Bertrand Kibler
email: bertrand.kibler@u-bourgogne.fr

Kamal Hammani

Claire Michel

Christophe Finot

Antonio Picozzi

Rogue waves, rational solitons and wave turbulence theory

Keywords: Nonlinear optics, Pulse propagation and temporal solitons, Coherence, Statistical optics, Optical turbulence

come

Introduction

The evolution of random nonlinear waves can be characterized by the spontaneous emergence of short lived high amplitude waves. These rogue waves events that "appear from nowhere and disappear without a trace" [1] are among the most studied phenomena in nature in these last years [START_REF]Discussion & Debate: Rogue Waves -Towars a Unifying Concept?[END_REF]. Besides the hydrodynamic context [START_REF] Kharif | Rogue Waves in the Ocean[END_REF][START_REF] Osborne | Nonlinear Ocean Waves and the Inverse Scattering Method[END_REF], rogue waves have been recently identified in various different fields, including optical waves [START_REF] Solli | [END_REF][6][7], capillary waves [8], superfluid helium [9] atmosphere [10] or microwaves [11]. Recent optical and hydrodynamics studies suggest that rogue wave events can be interpreted in the light of exact analytical solutions of 1D integrable nonlinear wave equations, the so-called Akhmediev breathers (ABs) [1][START_REF]Discussion & Debate: Rogue Waves -Towars a Unifying Concept?[END_REF][START_REF] Kharif | Rogue Waves in the Ocean[END_REF][START_REF] Osborne | Nonlinear Ocean Waves and the Inverse Scattering Method[END_REF]12], or more specifically their limiting cases of infinite spatial and temporal periods, the rational soliton (RS) solutions [13][14][15]. Because of this key property of localization in both the spatial and temporal domains, the RSs may be viewed as a kind of 'rogue wave prototype' [16]. The hierarchy of RSs has been found, in particular, in the framework of the integrable 1D nonlinear Schrödinger equation (NLS) equation, which is known to find several important applications in the framework of nonlinear optical waves [START_REF] Kivshar | Optical Solitons: From Fibers to Photonic Crystals[END_REF]. A remarkable property of RSs is that they are characterized by an increasing value of the central amplitude of the wave field, a feature that can be used to interpret the emergence of rogue wave events of higher amplitudes from a chaotic field [15]. The Peregrine soliton solution refers to the first order rational solution [START_REF] Peregrine | [END_REF]. It may be considered as a 'robust solution', in the sense that it can be excited even from non-ideal initial perturbations of the wave amplitude. In particular, its space-time profile may be closely approached into the nonlinear stage of the modulational instability, a feature that has been recently exploited in the context of nonlinear fiber optics to report its first experimental observation [19][20].

RSs are exact analytical solutions of integrable wave equations, and for this reason they may be regarded as a coherent and deterministic approach to the understanding of rogue wave phenomena. As a matter of fact, however, rogue waves events are known to spontaneously emerge from an incoherent turbulent state of the system. It is thus of a fundamental importance to study whether RSs can emerge from a turbulent environment (i.e., in more realistic oceanic conditions) [21,22]. In this respect, it is interesting to note that RSs have been recently identified in the midst of a modulationally unstable chaotic field [12,23]. However, besides these preliminary numerical observations, the problem of the existence of RS in a truly turbulent wave system has not been considered so far. Important questions, such as, e.g., the impact of the amount of incoherence in the system on the generation of RSs have not yet been considered. This actually constitutes a difficult problem, since the description of the turbulent wave system necessarily requires a statistical approach, whereas RSs are inherently coherent deterministic structures.

The present Letter is aimed at providing some physical insight into this vast problematic. We consider the emergence of rogue waves and RSs in a genuine turbulent wave system that can be described by the Wave Turbulence (WT) theory [24][START_REF] Zakharov | Kolmogorov Spectra of Turbulence I[END_REF][START_REF] Zakharov | [END_REF]. This theory is known to provide an accurate statistical description of random nonlinear waves in their weakly nonlinear regime of interaction. We address here the following important issue: Is the coherent description of rogue waves provided by RSs consistent with the WT description of the random wave? For this purpose, we consider a rather simple, nearly integrable, NLS model in which rogue wave events have been recently identified in the context of optics [27][28]. In particular, we recently showed that the amount of incoherence in the system has a deep impact on the properties of rogue waves, which may exhibit either intermittent or sporadic behaviors depending of the system's energy [28]. We showed that, by increasing the incoherence in the system, a transition occurs from the purely coherent and deterministic (quasi-)soliton regime toward the fully incoherent turbulent regime. From a different perspective, this last turbulent regime has been accurately described by using the WT theory [29][30], which thus brings the question of the existence of rogue wave events in the framework of the WT regime of the incoherent wave. We note in this respect that caution should be exercised when drawing conclusions as regard the applicability of the WT theory. It is indeed well-known that the existence of a permanent large scale coherent structure (such as a stable soliton or a condensate) leads to a breakdown of the WT theory [START_REF] Zakharov | [END_REF]31].

However, contrary to solitons, rogue waves are, by nature, very short and very rare events. In this way, although the WT theory is inherently unable to describe rogue waves, their occurrence does not invalidate the applicability of the WT theory. We show that rogue waves can emerge in the genuine turbulent state of the random field and that their coherent deterministic description provided by RSs is compatible with an accurate WT description of the random waves. In particular, the nearly Gaussian statistics for the field amplitudes inherent to the WT theory is compatible with the asymmetric long tail observed in the pdf of the maxima of the field intensity.

Furthermore, the simulations reveal that even in the weakly nonlinear regime, the nonlinearity can play a key role in the emergence of an individual rogue wave event. In this way we report a readily accessible optical setting in which the formation of spatiotemporal localized RS structures can be observed and studied in the WT regime of interaction.

NLS model

We consider the one-dimensional NLS equation in the presence of third-order dispersion (TOD),

u u t u i t u z u i 2 3 3 2 2 2 1 - ∂ ∂ + ∂ ∂ - = ∂ ∂ σ (1)
This equation is known to provide an accurate description of light propagation in optical fibers near by the zero-dispersion wavelength [START_REF] Kivshar | Optical Solitons: From Fibers to Photonic Crystals[END_REF]. In writing Eq.(1), we normalized the problem with respect to the nonlinear length L 0 = 1/γP and time τ 0 = (β 2 L 0 ) 1/2 , where γ is the nonlinear coefficient, P the average power of the field and β 2 the second-order dispersion coefficient. In these units, the normalized TOD coefficient reads ) [START_REF] Zakharov | [END_REF][START_REF] Michel | An accurate description of the validity of the WT theory for Eq.(1) requires an improved criterion[END_REF]. Equation ( 1) is known to admit quasi-soliton solutions: the TOD term ( 0 ≠ σ ) breaks the integrability of the NLS equation, and the standard soliton solution slowly loses its power through a process analogous to Cherenkov radiation [START_REF] Zakharov | [END_REF]33].

β L /(6 β σ 3/
In a recent work [28], we showed that the NLS Eq.(1) exhibits a process analogous to wave condensation [24,31,[34][35][36][37]: by studying the long term evolution of the wave, we identified a transition from the quasi-soliton state at small energies H, toward the fully incoherent WT state at high energies. For completeness, we reported in Fig. 1(a) the condensation curve published in [28]. It can be interpreted by recalling that the energy H provides a natural measure of the amount of incoherence in the system: at high energies the system is too incoherent to generate a coherent quasi-soliton structure. We recall that the condensation curve is obtained by varying the energy H, while the power ('number of quasi-particles') of the field N is kept constant. As discussed in detail in Ref. [28], the condensation curve is characterized by three distinct regimes:

(i) persistent and coherent rogue quasi-solitons at small energies H, (ii) intermittent-like rogue quasi-solitons that appear and disappear erratically at intermediate energies H, and (iii) sporadic rogue waves events that emerge from turbulent fluctuations as bursts of light at high energies.

Accordingly, it is only in the regime (ii) and the purely WT regime (iii) that the spontaneous emergence of extreme events was reported. Typical space-time intensity patterns in which rogue wave events have been identified are illustrated below in Fig. 1(b-c).

Temporal analysis and rational solitons

In this section we investigate the temporal properties of the extreme events identified in the regimes (ii) and (iii) of the condensation curve [Fig. 1(a)]. We underline that several rogue wave events identified in regime (ii) and (iii) verify the standard hydrodynamic criterion [START_REF] Kharif | Rogue Waves in the Ocean[END_REF], which defines a rogue wave as a wave that exhibits a maximal intensity higher than twice the average intensity among one third of the highest waves in the PDF of intensity maxima [28]. We start our analysis by considering the regime (ii), which is characterized by an intermittent-like behavior of the quasi-soliton structures, in the sense that it appears and disappears erratically during the propagation [28]. Because of its interaction with the turbulent fluctuations, the 'lifetime' of the quasi-soliton fluctuates significantly, so that the pdf of the intensity maxima exhibits an Lshaped distribution reminiscent of typical distributions characterizing extreme wave events [28].

Filtering of rogue waves from fluctuations

We identified several extreme events in the high intensity tail of the pdf distribution. A typical extreme event is reported in Fig. 2(a). It exhibits a maximum intensity of 22.9, which is much larger than 6.7, i.e., the value of the average of the maximum intensity detected in the long term evolution of the system (over 500 L 0 ) [28]. In order to further analyze the properties of this extreme event, we calculated the corresponding spectrogram of the field at z = 1560.4 L 0 [see Fig. 2(b)]. The spectrogram constitutes a convenient tool for the identification of possible correlations between the spectral and temporal components of a field (see, e.g., [38]). Here, it reveals that the extreme event exhibits a high degree of localization in both the temporal and spectral domains. This allows us to accurately filter the extreme event from the surrounding turbulent fluctuations. The corresponding spectral and temporal filters used here are indicated in Fig. 2(b) by dashed lines. We underline that the temporal and frequency ranges of the filter do not affect our results in a significant way. Note that the spectral filter centered on the pump frequency also suppresses the dispersive wave radiated from the quasi-soliton, which is generated in the high-frequency edge of the spectrum (i.e., in the normal dispersion regime) [33].

This filtering procedure allows us to compare the structure of the extreme event with the analytical RS solutions of the NLS equation.

Comparison with RS solutions

The integrable NLS equation exhibits a large variety of analytical solutions. Among them one finds the hierarchy of RS solutions recently derived in Ref. [15] by using a modified Darboux transformation. The hierarchy of the solutions starts from the fundamental Peregrine soliton solution [START_REF] Peregrine | [END_REF]. A remarkable property of RSs is that they are characterized by an increasing value of the central amplitude of the wave. RSs are described with the following basic structure characterized by the ratio of two polynomials [15,[39][40]: u j = [ (-1) j + ( G j + izH j ) / D j ] exp(iz), where G j , H j and D j are polynomials of both the spatial (z) and temporal (t) variables, where j refers to the order of the solution. Note that explicit forms for the solutions, from the first-order to the fourth-order, have been given explicitly in Refs. [15,39]. Previous theoretical and numerical studies have also demonstrated that RSs are robust with respect to various types of perturbations [23,41]. Perturbed solutions that remain in the class of RSs have been also obtained by using an extended NLS equation with perturbing terms frequently encountered in the study of nonlinear optical waves. In particular, the role of TOD considered here has been analyzed in [41]. This study revealed that, for the small values of the TOD parameter considered here, the TOD term does not qualitatively affect the RS solution. Moreover, these solutions have been detected as the highest amplitude parts of a chaotic field by realizing simulations of the NLS equation starting from a continuous wave with superposed random fluctuations [12]. More generally, Calini and Schober have demonstrated that homoclinic orbits of the periodic solutions of the NLS equation persist in the perturbed system and some of their properties can be identified in the chaotic regime [42].

We now compare the extreme event filtered out from the turbulent fluctuations in Fig. 2(b) with different orders of analytic RSs. In order to compare them, the filtered field u(t) is normalized in such a way that the power N contained in the reduced temporal window is the same as that of the analytical RS solution. Figure 3(a) reports the comparison between the corresponding extreme event detected in the simulation and the second order RS solution, which provided the best agreement with the simulations. The fact that the second order RS provides a better agreement with respect to the first and third orders RSs stems from the fact that its maximum intensity (I 0 RS = 25) is closer to the maximum intensity of the field detected in the simulations (I 0 num = 22.9), while the intensity maxima of |u 1 | 2 and |u 3 | 2 are respectively 9 and 49. We remark in Fig. 3(a)

that the intensity profile of the central pulse is in good agreement with the analytic RS solution, while the presence of turbulent fluctuations lead to an appreciable discrepancy in the side-lobes of the RS solution. Note in particular that a quantitative agreement between the numerics and the RS is obtained for the value of the pulse peak (i.e., I 0 num = 25.2, I 0 RS = 25). This good agreement is not due to the renormalization procedure, which only affects the integrated value of the wave amplitude over the numerical time window.

We also analyzed in our simulations an essential property of a rogue wave event, namely its degree of localization in the spatial and temporal domains [see the space-time profile in Fig.

3(b)

]. We obtained a temporal FWHM of ∆t num = 0.23 τ 0 and a spatial FWHM of ∆z num = 0.23 L 0 , which are in good agreement with the corresponding values of the analytical RS solution,

∆t RS = 0.3 τ 0 , ∆z RS = 0.3 L 0 . Given the large amount of fluctuations surrounding the extreme even, we may consider this qualitative agreement as satisfactory. (b) Spatio-temporal intensity profile of the filtered rogue wave event detected in the numerical simulations (see Fig. 2).

We have also performed this analysis for rogue wave events detected in the regime (iii), in which the system enters into the fully incoherent and weakly nonlinear regime. The spatio-temporal intensity pattern |u(z,t)| 2 reveals that very short-lived rogue wave events may still emerge from the turbulent field, although these extreme events become rare [see Fig. 1(c)]. In the space-time zoom pattern reported in Fig. 4(a), the extreme event exhibits a maximum intensity of I 0 num = 17.1. This value is lower than the previous one considered in regime (ii), but it is still much larger than 6.7, which refers to the average of the maximum intensity detected in the long term evolution of the system [28]. Proceeding as in regime (ii), we report the spectrogram of the field at z = 1441.6 L 0 in Fig. 4(b). We remark that, in spite of the large amount of fluctuations inherent to the regime (iii), the extreme event can still be identified and is characterized by a high degree of localization in both the temporal and spectral domains.

The space-time profile of the filtered field is compared with the second order analytical RS in Fig. 5(a). Globally, we may note that the agreement with the RS is poorer with respect to the previous analysis in regime (ii), as revealed by the comparison of Fig. 3(a) and Fig. 5(a). This observation has been confirmed through the analysis of several rogue wave events taken in regimes (ii) and (iii), and it can be simply interpreted as a consequence of the fact that the amount of turbulent fluctuations in regime (iii) is higher as compared to regime (ii). Note however in Fig. 5 Finally note that, following the above filtering procedure, we analyzed several rogue wave events detected in both regimes (ii) and (iii), which confirmed the good agreement between their intensity profiles and the corresponding RS solutions.

Spectral analysis and wave turbulence theory

In the framework of relatively small assumptions, the WT theory describes the spectral evolution of statistically homogeneous random waves in their weakly nonlinear regime of interaction, |H NL /H L | « 1 [43][44][45]. This theory has been essentially developed with the aim of describing fully developed turbulence in a dissipative system driven far from equilibrium by an external source [24][START_REF] Zakharov | Kolmogorov Spectra of Turbulence I[END_REF][START_REF] Zakharov | [END_REF], as it occurs, e.g., in some laser systems [46]. However, the kinetic equations also describe the nonequilibrium evolution of random nonlinear waves in a conservative and reversible (Hamiltonian) system. In analogy with kinetic gas theory, a closed system of incoherent nonlinear waves is expected to exhibit a thermalization process, which is characterized by an irreversible evolution of the system towards a thermodynamic equilibrium state. The WT theory describes the essential properties of this irreversible evolution towards the Rayleigh-Jeans equilibrium distribution [START_REF] Zakharov | Kolmogorov Spectra of Turbulence I[END_REF]. This thermalization process has been studied in the framework of NLS-like equations in various different optical configurations [47], including supercontinuum generation [48][49], spontaneous repolarization [50], discrete systems [51], as well as in various optical media characterized by different nonlinearities [52][53][54].

In the WT theory the system evolves in the weakly nonlinear regime (|H NL /H L | « 1), so that linear dispersive effects dominate the interaction and bring the random wave amplitude u(z,t) close to a state of Gaussian statistics. This is in apparent contradiction with the intuitive idea that extreme wave events are usually associated to a deviation from Gaussian statistics. Actually, as reported in our previous work [28], the field amplitude u(z,t) can exhibit a Gaussian statistics, while the existence of extreme events manifests itself through an asymmetric long tail distribution in the pdf of the intensity maxima. Our aim in this section is to show that the rogue wave events analyzed in the previous section can emerge from turbulent fluctuations whose spectral evolution is accurately described by WT theory.

The long term evolution of the NLS Eq.( 1) has been recently shown to exhibit a process of anomalous thermalization [29][30]. It is characterized by an irreversible evolution of the field toward an equilibrium state of a fundamental different nature than the usual Rayleigh-Jeans distribution. Below we briefly sketch the essential properties of this anomalous thermalization and refer the reader to Refs. [29][30] for more technical details. In substance, when applied to the NLS Eq.( 1), the WT theory reveals the existence of a local invariant in frequency space, )

( z q n z n J ω ω ω - - = , , ( ) , ( )
= z n where z) , ( u ) , ( 2 ω ω
is the averaged spectrum of the field amplitude, and q = -1/3σ. The invariant ) (ω J is 'local' in the sense that it is verified for each individual frequency ω in frequency space. This local invariant originates in the following degenerate resonance of the system: the frequencies (ω, q-ω) resonate with any pair of frequencies (ω', q-ω') because k(ω) + k(q-ω) = q 2 /6. Exploiting the existence of the invariant ) (ω J , one obtains the following WT kinetic equation governing the evolution of the averaged spectrum of the field:

∫ - + - = ∂ 1 1 1 z ] , [ 3 2 z) , n( ω ω ω ω ω σ π ω d q J n F (2)
with the functional

{ } 1 1 1 1 ) ( ) ( ) )( ( ] , [ 1 1 1 1 1 1 - - - - - - - - + - - = ω ω ω ω ω ω ω ω ω ω ω ω J n n J n n J n J n n n J n F
, where ' ω n ' stands here for ) , ( z n ω . This kinetic equation has been integrated numerically and its evolution has been compared with the simulation of the NLS Eq.(1). We considered here both regimes (ii & iii) of interaction previously analyzed for the following values of H = 15.5 and H = 19.5.

The initial condition in the NLS Eq.( 1) is a Gaussian spectrum with random spectral phases. The same Gaussian spectrum has been considered as initial condition in the kinetic Eq.( 2). We report in Fig. 6 the NLS spectrum (red dashed line) and the corresponding kinetic spectrum (blue solid line) at the propagation distance in which the rogue wave events have been identified. We remark that a quantitative agreement is obtained between the NLS simulation and the kinetic simulation, without using any adjustable parameter.

It is interesting to note that the existence of the rogue wave event leads to a deviation between the NLS spectrum and the WT prediction in the very far tail of the spectrum (at -80dB). This is illustrated in Fig. 6(a), which reports the NLS spectra just before (gray), during (red), and just after (green) the excitation of the rogue wave. The small deviation is only observed during a very short propagation distance, typically less than one L 0 . As will be discussed in the next Sec. 5 [see Fig. 7(b)], this small effect is a spectral manifestation of the rogue wave event, which, by nature, cannot be captured by the WT theory.

We finally note that, in its asymptotic evolution, the spectrum of the field tends to relax toward a 'local equilibrium state' of a different nature than the thermodynamic equilibrium state. In particular, it violates the property of energy equipartition: because of the existence of the local invariant J(ω), the local equilibrium spectrum exhibits a highly asymmetric shape superimposed on a constant spectral pedestal [30]. A satisfactory agreement is obtained, without using any adjustable parameter.

Influence of the nonlinearity

In the previous section we have shown that, despite the emergence of rogue wave events, the spectral evolution of the incoherent wave has been found in quantitative agreement with the WT theory. We have also shown in Section 3 that some rogue wave events exhibit properties reminiscent of the RS solutions. In this Section we shall see that even if one considers the weakly nonlinear regime of interaction, the nonlinearity plays an important role in the dynamics of emergence of an individual rogue wave event.

To assess the influence of the nonlinearity on the formation of the extreme event, we compare the NLS simulation of the rogue wave event analyzed in Fig. 3 with an identical simulation in which the nonlinearity is switched off two nonlinear lengths before the occurrence of the extreme event (-2 L 0 ). More specifically, the extreme event occurs at z = 1560.4 L 0 in Fig. 3, we thus started the same NLS simulation at z = 1558.4 L 0 by removing the nonlinearity (γ = 0). The results are reported in Fig. 7(a). Note that we realized here the same filtering and renormalization procedures as those discussed in Fig. 3. We clearly note that the nonlinearity plays an important role in the formation of the extreme event. In particular, contrary to the nonlinear regime (see Sec. 3), the value of the maximum wave amplitude reached in the linear regime (I 0 lin ~ 11.7 before renormalization) no longer satisfy the standard rogue wave criterion used in the context of hydrodynamic waves [START_REF] Kharif | Rogue Waves in the Ocean[END_REF]. Furthermore, the temporal and spatial localizations of the detected 'linear event' are ∆t num = 0.29 τ 0 and ∆z num = 0.1 L 0 : These values deviate in a significant way from the corresponding RS's values. This reveals that the detected rogue wave event does not result from a simple superposition of linear waves. Corresponding wave spectra (in 10xlog 10 -scale) of the field in the nonlinear regime (red solid line) and in the "linear" regime (blue dashed line). Spectrum of the second order RS solution is also shown (black circles).

We also report in Fig. 7(b) the corresponding numerical spectra of the fields in the linear and nonlinear regimes considered in Fig. 7(a). Note that these spectra do not account for the filtering procedure discussed in Sec. 3. We can remark that both spectra are almost indistinguishable, so that they cannot be used to detect easily the existence of the rogue wave event. This point deserves to be discussed in relation with the fact that the Peregrine soliton and RSs are known to be characterized by a specific triangular-shaped spectrum that appears at an early stage of their evolution [55], a property that was confirmed experimentally [19][20]. For this reason, such triangular-shaped spectra were proposed as a warning signal for the emergence of extreme wave events in oceans [55,56]. The analysis reported here indicates that this suggestion is not relevant when the extreme wave event emerges from a turbulent environment in a perturbed-NLSE system. Indeed, the slight difference observed in the far tail of the spectrum for H = 15.5 in regime (ii) becomes undetectable in the highly incoherent regime (iii), as illustrated in Fig. 6(b)

for H = 19.5.

Conclusion

In summary, through the analysis of the long term evolution of the wave system, we investigated the spectral and temporal properties of the incoherent field in its highly incoherent regime of interaction. We showed that intermittent-like rogue quasi-solitons [regime (ii)] and sporadic rogue wave events [regime (iii)], both exhibit properties reminiscent of the hierarchy of the RS solutions. This coherent and deterministic description of rogue waves coexists with the statistical description of the random field, which is found in quantitative agreement with the WT theory without using adjustable parameters. We also showed that the nonlinearity can play an important role in the formation of an individual rogue wave event, a feature that should deserve to be analyzed in further details, in relation with the recent work [57]. The complementary temporal and spectral analyses of the turbulent field and of the rogue wave events indicate that the localized RS coherent structures can be observed experimentally during the natural process of optical wave thermalization to equilibrium. It would be interesting to extend this work to the study of RSs in a forced-dissipative system driven far from thermal equilibrium by an external source [START_REF] Zakharov | Kolmogorov Spectra of Turbulence I[END_REF]58].

Figure 1 : 5 [

 15 Figure 1: (a) Condensation-like curve: Average of the maximum intensity

Figure 2 :

 2 Figure 2: (a) Zoom on the space-time intensity pattern reported in Fig. 1(b)

Figure 3 :

 3 Figure 3: (a) Comparison of the filtered rogue wave event detected in regime (ii) in

  (a) that the central part of the pulse is still in good agreement with the analytical RS solution. In particular, the value of the peak pulse in the simulations I 0 num = 25.4 is very close to the corresponding value of the RS, I 0 RS = 25. Conversely, the significant discrepancies in the side-lobes can be ascribed to the large amount of incoherent fluctuations ( H ~ 20) that characterizes the weakly nonlinear regime (iii). We also compared the temporal and spatial localization of the extreme event detected in the simulation with the corresponding localizations of the RS solution. We obtained at FWHM ∆t num = 0.24 τ 0 and ∆z num = 0.21 L 0 , which are still in rather good agreement with the corresponding RS's values (∆t RS = 0.3 τ 0 , ∆z RS = 0.3 L 0 ).

Figure 4 :

 4 Figure 4: (a) Zoom on the space-time intensity pattern reported in Fig. 1(c)

Figure 5 :

 5 Figure 5: (a) Comparison of the filtered rogue wave event detected in

Figure 6 :

 6 Figure 6: (a) Spectrum (in 10xlog 10 -scale) obtained by integrating the NLS Eq.(1)

Figure 7 : 3 (

 73 Figure 7: (a) Comparison of the rogue wave event analyzed previously in Figs. 3

Acknowledgments: This research was supported by the Agence Nationale de la Recherche (COSTUME project, ANR-08-SYSC-004-03; MANUREVA project, ANR-08-SYSC-019) and by the Conseil Régional de Bourgogne.


Éric De

La Clergerie
email: eric.de_la_clergerie@inria.fr

Benoît Sagot
email: benoit.sagot@inria.fr

Rosa Stern
email: rosa-devi.stern@inria.fr

Pascal Denis
email: pascal.denis@inria.fr

Gaëlle Recourcé

Victor Mignot Alpage

Extracting and Visualizing Quotations from News Wires

We introduce SAPIENS, a platform for extracting quotations from news wires, associated with their author and context. The originality of SAPIENS is that it relies on a deep linguistic processing chain, which allows for extracting quotations with a wide coverage and an extended definition, including quotations which are only partially quotes-delimited verbatim transcripts. We describe the architecture of SAPIENS and how it was applied to process a corpus of French news wires from the AFP news agency.

Introduction

The SAPIENS platform was designed to give a preview of what NLP resources and techniques would bring to a larger domain application, namely a service for press agencies, offering production, analysis, search and synthesis tools to journalists handling on a daily basis a large amount of information in the form of news wires. 1 SAPIENS focuses on quotations detection, as information sourcing constitutes a major part of press agencies' work; quotations thus represent a significant part of news wires content. The user's need in this context lies in the retrieval of those quotations in order to synthesize information on a particular topic with regards to the persons or entities -such as organisations -who expressed any kind of verbal utterances about it. Automatization appears to be very desirable for such a task; the main requirements of the system are an exhaustive coverage of various forms of quotations found in texts, as well as their correct attribution to entities who are to be recognised.

SAPIENS has been applied on a corpus of news wires from the Agence France-Presse (France-Press Agency, AFP). The AFP produces every day 6000 news in six languages (French, English, German, Spanish, Arabic, Portuguese). The average size of a news item is 250 words. Currently, SAPIENS focuses only on French language.

Related Work

Automatic extraction of quotations is not among the most explored fields in NLP applications, despite the interest it raises for domain related tools such as news exploring 1 SAPIENS has been developed within the Scribo project, funded by the French "pôle de compétitivité" System@tic (web page: http://www.scribo.ws). or sentiment detection.Nevertheless, we can mention several applications developed in this perspective: Google InQuotes2 , News Explorer3 , Excom 4 . Like SAPIENS, News Explorer aims at the detection of quotations in news -although SAPIENS is specialized for press agency news wires -and their author; it is based on word lists and pattern matching. Excom implements NLP techniques and takes into account quotations surrounded by typographic quotes, which is also the case with News Explorer and InQuotes. The latter indexes quotations based on word-spotting but is limited to a predefined list of authors. By proposing an approach using advanced NLP techniques for the detection of complex types of quotations and wide entities recognition, SAPIENS addresses these limitations and implements a broader notion of quotation, i.e., not only text segments surrounded by quotes.

Overall Architecture

Quotations and the related issue of reported speech (hereafter RS), currently treated in the context of journalistic corpora, can be described at different levels: a surface level, which gives several indications for detection by automatic tools, and a deeper, linguistic and discursive level. The surface level points out some markers such as typographic quotes and the presence of certain verbs close to them; these verbs can be grouped in a list which can be drawn up by observation of corpora or produced by various linguistic studies on RS. Example 1 illustrates a simple verbatim quotation, that is the indirect object of the verb "s'engager" (to promise).

(1) Ségolène Royal s'est engagée mardi, au stade Charléty à Paris, à "rassembler toutes les énergies d'où qu'elles viennent". (AFP-May 1 s t 2007) Ségolène Royal promised on Thursday, at the Charléty Stadium in Paris, to "put together all the help we can get, wherever it comes from".

However, the description of the deeper level shows several features of quotations usage and structure which are not captured by this surface approach. This is especially true for quotations in journalistic texts, which have the particularity to mix very often direct and indirect RS. This mixed type correspond to a very precise preoccupation of the journalist, who has to distinguish, at the word level, which parts of a speech were actually uttered and which parts he is indirectly reporting. This is illustrated in Example 2, where the quotation is between brackets.

(2) Elle rappelle que [les "premiers jalons" de la scolarisation des handicapés "furent posés par The direct RS parts are surrounded by quotes and constitute verbatims. Quotations are consequently not only those verbatims, which can be embedded in a larger textual area containing RS. The verbatims should always appear as such, even outside a detected segment of reported speech, in the final application, as they are for the user, i.e. the journalist, the core element of sourced utterances. By enlarging the definition of quotations beyond the verbatims, SAPIENS allows for quoted words to make sense in a broader context, corresponding to the original circumstances of utterance and thus giving consistency to the information retrieved. More generally, quotations are relevant only when associated with their author, i.e., the person -or in some cases the organization -who originally uttered the reported speech. Other relevant information can be extracted in order to make the detection tool as relevant and useful as possible (e.g., the location, date and audience of the utterance, such as "mardi, au stade Charléty à Paris" in Example 1). The extraction of such information is best achieved when full syntactic structures are available: this enables the extraction of arguments and modifiers of quotation verbs such as "déclarer" (to declare), and lead to better anaphora resolution results (which is required when, e.g., the author of a quotation verb is referred to with a pronoun, as illustrated in Example 2 with the pronoun elle).

SAPIENS' processing chain thus relies on a full-featured linguistic processing chain, NewsProcess, which includes a series of modules for handling news wires data both at the surface level through a pre-processing phase and at the deeper linguistic level during the parsing and post-processing phase. This allows NewsProcess to extract the relevant information and to store it in a database, which is in turn accessed by a visualization environment (see Section 6). The linguistic processing chain in itself can be split in three main phases:

1. pre-processing with SXPipe (Section 4) -tokenization, segmentation in sentences, detection of a first set of "named entities" such as URLs, addresses, numbers and other numeric units, sequences in foreign languages, etc.; -(standard) named entities recognition (such as persons, locations, organizations, etc.); -verbatim quotations extraction; 2. deep parsing with FRMG (Section 5) 3. post-processing, and in particular -anaphora resolution (Section 5.1) -quotation extraction (based both on verbatim quotations and on parsing results) (Section 5.2)

Pre-processing with SXPipe

SXPipe [START_REF] Sagot | From raw corpus to word lattices: robust pre-parsing processing with SXPipe[END_REF][START_REF] Sagot | SXPipe 2: architecture pour le traitement présyntaxique de corpus bruts[END_REF] is a set of tools which performs (1) "named entities" recognition: pretoken named entities (URLs, emails, dates, addresses, numbers. . . ), (2) tokenization and segmentation in sentences, (3) token-based named entities (phrases in foreign languages. . . ), ( 4) non-deterministic multi-word units detection and spelling error correction, and ( 5) lexicon-based patterns detection, including but not limited to named entities.

The most relevant parts of this pre-processing chain in the context of SAPIENS are classical named entities recognition (persons, locations, organizations, companies, products and brands, artworks) and verbatims extraction. They both belong to the 5th step, and are detailed in the two next sections.

Named Entities Recognition

While developing SAPIENS, a new module for standard named entities detection has been developed in SXPipe's dag2dag framework [START_REF] Sagot | SXPipe 2: architecture pour le traitement présyntaxique de corpus bruts[END_REF]. This framework allows for context-free patterns definitions and for the use of dedicated gazetteers, while remaining very efficient in terms of processing time.

The first step of this module is the generation of gazetteers. For location names, we us the Geonames database5 and filter it using criteria defined according to the nature of the corpus.

For each retained location name, we store the Geonames id and normalized name, as well as the lcoation latitude and longitude. Moreover, we compute a reasonable scale level to be used in the final interface when showing the location in Google Maps.

For other kinds of named entities (persons, organizations, companies, products and brands, artworks), we extract information from the French Wikipedia. 6 We manually define a mapping from a set of Wikipedia "categories" to one of the above-mentioned named entities types. This allowed to type the title of each relevant Wikipedia article and to select entity pages. For each entity, variants are extracted from redirection pages variants (e.g., CIA in addition to Central Intelligence Agency, or Marie-Ségolène Royal in addition to Ségolène Royal). A "short description" is extracted from the heading of the article (in the case of Ségolène Royal, femme politique française (22 septembre 1953, Dakar -)). Variants allow us to segment person names into the first name, a possible middle name, the last name, and a gender if possible. New variants are then computed, in particular the omission or abbreviation of first and middle names, as in M.-S. Royal or Royal. 7Both lexicons are corrected and enriched by a blacklist and a whitelist of named entities, both manually drawn up. The result is a large lexicon that contains over 1 million entries (variants), associated with a normalized form, a reference URI and a "description" (e.g. date of birth, position...).

A context-free grammar consisting of 117 rules has been developed for defining patterns based on these gazetteers, as well as on specific lists for identifying relevant contexts (e.g., ville, village, localité, i.e., city, village, locality); other lists used by the grammar are a large list of first names, a list of possible titles such as Dr., Mme, and others. Disambiguation heuristics have been activated, so that the amount of ambiguities added by this named entities module is as low as possible, although not null. The following verbatims extraction step then allows for some more disambiguation. For example, if an entity is ambiguous between a location and a person name, but is later found in the position of a verbatim author, it is disambiguated by the verbatims extraction component as a person name.

The result is a fast and high-quality named entities detection tool, integrated within SXPipe. Based on an evaluation conducted over a manually annotated corpus of 1544 entities occurrences 8 , this tool achieves a 0.77 f-score, which is rather satisfying for French although giving good scope for improvement.

Verbatims Extraction

The SXPipe pre-processing chain achieves the extraction of verbatim quotations at a surface level with a dedicated module which uses symbolic patterns. The extraction is first done by identifying all parts of text surrounded by typographic quotes, i.e. verbatims. The patterns of this module allow us to detect more interesting elements usually related to a quotation when they are present, mainly the predicate supporting the quotation 9 and the author of the quotation. The latter can be of two kinds: a named entity, which we propose as a candidate for the role of quotation author according to its distance to the predicate-verbatim set, or a clitic pronoun, when found in an incident clause. This particular position of the pronoun indeed guaranties the correct detection of the quotation author, which can thus be identified later in the processing chain by the anaphora resolution module. Similarly, the candidate for the role of author can later on be confirmed or rejected by the syntactic analysis. As mentioned in 4.1, in case of a type ambiguity on a named entity, its identification as a quotation author is used to assign a type to it. Some patterns are applied to link several chunks of verbatims scattered in a sentence but which belong to the same quotation; this link can later be used after the parsing step as an indication about the extension of the current RS area.

Parsing and Post-processing

The NewsProcess processing chain is organized as a sequence of processing modules called either offline or through a webservice. Strictly speaking, the pre-processing by SXPipe is embedded within the first of these modules, which takes SXPipe's output as an input for the FRMG parser; the parsing result is then enriched by a series of postprocessing modules which organize all the information retrieved along those steps. In particular, anaphora resolution is achieved, named entities are stored in a database with their normalized form and description ; quotations detected at the syntactic level are then aligned with verbatims.

Deep parsing is performed by the FRMG parser [START_REF] Thomasset | Comment obtenir plus des méta-grammaires[END_REF], a symbolic parser based on a compact TAG for French that is automatically generated from a meta-grammar. FRMG relies on the morphological and syntactic lexicon Lefff [START_REF] Sagot | The Lefff 2 syntactic lexicon for French: architecture, acquisition, use[END_REF].The output of FRMG is a shared dependency parse forest that represents all derivation structures that the grammar can build for the input sentence. 10 This forest is then disambiguated by a heuristicbased module that outputs a unique dependency tree. A resulting dependency tree is shown in Figure 1 for the sentence "soyons réalistes", a-t-il déclaré. ("be realist", he has declared.), with be realist being a sentential argument and a citation governed by to declare. A fragment of the underlying DEP XML format used to represent these dependency trees [START_REF] Villemonte De La Clergerie | Convertir des dérivations TAG en dépendances[END_REF] is shown in Figure 2. The DPath language (section 5.2) is used to extract information from this XML representation.

Anaphora Resolution

Next in the NewsProcess chain is the anaphora resolution module. This module uses the information collected by the earlier processing modules, including named entities and morphosyntactic features as extracted by SXPipe (I.e. persons gender), as well as deep grammatical analysis provided by FRMG.

Our resolution system concentrates exclusively on third person singular pronouns (e.g., il, elle, le, la, etc.), which are the most relevant in the context of quotations. This excludes possessive and demonstrative pronouns, as well as plural anaphora. The latter are more tricky in that they often take disjoint antecedents and moreover, sentiments expressed by a collective entity are not considered as quotations by the AFP guidelines, since they are not strictly sourced.

Technically, we model anaphora resolution as the task of mapping the identified referential pronouns onto one of the entities detected by the previous modules. Pleonastic il pronouns have been filtered out by the ILIMP system of [START_REF] Danlos | ILIMP: Outil pour repérer les occurrences du pronom impersonnel il[END_REF] which has been integrated within SXPipe. Following [START_REF] Lappin | An algorithm for pronominal anaphora resolution[END_REF] or [START_REF] Mitkov | Robust pronoun resolution with limited knowledge[END_REF], we model resolution as a two-step process, whereby: (1) we apply a series of hard constraints which has the effect of eliminating candidates semantically incompatible, and (2) we rank of the remaining candidates on the basis of salience preferences.

Among the hard constraints, we check compatibility in terms of gender, number, person and semantic typing by filtering all antecedent candidates whose gender (resp., number, person, and entity type) is incompatible with that of the anaphor. 11 We also filter out all entities that do not have any occurrence preceding the pronoun in the text; this in effect excludes possible cases of cataphora. For gender determination, we rely on the information provided by SXPipe, potentially updated by FRMG. Gender is assigned to an entity based on the genders of its occurrences using a simple majority vote.When gender information is not provided for an occurrence, we "back-off" to a simple gender guesser that tries to classify occurrences based on their surface form. In particular, the guesser relies on honorifics (e.g., Mme, M., le président).

The ranking of the remaining antecedent candidate entities12 is performed based on how well each candidate meets certain salience preferences. These preferences include proximity (in terms of sentence distance), grammatical functions as provided by FRMG's output (in particular, subject, object, indirect object), the number of occurrences of the entity that precede the pronoun (i.e., how often is an entity repeated prior to the pronoun), and the appearance inside a quote. When a full parse fails to be given for a sentence, we assign grammatical functions following the order of the text: the first NP is labeled subject, the second NP object and the third NP indirect object. Each of these preferences is associated with a weight, based on a scoring inspired from [START_REF] Lappin | An algorithm for pronominal anaphora resolution[END_REF] and determines the final resolution for each pronoun. The information is then used later to assign the detected quotations to the adequate entity (cf. section 5.2).

< c l u s t e r i d = " E1c_7_8 " l e f t = " 7 " r i g h t = " 8 " t o k e n = " d é c l a r é " l e x =" E1F8 | d é c l a r é " / > < c l u s t e r i d = " E1c_1_2 " l e f t = " 1 " r i g h t = " 2 " t o k e n = " s o y o n s " l e x =" E1F2 | s o y o n s " / > <node d e r i v = " E1d000148 " x c a t =" S " i d = " E1n023 " c a t = " v " t r e e =" 186 " lemma=" d é c l a r e r " c l u s t e r = " E1c_7_8 " form=" d é c l a r é " / > <node d e r i v = " E1d000010 " x c a t =" S " i d = " E1n005 " c a t = " v " t r e e =" 198 " lemma= " ê t r e " c l u s t e r = " E1c_1_2 " form= " s o y o n s " / > < edge i d = " E1e008 " s o u r c e = " E1n023 " t a r g e t =" E1n005 " t y p e =" s u b s t " l a b e l = " xcomp "> Fig. 2. Fragment of DEP XML

Quotation Extraction

As mentioned earlier, one of the main features of journalistic quotations is their mixed characteristic. It is indeed very common to find, in journalistic content, a mixed type of quotations, with both typographic quotes and for instance a finite subordinate clause containing the RS. It is also frequent that not the whole RS is between quotes, but only one or several chunks of it, as in Example 2. Besides, those chunks do not necessarily correspond to constituents. Thus, the simple matching of text surrounded by quotes does not provide a complete retrieval of RS parts. This is why SAPIENS expands verbatims by reconstructing a coherent RS based on parsing results, hence putting forward information not directly retrievable by the user, while still distinguishing between different types of speech reporting. Linguistic studies about RS offer different ways for us to define those configurations, and thus quotations, in the current context of journalistic corpora. They usually distinguish between various forms of RS, mainly direct and indirect, based on the presence or absence of typographic signs and particular syntactic structures, among other criteria. Without discussing here detailed aspects of RS theories, we can mention the most frequent configurations used for reporting speech, especially in journalistic content. In those constructions, the RS part is considered to be the grammatical object of the verb introducing it. As such, it can be realized as a noun phrase or a finite subordinate clause. It is also considered as the object, although at a weaker degree, when the RS verb appears in an incident clause, after or in the middle of the quoted text. For a more precise and complete study of quotations in news wires and of formal features of quotation syntactic structures, we refer to [START_REF] Sagot | A lexicon of french quotation verbs for automatic quotation extraction[END_REF] and [START_REF] Danlos | Analyse discursive des incises de citation[END_REF].

When the dependencies produced by FRMG contains such configurations, the quotation extraction module looks up the list of 230 quotation verbs at our disposal and whose making is described in [START_REF] Sagot | A lexicon of french quotation verbs for automatic quotation extraction[END_REF]. The module then appoints the sentence as an RS segment if the verb head of the main clause appears in it; the verb object, whether it is an NP or a subordinate clause, is selected as the quotation segment, while the subject of the verb is selected as the author. A few patterns were defined using a Perl-based query-langage over dependencies inspired by XPath, an exemple being given below to retrieve edges linking an active-voice citation verb (as source) with a sentential object (is_xcomp): Adverbial and prepositional clauses are finally examined in search of possible other quotation satellites, such as the date of utterance or the audience in front of which it was uttered. If previously detected verbatims are included in the current sentence, the RS segment is extended from the beginning of the clause containing the first quote to the end of the clause containing the last one. Thus the quotation can include inserted nonverbatim chunks, and stretch out on several clauses. Besides, the presence of verbatims in a sentence forces the appointment of the sentence as an RS segment even when no specific configuration or quotation verb could be found by the parser. In such a case the same extension is applied in order to put the verbatim back in a syntactical interpretable context.

RS are also frequently introduced without a specific verb, mainly in prepositional attribution phrases; in this case they are found before or after prepositional phrases such as "selon X" or "pour X" ("according to X", "for X"). The parser also looks for these configurations. The clause or clauses introduced by the prepositional phrase is or are selected as the quotation, and the NP following the preposition is selected as its author.

We have performed a limited evaluation of our work, mostly to guide our future efforts. We manually sampled 40 quotations from 40 different news items and evaluated both the span of the quotation and the correctness of the author. 32 quotations are found and in 19 cases, both the span and the author of the quotation are correct. Most other quotations lack an author (12 cases) or receive an incorrect one (7 cases, incl. 2 because of an erroneous anaphora resolution); 4 receive an incorrect span. More interestingly, 28 quotations exhibit patterns that would prevent a parsing-free processing chain from detecting the entire quotation span sucessfully (in most cases because not all the quotation lies between quotes, as explained above and illustrated by Example 2). Thanks to the use of the parser, SAPIENS correctly identifies the span of 21 of those 28 cases.

Web Interface for Visualization

The SAPIENS Web interface provides a visualization of AFP news items with a focus on detected quotations and related named entities. The access is organized by quotations authors: one can choose among entities, showed in a cloud, to whom one or more quotations have been assigned. An access via a search menu will soon be available, in order to enable search of quotations made by a particular person, as well as a keyword search for the retrieval of quotations related to a particular topic. On this latter possibility, we can argue that the association between a topic and a quotation will be larger and thus richer than the one offered for instance by InQuotes: InQuotes makes out this link only if the keyword itself is present within the quotation, whereas in SAPIENS' case the keyword is part of the news item metadata among other related terms which can thus be linked to the quotation in an indirect although relevant fashion. This possibility of linkage is also due to the thematic homogeneity of a news item. Once an entity has been chosen, the user is directed to a clickable list of news items including quotations from the selected author. It gives access to the enriched view of each of these news items, i.e. with a set of highlighted text elements: quotation(s), with distinction between verbatims and non verbatim parts, the named entity selected as quotation author -if the author is referred to with a pronoun, a tooltip indicates to which entity the anaphora has been resolved; all entities detected in the news item can be highlighted, and a link is provided for each of them, to Google Maps for locations and to the corresponding Wikipedia page for the other types of entities.

Conclusions and Perspectives

In this paper, we introduced SAPIENS, a platform for quotations extraction that relies on a deep linguistic processing chain. In particular, we have described different modules for named entities extraction, verbatims extractions, deep parsing, anaphora resolution and quotation extractions, as well as a visualization interface. We showed how we applied this chain on a corpus of news wires from the Agence France-Presse (AFP) news agency. All components of SAPIENS, including the processing chain and the resources it relies on, are free software. The information made available by SAPIENS are richer and more accurate than other systems such as Google InQuotes, in part thanks to the use of a deep parser within the chain.

In the future, SAPIENS should evolve into an operational tool used by AFP journalists. More precisely, the SAPIENS webservice will be queried by the news items editor used by journalists as soon as a news item is written, in order to automatically provide a list of descriptors to be used as metadata; these disambiguated descriptors may include named entities, topics 13 , quotations associated with their author, or others; the journalist will then validate or correct these descriptors, which are meant to be used for sub-wires generation and for indexing purposes.

  le plan Handiscol en 1999"]. (AFP-May 3 r d 2009) She recalls that [the "first steps" towards the schooling of disabled people "were achieved by the Handiscol plan in 1999"].

Fig. 1 .

 1 Fig. 1. FRMG dependencies for "'be realist', he has declared"

  d p a t h is_xcomp { $ c i t a t i o n _ v e r b s ->{$_->s o u r c e ->lemma } } { $_->a p p l y ( d p a t h s o u r c e i s _ a c t i v e ) }

Fig. 3 .

 3 Fig. 3. Example of an enriched news item as visualized in SAPIENS

http://labs.google.com/inquotes/

http://press.jrc.it/NewsExplorer/ -A description of the system can be found in[START_REF] Pouliquen | Automatic detection of quotations in multilingual news (european commission -joint research centre)[END_REF].

http://www.excom.fr/

Freely available at http://www.geonames.org

A full dump can be downloaded freely at http://download.wikimedia.org/frwiki/ latest/frwiki-latest-pages-articles.xml.bz2

A candidate such as Royal, i.e. an isolated last name, is discarded during the disambiguation step unless it refers to an entity mentioned earlier in the same news item in a more extended form, e.g. Ségolène Royal.

This evaluation corpus is however restricted to person, location and organization names.

A list of 230 quotation verbs has been acquired mainly by corpus examination and semiautomatic extraction, detailed in[START_REF] Sagot | A lexicon of french quotation verbs for automatic quotation extraction[END_REF].

More precisely, but this is outside the scope of this paper, the actual derivation forest is transformed into a dependency one.

[START_REF] Villemonte De La Clergerie | Convertir des dérivations TAG en dépendances[END_REF] Currently, only PERSON entities are considered, but the constraint can easily be relaxed to include other entity

types.12 There are a few cases in which the application of the above filters results in an empty set of candidates; the anaphora is left unresolved in those cases.


Elsa Tolone
email: elsa.tolone@univ-paris-est.fr

Benoît Sagot
email: benoit.sagot@inria.fr

Using Lexicon-Grammar Tables for French Verbs in a Large-Coverage Parser

Keywords: Syntactic lexica, Lexicon-Grammar, parsing, evaluation

In this paper, we describe the integration of Lexicon-Grammar tables for French verbs in the large-coverage FRMG parser and the evaluation of the resulting parser. This integration required a conversion step so as to extract the syntactic information encoded in Lexicon-Grammar tables and represent it in the NLP lexical formalism used by FRMG, i.e., the Alexina framework (that of the Lefff lexicon, on which the standard version of FRMG relies). We describe the linguistic basis of this conversion process, and the resulting lexicon. We compare the results of the FRMG parser on the EASy reference corpus depending on whether it relies on the verb entries of the Lefff or those of the converted Lexicon-Grammar verb tables.

Introduction

Lexicon-Grammar tables are currently one of the major sources of syntactic lexical information for the French language. Moreover, several Lexicon-Grammar tables exist for other languages, such as Italian, Portugese, Modern Greek, Korean, and others. Their development was initiated as early as the 1970s by Maurice Gross, at the LADL and then the IGM (Université Paris-Est) [START_REF] Gross | Méthodes en syntaxe: Régimes des constructions complétives[END_REF][START_REF] Boons | La structure des phrases simples en français : Constructions intransitives[END_REF][START_REF] Guillet | La structure des phrases simples en français : Les constructions transitives locatives[END_REF]. Lexical information is represented in the form of tables. Each table puts together elements of a given category (for a given language) that share a certain number of defining features, which usually concern subcategorization. These elements form a class. These tables are represented as matrices: each row corresponds to a lexical item of the corresponding class; each column lists all features 1 that may be valid or not for the different members of the class; at the intersection of a row and a column, the symbol + (resp. -) indicates that the feature 1 For example, the feature N0 V means "possible head of an intransitive construction with initial subject noun phrase"; the feature [passif] means "passive diathesis possible". corresponding to the column is valid (resp. not valid) for the lexical entry corresponding to the row. As far as the French language is concerned, 61 tables for simple verbs have been developed, as well as 59 tables for predicative nouns, 65 tables for idiomatic expressions (mostly verbal), and 32 tables for (simple and idiomatic) adverbs. Current tables suffer from various types of inconsistency and incompleteness. In particular, defining features are not represented in the tables. 2 To remedy this situation, tables of classes are being developed at IGM for each category, and notably for verbs, which associate the set of their defining features with each class [START_REF] Paumier | De la reconnaissance de formes linguistiques à l'analyse syntaxique[END_REF]. Preliminary results of this long-term effort allowed us to convert verb tables into a format suitable for their use within a large-scale parser for French, the FRMG parser [START_REF] Thomasset | Comment obtenir plus des méta-grammaires[END_REF]. This format is that of the Alexina framework, in which the lexicon used by the standard FRMG was developed. This lexicon is the Lefff (see below).

This paper is organized as follows. Section 2 briefly describes the lglex lexicon. Section 3 introduces the Alexina format and the Lefff NLP syntactic lexicon for French. Section 4 provides an overview of the interpretation and conversion process that allowed us to build an Alexina version of lglex. Then section 5 describes how we coupled this converted lexicon with the FRMG parser, and section 6 compares the results of the FRMG parser on the EASy reference corpus depending on whether it relies on the verb entries of the Lefff or those of the converted lglex (i.e., on converted Lexicon-Grammar verb tables). Finally, several further steps for this work are evoked in section 7.

The Verbal Lexicon lglex

A table of classes groups the list of all syntactic features identified for the corresponding category as columns, and the rows list all classes defined for this category. At the intersection of a row and a column, the symbol + (resp. -) indicates that the corresponding feature is valid (resp. not valid) for all elements of the class (i.e., for all entries of the corresponding table). The symbol o indicates that the feature is explicitly coded in the corresponding table, because it is valid only for some of its entries. Finally, the symbol ? means that this cell has not been filled in yet.

The development of the table of verb classes and that of noun classes is close to completion [START_REF] Constant | A generic tool to generate a lexicon for NLP from Lexicon-Grammar tables[END_REF], since the coding ? is now only used when a given feature has not yet been studied for a given class. Thanks to this work which makes all syntactic features of verbs in the Lexicon-Grammar tables consistent and explicit, it was possible to build a structured version of the tables, available in text or XML format, and called the lglex lexicon [START_REF] Constant | A generic tool to generate a lexicon for NLP from Lexicon-Grammar tables[END_REF]. 3 The construction of lglex relies on the LGExtract tool, that takes as input the tables of a given category, the corresponding table of classes and a configuration file. This file defines how each feature (as extracted from the table of classes, or, in the case of features that are coded o, extracted from the corresponding table) contribute to building the lglex entry.

Our conversion process starts from lglex verbal entries and turns them into entries in the Alexina format, i.e., the same as the format of the syntactic lexicon Lefff .

The Lefff Syntactic Lexicon and the Alexina Format

The Lefff (Lexique des formes fléchies du français -Lexicon of French inflected form) is a large-coverage syntactic lexicon for French [START_REF] Sagot | The Lefff 2 syntactic lexicon for French: architecture, acquisition, use[END_REF][START_REF] Sagot | Améliorer un lexique syntaxique à l'aide des tables du Lexique-Grammaire : Constructions impersonnelles[END_REF] 4 . It relies on the Alexina framework for the acquisition and modeling of morphological and syntactic lexicons. To represent lexical information, an Alexina lexicon relies on a two-level architecture:

-the intensional lexicon associates (among others) an inflection table and a canonical sub-categorization frame with each entry and lists all possible redistributions from this frame; -the compilation of the intensional lexicon into an extensional lexicon builds different entries for each inflected form of the lemma and every possible redistribution.

For example, consider the following (simplified) intensional entry: clarifier1 Lemma;v;<Suj:cln|scompl|sinf|sn, Obj:(cla|scompl|sn)>; %ppp_employé_comme_adj,%actif,%passif, %se_moyen_impersonnel,%passif_impersonnel

It describes an entry of the verbal lemma clarifier (clarify) which is transitive (two arguments canonically realized by the syntactic functions Suj and Obj listed between brackets), and which allows for the functional redistributions past participle used as an adjective, active (the default distribution), impersonal middle-voice "se" construction, impersonal passive, and passive.

The different syntactic functions are defined in the Lefff by criteria close to that used by the authors of the verb valency lexicon DICOVALENCE [START_REF] Van Den Eynde | Le dictionnaire de valence DICOVALENCE : manuel d'utilisation[END_REF], i.e., they rely for a large part on cliticization and other pronominal features. The Lefff uses the following syntactic functions: Suj (subject), Obj (direct object), Objà (indirect object canonically introduced by preposition "à"), Objde (indirect object canonically introduced by preposition "de"), Loc (locative), Dloc (delocative), Att (attribute), Obl or Obl2 (other oblique arguments). Defining criteria for these functions are described in [START_REF] Sagot | Améliorer un lexique syntaxique à l'aide des tables du Lexique-Grammaire : Constructions impersonnelles[END_REF].

Each syntactic function can be realized by three types of realizations: clitic pronouns, direct phrases (nominal phrase (sn), adjectival phrase (sa), infinitive phrase (sinf), completive (scompl), indirect interrogative (qcompl)) and prepositional phrases (direct phrases preceded by a preposition, such as de-sn, à-sinf or pour-sa). 5 Finally, a function whose realization is not optional has its realizations list between brackets.

Complementary syntactic information (control, mood for completives, etc.) are represented by macros (@CtrlSujObj, @ComplSubj, etc.) whose formal interpretation varies according to the context of use. An LFG modeling of these macros is provided with the Lefff .

Conversion of the Verbal Lexicon lglex into a Lexicon in the

Alexina Format

Sketch of the Conversion Process

Each entry in lglex is associated with a set of constructions that can be classified into several types: We developed a method for aligning two constructions, i.e., for building correspondences between arguments despite their surface differences 6 and their possible deletion. This method allows us to identify and align the MEBC and its variants, which we put together in a single entry of the final lexicon, called canonical entry. Among the other constructions, those that correspond to standard redistributions ([passif par],

[extrap]. . . ) lead to the inclusion of the corresponding redistribution in the canonical entry. 7 Other constructions lead to the creation of extra entries, because they correspond to secondary entries (5th type in the enumeration above) or because they involve redistributions that have not yet been identified in the Alexina format.

Once the entries to be produced are identified, we build sub-categorization frames. First, we build the frame corresponding to the maximal construction for each entry (the 6 For example, Qu P vs. N1, or à N1 vs. Prép N1 if in addition it is known that Prép can be à. 7 In the table of classes, the feature [passif par] (the standard passivability) is not yet correctly described, even for transitive classes. Considering this lack of information as a negative information (non-passivable), as done for other features, leads to a really incomplete lexicon. Therefore, we decided to add the corresponding %passif redistribution to all entries that have an argument whose syntactic function is Obj (direct object). Note that direct complements of the entries of table 32NM do not receive the function Obj (see below). Therefore, our heuristics is valid, apart from rare cases of non-passivability such as regarder (often to look at, but also to concern) in the sense of concerner (to concern).

MEBC for the canonical entry, and their unique construction for secondary entries). The realizations of these syntactic functions are built in two steps. First, the kind of phrase (nominal, infinitive, etc.) is determined. Then, possible introducers are extracted from the set of corresponding prepositions and other introducers (e.g., et -and). For the canonical entry, all variants of the MEBC lead to modifications of the resulting sub-categorization frame, by adding realizations and making some arguments optional.

Other types of information are then added so as to finalize the entry, such as the originating table and the corresponding row number, as well as a frequency information extracted from the DELA. Finally, syntactic macros concerning the auxiliary, the mood of completive arguments, idiomatic clitics (se, en, ne, etc.) and control phenomena are extracted and added to the final entry.

Resulting Lexicon

The resulting verbal lexicon contains 16,903 entries for 5,694 distinct verb lemmas (on average, 2.96 entries per lemma). As a comparison, the Lefff only contains 7,072 verbal entries for 6,818 distinct verb lemmas (on average, 1.04 entries per lemma). The resulting lexicon extracted from lglex, despite the fact that it describes fewer verbal lemmas, has a larger coverage in terms of syntactic constructions and therefore is much more ambiguous. At the extensional level, the Lefff has 361,268 entries whereas the lexicon extracted from lglex has 763,555 entries.

The construction of this lexicon from lglex according to the process described in this section is achieved by a perl script that contains less than 1,000 lines. The conversion in itself, i.e., the execution of the script of the whole lglex, takes less than a minute. 8Therefore, if a new version of the Lexicon-Grammar French verb tables or of the corresponding table of classes is released, building the new corresponding Alexina-format lexicon is a matter of seconds, and does not require any new development.

Integration in the FRMG Parser

The main goal of this work is to allow the use of the linguistic data coded in Lexicon-Grammar tables for French to be used as a lexical database for a French parser. Among the various parsers that rely on a syntactic lexicon in the Alexina format, we chose the FRMG parser [START_REF] Thomasset | Comment obtenir plus des méta-grammaires[END_REF]. It relies on a compact factorized Tree Adjoining Grammar (TAG) generated from a meta-grammar, and on the Lefff . The compilation and execution of the parser is performed by the DYALOG system [START_REF] De La Clergerie | DyALog: a tabular logic programming based environment for NLP[END_REF]. The result of the parsing itself is a derivation shared forest, that undergoes a symbolic (weight-based) disambiguation process so as to output only one parse. In case a sentence is not covered by the grammar and the lexicon, FRMG outputs several partial parses that cover disjoint parts of the sentence (however, no attempt is made to reassemble these partial parses into a global parse). FRMG takes as its input the result of the presyntactic processing chain SXPipe [START_REF] Sagot | SXPipe 2 : architecture pour le traitement présyntaxique de corpus bruts[END_REF], which converts a raw text into a lattice of forms known by the lexicon (namely, the Lefff ). 9The integration of the Alexina-format lexicon extracted from lglex in the FRMG parser is straightforward: in its standard configuration FRMG's lexer performs calls to a lexical database built from the Lefff . We shall call this standard parser FRMG Lefff . What is required to use the lexical information from Lexicon-Grammar verb tables is to replace verbal entries in the Lefff by those of the lexicon built from lglex while keeping other Lefff entries, to build the corresponding lexical database, and to tell FRMG to use it rather than the default Lefff -only one.

However, several verbal entries which are not covered by lglex had to be added as well: entries for auxiliaries and semi-auxiliaries, some raising verbs, impersonal verbs and light verbs. The result is a variant of the FRMG parser, that we shall call FRMG lglex , to distinguish it from the standard FRMG Lefff .

Evaluation and Discussion

We evaluated both FRMG Lefff and FRMG lglex by parsing the manually annotated part of the EASy corpus [START_REF] Paroubek | EASy : campagne d'évaluation des analyseurs syntaxiques[END_REF], i.e., 4,306 sentences of diverse genres (journalistic, medical, oral, questions, literature, and others).

We used the metrics defined and used during the first French parsing evaluation campaign EASy, which took place at the end of 2005 [START_REF] Paroubek | Data, Annotations and Measures in EASy, the Evaluation Campaign for Parsers of French[END_REF]. These metrics rely on both (nonrecursive) « chunks » and « relations » (dependencies between full words), for which the standard measures (precision, recall, f-measure) are applied. In this paper, we simply provide f-measures.

Before discussing the results of these experiments, some precautions must be taken:

-the conversion process described in this paper and its still preliminary implementation certainly contain errors, and we evaluate a variant of FRMG that relies on converted entries extracted from Lexicon-Grammar tables, not directly on Lexicon-Grammar entries from the tables; -the Lefff was developed in parallel with EASy campaigns, unlike Lexicon-Grammar tables; some choices in the EASy annotation guide may have influenced choices made during the development of the Lefff , whereas it is obviously not the case for Lexicon-Grammar tables; -as mentioned in the previous section, lglex had to be completed by various lexical entries from the Lefff , but other entries may still need to be added.

Comparative results for both parsers are shown on Table 1, with detailed results for some illustrative sub-corpora. As can be seen, results are for now a bit better for FRMG Lefff . We do not think that this result questions the relevance of using Lexicon-Grammar tables in a parser, especially given the above-mentioned precautions. In particular, we remain convinced that using as rich a lexical resource as possible is an efficient way to improve the quality of a parser, as has been shown for example by the results of the work described in [START_REF] Sagot | Error mining in parsing results[END_REF]. However, parsing times are more than twice as high with FRMG lglex as with FRMG Lefff (median average time per sentence: 0.62 s vs. 0.26 s), which is certainly a consequence of the higher average number of entries per lemma, which is three times higher in the lexicon extracted from lglex than in the Lefff (see above). In fact, these higher parsing times necessarily lead to a higher ratio of parsing failures because of reaching the timeout, which leads to the construction of partial parses whose quality can only be lower.

Nevertheless, on several sub-corpora, FRMG lglex performs better in terms of chunk fmeasure; but results on relations are better with FRMG Lefff , apart from two sub-corpora. A careful study of the results shows the following interesting facts:

-FRMG lglex performs better than FRMG Lefff on several relations, such as "adjective modifier" and "adverb modifier", and also on two relations for which results are anyway quite low ("preposition modifier" and "apposition"); -the relation "(subject of object) attribute" is that for which the difference in terms of recall is the highest (34.0% vs. 58.5%); -the high number of verb arguments listed in lglex's sub-categorization frames tends to fool the usual disambiguation heuristics according to which "arguments are preferred to modifiers": any phrase that can be parsed as a verbal argument tends to be done in this way. For example, in a sentence such as [...] on estime que cette décision [ferait] dérailler le processus de paix (it is estimated that this decision would derail the peace process), FRMG lglex considers de paix (peace genitive ) as an argument of estimer (estimer qqch de qqch/qqn -to estimate something about something/somebody), whereas FRMG Lefff gets the correct parse.

In the short term, the following statement can be made. Many sentences get a full parse from FRMG lglex but not from FRMG Lefff , and vice versa. For example, on the general_lemonde sub-corpus, 177 sentences are fully parsed by both parsers, 85 only by FRMG Lefff , 76 only by FRMG lglex , and 111 by neither of them. Since experience shows that partial parses lead to worse results (approx. 10 points lower in terms of f-measure on EASy relations), an interesting experiment would be to couple both parsers in such a way that if only one of them builds a full parse for a given sentence, this parse is kept (what should be done in other cases remains an open question). The results of such a "meta-parser" should be better than those of both parsers.

In the long term, it is important to benefit from this complementarity between both resources. It will be interesting to study the differences between errors made by both parsers, in particular thanks to techniques such as those described in [START_REF] Sagot | Error mining in parsing results[END_REF]. This could lead to an improvement for both resources, and in particular the lexicon converted from lglex. Perhaps we will realize that most errors come from the conversion process; but some errors may come from errors in Lexicon-Grammar tables, and may therefore allow us to improve them.

Conclusion and Future Work

In this paper, we introduced a methodology and a tool for converting the textual version of Lexicon-Grammar tables into an NLP lexicon based on the Alexina framework, i.e., in the same format as the Lefff syntactic lexicon for French, which is used by the FRMG parser. The relevance of the resulting lexicon is confirmed by its use for parsing the evaluation corpus of the French parsing evaluation campaign EASy.

The first step described here has allowed us to identify several problems in the input data (tables and tables of classes), but also several simplifications and approximations in the conversion process. Therefore, there is space for significant improvements, that could eventually lead to the construction of a syntactic lexicon for French based on Lexicon-Grammar tables. Such a lexicon would improve the quality of existing tools and resources, e.g., by fusion with other lexical resources and by integration in a largecoverage parser.

However, as mentioned in the introduction, we intend to enlarge the scope of our approach by applying the same approach on French to Lexicon-Grammar tables for other categories, but also on tables for other languages, as soon as the corresponding tables of classes become available. The next step, which should be taken soon, will deal with French predicative nouns, verbal idiomatic expressions and adverbs.

  1. the "base" construction(s), defining feature for the originating class of the entry; 2. "extended base" constructions, obtained by adding extra arguments to the base construction; in practice, these constructions are all intermediate constructions between the base construction and a construction called "maximal extended base" construction, or MEBC; 3. constructions that are variants of the base construction, obtained by deleting one or several arguments, or by changing the realization type (e.g., Qu P can become V

i inf W, as for the direct object of savoir -to know -, that can be a finite phrase but also an infinitive phrase); 4. constructions that are in fact redistributions, such as [passif de], that denotes the possibility of having a passive with an agent introduced by de (cf. Pierre est aimé de Marie -Pierre is loved by Marie) or N 1 est Vpp de ce Qu P (cf. Marie est étonnée de ce que Pierre soit là -Marie is surprised that Pierre is here) ; 5. constructions that should seemingly have led to distinct entries, called "secondary entries", such as neutral constructions of transformations like N 1 se V de ce Qu P (cf. Luc se félicite d'avoir réussi à séduire Léa vs. Max félicite Luc qu'il ait réussi à séduire Léa -Luc is very pleased he succeeded in seducing Léa vs. Max congratulates Luc for having succeeded in seducing Léa).

  The syntactic function of each argument is obtained by the following heuristics. First, the first argument always receives the function Suj (subject). The first post-verbal argument, if it is direct, receives the function Obj, apart from entries of table 32NM. Then, an argument introduced by à (resp. de) receives the syntactic function Objà (resp. Objde), except if an additional indicator contradicts this choice (e.g., for an N 1 argument introduced by à, the feature à N 1 = Ppv =: le shows it must receive the syntactic function Obj, as in Il apprend à conduire / Il l'apprend -He is learning how to drive / He is learning it). Arguments introduced by Loc have the syntactic function Loc, except those of the form Loc N i source or for which Loc N i =: de N i source is a valid feature, which receive the syntactic function Dloc. Finally, other arguments are considered as Att if they are direct, and as Obl if they are introduced by a preposition (Obl2 if an Obl already exists).

Table 1 .

 1 EASy results for FRMG Lefff and FRMG lglex , expressed in terms of f-measure. For reasons of space, figures are given for the whole EASy corpus and for only a sample of sub-corpora.

		Chunks		Relations
	Sub-corpus	FRMG Lefff FRMG lglex FRMG Lefff FRMG lglex
	general_lemonde	86.8%	82.8%	59.8%	56.9%
	general_senat	82.7%	83.1%	56.7%	54.9%
	litteraire_2	84.7%	81.5%	59.2%	56.3%
	medical_2	85.4%	89.2%	62.4%	58.6%
	oral_delic_8	74.1%	73.6%	47.2%	48.5%
	questions_amaryllis	90.5%	90.6%	65.6%	63.2%
	EASy corpus overall	84.4%	82.3%	59.9%	56.6%

This also motivated the work described in[START_REF] Gardent | Maurice Gross' Grammar Lexicon and Natural Language Processing[END_REF]. A comparison between the textual version of the tables, that is used in the present work, and the work of[START_REF] Gardent | Maurice Gross' Grammar Lexicon and Natural Language Processing[END_REF] can be found in[START_REF] Constant | A generic tool to generate a lexicon for NLP from Lexicon-Grammar tables[END_REF].

Partial on-line distribution under the LGPL-LR license at http://infolingu. univ-mlv.fr/english, Language Resources > Lexicon-Grammar > View.

On-line distribution under the LGPL-LR license at http://gforge.inria.fr/ projects/alexina/

à-scompl and de-scompl represent realizations of the form à/de ce que P.

On a 2.4 GHz machine using Ubuntu Linux.

SXPipe includes, among others, modules for (deterministic) sentence splitting and tokenization, as well as non-deterministic spelling error correction, named entity detection and identification of compound forms.