prior. This procedure is repeated until convergence. An example of the segmentation of the left ventricle in echocardiography is given in section 6.1.

Resolution schemes for active contour segmentation

The statistical criteria introduced above are generic and allow to well describe numerous medical image segmentation problems. However they imply the estimation of the optimal domain using an appropriate resolution method. This is the key part in variational approaches and we here propose to focus on two main efficient methods to solve the previous optimization problems.

Methods based on the evolution of a deformable model

These methods are based on the computation of an evolution equation that will drive an active shape towards the boundary of the object to segment. Such a deformation is directed by a geometric partial differential equation (PDE). Let us denote by Γ(s, τ ) the active contour where s is a parameter of the contour and τ is an evolution parameter. The contour evolves according to the following well known PDE: ∂Γ(s,τ ) ∂τ = F N where N is the normal vector and the velocity F must be deduced from each considered criterion.

In order to perform the computation of this PDE, several methods have been introduced. The first one is the well-known approach proposed in [START_REF] Chan | Active contours without edges[END_REF], which consists in transforming the initial criterion by introducing the level set function U and computing the associated Euler-Lagrange equations. The second one has been proposed by [START_REF] Jehan-Besson | DREAM2S: Deformable regions driven by an eulerian accurate minimization method for image and video segmentation[END_REF] and takes advantage of shape derivative tools introduced in [START_REF] Delfour | Shape and geometries[END_REF]. Let us suppose that the shape derivative of the criterion E(Ω) in the direction V may be written as follows:

< E ′ (Ω), V >= - ∂Ω speed(x, Ω)(V(x) • N(x))da(x) . (8)
If we want to minimize E, we can choose F = speed(x, Ω). On the contrary, to maximize the criterion, we take the opposite sign for the velocity.

Some other approaches are also worth mentioning. For example, some authors propose to directly take benefit of B-splines in the level set formulation [START_REF] Bernard | Variational B-spline level-set: A linear filtering approach for fast deformable model evolution[END_REF] allowing efficient resolution schemes, or to implement fast Newton-type minimization schemes based on second order derivatives in [START_REF] Bar | Generalized newton-type methods for energy formulations in image processing[END_REF].

Convexification method

This approach was proposed [START_REF] Bresson | Fast global minimization of the active contour/snake model[END_REF] for the classical non-convex variational segmentation problem:

min Ω1 E = Ω1 (I(x) -c 1 ) 2 dx + Ω\Ω1 (I(x) -c 2 ) 2 + λ ∂Ω1 g(x)da(x) ,
where c i is the mean value of the intensity within the corresponding region, and g(•) is some scalar function on the boundary.

The key idea now is (i) to reformulate this functional by introducing the characteristic function u of Ω 1 ; (ii) to use the co-area formula to re-express the boundary integral in terms of the TV semi-norm of u; and (iii) to relax u to live in [0, 1]. Altogether, this yields the non-smooth but convex functional: In [START_REF] Nikolova | Algorithms for finding global minimizers of image segmentation and denoising models[END_REF], the authors show that, for fixed c 1 and c 2 , if u * is a global minimizer of E GM , then for almost every α

min 0≤u≤1 E GM = Ω u(x)(y(x)-c 1 ) 2 +(1-u(x))(y(x)-c 2 ) 2 +λg(x)|∇u(x)| dx . (a) (b) (c)
∈ [0, 1], Ω C (α) := {x ∈ Ω : u * (x) > α} is a global minimizer of E.
The energy E GM can be solved using efficient nonsmooth convex optimization tools as proposed in [START_REF] Bresson | Fast global minimization of the active contour/snake model[END_REF].

In Fig. 1, we give a comparison between active contours and the convexification approach from [START_REF] Bresson | Fast global minimization of the active contour/snake model[END_REF] for a MRI slice of the 2009 MICCAI challenge database [START_REF] Radau | Evaluation framework for algorithm segmenting short axis cardiac MRI[END_REF] . Using active contours, and given that the energy E is non-convex, the final contour which is only a stationary point (not necessarily a minimizer even local). Using the convexification approach, the obtained u * is indeed a global minimizer, but must be thresholded using the parameter α. One of the advantage of convex optimization tools is the low computational cost of its resolution schemes. The introduction of more complex descriptors is also possible and an interesting application was proposed in [START_REF] Wojak | Introducing shape constraint via Legendre moments in a variational framework for cardiac segmentation on non-contrast CT images[END_REF] for cardiac segmentation with a prior shape based on Legendre moments.

Medical image segmentation examples

In this section we present some results on medical image segmentation using the criteria introduced in section 2. We propose different examples using both parametric and non parametric pdfs for different applications: echocardiography, brain MRI and perfusion MRI.

Noise and shape prior for cardiac echography segmentation

We propose to illustrate the interest of using shape prior on real echocardiographic images. We use a parametric Rayleigh model for the noise distribution with an anti-log-likelihood homogeneity criterion, and a shape prior term with invariant Legendre moments and an alternating minimization scheme. In order to deal with the shape variability of the heart on images, we choose α = 0.7 and β = 0.4 on eq. ( 6). Those parameters give the best results on quantitative and qualitative evaluation of the segmentation as shown in [START_REF] Lecellier | Les contours actifs basés région avec a priori de bruit, de texture et de forme : Application à l'échocardiographie[END_REF].

We conduct our experiment on both parietal and apical views and on contrast and classical echocardiography. The results on apical view for classical echography are depicted in Fig. 2. The importance of adding a shape prior in echocardiographic data is here demonstrated. In addition to this comparison, we compare also this method to another well-known segmentation method, the Active Appearance and Motion Models (AAMM) proposed by Bosch [START_REF] Bosch | Automatic segmentation of echocardiographic sequences by active appearance motion models[END_REF]. In structures. The noise model in MRI images is assumed to be represented by a Rician distribution. However, for large signal intensities the noise distribution can be considered as a Gaussian distribution (this is the case for the WM or the GM). For the CSF which has a low signal intensity, the noise model can be approximated by a Rayleigh noise.

In Fig. 3, we first compare the Chan-Vese method [START_REF] Chan | Active contours without edges[END_REF] to the (anti-)loglikelihood with Gaussian noise [START_REF] Martin | Influence of the noise model on level set active contour segmentation[END_REF] and divergence maximization using Kullback Leibler (KL) for the WM segmentation. We can note that the KL criterion acts as an extractor of the most prominent Gaussian in the initial mixture of Gaussians. The two other criteria separate the mixture without extracting a single Gaussian. In order to extract single Gaussian pdfs using the Chan-Vese method, a multiphase procedure can be advantageously used (see [START_REF] Angelini | Brain MRI segmentation with multiphase minimal partitioning: a comparative study[END_REF]). From a quantitative point of view, our method gives a dice coefficient of 0.91, a False

Positive Fraction (FPF) of 0.8% and a True Positive Fraction (TPF) of 84%

(computed on the whole volume). We can remark that our method gives a very small number of false positive voxels, at the price of a higher number of missing voxels. The last point is due to the regularization term which acts by minimizing the curve length. Some complementary results are depicted in [START_REF] Jehan-Besson | Biomedical diagnostics and clinical technologies : Applying high performance cluster and Grid Computing[END_REF].

Non parametric pdfs for perfusion MRI tracking

The perfusion MRI (p-MRI) has emerged as a primordial clinical investigation tool in the evaluation of cardiac diseases. Spatio-temporal tracking of myocardial dynamics during the first transit of the contrast bolus allows the identification of hypoperfused or ischemic regions. An automatic quantification tool relies on the accurate segmentation and tracking of the cardiac structures.

The main difficulty lies in the fact that the different regions (myocardium, left ventricle) are not homogeneous. We give here an example of tracking using non parametric pdfs. From an initial segmentation of the left ventricle, we track this structure along the sequence by minimizing the distance between the pdf of the intensity of the current region and the pdf of the intensity of the previous one.

In Figure 4, we show the evolution of the curve in one frame of the sequence and the joint evolution of the pdf of the inside region. It is interesting to see how the pdf converges towards the reference pdf as shown in Figure 4. This example shows that this tool can be used for segmentation tracking but some improvements are needed notably concerning the fact that the criterion needs both the inside reference pdf and an outside reference one. The outside reference pdf can be for example computed on the narrowband as proposed in [START_REF] Mille | Region tracking with narrow perception of background[END_REF] in order to be more representative. and a reference one (red or solid line) which is computed from the segmentation of LV in the previous frame (the pdf is the pdf of the intensity I within the region).

Discussion

Experimental results are given in order to prove the applicability of our general setting to medical image segmentation. Indeed, we can observe that various types of noise often contribute to degrade medical images (Gaussian, Poisson, Rayleigh). Our general framework allows the use of the noise models that are recovered by the exponential family. As studied in [START_REF] Lecellier | Regionbased active contours with exponential family observations[END_REF], the noise model has an influence on the accuracy of the segmentation and on its robustness to the choice of the regularization parameter. The examples show that relevant result are obtained both in MRI and echocardiographic images. When dealing with non homogeneous objects, we propose to rather take benefit of non parametric pdfs where no assumption is made on the distribution model. This has been exploited for tracking the LV in p-MRI sequences. Concerning parametric pdfs, the parameters of the noise models depend on the regions inside and outside the active contours and they are estimated automatically during the segmentation process using the ML (maximum likelihood) estimator. The only parameter to set is then the regularization parameter λ that allows to smooth the contour. Setting this parameter too high may lead to an under-segmentation of the structure and so its value is taken around 10 and 100 for the experimental results given above. However, experiments reported in [START_REF] Lecellier | Les contours actifs basés région avec a priori de bruit, de texture et de forme : Application à l'échocardiographie[END_REF] show that choosing the appropriate noise model allows the segmentation to be less sensitive to the choice of this parameter. As far as non parametric pdfs are concerned, the kernel parameter h allows to smooth the initial pdf. However, we set this value to 1 because we want an estimate of the pdf very close to the initial pdf for the accuracy of the tracking.

Let us mention that a recent trend in medical image segmentation consists in using the computed velocity of the active contour as a basis for an interactive segmentation tool, see for instance [START_REF] Bianchi | Dual B-spline snake for interactive myocardial segmentation[END_REF]. The tools reviewed above can then be exploited not only for automatic segmentation but also as a basis for an interactive segmentation process to guide the practitioner.

Figure 1 :

 1 Figure 1: Segmentation of a cardiac MRI slice obtained using the convexification approach [27] (a) and active contours [2] (c) (using the initial contour given in (b)).

Fig. 1 .

 1 (c) depends on the choice of the initial contour of Fig. 1.(b),

Fig. 2 (

 2 Fig.2(d), we present the segmentation result of the echographic image using AAMM. We also compute the mean distance between AAMM and expert segmentation (cross points on Fig.2 (e)), and the mean distance between active contours and expert segmentation (circle points on Fig.2 (e)). As depicted on Fig.2(e), active contours are closer to expert segmentation than AAMM. In addition, we compute Dice coefficient for both methods, on AAMM it is 0.74 and on active contour it is 0.83. Further quantitative evaluation results may be found in[START_REF] Lecellier | Les contours actifs basés région avec a priori de bruit, de texture et de forme : Application à l'échocardiographie[END_REF].

Figure 2 :

 2 Figure 2: Segmentation of the left ventricle in echocardiography using a Rayleigh model of the noise without any shape prior (a) and with a shape prior (b). The expert contour is given in (c) and the segmentation result of AAMM method[START_REF] Bosch | Automatic segmentation of echocardiographic sequences by active appearance motion models[END_REF] is given in (d). The graphic (e) gives the mean distance computed on 14 images between the AAMM and expert (cross points) and between the shape and noise method and expert (circle points).

  (a) Chan & Vese (b) log likelihood (c) KL maximization

Figure 3 :

 3 Figure 3: T1-weighted brain MRI segmentation results (extraction of the White Matter). Column (a): final contour and pdfs for the Chan & Vese method [2], column (b): for the log-likelihood method [1], column (c): for the maximization of the KL divergence.

  initial pdfs (initial contour) (g) final pdfs (final contour)

Figure 4 :

 4 Figure 4: Minimization of the distance between the current region pdf (blue or dashed line)

Acknowledgements

We would like to thank Dr. E. Saloux (CHU of Caen) for providing the echocardiographic images and Pr. M. Hamon (CHU Caen) for providing the perfusion MRI images. We also thank D. Tschumperlé and R. Clouard from GREYC Laboratory for their useful image processing libraries Gmic and Pandore.

[1] S. Zhu, A. Yuille, Region competition: unifying snakes, region growing, and bayes/MDL for multiband image segmentation, IEEE PAMI 18 (1996) 884-900.


A Bassoumi
email: amal.bassoumi@univ-orleans.fr

P Ouagne

J Gillibert

G Hivet

ANALYSIS OF THE BENDING BEHAVIOUR OF FLAX BASED REINFORCEMENTS USED IN SHAPE FORMING

The bending behaviour of woven perform was investigated in order to better understand the formation of some defects during sheet forming such as wrinkling and tow buckling. The fabric composition considering hybrid and pure flax fabrics as well as some test conditions like relative humidity were examined. On the one hand, the results show a drop of the bending stiffness with flax/PLA commingled fabric. On the other hand, the study points out that moisture enhances the bending rigidity especially in the case of pure flax fabric. However, an excess of humidity, for instance 100% relative humidity, leads to an opposite effect.

INTRODUCTION

Composite materials are considered as an essential component of the tomorrow's industry. Possessing good mechanical properties, they also reduce energy consumption thanks to a gain of weight. Besides, in a perspective of sustainable development, industry is attempting to replace existing ones by environmentally friendly composites. Disposal problems and the need to reduce the dependence on petroleum fuels, lead to an increasing interest for natural fibres based composites [START_REF] Dubrovski | Woven Fabric Engineering[END_REF] and particularly the flax based ones offer a good potential.

In addition to tensile and shear phenomena widely considered for carbon or glass reinforcements, the bending behaviour was generally neglected when considering the sheet forming simulation of highly non-developable parts [START_REF] Bilbao | Bending Test of Composite Reinforcements[END_REF]. For structural parts, the properties out of plan cannot be inferred from those in plan. The flexural behaviour of the reinforcement depends on yarns geometry, their mechanical properties and contact conditions. Therefore, we are dealing with a multi-scale problem [START_REF] Boisse | Composite reinforcements for optimum performance[END_REF].

The bending rigidity is a critical parameter regarding the out of plane deformations at both macroscopic and mesoscopic scale such as wrinkles formation and tow buckling. Some studies on process simulation showed the importance of this rigidity for either dry woven reinforcements or prepregs.

For a long time, the bending behaviour of textile clothing has been considered. In this context, Ghosh et al presented a critical review of various models with different yarn behaviour assumptions [START_REF] Ghosh | The Bending Behaviour of Plain Woven Fabrics. Part I: A Critical Review[END_REF][START_REF] Ghosh | The Bending Behaviour of Plain Woven Fabrics, Part II: The Case of Linear Thread-Bending Behaviour[END_REF]. However, the relationship between fabric and yarn bending rigidities is highly complex. On the contrary, there are few research works regarding composite reinforcements: Bilbao et al [START_REF] Bilbao | Bending Test of Composite Reinforcements[END_REF], Yu et al [START_REF] Yu | Analysis of flexible bending behavior of woven preform using non-orthogonal constitutive equation[END_REF] and Lomov et al [START_REF] Lomov | Carbon composites based on multiaxial multiply stitched preforms. Part 2. kes-f characterisation of the deformability of the preforms at low load[END_REF].

The aim of this paper is to study the influence of the fabric composition as well as test conditions on the bending stiffness of woven perform. In fact, two compositions have been considered: hybrid and pure flax fabrics. The effect of environmental conditions is evaluated regarding various relative humidities.

MATERIALS AND METHODS

MATERIALS

The dry reinforcements considered in this study are 4x4 hopsack fabrics (Figure 1). The first reference is pure flax based fabric with an areal weight of 494 g/m 2 and a thickness of 1.29 mm. The second reference is 40% flax/PLA commingled hopsack with an areal weight of 518 g/m 2 and a thickness of 1.38 mm.

BENDING TEST ON FABRICS

Our experimental work was carried out using a bending test based on the cantilever's principle, in which the fabric bends under its own weight. The improved device allows various loading cases related to different bending lengths [START_REF] Bilbao | Bending Test of Composite Reinforcements[END_REF][START_REF] Boisse | Composite reinforcements for optimum performance[END_REF].

The bending device used includes two modules: one mechanical and one optical. The first consists of two parts, one fixed (in the form of plate) and the other mobile composed of a set of removable strips rotatable around an axis coplanar with the fixed part. At the other end, the strips rely on a slide device for releasing them successively. To avoid friction between them, the strips are spaced by 2 mm using washers. After putting the sample on the horizontal assembly, a translucent blank holder plate is laid on it and clamped to the fixed plate which defines an embedded bond during bending.

The device allows at a growing number of released strips to increase the length of overhang. At a given length, the slide movement is stopped and an optical module comprising a CCD camera is used to capture the bending profile. After the test, a step of digital image processing is performed to extract by Framing-Filtering-Binarization the reference line. Then, using a calibration picture taken after the camera setting and knowing the real size of the image pixel, the scaling factor between the image space and the real space is determined. This information will be used to make the conversion pixel-mm. Then, by a direct method, the curvature C and the bending moment M can be evaluated at each point of the profile using the digital processing. Therefore, the M-C relationship can be estimated. However, as we are looking to a comparative study of the influence the reinforcement parameters, this paper will focus on the pierce rigidity.

The processed images can be used to determine the Peirce model [START_REF] Peirce | The geometry of cloth structure[END_REF][START_REF] Peirce | The 'handle' of cloth as a measurable quantity[END_REF] and thus the bending stiffness G. For this, the coordinates of the embedding bond and the free end points should be specified to calculate the θ angle (see Figure 2). For a fabric in cantilever configuration under gravity, Peirce defined the ratio c 3 :

with Ad and w are respectively the areal weight and the width of the fabric; g the earth's standard acceleration due to gravity. c has the unit of a length. It is named the bending length by Peirce.

Then, he suggested the following approximation:

with L and θ are respectively the length of the fabric bending part and the angle between the chord and the horizontal axis.

Thus, the stiffness goes to:

During the test, the sample is about 30 mm width and 300 mm length. Nonetheless, due to a twist effect in the bending fabric, two profiles (top and bottom) could be considered (see Figure 3).The following study focuses on the top profile. Its rigidity is denoted by Gs.

BENDING TEST IN VARIOUS RELATIVE HUMIDITY

As the materials studied in this work are based on natural fibres, the degree of moisture absorption may influence their mechanical properties and particularly the bending stiffness. The test samples are therefore prepared and submitted to different relative humidity RH environments. For the dried fabrics, the following protocol was used: the samples were dried for 24 h at 110 °C before being tested inside the oven where RH is about 14 %. Besides, fabrics conditioned at about 100 % of humidity (RH=99.9%) were also tested. Finally, three intermediates humidities were examined (RH= 33, 55 and 86 %). In this context, the samples were put in climatic enclosures airtight with a solution in the bottom and a sample holder. For the solution, we use water for 100 % RH and aqueous saturated salt solutions for 33, 55 and 86 % RH. During the tests the room temperature was between 20 and 23 °C. According to standard NF EN ISO 483 2006-01 [START_REF] Afnor | Plastics -Small enclosures for conditioning and testing using aqueous solutions to maintain the humidity at a constant value[END_REF], depending on the chemical salt used and the room temperature, an environment with controlled humidity can be created (Table 1). After being conditioned for 24 h, the fabrics were tested under ambient conditions (RH=63 % on average). The time taken for test including the placement of the sample is about 5 min. We point out that the references were placed in different atmospheres (oven or climatic enclosures) for 24 h. In fact, the evolution in time of the references weight in each atmosphere was carried out. The figure 4 shows the evolution of the moisture content MC of the two references at intermediates humidities. Such study allowed us to detect the equilibrium and the time needed to weight stabilisation.

with w is the weight ; w0 is the dry weight (the weight at time 0).

RESULTS AND INTERPRETATION 1. INFLUENCE OF THE FABRIC COMPOSITION

The fabric composition, considering hybrid and pure flax fabrics, was examined. Each time, five samples from the same roll were tested in the weft direction. Figure 5 represents the results of the bending rigidity of the 100% flax hopsack. It shows the variation of the rigidity Gs with bending length L. This can be used to check if the behaviour is linear elastic. In this case, the rigidity should be independent of the bending length [START_REF] Bilbao | Bending Test of Composite Reinforcements[END_REF].

The variation of the Gs amplitude ΔGs is about 79.68 % of the average which illustrates a non linear elastic behaviour with Assuming the general behaviour of Gs, it can be noted that the apparent stiffness is almost constant in the range of 100 to 180 mm Figure 5 The evolution of the bending stiffness Gs as a function of the bending length L for Hopsack 4x4 100% flax at ambient (RH=67.2% on average) Figure 6 The evolution of the bending stiffness Gs as a function of the bending length L for Hopsack 4x4 40% flax/PLA at ambient (RH=51.3% on average)

In the case of 40% Flax/PLA, the variation of the Gs amplitude ΔGs is about 95.41 % of the average which illustrates a non linear elastic behaviour as well (Figure 6). Nevertheless, the apparent stiffness is almost constant in the range of 100 to 160 mm. Considering that the bending stiffness is representative of the general behaviour of the material between 100 and 160 mm, we observed the effect of the composition in this range.

For flax/PLA commingled hopsack a significant loss of stiffness (66% on average) is observed in comparison to the 100% flax fabric. The rigidity goes from 31 N.mm 2 with pure flax to 10 N.mm 2 with hybrid flax. Thus, with 60% of PLA the fabric becomes more flexible. Such result is expected in the case of homogeneous isotropic linear elastic material because the vertical displacement is inversely proportional to the young's modulus. Actually, the young's modulus of PLA, which is about 3 ± 0.15 GPa [START_REF] Placet | Effect of hygrothermal treatment on the mechanical properties of natural fibres composites[END_REF], is significantly lower than the young's modulus of flax which is about 58 ± 15 GPa [START_REF] Baley | Fibres naturelles de renfort pour matériaux composites. Techniques de l'ingénieur Textiles à usage technique[END_REF].

L [mm]

Composite reinforcement shaping is a necessary step for process such as RTM and prepregs.

In RTM, the matrix will be injected after forming such is the case of the pure flax fabric. For thermoplastic composite (CFRTP), a hot sheet forming of commingled fabric such as flax/PLA could be used. After the hot forming, thermoplastic fibres will play the role of the matrix. By reducing the bending rigidity, the adding of PLA can affect significantly the fabric acceptable curvature. According to this study, the hybrid fabric is more likely to form deflects such as wrinkles [START_REF] Allaoui | Experimental and numerical analyses of textile reinforcement forming of a tetrahedral shape[END_REF]. In this context, we cannot make the same parts with RTM and sheet forming unless to enhance the stiffness of the flax/PLA reinforcement and one perspective is to act on the humidity effect.

INFLUENCE OF THE RELATIVE HUMIDITY

Due to the hydrophilic nature of flax fibres [START_REF] Raj | Interfacial studies of polylactic acid (pla)flax biocomposite from model surface to fibre treatment[END_REF], the evolution of bending properties with humidity was investigated. As it was observed before the apparent stiffness is almost constant between 100 and 160 mm. Thus, we will focus on a fixed bending length L=130 mm. Five relative humidities were examined: 14 %, 33 %, 55 %, 86 % and 100 % (Figure 7).

Figure 7 Effect of the relative humidity RH on the bending stiffness Gs

The graph shows that the rigidity increases as a function of a growing relative humidity until 86 % RH before dropping at 100 % RH. The water uptake is then advantageous for the rigidity up to a maximum relative humidity. The excess leads to an opposite effect. Up to 86 % RH, the rigidity growth could be explained by the plasticising effect of water possibly due to the presence of ''free water''. However, the excess of moisture increases the amount of ''bonded water'' in spite of free water [START_REF] Stamboulis | Effects of environmental conditions on mechanical and physical properties of flax fibers[END_REF].

Indeed, fabrics made from plant fibres are highly hygroscopic because they can host water in two forms: a free form which penetrates the cellulose network and is housed in capillaries and the spaces between fibrils; and a bound form attached to the cellulose molecules by chemical bonds. Polysaccharides are very hydrophilic [START_REF] Girault | Galactans and cellulose in flax fibres putative contributions to the tensile strength[END_REF]. Thanks to their hydroxyl group, they can host water molecules by Van der Waals and hydrogen bonds. In addition, the water molecules separate cellulose molecules. Hence, cellulose molecules are able to move more freely. The cellulose becomes more flexible and the insertion of water molecules in the hydrophilic network causes the swelling of the structure. The swelling can degrade the mechanical properties of the material by creating micro-cracks which can be confirmed by a SEM

RH %

100 % flax observation of the samples conditioned at 100% [START_REF] Stamboulis | Effects of environmental conditions on mechanical and physical properties of flax fibers[END_REF]. If a relative humidity of 100% results in a drop in the mechanical properties, a total water immersion can also cause a loss of stiffness [START_REF] Placet | Effect of hygrothermal treatment on the mechanical properties of natural fibres composites[END_REF][START_REF] Assarar | Influence of water ageing on mechanical properties and damage events of two reinforced composite materials: Flax-fibres and glass-fibres[END_REF]. As the sample conditioned at about 55% reveals the behaviour at ambient room conditions, moisture uptake can be disastrous (eg 100%) or advantageous (eg 86%). However, drying causes a loss of stiffness at either 14% or 33% RH. This is possibly due to the embrittlement of the fibre constituents after the removal of the plasticizer which is water [START_REF] Girault | Galactans and cellulose in flax fibres putative contributions to the tensile strength[END_REF][START_REF] Baley | Influence of the Absorbed Water on the Tensile Strength of Flax Fibers[END_REF]. In addition, the water removal can cause mechanical stress on the scale of the fibre due to changes in behaviour of the fibre components (cellulose, pectin, hemicellulose) [START_REF] Velde | Thermal and mechanical properties of flax fibres as potential composite reinforcement[END_REF]. Moreover, the drying effect can be explained by the formation of hydrogen bonds between the cellulose surfaces limiting interaction between the fibrils [START_REF] Hearle | The fractography of cotton fibres[END_REF][START_REF] Hill | Effect of drying and rewetting of wood on cellulose molecular packing[END_REF].

Previously, a gap of about 66 % in bending stiffness was noted between the two references under ambient conditions. Tested for various relative humidities, the 40% flax/PLA hopsack remains advanced by the pure flax fabric. In order to explain the drop in rigidity, the variation of samples water uptake with the air relative humidity was examined (Figure 8). Actually, at a given relative humidity, the moisture content differs from one reference to another. This is probably due to the difference in polar properties between PLA and cellulose. PLA is more hydrophobic than flax which is generally the case of the matrix in composite material [START_REF] Raj | Interfacial studies of polylactic acid (pla)flax biocomposite from model surface to fibre treatment[END_REF]. And a previous study has point out that the PLA moisture content is about 2 % in the case of total immersion [START_REF] Placet | Effect of hygrothermal treatment on the mechanical properties of natural fibres composites[END_REF].

CONCLUSION

The 40% flax/PLA reinforcement is more likely to generate defaults such as wrinkles during the sheet forming process because of a lower bending stiffness compared to the pure flax reinforcement. This can be explained by the PLA young's modulus which is lower than flax modulus as well as a less sensitivity to humidity.

This paper clearly shows that moisture enhances the bending rigidity especially in the case of 100% flax fabric. However, the study points out that the samples rigidity drops after conditioning in 100% relative humidity. This is probably due to fibre damage after an excessive water uptake. On the other hand, drying results in significant rigidity fall. The water removal embrittles the flax constituents and influence interfacial bonding between cellulose surfaces.

Figure 1

 1 Figure 1 The 4x4 hopsack fabric

Figure 2

 2 Figure2The bending test for fabric: For a given bending length L, the rigidity depends on θ angle.

Figure 3

 3 Figure 3 Top and bottom profiles

Figure 4

 4 Figure 4 The evolution in time of the moisture content at different relative humidities

Figure 8 .

 8 Figure 8. The evolution of the moisture content at the equilibrium with the relative humidity

Table 1

 1 Relative humidities according to the salt used

	Salt	RH for 20 °C
	Magnesium chloride: Mg Cl 2	33 %
	Calcium nitrate: Ca (NO 3 ) 2	55 %
	Potassium chloride: KCl	86 %

All things considered, we conclude that on the one hand, the environmental conditions during the process should be controlled. And on the other hand, acting only on the humidity, we cannot significantly improve the stiffness of flax/PLA reinforcement.


Ophélie Lacroix
email: ophelie.lacroix@univ-nantes.fr

On the Effect of Head Tagging on Parsing Discontinuous Dependencies in French

In this paper we aim at showing the strong impact of head tagging on syntactic dependency parsing. The rules of categorial dependency grammar used to parse French deal with discontinuous dependencies and long distance syntactic relations. Such parsing method produces a substantial number of dependency structures and requires too much parsing time. We show that a local tagging method can reduce these problems and help to solve the global problem of dependency parsing disambiguation. Then we adapt a tagging method (CRF) to types of the categorial dependency grammar. We obtain a dependency head preselection allowing us to reduce parsing ambiguity and to see that we can find distant relation of dependencies through local results of such method.

1 A dependency g → s is discontinuous if a word between the governor and the subordinate does not depend on the governor. These dependencies can cross others.

Introduction

Syntactic parsing is a well-known task in natural language processing. Its purpose is to attach syntactic structure to a sentence using a grammar. There are several types of syntactic structures. Among the syntactic structures used the most popular are the constituency and dependency structures. We choose in this work the dependency structures [START_REF] Mel | Dependency syntax : Theory and Practice[END_REF][START_REF] Tesnière | Éléments de syntaxe structurale[END_REF] because the order in French is flexible and admits many discontinuous constructions which are represented by discontinuous dependencies. The dependency representation allows us to highlight the syntactic functions binding words of the sentences. Notably, figure 1 presents the non-projective comparative relation moins que (less than). A dependency d is a binary relation between a governor g and a subordinate s (g d -→ s). We call head dependency type (head type) the name of the dependency pointing on the subordinate. Dependencies can be projective or discontinuous 1 . Discontinuous dependencies have always been an obstacle for dependency parsing. This is why we choose the class of categorial dependency grammar (CDG) [START_REF] Béchet | Dependency Structure Grammar. 18-34[END_REF][START_REF] Dekhtyar | Generalized Categorial Dependency Grammars[END_REF] which resolve this problem. We use in this work the CDG of French [START_REF] Dikovsky | Categorial Dependency Grammars: from Theory to Large Scale Grammars[END_REF] developed using CDG Lab [START_REF] Alfared | CDG Lab": a Toolbox for Dependency Grammars and Dependency Treebanks Development[END_REF]. The CDG Lab is an integrated environment for elaboration and maintainance of CDG grammars and corpora of dependency trees. Lab is integrated a parser for CDG. It allows 3 different methods of parsing : autonomous parsing, parsing by head type selection and parsing by approximation.

Parsing by head type selection consists in selecting the proper head dependency type for every word and computing the structure conforming to these choices.

In the head type selection mode, the head types are selected manually. This method drastically reduces the ambiguity of parsing. Our objective is to replace this manual choice by a stochastic procedure. So this objective may be seen as a problem of tagging the text with head types. First of all, this tagging should be adapted to the categorial dependency grammar of French we use. This task can be seen as a kind of supertagging [START_REF] Bangalore | Supertagging: Using Complex Lexical Descriptions in Natural Language Processing[END_REF] which assigns complex tags (with a rich description) on lexical units in order to disambiguate parsing. It is known to reduce ambiguity and parsing time. Here the difficulty of tagging consists of locally computing the correct head type for distant dependencies. The main difficulty of such tagging is to properly compute the head type not only in the case when the governor is local but even when it is distant. Very many methods have been developed for pos-tagging. Some of them improving dependency parsing [START_REF] Nasr | Grammaires de dépendances génératives probabilistes. Modèle théorique et application à un corpus arboré du franais. 115-153[END_REF][START_REF] Candito | Statistical French dependency parsing: treebank conversion and first results[END_REF]. In this parper, we choose CRF techniques and tools2 to train a French dependency tag model using the corpora developed in CDG Lab. Then, the tagging results are used in the place of manual head selection for parsing French sentences. In this paper, we statistically show the substantial effect of head type selection on parsing time and on the number of sucessful parses. We compare these results with results of autonomous parsing. This work is preliminary because the head type selection procedure uses a good splitting of the text into composite lexical units and also a tagging of morphosyntactic classes. So this is a part of a larger project where all these preliminary information will be computed by other stochastic procedures.

Categorial Dependency Grammar

The categorial dependency grammars [START_REF] Dekhtyar | Categorial Dependency Grammars[END_REF][START_REF] Dikovsky | Dependencies as Categories. 90-97[END_REF] are rather close to the classical categorial grammars [START_REF] Bar-Hillel | On Categorial and Phrase Structure Grammars. 99-115, Language and information[END_REF]. The novelty are the polarized valencies used to define discontinuous dependencies. The projective dependencies defined using the classical categories are constructed through the classical type elimination rules whereas the discontinuous dependencies are created through pairing of dual polarities (րց and ւտ). The rules of the CDG are presented in table 1.

L 1 C P 1 [C\β] P 2 ⊢ [β] P 1 P 2 I 1 C P 1 [C * \β] P 2 ⊢ [C * \β] P 1 P 2 Ω 1 [C * \β] P ⊢ [β] P D 1 α P 1 (

Grammar and Dependency Corpus for French

To parse French we use the categorial dependency grammar of French [START_REF] Dikovsky | Categorial Dependency Grammars: from Theory to Large Scale Grammars[END_REF]. It uses 117 French dependency types (corresponding to head types) distributed over 39 dependency groups. Then, we called head group the dependency group which can be derived from head type. As a matter of example, the dependency a-obj is the head type for the direct object (the object in accusative case), d-obj and g-obj are head types of indirect objects (respectively in dative and genitive cases). All the 3 are elements of the group OBJ. On the other hand, among the dependency types there are 27 discontinuous dependencies such as clitic, modifier, reflexive, apposition, negative and some other discontinuous dependencies.

We use a corpus counting 2778 dependency structures 3 over 35203 lexical units. The corpus was developed and is exploited by the members of the team TALN 4 of the LINA laboratory. We notice, though only 4% of dependencies in the corpus are discontinuous but 41% of dependency structures have at least one discontinuous dependency. So discontinuous dependencies are well enough represented in this French corpus. In this corpus, not only every lexical unit has a head type (belong into a head group) but it is also categorized by one of the 185 morphosyntactic classes of the categorial dependency grammar of French. We use 2 levels of the categorization: a more general one using 28 tags (hyper classes) and a more specific one using 86 tags (extended classes). The hyper morphosyntactic tagging gives a rudimentary lexical syntactic information whereas the extended one adds some semantic syntactically relevant information. As an example in figure 1, moins functions as an adverb in the lexical unit moins que (less than). It is tagged by Adv using the hyper tagging whereas it may be tagged with Adv-compar using the extended tagging. The lexical unit que is a junction tagged with Conj using the hyper tagging and which may be Conjcompar using the extended. This extended tagging shows that both members of the dependency are related through comparison. Figure 2

CDG Lab

As we have already mentioned, the CDG Lab parser has 3 complementary parsing methods :

autonomous parsing mode applied to raw french sentences. It computes both the correct head type and the proper morphosyntactic class. The sentence is split into lexical units and to this splitting is applied a CKY-based algorithm which searches all possible correct dependency structures. This parser treats a huge number of variants ; -parsing by head type selection is a semi-automatic mode. The user selects grouping lexical units into composite lexical units, selects proper morphosyntactic classes for them and head types (or head groups). Then the parser compute the dependency structures compatible with this selection. This mode drastically reduces the number of choices in the analysis ; -parsing by approximation mode is performed after the preliminary head type (or head group) selection. For every output dependency structure the user can positively or negatively annotate the and the parser reanalyses the sentence using these annotations.

Here, we consider the head type (or head group) selection mode. We observe that the manual tagging reduces the ambiguity of analyses. Generally, it garantees a very restricted number of solutions compatibles with the selection. The other benefit of this mode is a significant reduction of parsing time. By replacing the manual head type selection by an automatic head type selection we hope to attain both advantages. In this work, we focus on head type (and head group) tagging, which means that we know the lexical units decomposition and their morphosyntactic categorization on the training and tagging phase.

Head type Tagging

The most popular tagging procedures are pos-tagging and morphosyntactic tagging, both different from the head type tagging. Nevertheless, the tools for all of them may be identical. Among the various methods of tagging, the most popular are the stochastic graphical models such as Hidden Markov Model (HMM) [START_REF] Rabiner | A tutorial on hidden markov models and selected applications in speech recognition[END_REF], Maximum Entropy Model (MEMM) [START_REF] Ratnaparkhi | A maximum entropy model for part-of-speech tagging[END_REF] and Conditional Random Fields (CRF) [START_REF] Sutton | An Introduction to Conditional Random Fields for Relational Learning[END_REF]. In this work, we choose the CRF method because it is able to deal with a large number of tags and features and consider the notion of sequence.

Software and Feature Patterns

We use the Wapiti software [START_REF] Lavergne | Practical Very Large Scale CRFs[END_REF] to train our dependency model for tagging sentences. We use 15 features which apply to lexical units and their morphosyntactic classes. The window size we consider is of 5 lexical units containing the current one. For the classes we also have a window of 7 (both for hyper and extended classes). Features also consider the word suffixes and capital letters.

Experimentation and Evaluation

To evaluate the tagging we divide the corpus in 10 parts. Each experiment includes a training phase performed on 90% of sentences of the corpus and the tagging phase performed on the last 10%. Wapiti can yield the n best tagging sequences for each sentence: we choose to produce the 10 best. Then, for each lexical unit we evaluate the taggings with 1, 2, 5 or 10 best tags assigned. Sequences can be very similar from one to another, there are rarely 10 different tags for a lexical unit. We should decide whether among the 1, 1 to 2, 1 to 5 or 1 to 10 assigned tags there is the right one, that is we evaluate the accuracy on the top 1, 2, 5 and 10. The results of the evaluation are presented in table 2.

One may observe that when the number of assigned tags (per lexical unit) increases, the accuracy increases. because the ambiguity of tagging is minor. As it is shown in table 3, the average number of possible head groups is lower than that of head types for a given class.

The head groups score is not significantly better but can make a difference for parsing because assigning a head group to a lexical unit is equivalent to assigning the disjunction of the head types in this group. For example, when we assign to a lexical unit the group OBJ we actually assign the disjunction of 7 head types 5 . We will observe this difference through parsing evaluation. Moreover, the extended classes bring information improving the tagging of head types and groups. Then we choose to perform parsing using head types and head groups found using extended classes.

Dependency parsing and Evaluation

Parsing and evaluation process

Our objective is to replace the manual head type selection mode by the automatic selection using the CRF trained model. As a result of tagging, we have a corpus where each lexical unit is tagged by 1 to at most 10 head types or head groups. We parse all of the corpus using these head type or head group pre-selections. Both pre-selections reduce the ambiguity and so the number of the output dependency structures for each One of particular goals is to know whether among the dependency structures there is the best one6 . Currently, the output dependency structures are not sorted by the distance from the best one. So we use the best dependency structure to find the nearest output dependency structure. Nearest means having the maximum of correctly labelled dependencies as compared to the best one. We show the phases of this entire procedure in figure 3. For each sentence, the results are evaluated only considering the nearest dependency structure. By the way not all sentences are successfully analysed and obtain a dependency structure. There are 2 reasons for that :

the assigned head types (or head groups) contradict to the grammar categories, so the parsing fails ; -the parsing is avoided because of time limits (often because of the length of the sentence).

As a consequence, one of the evaluation criteria is the number of completed parses.

Results and discussion

First of all, we find the rate of sentences obtaining at least one dependency structure are the completed parses. And we are interested to see the evolution of parsing time and the average length of sentences for the completed and uncompleted parses. The experimentation results are presented in Table 4. On that one hand, these results allow to compare the performance of the autonomous parsing and of the parsing by head type selection. The important result is the impressive reduction of the parsing time. As a consequence, the rate of sentences for which the parsing fails because of time limit is close to zero. These few uncompleted parses correspond to very long sentences (> 41 lexical units per sentence). Note that there are fewer parses uncompleted because of time limits, but more parses uncompleted because of grammatical conflicts. Indeed, the wrong selection of head types or head groups can make fail the parsing because the sequence is ungrammatical.

From the results on parsing by head type and head group selection, one may observe that the number of completed parses increases when increases the number of possible head types or head groups. There are more chances to obtain the right head type or head group among various tagging possibilities. So the number of conflicts with the grammar categories decreases and the number of completed parses increases. The best results (for 10 possible head groups) gives 2548 completed parses among 2778 (91.7%), among which 2088 give the best dependency structure. Moreover, we saw that the head type and head group selections highly reduce the parsing time. At the same time it may increase with the growing number of alternative tags. The reason is clear : the more alternative head types or head groups are selected the more dependency structures are produced for one sentence. So for very long sentences the parsing fails with few head type or head group but succeeds with more. Respectively, the head group selection allows to parse more sentences but takes more time, because the groups often include several head types. So using the groups, we obtain more parsed sentences even though some parses are stopped because of time limit. The evaluation of the precision on the dependencies are presented in table 5.

The evaluation is performed on completed parses and uses the labelled (LAS) and unlabelled (UAS) attachment score. Similarly, the results are better when there is a larger choice of head types or head groups. As above, the more there are head type or head group choices the more we have chances to have a right dependency. As it concerns the discontinuous dependencies, one can see that the precision is not as good as in the case of all dependencies (both for head types and head groups). Nevertheless, the scores rest interesting. In particular, scores are better in the case of head type selection than in the case of head groups. The rate of discontinuous dependencies among all dependencies reach 4.3% to 4.6% with head type selection and 4.8% to 4.9% with head groups selection. We conjecture that some uncompleted parses of head types selection correspond to the difficult discontinuous cases. Sometimes, the more are possibilities of head type selection the easier is to find a parse. However, in some difficult discontinuous cases the right parses are not found. Nevertheless, parsing with head type (or head group) selection allows to find a good rate of correct dependencies (projective and discontinuous).

Related work

Here, we focus on one phase of dependency parsing. We based this work on a given morphosyntactic tagging and a given sorting of output dependency structures. That makes difficult the comparison with autonomous dependency parsing. Moreover, dependency parsing is often performed on the model derived from constituency parsing which does not reflect the non-projectivity. In a technically aspect, our work is close to supertagging which also reduces ambiguity and parsing time [START_REF] Clark | The Importance of Supertagging for Wide-Coverage CCG Parsing[END_REF][START_REF] Nasr | Non-lexical chart parsing for TAG[END_REF][START_REF] Sarkar | Combining Supertagging and Lexicalized Tree-Adjoining Grammar Parsing[END_REF].

Conclusion and Future Work

We show that from different points of view, the head type tagging is very usefull for dependency parsing. The first point is that it really reduces the parsing time. A large number of sentences for which parsing failed in autonomous mode finally succeed with the head type selection. We also obtain a good rate of completed parses. Finally, the number of sentences obtaining at least one dependency structure is noticeably greater. This makes more interesting the good precision score because the high precision concerns more representative cases of parsing success. As a result, the head type tagging really ameliorates the dependency parsing. Nevertheless, this amelioration is attained using given correct splitting of the sentences into lexical units and given correct morphosyntactic classes. One may also add the given good sorting of dependency structures by their distance from the optimal one which makes the work easier. To arrive at a completely autonomous parsing, one is obliged to make these tasks automatically. The question is whether the head type tagging will be efficient enough? Another question is whether the recall in autonomous parsing will be high enough to parse a great part of French sentences. A possible idea to obtain better results would be to compute partial dependency structures after failure and to use them in evaluation.

Fig. 1 .

 1 Fig. 1. Dependency structure for the French sentence "Il boit moins d'eau qu'avant." (He drinks less water than before).

  illustrate the information recovered from the annotated dependency structures for a particular sentence.

		clit-d-obj	qu				projective
			aux-d				dependency
	Y	pred avez -vous pensé	?	g	discontinuous dependency s g : governor s : subordinate
	PNclitd Vauxavoir PNpersn	Vtpz		QM	Extended Class
	PN	Vaux	PN	Vt		QM	Hyper Class
	clit-d-obj	S	pred	aux-d		qu	Head type
	CLIT	SENT	PRED	AUX	PUNCT	Head group

S ⚓

Fig.

2

. Dependency structure for the French sentence "Y avez vous pensé?" (Have you thought about it?) and hyper classes, extended classes, head types and head groups of each lexical unit.

  There are more possibilities to have the right tag among various possibilities. And the head group tagging gives best results

			type tagging	Head group tagging
	using	hyper classes extended classes hyper classes extended classes
	Top 1	87.8	91.1	90.4	91.6
	Top 2	90.0	93.2	92.5	93.7
	Top 5	92.9	95.5	95.1	96.0
	Top 10	94.6	96.6	96.4	97.1
	Table 2. Evaluation (accuracy) of head type and group tagging using Wapiti. Results
	represent the rate of lexical units correctly tagged among the 1, 1 to 2, 1 to 5 or 1 to
	10 assigned tags.

Table 3 .

 3 Average

	Average number of	head types (max.) head groups (max.)
	Per hyper class	13	(43)	7	(18)
	extended class	6	(31)	4	(16)

(and maximum) number of possible head types and head groups for a given hyper or extended class.

  Proceeding diagram. Training is performed on 90% of the corpus and tagging on the remaining 10%. The tagged part is parsed using the head type selection. The parser output several unsorted dependency structures and finds the nearest to the best dependency structure for each sentence.

	Corpus GS (french)	Wapiti		CDG LAB
			Parser
	10%	Training Tagging	French categorial dependency grammar Parsing with head type selection	Not sorted dependency structures	Sort	Best dependency structure for each sentence
	Fig. 3.

Table 4 .

 4 Number

	parsing

of completed parses (CP), number of uncompleted parses because head selection was not consistent with grammar's rules (UP-C) or because of parsing time (UP-T).

Parsing time is limited to 10s. Average number of lexical units (LU) per sentence in the three cases. Total parsing time for completed parses and both uncompleted parses.

Table 5 .

 5 LAS

			Autonomous parsing
	Nb of	All dependencies	Discontinuous dependencies
	types	LAS	UAS	LAS	UAS
	-	98.3	99.0	92.7	93.2
			Parsing by head type selection
	Nb of	All dependencies	Discontinuous dependencies
	types	LAS	UAS	LAS	UAS
	1	93.7	96.7	92.4	93.7
	1 to 2	95.1	97.3	94.3	95.5
	1 to 5	96.2	97.8	94.4	95.5
	1 to 10	96.4	97.9	94.5	95.4
		Parsing by head group selection
	Nb of	All dependencies	Discontinuous dependencies
	groups	LAS	UAS	LAS	UAS
	1	93.9	96.7	88.8	93.3
	1 to 2	95.1	97.2	90.0	93.7
	1 to 5	96.3	97.9	90.5	93.8
	1 to 10	96.7	98.0	91.1	94.3

and UAS for autonomous parsing compared to parsing by head selection. The evaluation is made on the best dependency structure (nearest to the original) produced by the parser for each completed parse. The labelled attachment score (LAS) is the rate of lexical units (apart from punctuations) bounded to the proper governor with the correct dependency label. The unlabelled attachment score (UAS) is the rate of lexical units bounded to the proper governor.

Conditional Random Fields.

2778 French sentences.

The corpus is not publicly available yet.

a-obj, o-obj, d-obj, l-obj, g-obj, a-obj-d, qa-obj.

The best dependency structure is that one associated to the sentence in the corpus.