D Georges

D Saletti

M Montagnat

P Forquin

P Hagenmuller

D Hébert

J-L Rullier

Influence of porosity on ice dynamic behavior as assessed by spalling tests

) is the only survey providing a robust and reproductible set of experiments about the dynamic tensile strength of ice, however the microstructure influence was out the scope of this experimental study. spherical pores present in the LP specimens are seen to contribute to this strength decrease.

Although fragmentation analysis did not allow to clearly assess the role of these porosities on the crack initiation and propagation processes, the numerous clues such as the high number of cracks detected, the tortuosity of crack paths and the presence of porosities on the crack surfaces seem to validate the hypothesis of porosities playing a key role during ice fragmentation.

Though, the hailstone microstructures are generally charaterised by a high level of porosity. It is the reason why the influence of this microstructural parameter on the dynamic behavior of polycrystalline ice needs to be investigated. The aim of this paper is to study the role of porosity on the tensile behavior of polycrystalline ice by applying the same experimental set-up and measurements processing than in [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF] to low-porosity (LP) and high-porosity (HP) microstructures. To do so, spalling tests with a Hopkinson bar apparatus were conducted and fragmentation processes were carefully analyzed by means of an Ultra High Speed Camera, an Automatic Ice Texture Analyser and a micro-Computed Tomograph. The experimental results show that the tensile strength is sensitive to the applied strain rate for both types of micro-structures over the range 24 s -1 to 120 s -1 . A weakening effect of porosity is also observed, the lowly porous specimens being significantly stronger than the highly porous ones. The large

Introduction

Dynamic interactions between ice and man made structures are of concern in many situations, such as icebreaker ships crushing ice floe in polar regions, serac falls, atmospheric ice impacting buildings, aircrafts or even space shuttles. For the latter, NASA classified atmospheric ice as a potential source of damage after the catastrophic Columbia space shuttle break down in 2003.

An accurate understanding of the ice dynamic strength failure is of interest to determine and to model the force generated during an impact and thus to provide relevant scaling of the structures of concern.

Dynamic confined compressive and tensile loadings are expected to developp in brittle materials under impact [START_REF] Forquin | A numerical study on the influence of free water content on the ballistic performances of plain concrete targets[END_REF][START_REF] Forquin | Brittle materials at high-loading rates: an open area of research[END_REF]. Ice is known to behave as a brittle material at high strain-rates [START_REF] Schulson | Creep and fracture of ice[END_REF], its mechanical response to dynamic confined compression and tension is thus essential and needs to be considered to get an accurate modelling. Up to now, with the improvement of computing capacities, numerous models have been developed to describe the behavior of polycrystalline ice during an impact event. Most of them adopted an elasto-plastic or elasto-visco-plastic approach, coupled with failure criterions [START_REF] Carney | A phenomenological high strain rate model with failure for ice[END_REF][START_REF] Pernas-Sánchez | Numerical modeling of ice behavior under high velocity impacts[END_REF]Tippmann et al., 2013;[START_REF] Dousset | Comportement mécanique dynamique de la glace: Contributions expérimentales et numériques pour le cas d'impacts de grêle sur structure aéronautique[END_REF]. The ice behavior is assumed to be pressure dependent and the volumetric and deviatoric response of ice is different according to the direction of loading, compression or tension. The first models were manually adjusted by changing the material input parameters, the hardening modulus, the plastic failure strain and the compressive and tensile failure pressures, until a good correlation is reached between numerical simulations and experimental data [START_REF] Kim | Modeling hail ice impacts and predicting impact damage initiation in composite structures[END_REF][START_REF] Keune | Development of a hail ice impact model and the dynamic compressive strength properties of ice[END_REF][START_REF] Park | Damage resistance of single lap adhesive composite joints by transverse ice impact[END_REF]. Thanks to the Split Hopkinson Pressure Bar technique (SHPB), the compressive yield stress sensitivity to strain-rate of ice was investigated [START_REF] Kim | Compressive strength of ice at impact strain rates[END_REF][START_REF] Shazly | High strain-rate behavior of ice under uniaxial compression[END_REF]Wu and Prakash, 2015). These experimental results, although scattered, reveal a strain-rate hardening behavior that has been implemented in recent modelling works [START_REF] Pernas-Sánchez | Numerical modeling of ice behavior under high velocity impacts[END_REF]Tippmann et al., 2013). These models are based on the strong hypothesis of a transition from a solid-to-liquid behavior of ice when reaching a tensile failure criterion. Above this threshold, ice is supposed to behave as a fluid, and not carry any shear or tensile stress. In most of the concerned models, the tensile failure stress is considered to be strain-rate insensitive and is either took from quasi-static experiment results or determined by a numerical parametric study. Indeed, for strain-rates lower than 10 -1 s -1 , the ice tensile strength remains constant and ranges between 0.5 MPa to 3 MPa, depending on the microstructural properties [START_REF] Petrovic | Review mechanical properties of ice and snow[END_REF]. However, other brittle materials, such as concrete and ceramics, are characterized by a dynamic tensile strength strongly dependent on the loading rate [START_REF] Schuler | Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates[END_REF]Erzar andForquin, 2011, 2014;Zinszner et al., 2015). In order to take that into consideration, [START_REF] Ortiz | Assessment of damage model and strain rate effects on the fragile stress/strain response of ice material[END_REF] adapted the initial Mazars model [START_REF] Mazars | Application de la mécanique de l'endommagement au comportement non linéaire et à la rupture du béton de structure[END_REF] to dynamic loadings and considered an ice tensile strength evolving similarly to the compressive strength with strain rate, but with values of strength one-tenth lower. While being the first attempt to catch the dynamic tensile behavior of ice, this approach was not based on any measurements performed under dynamic tensile conditions. This lack of knowledge is problematic as the tensile strength of ice material is the main driver of the fragmentation processes during impact events. This material property should be at the forefront among all the input parameters that should be identified in order to get satisfying modelling.

To our knowledge, only two studies experimentally investigated the response of ice dynamically loaded under tension. [START_REF] Lange | The dynamic tensile strength of ice and ice-silicate mixtures[END_REF] tested ice specimens via plate impact experiments and measured a tensile strength of 17 M P a at a strain rate of 10 4 s -1 . [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF] studied the strain rate sensitivity of ice dynamic tensile strength by performing spalling tests with a Hopkinson bar apparatus on isotropic polycrystalline ice. They observed a clear strain-rate hardening, the ultimate spalling strength was found to change from 2.3 M P a to 16.3 M P a for strain rates between 30 s -1 and 141 s -1 . Both studies have given little weight to the impact of defaults and specificities of the microstructures of the studied specimens. Under quasi-static tensile loading, grain size, crystallographic orientations and porosity, are expected to impact the mechanical response of polycrystalline ice [START_REF] Schulson | Creep and fracture of ice[END_REF]. In particular, [START_REF] Kermani | Bending strength and effective modulus of atmospheric ice[END_REF] and [START_REF] Timco | Flexural strength equation for sea ice[END_REF] showed that the presence of porosity in atmospheric and sea ice respectively, significantly decreases their quasi-static tensile strength.

Hailstone microstructures appear to be complex, and to strongly depend on the formation history, but clearly always present some porosity with a dispersed pore size distribution (see [START_REF] Macklin | Isotopic, crystal and air bubble structures of hailstones[END_REF] for instance). More broadly, in many quasi-brittle materials, cracks are supposed to be triggered on the microstructural defects under tensile loading, such as porosities, grain boundaries, inclusions, sintering defects, etc.. At high strain-rates in tension an intense multiple fragmentation occurs as a result of the activation of numerous microstructural defects [START_REF] Hild | On the probabilistic-deterministic transition involved in a fragmentation process of brittle materials[END_REF]. In polycrystalline ice, and more specifically in hailstones, these microstructural defects can either be porosities, grain boundaries, impurities, micro-cracks, for instance. As mentioned before, owing to the presence of a high and complex porosity in hailstones, porosities might be the dominating defect population influencing the behavior of ice under dynamic loading.

Quantifying how the defect of the microstructure can act upon ice fragmentation processes is therefore a key step to reach a better understanding of the behavior of ice under dynamic loading.

The present study will aim to evaluate how the porosity affects the dynamic tensile response of polycrystalline ice. To do so, two type of polycrystalline ice specimens, presenting different levels of porosity but similar grain size and shape, have been manufactured. The dynamic behavior of both types of specimen has been evaluated using the spalling technique on Hopkinson bar, according to the experimental procedure described in [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF]. The specimen growth method, the procedure for microstructure characterization and the spalling set-up are presented in section 2. In section 3.3, the dynamic tensile strength sensitivity to the strain-rate and porosity is analyzed. The influence of the porosity on the induced failure mechanisms is addressed in the discussion part via the analysis of crack initiation and propagation processes.

Materials and methods

Specimen growth and machining

The two studied materials are made of artificial polycrystalline granular ice grown in laboratory and are characterized by a microstructure with a low porosity (LP)(≈ 1 -2%) and a microstruc-ture with an high porosity (HP)(≈ 7 -10%) respectively. Both microstructures are obtained using two growth techniques inspired by the one described in [START_REF] Barnes | The friction and creep of polycrystalline ice[END_REF]. Specimens are grown out of isotropic seeds made of crushed ice (with a maximum particle diameter of 2 mm) surrounded by water at 0°C. The slurry is placed on a Peltier element (-15°C), in a 0°C room, to grow gently from bottom to top, and avoid internal stresses during freezing. To obtain the LP microstructure, the isotropic seed is pumped before adding the water. The air trapped between the snow grains is maintained in order to produce the HP microstucture. The LP specimens have no visible porosities and are slightly opaque, whereas large porosities are visible in HP specimens. After unmolding, the specimens are stored during 24 hours in a 0°C environment. This annealing stage aims to relaxe freezing stress and to homogeneize the grain size. Finally, after lathing and milling, 120 mm long and 45 mm diameter cylindrical specimens are obtained.

The geometric and density features of the specimens used in the spalling tests are listed in Table 1.

2.2 2D analysis of the microstructure : the Automatic Ice Texture Analyser (AITA)

Several LP and HP specimens, not tested here but assumed to be representative of the whole sets, were machined in thin square sections of approximately 50 × 50 cm 2 and 0.3 µm in thickness.

Owing to the birefringent property of ice, the optical method of AITA (Wilson et al., 2003) gives access to the orientation of the c-axis (the optical axis) of the hexagonal crystal cell. The current assumption of a relative isotropic behavior in the plane normal to the c-axis (the basal plane) renders sufficient the knowledge of c-axis orientations. The AITA provides the c-axis orientations at a pixel scale set here to 20 µm, and therefore offers orientation images that enable to extract the 2D microstructure fabric and the crystallographic texture (plotted with orientation color-scaled images, see Figure 5).

3D analysis of the microstructure : micro Computed X-ray Tomography (microCT)

MicroCT is a convenient non destructive method to collect the 3D microstructure of a biphasic material when phases are X-Ray contrasted, and hence the porosities size and shape. Quantify- ing damage in post-mortem specimens can also be achieved with microCT. Numerous scans with different resolutions were performed on HP and LP specimens in order to assess the homogeneity and the reproductibility of the pore structure. Here we present the scan configuration used with three HP specimens and three LP specimens scanned prior and after spalling tests. Detailed observations are given in the section 3.2 and 3.6.

Description of the microCT configuration (TomoCold)

Scans were performed in a cold room set at -20°C with the tomograph TomoCold DeskTom130

RX Solutions, specifically adapted to cold temperatures at the CNRM-CEN (Centres d'Etudes de la Neige), Grenoble. A voxel size of 27 µm was chosen, resulting from a compromise between the volume to be analyzed and the minimal resolution required to detect porosities in LP specimens.

The X-ray tube was powered by a current of 238 µA and a voltage of 60 kV . The detector was composed of 1920 pixels × 1536 pixels with a physical pixel size of 127 µm. Each scan consisted of four stacks composed of 1440 radiographs covering a 360°rotation for every stack. One radiograph was computed as the average of two frames captured at three frames per second.

The whole process for every scan lasted 1 h 15 min and the scanned specimens were subjected to spalling tests ( × h = 45 × 120 mm).

Image post-processing

A 3D image is reconstructed from the acquired radiographs. A ring filter with a 20 voxel kernel was applied in order to remove ring features that are artefacts from the acquisition. After reconstruction the scans are composed of approximately 4500 × 1660 × 1660 voxels, whose value spreads out between 0 (black) and 65536 (white). An enhancement of the contrast prior to conversion into 8 bit images was made in order to have reproducible grey level histograms. This operation allowed to apply identical thresholding method for each scan of the same microstructure (more below). Typical images (8 bits) of both microstructures are shown on Figures 1a and2a. Examples of corresponding grey level probability density function are highlighted for each microstructure.

The threshold step allows to separate the voxels into two phases, i.e. air and ice, accord- ing to their grey level value. This operation has to be conducted with caution to minimize the error related to the image noise. HP microstructure histograms present two distinct maxima associated with each phase. Assuming that images are undergoing a Gaussian noise (related to the microCT device), the threshold value minimizing the voxel error is the intersection between the two Gaussian functions fitting each phase (red curves on Figure 1c). Finding a relevant threshold is more tricky for histograms associated to LP specimens, as the porosity density and size are much smaller. To do so, a pseudo-maximum for the air phase is manually picked, the threshold value is chosen to be the middle value between this maximum and the ice phase maximum. See Figures 1b and2b to have an overview of the resulting binary images.

The segmentation stage has been performed on the binary images using SPAM (The Software for the Pratical Analysis of Materials), a Python package currently in development in the 3SR laboratory (Ref SPAM Eddy). During this stage each group of isolated or aggregated black voxels is labelled with a corresponding integer. Due to the presence of impulse noise (sparsely occurring white and black voxels) only labels whose volume exceeds 10 voxels, namely 0.19 mm 3 here, were taken into account and considered as porosities. The results of the analysis are presented in the Section 3.2.

The spalling technique

Experimental set-up

The spalling test on Hopkinson bar is a convenient technique to measure the tensile strength of quasi-brittle materials at strain-rate up to 200 s -1 [START_REF] Klepaczko | An experimental method for dynamic tensile testing of concrete by spalling[END_REF][START_REF] Erzar | An experimental method to determine the tensile strength of concrete at high rates of strain[END_REF][START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF] and to characterize the stress-strain relationship and tensile fracture energy of geomaterials [START_REF] Pierron | Ultra-high-speed full-field deformation measurements on concrete spalling specimens and stiffness identification with the virtual fields method[END_REF][START_REF] Lukić | On the processing of spalling experiments. part ii: identification of concrete fracture energy in dynamic tension[END_REF][START_REF] Forquin | A benchmark testing technique to characterize the stress-strain relationship in materials based on the spalling test and a photomechanical method[END_REF]. A short compressive pulse generated by the impact of a cylindrical projectile against an incident bar propagates along the bar. When it reaches the interface bar/specimen a part of it is reflected because of an impedance discontinuity whereas the other part is transmitted to the specimen. The transmitted pulse is then reflected on the free surface as a tensile pulse creating a dynamic tensile loading inside the specimen when the amplitude of the latter is higher than the compressive pulse one. The core of the specimen undergoes an elastic deformation up to brittle fragmentation due to an intense dynamic tensile stress. Obviously this method is suitable for materials which compressive strength is higher than the tensile strength as it is the case for ice in the quasi-static regime [START_REF] Schulson | Creep and fracture of ice[END_REF].

The configuration used here (Figure 3) is the same than the one described in [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF] where further informations can be found. The projectile is 50 mm long and 45 mm in diameter and has a spherical-cap-ended nose acting as a pulse shaper, in order to smooth the loading pulse [START_REF] Erzar | An experimental method to determine the tensile strength of concrete at high rates of strain[END_REF]. The incident bar is 1200 mm long with the same diameter as the projectile. Both the projectile and the bar are made of high-strength aluminium alloy (yield strength > 450 M P a) with a longitudinal wave speed C of 5078 m.s -1 , a density of 2800 kg.m -3 and an elastic modulus equal to 72.2 GP a. The Hopkinson bar is instrumented with a strain gauge to measure the compressive pulse applied to the specimen. A reflective paper is glued at the free-end of the specimen allowing the measurement of the particle velocity of this rear face by a laser interferometer. The tests are filmed with an ultra high speed (UHS) camera (Kirana model from Specialised Imaging). For each test, 180 images with an inter-frame of 1 µs are obtained, the sensor resolution used is 924 pixels × 768 pixels.

As the major difficulty being the ambient temperature of the spalling room that far exceeds the ice melting temperature, several arrangements were made. The specimens are stored in a freezer set at -30°C located nearby their final position in the experimental set-up. A protocol was established in order to ensure that less than 45 seconds elapse between the time when the specimen is taken out from the freezer and the time when it is loaded in the spalling test apparatus. The full time of handling was systematically recorded for every test and remained below 45 seconds. A cylinder made of the same aluminium alloy as the one of the input bar is glued on the specimen during its preparation in the cold room. This cylinder is 45 mm in diameter and two lengths were used, 30 mm and 40 mm. Its main roles are (i) to avoid a thermal shock between the ice specimen and the Hopkinson bar which is at room temperature; (ii) to delay the melting of the specimen on its face in contact with the bar. The post-mortem specimens were immediately taken back in the freezer after experiment when possible, namely if the fragmentation was not too intense.

Signal processing

Spalling strength to failure

As described in details in [START_REF] Erzar | An experimental method to determine the tensile strength of concrete at high rates of strain[END_REF] and [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF], from the signal measured one can use the linear acoustic approximation [START_REF] Novikov | The study of fracture of steel, aluminium and copper under explosive loading[END_REF] to deduce the ultimate spall strength σ T of the specimen prior to fracture :

σ T = 1 2 ρ ice C ice ∆V pb , (1)
where ρ ice is the specimen density and C ice the longitudinal wave velocity in the specimen.

The latter is computed by performing an inter-correlation between the rising stage of the strain gauge and laser signals to determine the time of propagation between the gauge location and the specimen free surface, the distance being perfectly known. ∆V pb represents the pullback velocity corresponding to the difference between the maximum velocity and the velocity at rebound that are measured on the rear face of the specimen.

The Novikov approximation is relevant under certain assumptions. The deformation prior to fracture is assumed to be purely elastic in the core of the specimen likewise in the fragment bounded between the first fracture plane and the free surface. The specimen is assumed to undergo 1D longitudinal stress only, dispersion effects are neglected. In addition, a linear response is supposed prior the tensile stress peak, and the compressive and tensile Young's moduli are supposed to be equal (Forquin and Lukic 2018).

Evaluation of the strain rate during tensile loading Gluing strain-gauges on an ice surface is challenging, especially in these experimental conditions where each second matters. The strain rate is estimated by means of elastic numerical simulations that are performed with the software ABAQUS-explicit. The material velocity profile of the free surface of each test (red curve in Figure 4a) is converted into an elastic profile (black curve in Figure 4a). This is achieved by keeping the slope of the tensile phase (that follow the maximum value of particle velocity profile) before the expected occurrence of spalling fracture characterized by the velocity rebound. By using the equation 1, a corresponding stress can be computed from the material velocity at a given time t. This stress profile is used as a loading pulse in the numerical simulations. The exact density and dimensions of each specimen was used for each computation. Figure 4b shows the type of curve obtained from the simulation to evaluate the strain rate in the tensile phase prior failure. For each test, the values are extracted from the results of the numerical simulation at the approximate location of the first appearance of cracks, thanks to the image sequence filmed during the test. The curve is valid up to the spall strength identified with equation 1. To get the minimum, maximum and mean value of the strain rate, the authors considered the stress interval which begins with the tensile phase (σ > 0) and ends with the ultimate spall strength measured (see gray zone in Figure 4b).

Experimental indicators of test validity

Different indicators were considered to assess the quality of each test. As the major risk is the initiation of cracks due to compressive loading, the images of the UHS camera were carefully analyzed in order to detect any compressive damage. The post-mortem specimen part near the ice-bar interface is also checked with naked eyes, when specimens were fragmented in few pieces.

Another source of error is the quality of the interfaces between (i) the aluminium insert and the specimen and (ii) the incident bar and the aluminium insert. For (i), the presence of water due to premature melting of the ice is possible. For (ii), the risk is a slight orientation mismatch between the bar and the insert, an alignment defect could lead to the generation of a moment at the interface. In both cases, although the specimen is still undergoing compression and tension, the input stress is not completely transmitted. The procedure used here to quantify the quality of these interfaces is the same as the one described in [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF]. The experimental ratio of the transmitted energy with the incident energy α exp is compared with a theoretical value α 0 function of the bar and specimen impedances. The quality of the interfaces is assumed to be satisfying when the ratio α exp /α 0 is close to 1. The ratios are presented in Table 2 for every succesful spalling test.

Results

2D characterization of the microstructure

The porosity being the parameter we focus on, we took care to provide specimens characterized by similar microstructures and crystallographic textures. Examples of thin sections analyzed with AITA are presented in Figure 5. We verified that the textures are isotropic and that grains are rather equiaxed. Grain areas have been measured by contour extraction and morphological tools from the orientation color-coded images obtained with AITA. The mean grain sizes in both microstructures range between 1 and 2 mm. This analysis shows that no significant difference is observed between the LP and HP microstructures and texture properties.

3D characterization of the microstructure with microCT

The low porosity specimens scanned for this study are LP10, LP11, and LP12, and the high porosity ones are HP12, HP13 and HP14. Figure 6 shows the distributions of porosity size and geometry for both microstructures as a function of a porosity equivalent radius. This equivalent radius is defined as the radius of a sphere whose volume is the one of the porosity. The coefficient of sphericity Ψ is computed as

Ψ = π 1/3 (6V p ) 2/3 A p (2)
with V p and A p the volume and the surface of the ideal ellipsoid fitting the porosity. The technique described in [START_REF] Ikeda | Three-dimensional study on the interconnection and shape of crystals in a graphic granite by x-ray ct and image analysis[END_REF] was applied to recover the length of the principal axes.

The main difference between the two microstructures is the presence of some large spherical porosities in the HP specimens, which equivalent radii exceed 0.3 mm. These large porosities are likely to exist prior to ice growth in the ice slurry mixture of HP specimens. Smaller porosities take random ellipsoid shapes and their formation is probably related to air trapped in the water. In the following, porosities will be splited into two populations : the population A (large spherical porosities) that only exist in HP specimens and the population B (small porosities with random ellipsoidal shapes), observed in both microstructures. Note that for a scan at a given resolution, the uncertainty on porosity size and shape increases as the porosity size decreases. However scans performed at higher resolutions (not presented here) confirmed the random shape feature associated with population B.

Tensile strength measurements

The specimens LP12 and HP14 failed during the compression phase and were thus dismissed. which are new tests. The strain rates range between 24 and 112 s -1 and between 41 and 120 s -1

for HP and LP specimens respectively. The measured spalling strengths, i.e. tensile strengths, vary between 0.8 to 3.0 M P a and from 1.9 to 5.3 M P a in the considered range of strain rate for HP and LP specimens, respectively.

The results presented in Figure 7 highlight an increase of the tensile strength with strain rate. A strength weakening with increasing porosity is also observable, LP ice appearing almost twice stronger than HP ice for the highest strain rates. Few tests on HP specimens exceed a strain rate of 80 s -1 as these specimens are more likely to fail in compression at high loading rates. Overall it is difficult for both microstructures to reach strain rates higher than 120 s -1 Spec Id V p (m.s -1 ) C ice (m.s -1 ) σ spall (M P a) ε (s

Fragmentation analysis from UHS camera

The UHS camera allowed to observe the crack propagation in the volume of the specimen during each test. Although a qualitative piece of information, it enables to distinguish two main scenarios as a function of the strain rate. At low strain rates the ice experiences a single fragmentation occurring randomly in the volume loaded in tension as it can be observed in Figures 8a and9a. At higher strain-rates the specimens undergo intense multiple fragmentations.

In Figures 8b and9b one can see several cracks oriented perpendicularly to the specimen axis expending in an initially restricted zone (white dashed-line rectangle). In the next steps of the test, this zone of damage spreads out toward the bar side of the specimens as observed on the last images. Finally, the higher the strain rate, the higher the crack density. However the quality of the images did not allow to find significant variations of the fragmentation pattern between LP and HP specimens.

Fragmentation analysis from AITA measurements

After spalling tests, post-mortem specimens were first scanned with the microCT (see section 3.6) and then brought back in cold rooms (-15°C) to perform thin sections and analyze the cracked zones by using the Automatic Ice Texture Analyser. Areas of interest were selected around the fracture planes which could be located by eye. As described in section 2.2, 0.3 mm thick thin sections were made but a great care was taken not to create additional cracks during the operation. Pictures of the post-mortem specimens are shown in Figures 10 and11, together with the corresponding thin sections analyzed with AITA. The cracks being very thin and therefore hardly visible on the pictures, there were manually highlighted by white lines added on the images. For specimens that fractured into two distinct fragments, a small gap was left between the two parts during the manufacturing of the thin sections (see Figures 10b and11b).

Although one main plane of fracture is always observable, numerous additional cracks seem to have been triggered during the tests, which orientations are roughly perpendicular to the specimen principal axis. In each thin section a branching phenomenon or cracks coalescence can be seen, especially in the LP10 specimen. No clear evidence appears in our observations about a likely influence of the microstructure in the crack junction/separation as no cracks follow the grain boundaries and no distinct direction shift could be observed at a triple junction. However, in the analyzed HP microstructures, the cracks seem to follow a route through the largest porosities or to be trigerred from these porosities. The crack tip is generally located in a porosity, at least on the 2D images and for cracks not crossing the entire specimen. These observations have to be considered with caution considering the high density of large porosities in the volume and the fact that these images provide only 2D information. Regarding LP specimens, no evidence about some relationship between porosities and crack initiation and propagation could be established, due to a too low spatial resolution of the AITA analysis and the high density of small pores.

Unfortunately, the measurement chains were not successful for LP10 and HP12 : it was not possible to process these tests to get the spalling strength. Nevertheless, they both experienced tension during the test and UHS camera analysis reveals that no compression fractures occurred.

Consequently their fragmentation pattern can still be presented in this paper as we consider they are representative of the micro-scale processes at play. 3.6 Fragmentation analysis from micro-CT measurements LP10, LP11, HP12 and HP13 specimens were scanned within a few hours following the spalling tests, using the set-up and conditions described in section 2.3. The intense fragmentation during the spalling tests of LP12 and HP14 specimens prevented from carrying them to the micro-CT device. LP11 and HP13 specimens fractured into two pieces, fragments were put together back by taking care of a good match between them prior to scanning. We can expect some cracks healed between the spalling test and the micro-CT scans, as commonly observed when ice is subjected to a temperature gradient [START_REF] Colbeck | Theory of microfracture healing in ice[END_REF].

Examples of microCT images of cracked zones are presented in Figures 12 and13. Except for fracture planes separating two fragments, the crack thickness appears not to exceed several microns. In addition, the grey values associated to crack volume lie in the ice value range, as shown on images (1) and (2) of Figure 12a, where impulse noise makes difficult or impossible to isolate the cracks. Consequently only the main fracture planes were efficiently identified. To do so, digital image correlation has been performed with SPAM on HP specimens by using the initial volumes scanned prior to spalling test and the fragmented volumes analyzed post-test.

The transformation matrix from DIC treatment allowed to adjust the position of the two volumes. The only difference between the two scanned volumes being the fragmentation pattern, the largest cracks could be identified by substracting the two 3D images. The software SPAM gives access to the exact position of each voxel in the volume, porosities in contact with the different fracture planes could thus be collected. Results are shown on images (2) and (3) of Figures 13a and13b. A simple thresholding method was applied for LP11 specimen to isolate the main fracture plane.

The crack observed in the LP11 specimen (Figure 12b) is almost perpendicular to the tensile loading direction, with no noticeable direction shift, and covers the entire specimen thickness.

The same pattern is observable on 2D images obtained with micro-CT for the LP20 specimen.

The situation is different for the fracture plane of specimen HP12 where the crack, although approximately perpendicular, is more tortuous and eventually stops before crossing the total thickness. Two cracks could be isolated in the HP13 specimen, one perpendicular to the speci-men axis and another oriented at around 30 -40°from this axis. The junction between these cracks occurred nearby the specimen surface. From qualitative observations, the crack surfaces seem to be slightly rougher in the HP microstructures than in the LP microstructures.

As for the 2D analyses performed in section 3.5, we can hardly conclude on a clear influence of porosity on crack initiation and propagation. However porosities were detected on the surface of each crack in every specimen analyzed from microCT 3D reconstructions.

Discussion

Strain-rate dependency of ice dynamic tensile strength

Results shown on Figure 7 evidence a strain-rate sensitivity of the dynamic tensile strength of ice, as already shown by [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF] for the microstructure with a low porosity. This strain-rate hardening is a common feature found in many other brittle materials, such as concrete, ceramics, or rocks [START_REF] Cho | Strain-rate dependency of the dynamic tensile strength of rock[END_REF][START_REF] Schuler | Spall experiments for the measurement of the tensile strength and fracture energy of concrete at high strain rates[END_REF]Zinszner et al., 2015;[START_REF] Saadati | On the tensile strength of granite at high strain rates considering the influence from preexisting cracks[END_REF]. Under quasi-static sollicitations, ice strength has been shown to be strain-rate insensitive and is rather subjected to microstructural property dependency [START_REF] Schulson | Creep and fracture of ice[END_REF][START_REF] Schulson | Brittle failure of ice[END_REF]. Based on results obtained from direct tensile tests and bending tests in the literature [START_REF] Petrovic | Review mechanical properties of ice and snow[END_REF][START_REF] Schulson | Creep and fracture of ice[END_REF][START_REF] Timco | A review of the engineering properties of sea ice[END_REF] , together with the results presented here, the transition between a strain-rate insensitive and a strain-rate sensitive response seems to occur approximately between 10 -1 s -1 and 10 1 s -1 . This transition phenomenon exists in many other brittle materials that show a probabilist behavior at low strain-rates and a deterministic behavior at higher rates of loading [START_REF] Hild | On the probabilistic-deterministic transition involved in a fragmentation process of brittle materials[END_REF][START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF]. Despite the narrow strain-rate range covered here (24 s -1 to 120 s -1 ), polycrystalline ice appears to follow the same trend, as the dispersion of tensile strength associated with spalling tests appears much lower than the one observed in the quasi-static regime [START_REF] Timco | Flexural strength equation for sea ice[END_REF].

To explain this macroscopic behavior, a point of view at a microscopic scale can be used. Indeed, microstructural defects (such as porosities, grain boundaries, micro-cracks, etc) are frequently considered as responsible for crack triggering in brittle materials under tension. The microscopic stress required to activate a critical defect is a complex function of the defect nature, size, orientation, etc... [START_REF] Jayatilaka | Statistical approach to brittle fracture[END_REF]. Under quasi-static conditions, a single crack is likely to be responsible for the complete specimen failure. In the dynamic range, brittle materials undergo a multiple fragmentation, as observed on ice during spalling tests (Section 3.4) with a crack density increasing with strain rate. [START_REF] Denoual | A damage model for the dynamic fragmentation of brittle solids[END_REF] and [START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF] introduced the concept of "critical defect obscuration" and "local weakest link hypothesis" to describe the fragmentation process in brittle solids and to predict the crack density and the tensile strength dependency with the applied strain rate. The theory lies on the growth of obscuration zones which correspond to areas in which stress-release waves develops due to unstable cracks activated from the non-obscured critical defects. At low strain-rates, damage propagates to the full specimen prior to local stress increase, preventing any additional crack triggering. At high strain-rate, the limited crack speed makes possible a local stress increase, leading to the activation of a large number of cracks that propagate in small zones up to crack coalescence. Only when damaged volumes link up will the complete fragmentation of the material occur, which results into a higher macroscopic strength. As a consequence, crack density and strength is expected to increase with strain-rate.

The observations performed here on polycrystalline ice are in agreement with [START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF] approach. Indeed, the high speed camera observations reveal an increase in the number of failure planes with strain rate (see Figures 8 and9). Cracks are approximately perpendicular to the loading direction, meaning that they are mainly opening in mode I as a result of a brittle response to the tensile loading.

3D images of post-mortem specimens (Figures 12b, 13a and 13b) reveal rough and irregular profiles of crack at the microstructure scale, while the linear elastic fracture mechanics theory would predict straight cracks perpendicular to the maximum tensile stress, as long as the cracks do not interact with each other. On top of the impact of porosity on the crack propagation routes discussed in Section 4.2, the crack roughness could result from the coalescence of several small cracks. Although the limitations of our observation methods (AITA and microCT) and possible microcrack proofing, prevent from a quantitative evaluation of crack density, the observation of a relatively high number of small cracks in the vicinity of the main fracture plane would be consistent with the former hypothesis. Furthermore, would a single crack be responsible for the specimen failure, the failure process would take the minimum time for the crack to propagate through the specimen, that can be estimated at around 20 µs (equal to r spec /0.38C ice , 0.38C ice being the supposed crack speed Ref) for specimen of radius 22.5 mm. In the case of specimen LP11, for instance, the time interval in the tensile phase to reach failure (roughly equal to σ spall /E ε) was about 9 µs, that is about twice shorter than the time for a crack to propagate from the specimen axis to its outer surface.

Based on these observations, we can hypothesise that the pullback velocity measured by the laser interferometer on the free surface of the specimen is indeed the result of the growth and interaction of several cracks, very likely triggered on critical defects that are supposed to be the porosities, and that the coalescence results into a macroscopic fracture plane.

Porosity effects on ice dynamic tensile strength

The strain-rate effect discussed above, although noticeable for both microstructures, is less pronounced for the HP microstructure. Both LP and HP microstructures have been designed to be similar in terms of grain size and shape, and crystallographic orientation, but to present two different porosities. The main difference between the two microstructures come from the presence, in the HP specimens, of large spherical porosities (population A). We therefore make the hypothesis that the difference observed in dynamic tensile strength between the two types of specimens arises, in a direct or indirect way, from the role of porosities. Porosities are microstructure defects and therefore potential areas of stress concentration during tensile loading.

Two processes could be involved, namely initiation of new cracks or/and the influence of porosities on crack propagation.

Crack initiation

Several studies point out a link between the size of a microstructural defect and a corresponding critical stress for crack nucleation. [START_REF] Liu | Influence of porosity and pore size on the compressive strength of porous hydroxyapatite ceramic[END_REF] showed that increasing the pore size for a given porosity induced a decrease in the compressive strength of porous ceramics. Chao et al. 1992 evidenced that the fracture strength distribution in sintered silicon nitride under tensile loading could be predicted from the pore size distributions. Recently, Forquin et al. (2019a) hypothesized that the porosities population found in an ultra-high performance concrete, a ceramic and porous ice could be considered to model single and multiple fragmentation properties of these materials.

Under dynamic loadings, as described in the DFH obscuration model [START_REF] Denoual | A damage model for the dynamic fragmentation of brittle solids[END_REF][START_REF] Forquin | A probabilistic damage model of the dynamic fragmentation process in brittle materials[END_REF], the differences observed in the dynamic responses of two materials having distincts microstructural properties would arise from the activation of different defect populations. In this study, if we assume that the porosities are the only critical defects of the microstructures considered and that the threshold stress for crack triggering is depending on the pore size, the porosity weakening effect could be due to a premature fragmentation in HP specimens. The porosities belonging to population A (present only in HP specimens) would initiate cracking phenomenoms at lower stresses than porosities from population B (present in both types of microstructures). At very high strain-rates (not reached here) and if the aforementioned hypothesis are still valid, one could expect similar dynamic behavior from LP and HP specimens as the pore size distributions for small porosities tend to be the same in both microstructures.

Although the 2D or 3D analyses of post-mortem specimens presented here are not accurate enough to clearly identify the role of porosities in crack triggering, we observed a large number of porosities from population A located along cracks in HP specimens. In addition, porosities from population B adjacent to cracks in LP specimens were also detected on the microCT images (see for instance the image 2 of Figure 12a) . On top of that, cracks propagate through the grains (see Figures 5a and5b) implying that grain boundaries or at a triple junction are not major initiation areas.

Crack propagation

As shown previously (Section 3.4), and as usually observed for quasi-brittle materials, the crack density is increasing with strain-rates. The main explanation comes from the limited crack velocity that restricts the growth of obscuration volumes making possible the activation of more cracks on non-obscured critical defects. However, under quasi-static loadings or at moderate strain-rates when the material is not highly fragmented (as the ones undergone by LP10, LP11, HP12 and HP13 for instance), crack propagation could be dependent on the presence of microstructural defects. [START_REF] Renard | 3d imaging of fracture propagation using synchrotron x-ray microtomography[END_REF] showed that mechanical heterogenities (such as pores and grains) in rocks may affect a fracture propagation by acting on the stress field near a crack tip under quasi-static loading. They observed an attraction phenomenom from porosities on the final crack path hence a subsequent amplitude of its out-of-plane fluctuations. [START_REF] Chen | Effect of pores on crack propagation behavior for porous si3n4 ceramics[END_REF] investigated the effect of pores on the stress-intensity factors of the crack tips in porous ceramics, by using the J-integral numerical method. Pores in front of the propagating cracks was found to promote crack propagation by enhancing the stress intensity factor of the crack tip. For ice material, [START_REF] Smith | The fracture toughness of porous ice with and without particles[END_REF]

Conclusion

Following on the work of [START_REF] Saletti | A study of the mechanical response of polycrystalline ice subjected to dynamic tension loading using the spalling test technique[END_REF], we performed spalling tests on polycrystalline ice.

Specimens with two different levels of porosity were considered in order to study the porosity effect on the dynamic response of ice under tensile loading. Fragmentation processes were also investigated on post-mortem specimens by means of an Automatic Ice Texture Analyser (AITA) and a micro-Tomograph (TOMOCOLD). A strain-rate hardening of the tensile strength and the crack density have been observed for both microstructures over the range 24 s -1 to 120 s -1 , as expected for a material exhibiting a brittle behavior. However, porosity seems to weaken the ice tensile strength, the strain-rate influence being less marked with highly porous ice. The presence of large spherical porosities in highly porous specimens is thought to be responsible of the porosity weakening observed, as no additional differences could be detected between the two microstructures. The role of these porosities has been discussed in term of crack initiation dependent material model for spherical ice impact simulation. International Journal of Impact Engineering, 57:43-54.

Wilson, C. J., Russell-Head, D. S., and Sim, H. M. (2003). The application of an automated fabric analyzer system to the textural evolution of folded ice layers in shear zones. Annals of Glaciology, 37:7-17.

Wu, X. and Prakash, V. (2015). Dynamic strength of distill water and lake water ice at high strain rates. International Journal of Impact Engineering, 76:155-165.

Zinszner, J., Forquin, P., and Rossiquet, G. (2015). Experimental and numerical analysis of the dynamic fragmentation in a sic ceramic under impact. International Journal of Impact Engineering, 76:9-19.

Figure 1 :Figure 2 :

 12 Figure 1: Slice of HP microstructure perpendicular to the specimen axis: (a) 8 bits image (b) Binary image (c) Probability Density Function of voxel grey levels

Figure 3 :

 3 Figure 3: Scheme of the spalling test set-up used in the experiments, from Saletti et al. (2019)

Figure 4 :

 4 Figure 4: (a) Rebuilt of the rear-face velocity to reproduce an virtual elastic loading in numerical simulations. (b) Interval of data taken into account to compute the mean strain-rate of a test (from Saletti et al. (2019))

Figure 5 :

 5 Figure 5: (a) and (b) Microstructures represented colour-coded with the [0001] crystallographic axis (c-axis) orientation of LP and HP specimens respectively, as measured with the Automatic Ice Texture Analyzer from thin sections.

Figure 6 :

 6 Figure 6: (a) porosity size distribution of LP11 (blue) and HP13 (red) specimens according to the porosity equivalent radius. Sphericity coefficient of each porosity for (b) LP and (c) HP specimens. The black dotted lines delimit the population A and B

Figure 7 :

 7 Figure 7: Tensile strength as a function of the strain rate. The displayed intervals on the curve correspond to the minimum and maximum values of strain rate measured during the tensile phase according to the elastic simulations. The marker (in between the intervals) corresponds to the mean values of the determined strain rates

Figure 8 :

 8 Figure 8: Fracture in LP specimens for two different strain rates.

Figure 9 :

 9 Figure 9: Fracture in HP specimens for two different strain rates.

Figure 10 :

 10 Figure 10: Post-spalling pictures and orientation color-coded microstructures of the cracked zones for two LP specimens. White lines on thin sections are manually added to make visible the crack network.

Figure 11 :

 11 Figure 11: Post-spalling pictures and orientation color-coded microstructures of the cracked zones for two HP specimens. White lines on thin sections are manually added to make visible the crack network.

Figure 12 :

 12 Figure 12: Observation of crack areas from microCT scans. a) specimen LP10 : (1) 16 bits 2D image of the crack area, (2) Focus on the crack path. b) specimen LP11 : (1) 16 bits 2D image of the crack area, (2) and (3) 3D crack visualisation according to XZ and YZ planes respectively.

Figure 13 :

 13 Figure 13: a) and (b): (1) 16 bits image of cracked zone, (2) and (3) 3D crack visualisation according to XZ and YZ planes respectively. The porosities in contact with crack networks are shown in white. Figures en cours de modification (suppression du bruit et amélioration du contraste pores/fissures)

  experimentally established a porosity weakening of ice fracture toughness, implying porosity would facilitate crack propagation. Here, rough and wavy crack paths described in section 3.6 tell us about a likely role of porosity on crack propagation prior to failure. The presence of large spherical porosities on the crack path (Figures11 and 13) could illustrate how porosities would distord the crack propagation resulting in the roughness and out-of-plane fluctuations observed on crack surfaces of HP specimens. Also, the redistribution of the stress-field ahead of a crack tip could potentially activate new micro-cracks on porosities into the vicinity of the crack (Ref). Based on the work of[START_REF] Smith | The fracture toughness of porous ice with and without particles[END_REF] and regarding the high density of porosities from population A, we can expect significantly lower fracture toughness in HP specimens compared to LP ones. Thus, micro-cracks coalescence is probably more efficient in the highly porous specimens, hence a faster damage propagation in the latters inducing lower tensile strength to failure.

Table 1 :

 1 Dimensions and densities of the specimens presented in this study. The calculation of the density using the mass and volume of the specimen delivers a typical uncertainty of individual values about ± 5 kg.m -3 .

	Spec Id Length (mm) Diameter (mm) Density (kg/m 3 )
	HP01	119.7	44.9	857
	HP02	120.2	44.9	840
	HP03	120.3	44.9	847
	HP04	119.6	44.9	818
	HP05	119.5	45.1	834
	HP06	119.7	45.1	844
	HP07	118.0	45.0	844
	HP08	119.8	45.2	834
	HP09	119.7	45.0	848
	HP10	120.0	44.9	843
	HP11	119.9	45.0	835
	HP12	119.0	45.0	833
	HP13	120.9	45.0	840
	HP14	120.6	45.6	805
	LP01	119.7	45.1	906
	LP02	119.9	45.1	917
	LP03	120.1	45.1	921
	LP04	119.9	45.0	908
	LP05	119.6	45.1	912
	LP06	119.2	45.0	906
	LP07	120.0	45.3	910
	LP08	120.6	45.2	918
	LP09	120.0	45.0	910
	LP10	119.0	44.9	908
	LP11	119.5	45.0	914
	LP12	110.7	44.8	908

Table 2 :

 2 Projectile velocity V p , acoustic wave velocity into the specimen C ice , spalling strength to failure σ spall and calculated strain rate in the tensile phase ε for LP and HP specimens, as obtained from the treatment of laser and strain-gauges signals. α exp /α 0 is the ratio between the experimental and theoretical transmitted energy

	-1 ) α exp /α 0

crack from a porosity is function of the porosity size, leading to a premature activation of the large spherical porosities in highly porous ice. This theory is supported by the high density of porosities located along crack paths. Rough crack surfaces observed in 2D and 3D analysis also show that porosities potentially accelerated the crack propagation and crack coalescence.

All these observations tend to confirm the role of porosity as a key parameter to describe the dynamic behavior of ice subjected to tensile loading.

Aknowledgements

The present work was developed in the framework of the Brittle's Codex chair (Fondation UGA) and thanks to the support from the CEA-CESTA and from the Labex OSUG@2020 (ANR 10 LABEX 56). The provided support and fundings are gratefully acknowledged by the authors.


Franck Dary
email: franck.dary@lis-lab.fr

Alexis Nasr
email: alexis.nasr@lis-lab.fr

The Reading Machine: a Versatile Framework for Studying Incremental Parsing Strategies

The Reading Machine, is a parsing framework that takes as input raw text and performs six standard NLP tasks: tokenization, POS tagging, morphological analysis, lemmatization, dependency parsing and sentence segmentation. It is built upon Transition Based Parsing, and allows implementing a large number of parsing configurations, among which a fully incremental one. Three case studies are presented to highlight the versatility of the framework. The first one explores whether an incremental parser is able to take into account top-down dependencies (i.e. the influence of high level decisions on low level ones), the second compares the performances of an incremental and a pipe-line architecture and the third quantifies the impact of the right context on the predictions made by an incremental parser.

Introduction

Syntactic parsers usually take as input text that has been processed at several levels. It has generally been segmented in sentences, tokenized, POS tagged, and possibly lemmatized and morphologically analyzed. All such steps are realized by other NLP modules that are usually organized in a sequential pattern, called a pipe-line. The pipe-line imposes a rational order on the modules: word boundaries, for example, have to be determined before a word can be associated to a POS tag and syntactic parsing usually comes after POS tagging, for POS tags group words that have close syntactic properties.

The pipe-line architecture offers many advantages, among which, the independence of the modules that compose it. The only constraint for their inter-operability is the compatibility of their inputs and outputs. Once this constraint is verified, each module can be built on any kind of model considered more suitable for the task to perform. Besides, in a pipe-line architecture, every module narrows down the search space of the following modules: a parser, for example, does not have to consider different tokenization hypotheses nor different POS tags for a word. Considering all such decisions can lead to a combinatorial explosion problem and yields huge search spaces.

The pipe-line architecture nevertheless has its limits. It is well known that some low level decisions (made by early modules of the pipe-line) can benefit from high level ones (made by late modules). Some tokenization decisions, for example, can depend on the syntactic structure of the sentence to parse, such as complex prepositions in French, as noted by [START_REF] Nasr | Joint dependency parsing and multiword expression tokenisation[END_REF]. Likewise, sentence segmentation can depend on syntactic structures, especially when punctuation is absent or unreliable, such as in speech transcriptions. Such top down dependencies cannot be taken into account in a strict pipe-line architecture. But they are arguably less numerous than bottom up dependencies and this is the reason why the pipeline architecture usually yields good results. One aim of this paper is to propose a framework, called the Reading Machine (RM), that is flexible enough to define several patterns for combining different NLP modules and explore different ways to link decisions made by these modules. We use in this paper the RM framework to define and compare several non sequential machines that model top down dependencies.

There is another, less immediate, reason for studying non sequential architectures, in link with human cognition. Psycholinguistic studies have shown that human language processing is incremental, i.e., people do not wait to see the entire sentence before they start trying to understand it (see [START_REF] Keller | Cognitively plausible models of human language processing[END_REF] for more details). Such findings have developed interest in using NLP tools to implement cognitively-plausible models of hu-man sentence processing (see [START_REF] Hale | Models of human sentence comprehension in computational psycholinguistics[END_REF] for a review). Various "linking hypotheses" have been proposed to relate the models' intermediate states when parsing a given sentence to the behavior of human subjects trying to understand that same sentence. The RM offers a framework to investigate such linking hypotheses by defining machines that implement them and observe their behaviour on human data. In this perspective, the RM has already been used for predicting eye-movements during reading: different RM architectures have been compared on their ability to accurately predict fixation time (Dary et al., 2021a,b). In order to illustrate the kind of experiments that can be conducted in such a perspective, we will define and compare machines that model different perceptual fields and measure their influence on an incremental parsing process.

Technically, RM is an extension of the transitionbased parsing algorithm (TBP) [START_REF] Yamada | Statistical dependency analysis with support vector machines[END_REF][START_REF] Nivre | An efficient algorithm for projective dependency parsing[END_REF]. The reason for this choice is mainly that TBP implements an incremental parsing strategy [START_REF] Nivre | Algorithms for deterministic incremental dependency parsing[END_REF]. We propose to extend this model to define a complete incremental NLP parser that integrates six tasks: tokenization, POS tagging, morphological analysis, lemmatization, syntactic parsing and sentence segmentation. RM borrows from TBP the two key notions of Configurations and Actions (also called Transitions), as well as a greedy algorithm that performs syntactic parsing. We extend these notions by defining an enriched version of a configuration and a richer set of actions. All linguistic decisions, such as word and sentence boundaries detection, POS tagging, lemmatization and, of course, syntactic parsing are realized by actions that are predicted based on configurations. The RM takes as input raw text and greedily predicts a sequence of actions that perform the six tasks mentioned above.

Related Work

Solving the circular dependencies that exist between parsing and other pre-processing steps, is an active area of research in the parsing literature. The solution that has been mainly investigated consists in jointly performing syntactic parsing and other pre-parsing steps. If we restrict ourselves to recent approaches to dependency parsing, solutions have been proposed both for graph-based parsing [START_REF] Yan | A Graph-based Model for Joint Chinese Word Segmentation and Dependency Parsing[END_REF][START_REF] John Sy Lee | A discriminative model for joint morphological disambiguation and dependency parsing[END_REF][START_REF] Dat | An improved neural network model for joint POS tagging and dependency parsing[END_REF][START_REF] Nasr | Joint dependency parsing and multiword expression tokenisation[END_REF][START_REF] Li | Joint models for Chinese POS tagging and dependency parsing[END_REF][START_REF] Zhang | Randomized greedy inference for joint segmentation, POS tagging and dependency parsing[END_REF] and transition-based pars-ing [START_REF] Yoshikawa | Joint transition-based dependency parsing and disfluency detection for automatic speech recognition texts[END_REF][START_REF] Bohnet | A transitionbased system for joint part-of-speech tagging and labeled non-projective dependency parsing[END_REF][START_REF] Alberti | Improved transition-based parsing and tagging with neural networks[END_REF][START_REF] Hatori | Incremental joint approach to word segmentation, POS tagging, and dependency parsing in Chinese[END_REF][START_REF] Honnibal | Joint incremental disfluency detection and dependency parsing[END_REF][START_REF] Constant | A transition-based system for joint lexical and syntactic analysis[END_REF][START_REF] Kurita | Neural joint model for transition-based Chinese syntactic analysis[END_REF][START_REF] Hui Wan | Ibm research at the conll 2018 shared task on multilingual parsing[END_REF].

Solutions to this problem differ vastly for these two approaches, mainly because of the different parsing strategies they adopt. This is why we have decided to restrict ourselves to TBP based papers in the remainder of this section.

There have been many propositions to realize simultaneously several linguistic tasks in TBP. Both [START_REF] Bohnet | A transitionbased system for joint part-of-speech tagging and labeled non-projective dependency parsing[END_REF] and [START_REF] Alberti | Improved transition-based parsing and tagging with neural networks[END_REF], for example, show how a transition system can be extended and trained to jointly predict POS tags and the dependency tree, improving both the accuracy of tagging and parsing. These systems are not strictly incremental across the tasks they realize for they process text that has already been segmented in words and sentences. Besides, the text has been pre-tagged in order to limit the size of the search space.

The closest approach to ours is [START_REF] Kurita | Neural joint model for transition-based Chinese syntactic analysis[END_REF], which is based on the work of [START_REF] Hatori | Incremental joint approach to word segmentation, POS tagging, and dependency parsing in Chinese[END_REF]. The authors propose an extension of the arc-standard transition system that is able to perform a fully joint prediction of word segmentation, POS tagging and dependency parsing. Their system takes a queue of symbols as input, and process it in an incremental fashion, consuming one symbol at a time. They conducted their experiments on Chinese, and were the first to use a neural network architecture using both word and character based embeddings to achieve fully joint prediction of these three tasks. They showed that their joint architecture was competitive with a pipeline architecture for word segmentation and POS tagging, but fell short on parsing.

For their participation in the 2018 CoNLL Shared Task [START_REF] Daniel Zeman | CoNLL 2018 shared task: Multilingual parsing from raw text to universal dependencies[END_REF], [START_REF] Hui Wan | Ibm research at the conll 2018 shared task on multilingual parsing[END_REF] also defined an extension of TBP that is close to ours. It is based on the arc-standard system enriched with a swap transition [START_REF] Nivre | Non-projective dependency parsing in expected linear time[END_REF], and is able to jointly perform word segmentation, POS tagging, morphological tagging and dependency parsing. They showed that such a system could get better scores than the shared task's baseline, while still being quite far from the top scoring systems. Their paper focuses on low or even zero resources languages (what the shared task was mainly about), and did not test whether or not the joint prediction of multiple tasks was improving the performances.

Our model has the following characteristics that distinguishes it form the approaches cited above.

The RM performs simultaneously six NLP tasks with the notable inclusion of sentence segmentation which is almost always pre-processed in parsing systems.

The RM allows us to build a machine that is strictly incremental across the six tasks it realizes. There are two reasons for this choice. The first is theoretical, we are interested to know how much information is present in top-down dependencies and whether they can be captured in an incremental setup. The second is related to psycholinguistics: we believe that the definition of a fully incremental RM offers a useful model for simulating human behaviour during reading.

The RM is flexible enough to design machines that implement different strategies in order to compare them. We propose, in section 5, a high-level description format that allows us to define machines that differ on a specific dimension and study the effect of this dimension on the performances of the machines.

The Reading Machine

As mentioned in the introduction, the reading machine is an extension of the TBP 1 framework. The details of this algorithm are well known and do not need to be repeated here. We will only introduce the terms that are important for the rest of the paper.

TBP is an algorithm that predicts the dependency syntactic structure of sentences. This task can be viewed as selecting for each word w of a sentence its syntactic governor (another word w of the sentence) as well as its syntactic function f . A directed arc, referred to as a dependency, is built from w to w, labeled with function f . The graph built at the end of the parsing process is a tree. The TBP algorithm builds the dependency tree by scanning the sentence word by word, in reading order. At each step, an action, is predicted and applied to the current configuration of the parser and yields a new configuration. The prediction is realized by a classifier that takes as input a configuration and computes a score for every possible action. The parser makes use of a stack containing words that need to be linked to words yet undiscovered.

Four types of actions are defined: SHIFT, pushes the current word on the stack, REDUCE, pops the 1 Several sets of actions have been proposed in the literature, the one used here is known as Arc Eager. stack, LEFT l , creates a left dependency, labeled l, whose governor is the current word and dependent is top element of the stack and RIGHT l , which creates a right dependency, labeled l, whose dependent is the current word and governor is the top element of the stack.

SEG NO NO NO NO NO YES SYN DET SUB ROOT DET OBJ PCT GOV +1 +1 0 +1 -2 -3 LEM @ @ s@ @ @ @ MRF DEF SG P3S DEF SG - POS DET N V DET N
Before giving a precise definition of the RM, in section 3.1, we describe the directions in which the TBP has been extended.

Tapes: The RM has one input tape, which is a read tape and an arbitrary number of output tapes which are read/write tapes.

The input tape contains the text to parse. It is character based: each cell of the tape contains a character. The text has not been linguistically preprocessed: it has not been segmented into sentences nor into words. The current position of the reading head of the input tape is called the character index.

Output tapes are word based: each cell of a tape refers to a word of the input text. Output tapes are used to write the predictions made by the machine, typically one tape per type of prediction. These tapes are synchronized: at all times, the head is at the same position for all tapes. This position is called the word index.

Table 1 represents the tapes of a machine after processing the text The boy hits the ball. The machine has 7 output tapes and one input tape, represented at the bottom.

Sliding Window: The reading head of the input tape takes the form of a sliding window. It is centered on the cell of the tape pointed by the character index and has access to an arbitrary number of cells to the left and to the right of this cell.

States and Transitions: TBP can be seen as a single state machine, in contrast RM are multi-state machines. Every state, or set of states, is devoted to a specific linguistic task and is linked to a classifier. The linking between states and classifiers can range from a single classifier for all states to one classifier per state. States are deterministically linked to each other through transitions that are labelled with action labels. At each step, the classifier of the current state predicts the next action to perform. The action is applied on the configuration and the transition labeled with this action is traversed to reach another state.

Actions: RM actions encompass standard Arc Eager actions for parsing and new actions have been defined for performing the other tasks.

Word tagging tasks (POS tagging and morphological tagging) are realized through a single action: TAG L (t), which simply writes symbol t on tape L at the word index position. For example, action TAG POS (DET) tags the current word as a determiner.

It is not straightforward to cast lemmatization as a classification task, due to the large number of classes (potentially all the lemmas of a language). Besides, lemmatization is, to a large extent, regular. In order to capture this regularity, the classifier that realizes the lemmatization task predicts editing rules of the form s1@s2 where s1 is a suffix of the word to lemmatize and s2 the suffix of the lemma.2 When applied to a word w, such a rule strips off suffix s1 from w and appends s2, as in the following example apply(s@, hits) = hit.

The actions predicted by the tokenizer are of four types: ADD n adds the n next characters of the input tape to the current word and moves the character index n positions to the right, IGNORE ignores the current character (typically spaces) and moves the character index to the right, WORD marks the current word as complete and SPLIT w W action moves the character index |w| positions to the right and adds the word sequence W in the buffer. This last action is used to expand contractions such as don't → do not.

Programming an oracle function for actions IG-NORE, WORD and SPLIT is straightforward because there is no ambiguity on which is correct at any time. However, the choice of ADD n is ambiguous: if we consider that the 8 next characters on the input tape are "academic", we want to add them to the current word. This could be done using several action sequences, such as "ADD 8 ", "ADD 4 ,ADD 4 " or "ADD 2 ,ADD 3 ,ADD 3 ,". In our experiments, we chose to limit the size of ADD n to n=6 and to program the oracle so that it adds the largest number of characters at once. During training, the correct action sequence would then be: "ADD 6 ,ADD 2 " Sentence segmentation is realized by a binary action EOS(YES/NO) which tags the current word as the end of the current sentence, or not. Once the end of a sentence has been detected, the deepest element in the stack is marked as the root of the sentence and the potential remaining elements of the stack are attached to the root, before emptying the stack. The complete set of actions is reported in Table 2.

State Action Description

Formal Definition

A RM, as any formal automata, has an input alphabet Σ T , which is a set of characters, a set of states S, a transition function δ, an initial state s 0 and a set F of final states. It also has N output alphabets Σ 1 , . . . Σ N associated to its N output tapes. Transitions between states are labelled with actions. Moreover, each state is associated, via function γ, to a classifier, which maps configurations to actions, along with a score.

Formally, we define a RM as a tuple T = (Σ T , N, Σ, S, s 0 , A, K, γ, δ, F ). We develop below the elements of the machine that deserve more explanation.

-A is a set of actions. Each action can write a symbol on an output tape, move the character head or the word head either to the left or to the right and push or pop the stack (see Table 2). -K is a set of classifiers, described in section 3.3 -δ : S × A → S is a deterministic transition function, also called a Strategy. Given the current state and its associated classifier, the action selected by the classifier is performed and control jumps to the destination state of the transition. The strategy defines the order in which the predictions are made. For instance a strategy could force the lemmatization task to happen after the dependency parsing task. Two different strategies are described in section 5.

γ : S → K is a function that maps each state of the RM to a classifier. This mapping allows several states to share a single classifier which allows in turn jointly training several processes.

Configuration

Configurations for a RM M and a text T are defined as (S, T, c, β 1,N , w, σ, H), where: -S is the current state of M .

-T is the input tape c is the character index β 1,N is a collection of output tapes.

w is the word index σ is a stack of word indexes, its purpose is the same as the stack in TBP.

-H is the sequence of transitions that have been predicted till now.

The set of all configurations for text T is noted C T .

An initial configuration for a text T is defined as follows: (s 0 , T, 0, β, 0, [], []), where all tapes in β are empty.

An accept configuration is defined as (s ∈ F, T, n c , β, n w , [], H), where n c and n w are respectively the number of characters and words in T .

Classifier

The classifiers that constitute the set K are functions that map a configuration to actions and scores.

The classifiers are independent of each other but they all take as input a configuration which contains all aspects of the current state of the RM, in particular, the content of all the tapes of the RM. The tapes contain all predictions already realized. Each classifier defines its own Feature Function which extracts from the input configuration all features considered useful for the type of prediction it realizes. We will not delve into the set of all possible features, let us just mention that most of them allow to access the content of a specific cell of a specific tape.

Training the RM

The training process of a RM is close to TBP training. It starts with a dependency tree that is decomposed into a sequence of (state, configuration, action) triples, by a static oracle. The difference with TBP is that the set of actions is considerably larger since it encompasses actions for all six tasks. This sequence is used to train the classifiers: every classifier receives examples corresponding to the states it is related to. The RM is trained using only correct examples, predicted by the oracle. In order to increase the robustness to error propagation, we use a dynamic oracle [START_REF] Goldberg | A dynamic oracle for arc-eager dependency parsing[END_REF] to extract a new set of training examples where the actions applied were the one predicted by the network. 3 The RM is therefore trained to predict the next action given potentially incorrect configurations.

Four epochs are devoted to the first part of the training process, followed by 26 more epochs in dynamic oracle regime. 4 At each epoch, the machine is used to decode the development set, and is saved if its score (mean score across all 6 levels) is the best so far. We used cross entropy as a loss function and Adagrad [START_REF] Duchi | Adaptive subgradient methods for online learning and stochastic optimization[END_REF] for optimization.

The classifiers used to predict the actions can be decomposed into three parts: the first part is devoted to feature extraction, it is composed of several encoders applied to different parts of the RM configuration. The output of these encoders are then concatenated yielding a dense vector representation of the current configuration, to which we apply a dropout of 0.5 and feed it into a Multi Layer Perceptron (MLP) composed of 2 hidden layers of respective sizes 3200 and 1600 with dropout 0.4 and ReLU activation. The output of the MLP is then fed into a decision layer, producting a probability distribution over the possible actions. The most probable action is predicted then applied to the configuration. A classifier can have up to 6 decision layers, one for every task. A schematic representation of the classifier structure can be found in They take as input a configuration and predict an action for up to 6 tasks. Figure 1.

The most complex part of the classifier is the transformation of the configuration into a vector: the input of the MLP. Depending of its feature function, the classifier extracts from the configuration elements that can be of different natures: the current state of the RM, tags or words read from the tapes, characters read from the input tape, previous action present in the history and words from the stack. All these elements are fed to specific Bi-LSTM that produce contextual representations, as in [START_REF] Kiperwasser | Simple and accurate dependency parsing using bidirectional LSTM feature representations[END_REF], that are in turn concatenated in the MLP input layer.

All feature values are represented by trainable embeddings of size 128. These embeddings are randomly initialized, except for word embeddings that are pretrained5 exclusively on the train set, in order to produce an embedding for unknown words (using words occurring only once in the train set).

The Bi-LSTM that take sequences of these embeddings as input are made of only one layer of size 64.

Designing Reading Machines

The precise definition of RM, introduced in section 3, allows us to design a large number of machines. Every machine is defined by a large number of features and comparing machines is not always easy. In this section we define a more abstract description that is based on four high-level features, and define seven machines that are compared in section 6. We first describe the four high-level features then give a description of the machines.

Strategy

As mentioned in section 3, the strategy of a RM is the structure of the underlying automaton: its number of states and transition function. A strategy dictates the order in which the predictions are made. Two strategies: INCR and SEQ, are defined, they are represented in Figure 2. The actions that label the transitions have been omitted for readability reasons.

The main difference between the two strategies comes from the loops on all states of the SEQ strategy. These loops model the sequential behaviour of the RM: the whole text is processed at a given level before switching to the upper level. In contrast, the INCR strategy processes a word at a given level then performs a prediction at the next higher level for the same word. This difference can be illustrated in the way the matrix of Table 1 is filled: the SEQ machine fills it line by line, bottom-up, while the INCR machine fills it column by column, from left to right.

Feature Span

The Feature Span of a machine specifies the part of the tapes that are accessible to each classifier in order to make a prediction. Three feature spans have been defined, they are represented in Figure 3. Each of the three rectangles represents, schematically, the tapes of an RM, as in Table 1. The black square corresponds to the current prediction and the hatched area to the content of the tapes available for the current prediction. The past-low (PA-LO) feature span only sees the tapes content for the lower level past predictions. Future-low (FU-LO) sees the past, current and future predictions for lower levels.

PAST HIGH (PA-HI) FUTURE LOW (FU-LO)

PAST LOW (PA-LO)

Figure 3: Three feature spans: the black square is the current prediction and the hatched area, the available features.

Past-high (PA-HI) have access to low, current and high-level predictions from the past.

In the PA-HI configuration, when the tagger, for example, has to select the POS tag of a word, it has access to the predictions made by all the modules, including the parser, for preceding words. The PA-HI feature span therefore offers an explicit way to model top down dependencies.

Number of Classifiers

As mentioned above, several states of a machine can share a single classifier to predict the actions associated to these states. The sharing of a single classifier by several states amounts to perform multi-task training, which "uses the domain information contained in the training signals of related tasks as an inductive bias. It does this by learning tasks in parallel while using a shared representation; what is learned for each task can help other tasks be learned better" [START_REF] Caruana | Multitask learning[END_REF].

In our case, when a single classifier is used, for example, to perform both POS tagging and parsing, the representation of a configuration built by this classifier is obtained by optimizing both tasks. Decisions made by the parser can therefore implicitly influence the tagger. The Number of Classifiers is, with the Feature Span, the two ways that will be tested to take into account top down dependencies.

Two extreme choices have been made with respect to this dimension, in the first one, all states share a single classifier while in the second each state defines its own classifier, yielding two different values: 1 and 6.

Window Span

The Window Span of a machine is simply the span of the sliding window that gives access to the text. A window span is defined by a pair of integers that indicate how many characters, to the left and to the right of the character index, are accessible. The window span corresponds to the sliding window introduced by [START_REF] George | The span of the effective stimulus during a fixation in reading[END_REF] used to model the perceptual span of a human reader.

Four different window spans have been defined: [-5,2], [-5, 5], [-5, 10] and [-5, 15]. We followed [START_REF] George | Asymmetry of the perceptual span in reading[END_REF] in choosing asymmetric windows.

Seven Machines

Given the four dimensions defined above and the number of values per dimension, a total of 48 different machines can be defined. We have selected, among these, seven machines that can be grouped in four subsets, as shown in Table 3. Machines in a subset generally differ from one another for a single dimension, the exception are the two machines of the first subset. These four subsets correspond to the four experiments that are described in the following section. The letter in the first column of the table indicates identical machines. They have been given several names in order to ease the comparisons in section 6. The feature function of the classifiers of each of these machines can be found in table 4.

Experiments

The experiments presented in this section aim at exploring three directions. The first one is the modelling of top-down dependencies. We have introduced two means for taking into account such dependencies in a RM: joint prediction of several tasks, using a single classifier, and the feature span of the classifiers. The two first experiments aim at studying whether these two techniques allow to effectively model such dependencies. The second direction compares the sequential and the incremental strategies and measure how much information a parser gets from the knowledge of the next words Table Features used in our RM architecture. "b.i" stands for the word at position word index+i in the buffer and "s.i" for the i th topmost word on the stack. Additional suffixes ".0" and ".-1" refer respectively to the leftmost and rightmost dependent.

POS, lemma and morphological analysis. The third direction aims at measuring the effect of the window span on the performances of an incremental RM.

The machines realize six types of predictions: tokenization, part of speech tagging, lemmatization, morphological analysis, syntactic parsing and sentence segmentation. Each of these predictions are evaluated by a specific metric using the evaluation script of the CoNLL 2018 shared task [START_REF] Daniel Zeman | CoNLL 2018 shared task: Multilingual parsing from raw text to universal dependencies[END_REF]. Besides the task specific metrics, we report the Morphology-Aware Labeled Attachment Score (MLAS) which takes into account word segmentation, morphological and POS tagging as well as syntax, as described in [START_REF] Daniel Zeman | CoNLL 2018 shared task: Multilingual parsing from raw text to universal dependencies[END_REF]. The MLAS allows us to compare the general performances of two machines, while the task specific metrics allow for a finer comparison of these machines.

Experiments have been conducted on French6 data, using the GSD corpora of the Universal De-pendencies collection [START_REF] Daniel Zeman | Universal dependencies 2[END_REF] version 2.7. In the official distribution of this corpus, the train/dev/test split is of respective sizes 364,349/36,775/10,298 words. In preliminary experiments, we found out that the test split was way too small to meaningfully compare machines. That's why we decided to use 10 fold crossvalidation: we realized ten different 80%/10%/10% train/dev/test splits and trained ten copies of each of our machines on these splits. The ten test sets were then decoded by the corresponding copy of the machine and the predictions were concatenated. This technique allowed us to compare the machines on their predictions on a test set of 427,763 words. We tested the significance of our comparisons using paired bootstrap resampling7 [START_REF] Koehn | Statistical significance tests for machine translation evaluation[END_REF], and reported in our tables the corresponding p-value, estimating the probability that in a pair of models, the model that appear to perform better is in reality a worse model. Unfortunately, the resampling script we used (the one used in the CoNLL 2018 shared task) is not able to produce p-values for the task of sentence segmentation, that is why the corresponding cells in tables 5,6 and 7 are empty.

Wide vs Narrow Feature Span

This experiment aims at studying if past high level predictions can help current low level predictions, which is the explicit means we have proposed to model top-down dependencies. In order to test this hypothesis, we compare machines PA-LO and PA-HI. Both machines differ on their Feature Span. PA-HI has access to past high-level predictions while PA-LO does not.

The results, displayed in Table 5, show that PA-HI yields lower results than PA-LO. This is true for the general MLAS measure, as well as sentence segmentation and morphological tagging. The differences obtained by the two machines on the other tasks are not significant. Contrary to what we expected, using past high level predictions does not seem to increase the performances of low-level modules. We do not have for the moment an explanation for this result. It could be explained by the errors made by PA-HI on earlier predictions which, in turn, provoke errors on current word predictions.

Multi Task vs Mono Task

The aim of our second experiment is to test the second means we have proposed to model top-down

Window Span

Our last experiment aims to study the influence of the Window Span on the performances of an incremental machine. Four machines are compared: [-5,2], [-5,5], [-5,10], [-5,15]. The best MLAS results are obtained by machine [-5,10] which defines a look-ahead of 10 characters for its predictions. It is interesting to note that low values of look ahead has a dramatic effect on the performances. This is partly due to the metrics used in which tokenization errors provoke errors on higher level modules. As expected, we observe diminishing returns as we increase the Window Span to the right, and going to 15 characters slightly decreases performances. These results are in line with [START_REF] George | The span of the effective stimulus during a fixation in reading[END_REF] who determined experimentally that the span of the window for humans is about four characters to the left of the current character and twelve characters to the right.

Task [-5,2] [-5,5] [-5,10] [-5,15 This paper introduced a versatile parsing framework, called the Reading Machine, that allows us to compare incremental parsers that implement different parsing configurations. We illustrated this with two cases. In the first one, we compared different ways to take into account top down dependencies across six tasks. In the second, we compared the effect of the look-ahead on the parsing performances. This work will be extended in several directions. The first one concerns the analysis of the results obtained in our two first experiments. More investigation is needed to explain the reason why using past high level predictions cannot help low level current ones. Likewise, we would like to understand if the better results of multi task learning comes from the modelling of top down dependencies. Two means will be used in order to answer this question: probing and the development of (small) specialized test sets that focus on such phenomena.

The sequential machines that have been proposed are greedy: a local decision taken by a machine is never questioned even when contradicted by future events. This behaviour is not appealing from an NLP perspective nor from a psycholinguistic one. In order to tackle this problem, we will introduce in the Reading Machine a backtrack mechanism that can predict left movements leading to the re-analysis of a previously analyzed part of the text.

The third direction consists in evaluating the model against human experimental data. The Reading Machine has already been used to predict reading time. We will continue further in this direction and use the Reading Machine to predict saccades. The strategies implemented in the RM described in this paper completely specify the order in which predictions are made. We plan to relax this constraint and let the RM learn strategies that optimize its performances. A RM would have the ability to decide the order in which to perform some tasks (specifically, POS tagging, lemmatization and morphological analysis).

  Adds the n next symbols to b.0. TOK IGNORE Ignores the next symbol. TOK WORD Marks b.0 as complete. TOK SPLIT w W Consume symbol sequence w. Add word sequence W in buffer. POS, MRF TAG L (t) Writes tag t to b.0 on tape L. LEM s@s' b.0 lemma := form -s + s . LEM CASE ul b.0 lemma to upper/lower case. SYN REDUCE Pop the the stack. SYN SHIFT Push b.0 on the stack. SYN RIGHT l Adds arc (s.0,b.0,l). Push b.0 on the stack. SYN LEFT l Adds arc (b.0,s.0,l). Pop the stack. SEG EOS(Y/N) Mark b.0 as an end of sentence, set sentence root, attach orphans to root then empty stack.

Figure 1 :

 1 Figure 1: General structure of the classifiers of a RM.They take as input a configuration and predict an action for up to 6 tasks.

Figure 2 :

 2 Figure 2: Two RM strategies that correspond to the order of predictions. Above, the INCR strategy and below the SEQ strategy.

  Definition of the machines used in the experiments. The letter in the first column indicates identical machines. NC stands for Number of Classifiers.

  6 classifiers is different. The classifier corresponding to a given linguistic level will only have the features of PA-HI corresponding to this linguistic level and inferior levels. For example, the classifier corresponding to MRF will only access columns FORM,ID,POS,MRF for targets b.-3 b.-2 b.-1 b.0 and will not have the distance feature.[-5,2] Same as[-5,10] but with window[-5,2].[-5,5] Same as[-5,10] but with window[-5,5].[-5,15] Same as[-5,10] but with window[-5,15].

Table 1 :

 1 Input and output tapes of a RM after processing the text The boy hits the ball.

	PCT

Table 2 :

 2 Actions used in our RM architecture. b.0 stands for the current word and s.0 for the word on top of the stack.

Table 5 :

 5 Wide vs Narrow Feature Span dependencies: multi task prediction. Two machines are compared: C1 which uses a single classifier to predict all tasks and C6 which uses a specific classifier for every task. The results are reported in Table6. The table shows that C1 outperforms C6 on the MLAS metric: on average, a multi-task setup performs better than a mono-task one. C1 is significantly better than C6 for parsing, morphological and POS tagging. While the two machines are equivalent on the other tasks. These results show that predictions based on representations of the machine configurations that are optimised for all tasks are beneficial for all tasks. It is tempting to con-

	Task	PA-LO PA-HI p-value
	MLAS	77.70 77.30	0.014
	Seg	96.65 96.57
	LAS	86.88 86.77	0.193
	UAS	89.13 89.03	0.183
	Lemma 98.04 98.01	0.22
	UFeats	97.02 96.87	0.003
	UPOS	97.02 96.93	0.051
	Words	99.60 99.64	0.02

Table 6 :

 6 Multi Task vs Mono Task6.3 Sequential vs IncrementalIn this experiment, two machines are compared, SEQ, a sequential machine that implements a pipeline architecture, and INCR that implements an incremental architecture. These two machines differ on two dimensions, their strategy as well as their feature span. The aim of this experiment is to measure to which extend the information given to a parser by the next words low level analysis (POS tagging, morphological tagging and lemmatization) help a parser. The SEQ machine implements a two words look-ahead: the parser has therefore access to the form, POS, lemma, and morphological analysis of the next two words.The results of this experiment are reported in Table7. As one can see, SEQ outperforms INCR on the MLAS metric: on average, SEQ gets better results than INCR. As was expected, it is the parser that takes advantage of the sequential strategy: both LAS and UAS are increased by around one point. The two architectures achieve equivalent performances on the low level tasks, meaning that early processing steps do not take advantage of the sequential architecture.

	Task	INCR	SEQ	p-value
	MLAS 77.93 78.60 0.000
	Seg	96.40 95.96
	LAS	87.08 87.56 0.000
	UAS	89.33 89.89 0.000
	Lemma 98.02 98.01 0.403
	UFeats 97.01 97.16 0.002
	UPOS	96.99 97.09 0.036
	Words	99.65 99.63 0.115

Table 7 :

 7 Sequential vs Incremental

Table 8 :

 8 Different values of Window Span 7 Conclusion and Future Work

	]

Of course, such a simple form of rules can only deal with suffixal flexional morphology. More complex morphological phenomena, in templatic morphology for example, ask for more elaborate types of rules.

Except for tokenization and sentence segmentation actions, because our dynamic oracle is not able to deal with incorrect segmentation.

4 All hyper-parameters have been optimized for the development set described in section 6.

Using GloVe[START_REF] Pennington | Glove: Global vectors for word representation[END_REF], implementation: https://github.com/stanfordnlp/GloVe.

The same experiments can be replicated on any language of the UD collection. Comparing the respective merits of the different machines across languages is a very interesting but very resource demanding task (mainly for optimizing the hyper-parameters for each language) and we leave this for future work.

Using implementation of[START_REF] Popel | Udapi: Universal api for universal dependencies[END_REF].

Acknowledgments

This work was granted access to the HPC resources of IDRIS under the allocation 2020-AD011011708 made by GENCI.