L Zaccarelli

G Soldati
email: gaia.soldati@ingv.it

A Michelini
email: alberto.michelini@ingv.it

Variations of crustal elastic properties during the 2009 L'Aquila earthquake inferred from cross-correlations of ambient seismic noise

We retrieve seismic velo city variations within the Earth's crust in the region of L'Aquila (central Italy) by analyzing cross-correlations of more than two years of continuous seismic records. The studied period includes the April 6, 2009, M w 6.1 L'Aquila earthquake. We observe a decrease of seismic velocities as a result of the earthquake's main shock. After performing the analysis in different frequency bands between 0.1 and 1 Hz, we conclude that the velocity variations are strongest at relatively high frequencies (0.5-1 Hz) suggesting that they are mostly related to the damage in the shallow soft layers resulting from the co-seismic shaking.

Introduction

On April 6, 2009 a M w 6.1 earthquake struck the central Apennines region near L'Aquila (Italy) causing severe damage and more than 300 fatalities [Scognamiglio et al.,2 0 1 0 ] . This area had been long recognized as seismically active [seet h eo ffi c i a ls e i s m i ch a z a r d map of Italy, MPS Working Group ,2 0 0 4 ]a n da no c c u r r e n c eo fas t r o n ge a r t h q u a k ei n the central Apennines could not be considered as totally unexpected. Before the main shock, an increase in the rate of seismicity started on September 2008 and many small size events (about 300 with M L ≤ 2.5)occurredbeneaththeL'Aquilacityarea. Thisforeshock sequence culminated with a M L =4 .1 earthquake on March 30, 2009. In the following days, the seismicity decreased until two earthquakes (M L =3 .9 and M L =3 .5)o c c u r r e d just a few hours before the L'Aquila main shock. In agreement with the extensional tectonics of the central Apennines, the focal mechanism of the L'Aquila earthquake has been determined to be a normal fault on a South-West dipping plane with the rupture area of ∼20x15 km 2 and the dipping angle of about 50 degrees [Cirella et al.,2 0 0 9 ] . T h e main shock was followed by an aftershock sequence that included 33 earthquakes greater than M L =4.

In this study, we use a recently proposed monitoring technique based on ambient seismic noise. The idea of this method is to use signals reconstructed from repeated crosscorrelations of continuous seismic records as virtual seismograms generated by highly repeatable sources. In case of well distributed noise, the reconstructed virtual sources are close to point forces and the cross-correlations functions can be considered as Green In a seismogram or in a correlation function, the delay accumulates linearly with the lapse time when the wave speed changes homogeneously within the medium. As a consequence, a small change can be detected more easily when considering late arrivals.

This makes the use of coda waves particularly suited to measure temporal variations.

This can be done either by using the so-called stretching technique [e.g., Wegler and Sens-Schönfelder ,2007]orwithamethodthatwasinitiallydevelopedforrepeated earthquakes (doublets) by [START_REF] Poupinet | Monitoring velocity variations in the crust using earthquake doublets: an application to the Calaveras Fault, California[END_REF]. Here, we use this latter approach that has been specifically adopted to make measurements from the noise cross-correlations [e.g., However, records of one of these stations contained too many gaps and we finally decided to use three stations: CAMP and FIAM from INSN and AQU from MedNet (Figure 1).

The longest period of data availability at these three stations was between March 27, 2008 and April18, 2010.

We re-sampled time series recorded at the three stations in order to get a perfect time synchronization and filled existing small gaps via a linear interpolation. Then, we preprocessed the vertical component seismograms by whitening their spectra between 0.1 technique to the cross-correlations of the seismic noise. The main idea of the method is that the noise cross-correlations computed from subsequenttimewindowscanbeanalysied similar to records from earthquake doublets. When analyzinglongtimeseries,wecompare asinglereferencecross-correlationwithmanysubsequentcurrent functions. The reference cross-correlation CC R for a particular station pair is obtained from stacking all available cross-correlations for this pair and, therefore, is representative of the background crustal state. The current cross-correlations CC C are obtained from stacking a small sub-set of cross-correlations representative of a state of the crust for a given short period of time.

There is a trade-off between the length of the stack required toh a v es t a b l ee s t i m a t e so f the CC C and the time resolution for detecting the variations. To find an optimal stacking duration for the current function we tested different lengthsbetw een10and100days. F or each tested stacking length, we computed all possible functions CC C by applying moving windows shifted by two days. Then, we computed the correlation coefficient r between the reference function CC R and every CC C .T h ed i s t r i b u t i o no fr characterizes the similarity between CC R and CC C for a given stacking length. We represent the overall degree of similarity by the mean and the standard deviation of this distribution. Figure 2 shows these parameters for the three station pairs. We observe thatt h ed e g r e eo fs i m i l a r i t y

DRAFT N o v e m b
∆t t = - ∆v v (1)
where ∆v v is the relative uniform seismic velocity perturbation that can be estimated in the second step from a single station pair k via linear fitting of the following equation:

δt k i = - ∆v v k • t i (2)
In order to obtain one estimates representative of the entirec r u s t a lv o l u m e ,w em e r g e d together the delays δt k i measured from the three station pairs before proceeding witht h e second step of the analysis. We computed the median value δt i of the delays δt k i for every ith window, and we inserted it into (2) to estimate of ∆v v for the entire region encompassed by the three stations. When performing this analysis, we removed the central part of the cross-correlations containing direct waves (group velocities faster than 2.5 km/s; see To estimate uncertainties of our measurements, we followed the method proposed by Clarke et al.

[2011] and performed a synthetic test on the L'Aquila noise cross-correlations.

We p erturb ed the reference cross-correlation function by stretching its waveform and simulating different values of velocity variations (from 0.01% to 0.5%). Then, we added ar a n d o mn o i s ew i t has i g n a l -t o -n o i s er a t i oo f5( t h a ti st h em ean value measured from the observed cross-correlations). Finally, we applied the MWCS technique to measure the apparent velocity variations ∆v v between the perturbed cross-correlations and the original CC R .T h eR M Sd e v i a t i o n sb e t w e e nt h ee s t i m a t e dv e l o c i t yv a r i a t i ons and those introduced through stretching characterize the uncertainties of our measurements.

To investigate the depth extent of the measured crustal velo city perturbations, we Our results are based on current cross-correlation functions stacked over a 50 day period and, therefore, do not have the time resolution required to identify possible short-term precursory variations and to separate them from the co-seismic effect. On the other hand, with stacking large data volumes our estimation of the co-seismic velocity reduction is inherently very robust. The observed velocity reduction is larger at higher frequencies.

Therefore, we prefer the hypothesis the perturbation is mainly due to damaging of shallow soft sedimentary layers by the co-seismic strong ground motion [e.g., Wu et al.,2009]. This effect may be also enhanced by the presence of fluids.

We compare the co-seismic p erturbation observed during the L'Aquila earthquakes with other cases when the co-seismic crustal velocity variationsweremeasuredfromnoisecrosscorrelations (Table 2). The co-seismic velocity drop measured for the L'Aquila earthquake (∼ 0.3%)i ss i gn i fi c an t l yl ar ge rt h ant h ev al u e sm e as u r e dw i t h i nas i milar frequency band for the M w 6.0 Parkfield and the M w 7.9 Wenchuan events (∆v/v ∼ 0.08% as reported by [2010], respectively). At the same time, a stronger variation (∼ 0.6%)hasbeenobservedwith the stretching technique and frequencies higher than 2 Hz during the M w 6.6 Mid-Niigata earthquake. The results of this comparison suggest that the level of measured co-seismic velocity variation is not a simple function of the total moment release during an earthquake but is controlled by different factors such as local geological conditions and, possibly, focal mechanism and source depth. Also, the frequency range used in the analysis controls the depth extent of the measured anomaly.

DRAFT N o v
Finally, the aperture of the used seismic network (i.e., the distance between the station pairs) can play an important role. So far, the velocity variations reported in this study were measured over a relatively large area. Therefore, they may be less sensitive to the processes occurring in the immediate vicinity of the fault, where stress-induced velocity perturbations are expected to be most important.

  functions [e.g., Weaver and Lobkis ,2 0 0 1 ;Shapiro and Campillo,2 0 0 4 ;Sabra et al.,2 0 0 5 ; DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT Shapiro et al.,2 0 0 5 ] . H i g h l ya c c u r a t et e m p o r a lm o n i t o r i n gc a nb ea l s op e r formed even with inhomogeneous noise sources distributions when a perfect reconstruction of the Green function is not achieved [e.g., Hadziioannou et al.,2009] . T h ec h an ge softh etra v e lti m e s measured from the noise cross-correlations reflect variations of the elastic properties in the propagating media, i.e., in the Earth's crust. This approach has been recently applied to monitor active volcanoes [e.g., Sens-Schönfelder and Wegler ,2 0 0 6 ;Brenguier et al., 2008a; Duputel et al.,2 0 0 9 ;Mordret et al.,2 0 1 0 ]a n dl a r g es e i s m o g e n i cf a u l t s[ e . g . ,Wegler and Sens-Schönfelder ,2007;Brenguier et al.,2008b ;Chen et al.,2010]an dtod e te c t seasonal changes in the Earth's crust resulting from thermoelastic variations [e.g., Meier et al.,2 0 1 0 ] .

and 1

 1 Hz and by normalizing their amplitude through a one-bit normalization. In this way, the contributions arising from strong transient phenomena were reduced in both time and frequency domains [e.g., Bensen et al.,2 0 0 5 ;Brenguier et al.,2 0 0 8 b ] . F i n a l l y , we computed cross-correlations between the three pairs of stations for every hour of the available recordings. DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT 3. Measurement of seismic velocity variations We adopted the Multi Window Cross-Sp ectrum (MWCS) analysis [e.g., Clarke et al., 2011]. This technique was first proposed by Poupinet et al. [1984] for retrieving the relative velocity variation between earthquake doublets. Brenguier et al. [2008a, b] applied this

Table 1 )

 1 b ecause they may b e sensitive to the changing p osition of the noise sources [e.g., Froment et al.,2 0 1 0 ] . R e l a t i v ev e l o c i t yv a r i a t i o n sw e r et h e nc o m p u t e db ytaking into DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT account the coda of the cross-correlation up to a length of 60 sw he rethes ignalde c re as e s to values close to the noise level.

  performed the MWCS analysis inside three different frequencyb a n d s : [ 0 . 1 -1 ] ,[ 0 . 1 -0 . 6 ] , and [0.5-1] Hz. It has been shown both theoretically and observationally that at these frequencies the coda of seismograms and correlation functions are mainly composed of surface waves [e.g., Hennino et al.,2001;Margerin et al.,2009]. W ethereforeexpectthat the sensitivity of the coda waves to a velocity change at depthd e p e n d so nt h e i rs p e c t r a l content with shorter periods sensitive to shallower structures and longer periods sampling deeper parts of the crust. The measurement results for the three frequency bands are presented in Figure 3 and show a sudden velocity decrease at the time of occurrence of the L'Aquila main shock. The amplitude of this velocity drop is largest at frequencies DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT higher than 0.5 Hz and decreases at lower frequencies. This indicates that a large part of the observed variations have their likely origin within the shallow crustal layers. 4. Discussion Al i m i t e dn u m b e ro fa v a i l a b l es t a t i o n s( o n l yt h r e e )a n dt h ef act that only one of them is located in the immediate vicinity of the earthquake fault did not allow us to identify exact regions that produced the observed velocity variations. Also, the dataset used in this study did not allowu st om a k e robust measurements with refined time resolution. A denser network covering the source area would be required to obtain better space and time resolutions [e.g., Brenguier et al.,2 0 0 8 a ] . T h e r e f o r e ,w ei n t e r p r e th e r eo n l yt h em o s t robust average features. The results presented in our study show that the L'Aquila mains h o c kc a u s e dad etectable reduction of seismic velocities within the surrounding crust. We observe that the velocity dropped by 0.3%, which is more than 3 times largert h a nt h efl u c t u a t i o n s observed before the main shock. Co-seismic velocity reductions can be attributed to increasing crack and void densities in the shallow crustal structure and/or to reduced compaction of the near-surface granular material. The presence and migration of fluids can further contribute to modification of the seismic properties in the shallow crust. Our results can be compared with other studies that have addressed changes of the crustal parameters prior and after the L'Aquila earthquake. Amoruso and Crescentini [2010] used strain measurements obtained in the Gran Sasso laboratory during the two years prior to the main shock to infer that no anomalous signal was observed. They concluded DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT that the possible earthquake nucleation zone was confined to av olumelessthan100km 3 . In contrast, v p /v s anomalies have been reported by Di Luccio et al. [2010] in the weeks prior to the main shock with an abrupt variation after the M L =4 .1 foreshock occured on March 30. Similar results were obtained by Lucente et al. [2010] who used shear wave splitting in addition to v p /v s ratios. They attribute the velocity anomalies occurring in the week prior to the main shock to a complex sequence of dilatancy-diffusion processes in which fluids play a key role. Terakawa et al. [2010] inverted the stress field obtained from the aftershock sequence focal mechanisms to determine the fluid pressure and to conclude that the spatial pattern of the sequence is driven mainly by fluid migration.

X- 1 1

 1 e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT Brenguier et al. [2008a] and Chen et al.

  Amoruso, A., and L. Crescentini, (2010), Limits on earthquake nucleation and other pre-seismic phenomena from continuous strain in the near field of the 2009 L'Aquila earthquake, Geophys. Res. Lett., 37,L 1 .D., M.H. Ritzwoller, M.P. Barmin, A.L. Levshin, F.Lin,M.P .Mosc hetti,N.M. Shapiro, and Y. Yang (2007), Processing seismic ambient noise data to obtain reliable broad-band surface wave dispersion measurements, Geophys. J. Int., 169,1 2 3 9 -1 2 6 0 , doi: 10.1111/j.1365-246X.2007.03374.x. Brenguier, F., M. Campillo, C. Hadziioannou, N. M. Shapiro, R. M. Nadeau, and E. Larose (2008a), Postseismic relaxation along the San Andreas fault at Parkfield from continuous seismological observations, Science, 321,1 4 7 8 -1 4 8 1 . Brenguier, F., N. M. Shapiro, M. Campillo, V. Ferrazzini, Z. Duputel, O. Coutant, and A. Nercessian (2008b), Towards forecasting volcanic eruptions using seismic noise, Nature Geoscience, 1,1 2 6 -1 3 0 . Chen, J. H., B. Froment, Q. Y. Liu, and M. Campillo (2010), Distribution of seismic wave speed changes associated with the 12 May 2008 Mw 7.9 Wenchuan earthquake, Geophys. Res. Lett., 37,L 1 ., and 29 others (2009), The 2009 L'Aquila (central Italy) M w 6.3 earthquake: Main shock and aftershocks, Geophys. Res. Lett., 36,L 1 8 3 0 8 , doi:10.1029/2009GL039627. Cirella A., A. Piatanesi, M. Cocco, E. Tinti, L. Scognamiglio, A. Michelini, A. Lomax, and E. Boschi (2009), Rupture history of the 2009 L'Aquila (Italy) earthquake from nonlinear joint inversion of strong motion and GPS data, Geophys. Res. Lett., 36,L 1 9 3 0 4 , DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT Terakawa, T., A. Zop orowski, B. Galvan, and S. Miller, (2010), High-pressure fluid at hypocentral depths in the L'Aquila region inferred from earthquake focal mechanism, . C., and R. S. Crosson, (1990) Determination of teleseismic relative phase arrival times using multi-channel cross-correlation and lest squares, Bull. Seismol. Soc. Am., 80,1 ,1 5 0 -1 6 9 . Weaver, R. L. and O. I. Lobkis (2001), Ultrasonics without a source: thermal fluctuation correlations at MHz frequencies, Phys. Rev. Lett., 87,1 3 4 3 0 1 , doi:10.1103/PhysRevLett.87.134301. Wegler, U., Sens-Schönfelder C. (2007), Fault zone monitoring with passive image interferometry, Geophys. J. Int., 168,1 0 2 9 -1 0 3 3 . Wu, C., Z. Peng, and Y. Ben-Zion (2009), Non-linearity and Temporal Changes of Fault Zone Site Response Associated with Strong Ground Motion, Geophys. J. Int., 176, 265-278, doi: 10.1111/j.1365-246X.2008.04005.x. DRAFT N o v e m b e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT

Figure 1 .Figure 2 . 1 0. 6 ]

 1216 Figure 1. Map of the central Apennines showing the location of the L'Aquila epicenter (black

  short stacking durations and then it tends to stabilize. We selected av a l u eo f5 0d a y sa ss t a c k i n gl e n g t hf o rc o m p u t i n gt h ec u r r e n tc o r r e l a t i o nf u n c t i o n s .The MWCS analysis consists of two computational steps [e.g., Clarke et al.,2 0 1 1 ] . I n the first step, we estimate for a station pair k delay times δt k i between CC R and CC C

	within a set of time windows centered at t i .I nc a s eo fu n i f o r mv e l o c i t yp e r t u r b a t i o n s ,
	the measured delays δt k i are expected to be a linear function of time t i with a slope
	corresponding to the relative time perturbation:

e r4 ,2 0 1 1 ,7 : 1 5 p m DRAFT increases rapidly for

Table 1 .

 1 Parameters of the three inter-stations paths used in the study. The Rayleigh wave arrival times are roughly estimated considering a group velocity of 3 km/s [Chiarabba et al.,2009]). Parts of the correlation functions with group velocities faster than 2.5 km/s we excluded from the analysis to avoid the influence of the noise source variability in direct arrivals.

	stations	distance Rayleigh arrival cutoff
		km	s	s
	AQU_CAMP	20	6.67	±7.5
	AQU_FIAM	26	8.67	±10
	CAMP_FIAM	38	12.67	±15

Table 2 .

 2 Comparison between the L'Aquila event and other earthquakesw h e r ec o -s e i s m i c velocity variations were measured from noise cross-correlations. Values of velocity variations are from Brenguier et al. [2008a], Wegler and Sens-Schönfelder [2007], and Chen et al. [2010], for the Parkfield, the Mid-Niigata, and the Wenchuan earthquakes, respectively.

	Earthquake M w depth focal mechanism ∆v/v frequency stations
			km		%	Hz
	L'Aquila	6.1 8.8	normal	0.15	0.1-0.6	3
					0.3	0.1-1
					0.4	0.5-1
	Parkfield 6.0 7.9	strike-slip	0.08	0.1-0.9	13
	Mid-Niigata 6.6	5	thrust	0.6	> 2	1
	Wenchuan 7.9	19	thrust	0.08	0.3-1	> 30

Acknowledgments. The data used in this study were provided by the Istituto Nazionale di Geofisica e Vulcanologia. We thank G. Moguilny for maintaining the Cohersis cluster on which all computations were performed. This work was supported by Agence Nationale de la Recherche (France) under contract ANR-06-CEXC-005 (COHERSIS) and by a FP7 ERC Advanced grant 227507 (WHISPER).


Pierre Rodiere

Thierry Klein

Louis Lemberger

Klaus Hasselbach

Zhao-Sheng Kacmarcik

H Q Wang

X Y Luo

H H Lu

Wen

P Rodière

A Demuer

J Kačmarčik

Z S Wang

H Q Luo

X Y Lu

H H Wen

F Gucmann

C Marcenat

Scaling of the physical properties in Ba(Fe,Ni)2As2 single crystals: Evidence for quantum fluctuations

come

I. INTRODUCTION

The discovery of superconductivity up to 55K in ironbased pnictides [1] has generated tremendous interest. Even though the symmetry of the order parameter in this multi-band system is not yet determined with certainty, a popular model is based on magnetic fluctuations associated with a sign reversal of the order parameter between the hole and electron sheets of the Fermi surface (so called s± model [2]). It has then been suggested by V.G.Kogan [3,4] that the critical temperature (T c ) could be strongly suppressed not only by scattering breaking the time reversal symmetry (spin-flip scattering) but by any scattering mechanism. As a consequence, for T c << T c,0 (T c,0 being the critical temperature in the absence of scattering) and an average of the order parameter over the Fermi surface being equal to zero, the superfluid density (ρ s ) is expected to vary as:

ρ s ∝ 1/λ 2 ∝ T 2 c -T 2 (1)
leading to a London penetration depth (λ) scaling as : λ(0) ∝ 1/T c and ∆λ(T ) = λ(T ) -λ(0) ∝ T 2 /T 3 c (for T → 0). Moreover, the slope of the upper critical field close to T c , H c2 = -(dH c2 /dT ) |T →Tc is then expected to be proportional to T c and finally the specific heat jump at T c , ∆C p ∝ T 3 c . Some indications for the ∆λ(T ) [5] or H c2 and ∆C p [6] scalings have been observed in various pnictides but a systematic analysis of the evolution of all those quantities on a given system was still lacking.

Moreover, the dependence of ρ s (0) on T c remains controversial. It has been initially suggested [7] that ρ s (0) could scale as T c but, measurements in overdoped Ba(Co x Fe 1-x ) 2 As 2 rather suggested that ρ s (0) could be either proportional to T 2 c [8] or, on the contrary, almost T c independent [9]. Those later measurements also indicated a strong reduction of the superfluid density in underdoped samples, which has been attributed to the coexistence of superconductivity and magnetism.

It is worth noting that somehow contradictory results have also been observed in cuprates, emphasizing the fact that the ρ s (0) vs T c dependence can be very sensitive to the sample quality and/or dimensionality [10]. As in pnictides, initial measurements suggested that ρ s (0) ∝ T c in samples close to optimal doping [11] and this dependence found a straightforward explanation in this quasi 2D system assuming that T c is close to the Kosterlitz-Thouless-Berezinskii transition temperature T c ∼ T KT D = Φ 2 0 t/8πµ 0 λ 2 (t being the interlayer spacing). However, strong deviations from this behavior have been observed in highly underdoped samples for which ρ s (0) was found to scale as T ζ c with 1.6 < ζ < 2.3 in thick films [12] and ultraclean crystals [13,14] or ζ ∼ 1 in very thin films [10]. This change in ζ from ∼ 2 to 1 has been attributed to a dimensional crossover associated to the proximity of a quantum critical point [15].

We present here a detailed analysis of the doping dependence of T c , λ(0), ∆λ(T ) and specific heat in the Ba(Ni x Fe 1-x ) 2 As 2 system. The measurements have been carried out in a series of Ba(Ni x Fe 1-x ) 2 As 2 single crystals grown by self flux method. Details on the sample elaboration are given in [16]. We will show that λ(0) ∝ 1/T 0.85±0.2 c , ∆λ(T ) ∝ T 2.3±0.3 (for T < T c /3) and ∂∆λ/∂T 2 |T →0 ∝ 1/T 2.8±0.3 c in both underdoped and overdoped samples. Moreover, H c2 decreases with T c in overdoped samples but increases with decreasing T c for underdoped samples. Those results strongly suggest the presence of pair breaking effects and we will show that they can be consistently described assuming that those pair breaking effects are associated with the proximity of superconducting quantum critical points.

II. LONDON PENETRATION DEPTH

A. Lower critical field measurements

The local field has been measured by placing the samples on miniature GaAs-based quantum well Hall sensors. The external field was increased up to H a and swept back to zero in order to measure the remanent field (B rem ) trapped in the sample after the field cycle. All measurements were performed for H a c. In the Meissner state, the external field is fully screened out and B rem is equal to zero. Vortices start to penetrate into the sample for H a > H p (the first penetration field) and remain partially pinned in the sample when the field is swept back to zero, leading to a finite B rem value (see Fig. 1a). For H a > H p , the remanent fields increases approximatively as (H a -H p ) 1/γ with 1/γ ∼ 1.5 -2.5 and H p as hence been obtained by linearly extrapolating B γ rem to zero (see Fig. 1a). In order to avoid spurious effects associated to strong pinning preventing the vortex diffusion to the center of the sample (and hence the absence of any signal on probes located close to the center of the sample) H p has been measured on several locations with an array of miniature probes. As expected the measured H p value (slightly) increases as the distance between the probe and the sample edge increases. The H p values reported in Table 1 have been obtained with probes located at ∼ 5 to 10µm from the edge and we estimate to ∼ 20 % the possible overestimation of this field.

This first penetration field is smaller than the lower critical field (H c1 ) due to the expulsion of the flux lines for H a < H p which increases the local field in the vicinity of the sample edges so that H c1 = αH p with α > 1. In the presence of geometrical barriers (GB) [17], α GB ≈ tanh(βd/w) -1/2 where β varies from 0.36 in strips to 0.67 in disks (d and w being the thickness and width of the sample, respectively) whereas for elliptical samples (i.e. without geometrical barriers) the standard "demagnetization" factor α elliptical = 1/(1 -N ) ∝ w/d. All samples were chosen to present very similar aspect ratios (see Table 1) leading to very similar corrections for the whole series whatever the origin of α. In the following, we approximated the samples by disks leading to 2.4 < α GB < 2.8 from one sample to the other (see Table 1). However, it is important to note that a standard "demagnetization" correction would lead to 2.7 < 1/(1 -N ) < 3.3 for our d/w values (∼ 1/4) and would hence only lead to an overestimation of H c1 by ∼ 12% i.e. an underestimation of λ of ∼ 6%. In the following, to evaluate the error bars, the uncertainty on α 3) introducing only one free parameter (corresponding to the absolute value at zero T ) for the whole set of data (see text for details). The shaded cones correspond to the values expected from the amplitude of the specific heat jump at Tc (see Fig. 4) and the slope of the upper critical field (see Fig. 5 and text for details).

is taken to ±20%. The temperature dependences of H c1 (for the indicated x values) are displayed in Fig. 1b.

Finally, λ(0) has been deduced from the upper and lower critical fields writing : [18], see section III) and µ 0 H c1 = (Φ 0 /4πλ 2 ).(Ln(κ) + c(κ)) where κ = λ/ξ TABLE I. x, d, w and l are the composition, thickness, width and length of the Ba(NixFe1-x)2As2 samples, respectively. The first penetration field Hp has been defined as the field above which a remanent field is observed in the sample and the lower critical field Hc1 (see Fig. 1) is deduced from Hp introducing demagnetization corrections due to geometrical barriers (µ0Hc1[G] = αGB × µ0Hp[G] (see text). λ is the London penetration depth (the values between brackets are deduced from specific heat measurements) and β = ∂λ/∂T 2 (see Fig. 4). Hc2 is the upper critical field (see Fig. 5, the values deduced from the irreversibility field are marked by an * ). All values are given for T → 0. ∆Cp/Tc is the amplitude of the specific heat jump at T = Tc (in mJ.mol -1 .K -2 ). Gi is the Ginzburg number (see text) and Tc the critical temperature. Measurements techniques : HP=Hall Probe, Cp=Specific Heat and TDO=Tunnel Diode Oscillator.

µ 0 H c2 = Φ 0 /2πξ 2 (with H c2 (0) ∼ 0.7.T c .(dH c2 /dT ) |T →Tc
x d(µm) w(µm) l(µm) µ0Hc1 ∼ αGB × µ0Hp λ(nm) β(nm/K 2 ) µ0Hc2(T) κ ∆Cp/Tc Gi(10 [9]. Our measurements do hence not support the scenario of a sharp increase of λ(0) due to the presence of a magnetic gap in underdoped samples but rather suggest that only a small fraction of the Fermi surface is affected by the antiferromagnetic coupling.

Note that (dH c1 /dT ) |T →Tc (and hence λ(0)) can also be deduced from specific heat measurements (see section III). Indeed, the amplitude of the specific heat jump at T c is equal to :

∆C p = (µ 0 T c ).(dH c /dT ) 2 |T →Tc ∼ (µ 0 T c ).(dH c2 /dT ) |T →Tc .(dH c1 /dT ) |T →Tc /[ln(κ + 0.5].
Deducing H c2 (T ) from the shift of the anomaly under magnetic field (see section III.A), one directly obtains (dH c1 /dT ) |T →Tc and λ Cp (0) can then be calculated using the same procedure as above, assuming that

H c1 (0) ∼ 0.7.T c .(dH c1 /dT ) |T →Tc . The corresponding H c1 (T → T c ) = (T -T c ) × (dH c1 /dT ) |T →Tc and λ Cp (0)
values have been reported on Fig. 1b (shaded cones) and Fig. 2a (crosses), respectively. It is important to note that those values do not depend on any demagnetization correction. As shown in Fig. 2a, the as-deduced λ Cp values are in reasonable agreement with those deduced from H p (λ Hp ) measurements (λ Hp /λ Cp ∼ 0.7) and both measurements lead to very similar dependences on T c .

The most remarkable feature is the very large variation of the superfluid density which varies over one order of magnitude for T c values ranging from ∼ 6.8K to ∼ 20.2K. Such a strong dependence is unexpected in conventional superconductors, but strongly suggests the presence of pair breaking effects.

B. Tunnel Diode Oscillator Technique

The samples were glued at the end of a sapphire rod which was introduced in a coil of inductance L. The variation of the London magnetic penetration depth induces a change in L and hence a shift of the resonant frequency δf (T ) = f (T )-f (T min ) of a LC oscillating circuit (14MHz) driven by a Tunnel Diode. This shift, renormalized to the one corresponding to the extraction of the sample from the coil (∆f 0 ) is then equal to the fraction (δV /V ) of the sample which is penetrated by the field. For H c, δV is related to the in-plane penetration depth λ ab through some calibration constant depending on the sample geometry. However, this constant can be altered by edge roughness effects (see discussion in [20]) and we have hence decided to perform all measurements with H ab. Indeed, the surfaces parallel to the ab-planes are much flatter and δV /V is, in this case, directly given by

δV /V ∼ 2(λ c /w+λ ab /d) = δV /V ∼ 2/d×[λ ab +(d/w)λ c ]
without any geometrical correction (λ c being the penetration depth parallel to the c-axis). In contrast to H c1 measurements for which we used rather "thick" (d/w ∼ 1/4) samples in order to reduce the uncertainty related to geometrical corrections, we have, in this case, selected very thin samples (d/w << 1) (see Table 1) so that λ ab + (d/w)λ c = λ mix ∼ λ ab (for weakly anisotropic systems [19]). The temperature dependence of the penetration depth is clearly non exponential in all measured samples but can be well described by a power law : ∆λ mix (T ) = λ mix (T ) -λ mix (0) = A.T ∼2.3±0.3 for T ≤ T c /3 (see Fig. 3). A very similar behavior has been reported in a large number of pnictides in both 1111 and 122 systems [5] (as well as in Fe(Se,Te), see [20] and references therein). This dependence is another clear indication for the presence of pair breaking effects but it is also important to note that the slope of the ∆λ vs T 2 curve, ∂∆λ/∂T 2 |T →0 is proportional to 1/T 2.8 c (see discussion in section IV.A).

III. UPPER CRITICAL FIELD

A. Specific heat measurements Finally, C p measurements have been performed in magnetic fields up to 28 T using an high sensitivity AC technique (typically 1 part in 10 3 ). Heat was supplied to the sample by a light emitting diode via an optical fiber and the corresponding temperature oscillations were recorded with a thermocouple. In order to obtain quan- titative C p values, special care has been taken in the calibration procedure to measure a copper standard and the addenda in the exact same conditions. For x = 3.4, 4.2 and 6.5 % well defined specific anomalies were obtained in zero field (see Fig. 4) and this anomaly progressively shifted with magnetic field. T c2 has hence been defined as the temperature corresponding to the mid point of the transition for a given value of the external field. The transition became broader and weaker for x = 2.9 % (not shown) and finally too weak (and/or broad) to allow any accurate determination of H c2 from specific heat measurements for x = 2.6 % and x = 7.4 %. The H c2 (T ) values have been reported in Fig. 5 and the corresponding H c2 values are displayed in Fig. 6b together with the T c versus x data.

B. Transmittivity measurements

In order to obtain the upper critical field for the two low T c samples, we performed transmittivity measurements (T H ). The AC component of the local induction on the Hall probe was recorded in presence of an AC modulation field (h ac ∼ 1G, ω ∼ 200 Hz) and T H has been defined as : T H = (B AC (T )-B AC (T <<Tc))

(B AC (T >Tc)-B AC (T <<Tc)) . The irreversibility field (H irr ) was defined as the onset of diamagnetic response (i.e. locus of minimal observable screening current). Writing the Ginzburg-Landau free energy functional in terms of Lowest Landau Level (LLL) eigenfunctions, H c2 can then be deduced from H irr through [21] :

(1 -h)(1 -t 2 ) 1/3 = (th) 2/3 × CGi 1/3
(2

)
where t = T /T c , h = H irr (T )/H c2 (T ), C is a constant depending on the amount of disorder present in the sample and Gi =

1 8 [k B T c /ε 0 ξ(0))]
2 is the Ginzburg number (see Table 1) with ε 0 = (Φ 0 /4πλ(0)) 2 the vortex line energy and the anisotropy [19].

As shown in Fig. 5, the H c2 (T ) values (diamonds) deduced from H irr (T ) (crosses) taking CG 1/3 i ∼ 1 are in very good agreement with the values deduced from the specific heat measurements (squares) for both x = 3.4 and x = 6.5 %. Note that the irreversibility line lies significantly below the H c2 (T ) line, clearly suggesting the presence of vortex liquid phase in this systems [START_REF] Pribulova | Canfield[END_REF]. The corresponding C value (∼ 15) is very close to the one obtained in (Ba,K)Fe 2 As 2 [23] and we have calculated the H c2 values for x = 2.6 and 7.4 % using this C value (i.e. taking CG 1/3 i ∼ 1.1 ± 0.2 and CG 1/3 i ∼ 0.8 ± 0.2 for x = 2.6 and x = 7.4, respectively) We hence confirmed the decrease of H c2 with T c in overdoped samples and the increase of H c2 for T c → 0 for low doping contents (see also Fig. 6b). Note that a similar behavior has been reported by Vinod al. [24] in Ba(Ni x Fe 1-x ) 2 As 2 . Even though the determination of H c2 from transport measurements may be altered by fluctuation effects, those measurements also suggested that H c2 could be proportional to T c in overdoped samples and that the H c2 /T c ratio increases in underdoped samples. Finally, note also that a different scaling has been recently obtained in overdoped BaFe 2 (As,P) 2 samples in which H c2 rather scales as T 2 c [25] (see discussion in section IV.B).

IV. DISCUSSION AND CONCLUDING REMARKS

In summary, we have shown that : i) the penetration depth λ strongly varies with the critical temperature of the sample, ii) λ(0) scales as T 0.85±0.2 c for both underdoped and overdoped samples, iii) the temperature dependence of λ is non exponential but varies as ∆λ ∝ T 2.3±0.3 for T < T c /3 , iv) the slope of the upper critical field decreases with decreasing T c in overdoped samples but increases with decreasing T c in underdoped samples.

Points i) and iii) strongly suggest that pair breaking effects are important. As pointed out by V.G.Kogan [3,4], in the s± model, the Cooper pairs are expected to be be very sensitive to all scattering events and the superconducting condensate is hence progressively destroyed on both side of the superconducting dome, in agreement with the observation of a non residual Sommerfeld coefficient in specific heat data in Co-doped samples [30]. (small open symbols) and Tc(∆Cp/Tc) 0.5 (large open symbols) as a function of doping in both Ba(Fex,Ni1-x)2As2 (present work, (black) circles) and Ba(Fex,Co1-x)2As2(blue) squares). The x values in Co-doped samples have here been rescaled by a factor ∼ 0.6. (b) Left scale : slope of the critical field H c2 = dHc2/dT |T →Tc (solid lines in Fig. 5b) as a function of the composition (x) in Ba(NixFe1-x)2As2 single crystals where Hc2 has been deduced from specific heat measurements (open squares) and from the irreversibility field (solid squares). Right scale : critical temperature Tc (solid circles) as a function of x.

However, it is still unclear whether the system lies close to the critical disorder for which T c → 0 and whether the gap vanishes or not. Alternatively, those pair breaking effects can be associated with quantum fluctuations [15]. Those fluctuations require a finite value of the coupling strength even for T c → 0 [28]. They can hence not be observed in a standard BCS superconductors but can in the presence of pair breaking effects as superconductivity only develops above some finite value of the coupling strength in this case. The scaling properties associated with those two scenarios (strong pair breaking effects close to critical disorder and superconducting quantum fluctuations) are discussed below.

A. Strong pair breaking effects for < Ω >= 0 As discussed by V.G.Kogan [3,4], the superfluid density is expected to vary as (T c (x) 2 -T 2 ) (Eq.( 1)) for an average of the order parameter over the Fermi surface < Ω >= 0 and vanishingly small critical temperatures (see also [26]). Writting 1/λ(T ) 2 = 1/(λ(0) + ∆λ(T )) 2 ∼ (1/λ(0) 2 )×(1-2∆λ(T )/λ(0)) (for ∆λ << λ(0)) one then expects that ∆λ(T ) ∼ βT 2 with β = λ(0)/2T 2 c . The exponent n slightly larger than 2 observed experimentally can be attributed to a non zero gap value [26] but in order to compare the different samples within each other, we assumed in the discussion below that n = 2. Neglecting the -small -variation of ln(κ) with x one also expects that :

H c1 (x, T ) = K(x) × (T c (x) 2 -T 2 ). (3)
This equation leads to a very satisfying agreement to the data introducing only one single adjustable parameter (K(x) = K 0 ) for the whole set of x values (see solid lines in Fig. 1b). As mentioned above, the aim is here not to obtain the best fit to the data (the agreement could for instance be improved by adjusting the exponent n) but to emphasize that the whole set of data can be reproduced in a very satisfactory way only assuming that Eq.( 1) is valid. Eq.( 1) also suggests that λ(0) ∝ 1/T c in very reasonable agreement with the λ(0) = A/T 0.85 c scaling observed in Fig. 2a (point ii)). One then expects β = λ(0)/2T 2 c = B/T 2.85 c in very good agreement with the experimental data (see Fig. 2b). TDO measurements hence also lead to λ(0) ∼ A/T 0.85 c . The corresponding A value is on the order of ∼ 5600 nmK 0.85 e.g. about two times larger than the one obtained from H c1 measurements (A ∼ 2800 nmK 0.85 ) but in very fair agreement with the one deduced from C p measurements (∼ 4000 nmK 0.85 , see corresponding λ(0)/2T 2 c values in Fig. 2b). It is important to note that, this scaling law has been obtained through three independent techniques (with an average A value ∼ 4100 nmK 0.85 ). Note that much larger β values (from ∼ 1.2 nm/K 2 in the optimally doped sample to ∼ 45 nm/K 2 for x = 7.2%) have been obtained by Martin et al. [29] in Ni doped crystals but those values would correspond to λ(0) ranging from ∼ 900 nm to ∼ 1600 nm (in the pair breaking scenario) i.e. much larger than any experimental value.

The scaling properties of the magnetic penetration depth are hence in very reasonable agreement with the strong pair breaking model suggested by V.G.Kogan [3,4] and it is reasonable to attribute, in this scenario, the small deviations from the expected scaling laws to the non zero gap value. However, it is important to note that this model assumes a very strong reduction of T c suggesting that T c,0 could largely exceed 100 K in pnictides in the absence of scattering which remains very puzzling. Moreover, sample dependent parameter (such as the density of states or the Fermi velocity) enter in the prefactors of the scaling functions and it is hence quite surprising to obtain one single A value (i.e. K value for the H c1 data) for all doping contents [START_REF] Liu | ARPES measurements in Ba(FexNi1-x)2As2 samples clearly indicated a strong variation of the band filling with x[END_REF]. Moreover, even though V.G.Kogan pointed out in [4] that the H c2 ∝ T c dependence expected for < Ω >= 0 would actually be reversed (H c2 ∝ 1/T c ) for < Ω > = 0, the strong difference in H c2 (T c ) between underdoped and overdoped samples (point iv)) and not in λ(0) vs T c , can hardly be explained in the framework of this model.

B. Proximity of a superconducting quantum critical point

In the presence of quantum fluctuations, static and dynamical properties are inextricably mixed, so that the value of the dynamic exponent z directly enters in the scaling properties of the thermodynamical properties [15]. However, for d=2 (d being the dimension), z cancels out in the ρ s (0) vs T c scaling and ρ s (0) ∝ T c for all z.

the other hand, for d=3, d + z ≥ 4 (i.e. larger than the Gaussian end point value) and the superfluid density is expected to vary as : ρ s (0) ∝ |p-p c | where p is the parameter driving the transition (here the doping content) and p c its critical value. The critical temperature varies as : T c ∝ |p -p c | Ψ where the shift exponent Ψ is related to z through Ψ = z/(z + 1) [15] and one expects :

ρ s (0) ∝ T (z+1)/z c ( 4
)
with z = 2 in standard superconducting quantum critical points and z = 1 in the presence of nodes in the superconducting gap [28]. One then expects either ρ s (0) ∝ T 1.5 c for z = 2 or ρ s (0) ∝ T 2 c for z = 1. The change from ρ s (0) ∝ T c to ρ s (0) ∝ T 2 c with the sample thickness in underdoped YBaCuO has hence been interpreted as a dimensional crossover from 2D thin samples to 3D samples with z = 1 [10].

In our case, ρ s ∝ T 1.7±0.4 c and it is hence impossible to distinguish between the z = 1 and z = 2 cases (d = 3). On the other hand, 1/ξ 2 0 is also expected to scale as T 1/Ψ c and, as for the strong pair breaking model discussed above, it would be difficult to explain the different H c2 (T c ) dependences observed for underdoped and overdoped samples assuming that they are in the clean limit (H c2 ∝ 1/ξ 2 0 T c ). This difference can however be understood in the dirty limit for which ξ ∼ (ξ 0 l) 0.5 where l and ξ 0 are the mean free path and coherence length without disorder, respectively. A non symmetric l(x) dependence would lead to different H c2 dependence for underdoped and overdoped samples. Note that some difference would also be expected for λ ∼ λ 0 (ξ 0 /l) 0.5 (λ 0 being the penetration depth without disorder) but this difference is much weaker than for H c2 and remains within our error bars.

Interestingly, l is expected to cancel out in the ξλ product which is equal to ξ 0 λ 0 for both clean (l > ξ 0 ) and dirty (l < ξ 0 ) samples and one expects : (small open circles) present very similar dependence on the doping content clearly suggesting that 1/ξλ ∝ T 3/2 c i.e. that z = 2. Moreover, they both decrease roughly linearly with x on either side of the superconducting dome in good agreement with Eq.2.

Moreover, as pointed out in section II.A, the jump of the specific heat at T c : ∆C p /T c ∝ [1/ξλT c ] 2 and we have also reported on Fig. 6a the T c ∆C p /T c val-ues (large open circles) deduced from our specific heat measurements. As shown, this quantity consistently follows the expected behavior. Moreover, one can similarly plot 1/ξλ, T 1.5 c and T c ∆C p /T c as a function of doping for Ba(Fe x Co 1-x ) 2 As 2 samples (squares) taking λ values from [8] and [31], H c2 data from [24] and T c ∆C p /T c values from [6]. As shown, very similar scalings are obtained in both systems (the x values in Co-doped samples have here been rescaled by a factor ∼ 0.6 to take into account the difference in the electronic valency between Co and Ni atoms) emphasizing the strong similarity between the two systems.

FIG. 1 .

 1 FIG. 1. (a) B γ rem as a function of the applied field for the indicated temperature in Ba(NixFe1-x)2As2 with x = 3.4% (Brem being the remanent field trapped in the sample after a field excursion up to Ha -see text for details -and γ is an exponent ∼ 0.4 -0.6). The first penetration field is deduced from the linear extrapolation of B γ rem to zero. Inset (color online) : Same as main panel for different x values at T = 1.3K (the different curves are shifted vertically by 0.2 for clarity). (b) Temperature dependence of the lower critical field Hc1 in Ba(NixFe1-x)2As2 single crystals (for the indicated doping concentrations x). The solid lines are the values expected from Eq.(3) introducing only one free parameter (corresponding to the absolute value at zero T ) for the whole set of data (see text for details). The shaded cones correspond to the values expected from the amplitude of the specific heat jump at Tc (see Fig.4) and the slope of the upper critical field (see Fig.5and text for details).

FIG. 2 .

 2 FIG. 2. (a)London penetration depth at T → 0 (λ(0)) as a function of the critical temperature Tc in Ba(NixFe1-x)2As2 crystals deduced from Hc1 measurements (squares, see Fig.1) and specific heat measurements (crosses, see text for details). The thick line is a guide to the eyes varying as 1/T 0 c .85. (b) Slope of the ∆λ vs T 2 curve (see Fig.3) as a function of Tc in samples from the same batch deduced from TDO measurements (squares). The crosses correspond to λ(0)/2T 2 c (see text for details) introducing the λ(0) values deduced from Cp measurements (see upper panel).

FIG. 3 .

 3 FIG. 3. London penetration depth λmix = λ ab + (d/w)λc (∼ λ ab for w >> d) as a function of (T /Tc) 2 in Ba(NixFe1-x)2As2 single crystals for the indicated x values. As in Fig.2, closed, half-closed and open symbols refer to underdoped, optimally doped and overdoped samples, respectively. Inset : best fit values for the exponent n, assuming that ∆λ ∝ T n .

FIG. 4 .

 4 FIG. 4. Temperature dependence of the field dependent part of the specific heat for the indicated field values in

FIG. 5 .

 5 FIG. 5. Temperature dependence of the upper critical fieldHc2 deduced from the mid-point of the specific heat anomaly (squares, see also Fig.2for symbol correspondance). The crosses correspond to the irreversibility field (Hirr) deduced from the onset of diamagnetic screening and circles to Hc2 values deduced from Hirr (see text for details).

FIG. 6 .

 6 FIG. 6. (color online) (a) (closed symbols), T 1.5 c

1 /

 1 ξλ ∝ T (z+1)/z c ∝ |x -x c | (5)on both sides of the superconducting dome, independently of the sample quality. Note that, two quantum critical points are present in this scenario, corresponding to the two end points of the dome. As shown in Fig.6a, 1/ξλ (closed circles) and T 3/2 c

  ) are obtained on both sides on the superconducting dome in striking contrast with the result obtained by Gordon et al. in Ba(Ni x Fe 1-x ) 2 As 2

											-4 ) Tc(K) measured by
	2.6 70	260	390	30 ∼ 2.8 × 11	530	-	23 *	150	-	4.0	6.8	HP
	2.6 140	340	450	25 ∼ 2.6 × 09	620	-	-	-	-	-	6.0	HP
	2.6 20	1040 1420	-	-	24	-	-	-	-	5.3	TDO
	2.9 50	160	250	70 ∼ 2.6 × 27	350 (570)	-	35	120 10-12	2.9	11.0	HP+Cp
	2.9 20	70	80	80 ∼ 2.6 × 30	330	-	-	-	-	-	11.2	HP
	2.9	5	450	570	-	-	2.9	-	-	-	-	11.1	TDO
	2.9 10	700	950	-	-	2.0	-	-	-	-	11.2	TDO
	3.4 90	280	320	100 ∼ 2.6 × 38	290 (410)	-	46	100 14-16	2.9	16.0	HP+Cp
	3.4 60	210	290	110 ∼ 2.7 × 43	270	-	-	-	-	-	15.6	HP
	3.4 50	580	630	-	-	1.2	-	-	-	-	14.6	TDO
	3.4	5	330	640	-	-	1.4	-	-	-	-	15.0	TDO
	3.4 10	470	820	-	-	1.6	-	-	-	-	15.8	TDO
	4.2 70	300	340	240 ∼ 2.8 × 85	180 (270)	-	52	80 24-28	1.7	20.2	HP+Cp
	4.2 10	45	45	180 ∼ 2.8 × 62	210	-	-	-	-	-	19.6	HP
	4.2 10	300	590	-	-	0.6	-	-	-	-	18.8	TDO
	6.5 90	280	380	80 ∼ 2.4 × 35	310 (400)	-	28	90 13-15	1.2	13.5	HP+Cp
	6.5 100	250	300	70 ∼ 2.7 × 26	340	-	-	-	-	-	12.5	HP
	6.5 20	850	900	-	-	3.2	-	-	-	-	10.8	TDO
	6.5 20	310	630	-	-	5.3	-	-	-	-	9.9	TDO
	7.4 80	280	340	45 ∼ 2.6 × 17	420	-	13 *	80	-	1.3	8.6	HP
	7.4 50	190	220	50 ∼ 2.8 × 18	400	-	-	-	-	-	9.0	HP
	7.4 40	540	900	-	-	17	-	-	-	-	6.5	TDO

and c(κ) is a κ dependent function tending towards ∼ 0.5 for large κ values. κ has hence been deduced from the H c2 /H c1 ratio (see table

1

) and the corresponding λ(0) = κξ(0) values have been reported on Fig.

2a

as a function of T c . As shown, similar values (λ(0) ∼ 1/T 0.85±0.2 c

This work has been supported by the French National Research Agency, Grant No. ANR-09-Blanc-0211 SupraTetrafer. This work has been supported by the joined PHC grant No.23073WF from the French government and by the Slovak Research and Development Agency, Grant No. SKFR-0024-09.


Cédric Lopez
email: lopez@lirmm.fr

Violaine Prince
email: prince@lirmm.fr

Mathieu Roche
email: mroche@lirmm.fr

NOMIT: Automatic Titling by Nominalizing

The important mass of textual documents is in perpetual growth and requires strong applications to automatically process information. Automatic titling is an essential task for several applications: 'No Subject' e-mails titling, text generation, summarization, and so forth. This study presents an original approach consisting in titling journalistic articles by nominalizing. In particular, morphological and semantic processing are employed to obtain a nominalized form which has to respect titles characteristics (in particular, relevance and catchiness). The evaluation of the approach, described in the paper, indicates that titles stemming from this method are informative and/or catchy.

Introduction

A title establishes a link between a reader and a text. It has two main functions. First of all, a title can be informative (it conveys relevant information about the text content and aim), and second, it can be catchy or incentive [START_REF] Herrero | Syntaxe, sémantique et pragmatique des titres des nouvelles de la presse française construits en forme de phrase nominale ou averbale: aspects cognitifs et communicatifs[END_REF]. A heading is said to be catchy when it succeeds in capturing the reader's attention on an aspect of the announced event, in a ingenious, metaphoric, enigmatic, or shocking way. From a syntactic point of view, a title can be a word, a phrase, an expression, a sentence, that designates a paper or one of its parts, by giving its subject.

Titles are used within applications such as automatic generation of contents, or summarization. So, it is interesting to automate the process that produces relevant titles by extracting them from texts, and supplying other applications with such data, while avoiding any human intervention: Direct applications (as automatic titling of "no object" e-mails) are thus possible.

The point is that several titles can be relevant for a same text: This constitutes the main difficulty of automatic titling. Some writers prefer informative titles, whereas others prefer catchy ones. Others juggle with both criteria according to the context and the type of the publication. So, evaluation of automatic titling is a complex step requiring a human intervention. Indeed, how can titles relevance be estimated ? How an automatic title can be compared to a human-written ("real") title, knowing that both can have a very different morphosyntactic structure?

Automatic titling is a full process, possessing its own functions. It has to be sharply differentiated from summarization and indexation tasks. Its purpose is to propose title(s) that have to be short, informative and/or catchy, and keep a coherent syntactic structure. NLP 1 methods will be exploited in order to abide by language morphosyntactic and semantic constraints in titling.

In this paper, we describe an approach of automatic titling relying on nominalization, i.e. rules transforming a verb phrase into a noun phrase (e.g. "the president left" is nominalized into " President's Departure"). This study raises two crucial questions:

(1) Determining sentences and phrases containing relevant information (2) Nominalizing a chosen item and using it as a title. Example: From the following pair of sentences "The disappointing perfor-mance, on Sunday October 9th, of Ségolène Royal, amazed the French citizens. For months, they defended their candidate on the Web.", containing the relevant information about an article in the French press in 2007, the idea is to built the following title: "Ségolène Royal: Surprise of the French citizens". In fact, other titles could apply such as "Ségolène Royal's Disappointing Performance" or "Surprising the French Citizens", but notice that both are less informative, since they drop a part of the information.

This article is organized as such: The following section briefly positions automatic titling in its research environment and describes previous work (section 2). The next one describes NOMIT, our approach of automatic titling by nominalization, which consists in three successive steps: Extracting candidate headings from the document (section 3.1), processing them linguistically (section 3.2), and last, selecting one among the produced headings, which will play the role of the system heading suggestion (section 3.3). Finally, the results of NOMIT evaluation are presented and discussed (section 4).

Previous Work

Automatic titling of textual documents is a subject often confused with summarization and indexation tasks. While a summary has to give an outline of the text contents, the title has to indicate the subject of the text without revealing all the contents. The process of summarization can use titles, as in [START_REF] Blais | Discourse automatic annotation of texts: an application to summarization[END_REF][START_REF] Massih | Automatic text summarization based on wordclusters and ranking algorithms[END_REF], thus demonstrating their importance. Automatic summarization provides a set of relevant sentences extracted from the text: The total number of sentences is diminished, but sentences are not shortened by themselves. Ultimately reducing the number to one does not provide a title, since the latter is very rarely a sentence, but needs to be grammatically consistent. It is also necessary to differentiate automatic titling from text compression: Text compression might shorten sentences but keep the original number of sentences [START_REF] Yousfi | Sentence compression as a step in summarization or an alternative path in text shortening[END_REF]. Mixing both approaches appears as a very costly process to undertake, more adapted to a summarization task, when titling might be obtained by less expansive techniques.

Titling must also be differentiated from indexa-tion because titles do not always contain the text key-words: Headings can present a partial or total reformulation of the text, not relevant for an index, which role is to facilitate the user's search and retrieval. Once again, the construction of an index can use titles appearing in the document. So, if determining relevant titles is a successful task, the quality of indexation will largely be improved. An automatic titling approach, named POSTIT, extracts relevant noun phrases to be used as titles (Lopez et al., 2011b). One of its benefits is that long titles, syntactically correct, can be proposed. The main inconvenience is that it cannot provide original titles, using a funny form for example, unless this one already appears in the text (which can be rather scarce, even in newspapers articles). In the same environment, a variant of this approach, called CATIT, constructing short titles, has been developed by the same authors (Lopez et al., 2011a). It tries to built titles which are relevant to the texts. It evaluates their quality by browsing the Web (popular and recognized expressions), as well as including those titles dynamic context. Applied to a corpus of journalistic articles, CATIT was able to provide headings both informative and catchy. However, syntactical patterns used for titles building were short (two terms) and experience showed that longer titles were often preferred.

Another approach, presented by [START_REF] Banko | Headline generation based on statistical translation[END_REF], consists in generating coherent summaries that are shorter than a single sentence. These summaries are called "headlines". The main difficulty is to adjust the threshold (i.e., the length of the headline), in order to obtain syntactically correct titles. This is the main difference with our method NOMIT, which ensures that its produced titles are always syntactically correct.

If a system were to produce informative, catchy, and variable-sized (in number of words) titles, the nominalization of constituents seems to be an interesting approach. Nominalization is a process transforming an adjective or a verb into a noun or noun phrase. In a nominalized constituent, the time of the event is not in touch with the time of the speech of the event (for example, "President's departure" does not infer that the president already left, contrary to "The president left"). In some languages such as German and French, nominalization answers an ac-tivity of conceptualization and conciseness. In a title, it allows to focus, according to the context of the author, on the dimension of the event considered the most relevant. [START_REF] Moirand | Le rôle anaphorique de la nominalisation dans la presse écrite[END_REF] already noticed that in French journalistic articles, numerous titles appear with a nominalized form. This observation was recently confirmed by [START_REF] Herrero | Syntaxe, sémantique et pragmatique des titres des nouvelles de la presse française construits en forme de phrase nominale ou averbale: aspects cognitifs et communicatifs[END_REF]. It is thus interesting to study automatic titling by nominalization of constituents when dealing with languages where it is often used. In English, the method stays the same, but the pattern changes: English headings patterns incline towards progressive present (e.g. "Tempest looming"), an infinitive form with a past participle (e.g. "Conference to be held"), and always with a deletion of articles. This paper focuses mostly on French because of its available data, but a shift in languages and patterns is contemplated in a further step.

NOMIT: Titling by Nominalizing

Since nominalization converts a sentence into a noun or a noun phrase, it can always be described by a transformation. Some transformations are easy-todo, in particular, transforming verb participles into names or adjectives (such as defined by [START_REF] Dubois | Eléments de linguistique française: syntaxe[END_REF]). For example, "arrivé(e)" (arrived is a French verbal participle which is equal to its nominalized shape "arrivée" (arrival). Others are more complex, for example the past participle "parti" (gone) which nominalized form is "départ" (departure). For these last ones, the use of a lexicon is necessary.

The nominalization process embedded in NOMIT develops three successive stages. The first one concerns the extraction of candidates according to a classical process in NLP: Data preparation, morphosyntactic labeling, selection of the data to be studied. The second phase consists in performing a linguistic process, including morphosyntactic and semantic aspects. Finally, the third phase focuses on selecting a relevant title. Figure 1 presents the global process, detailed in the following sub-sections.

We chose to focus our study on journalistic articles stemming from Le Monde (year 1994), a famous French daily paper, since their electronic form is available for scientific investigation. Note that the method presented in this paper is applicable to all

Extracting Candidates

This first phase consists in extracting the candidates (cf. section 3.2), which will be considered as potential titles after a linguistic treatment. It consists, in turn, of four steps. The first step determines the article relevant data (i.e. fragments or reformulations representing at best the main information emanating from the text).

The described approach relies on the assumption that good candidate phrases can be found in the first two sentences of the article. Actually the best covering rate of the words of real titles is obtained with these first sentences (see [START_REF] Baxendale | Man-made index for technical literature -an experiment[END_REF], [START_REF] Vinet | L'aspect et la copule vide dans la grammaire des titres[END_REF], [START_REF] Jacques | Titres et structuration des documents[END_REF], and (Lopez et al., 2011b) regarding the POSTIT approach), justifying this choice. So, here, the selection of relevant sentences (cf. Step 1.b (cf. Fig. 1) consists in labeling these two sentences via SYGFRAN [START_REF] Chauché | Classifying texts through natural language parsing and semantic filtering[END_REF], a morphosyntactic parser that tags words. Thus, the presence of a "auxiliary + past participle" form syntactic pattern is tested2 (for example, "a augmenté" meaning has increased). If such a pattern is recognized in the sentence, then it is retained and goes into the following stages. Otherwise, the sentence is ignored. Then, sentences are pruned according to two heuristics. [START_REF] Knight | Summarization beyond sentence extraction: A probabilistic approach to sentence compression[END_REF] have studied sentence compression by using a noisy-channel model which consists in making the following hypothesis: The sentence to be compressed was formerly short and the author has extended it with additional information (noise). Sentence compression, could, at a first glance, appear as a possible clue, however, our approach does not aim at reducing at most the treated sentence. Indeed, elements which can be pruned to obtain a good summary do not always need to be pruned to obtain a good title. So, the NOMIT sentence pruning step (cf. Fig. 1, step 1.c) does not only preserve the governors3 . Here, the text is pruned according to three heuristics, inspired from [START_REF] Yousfi | Sentence compression as a step in summarization or an alternative path in text shortening[END_REF], focusing on the function and position of constituents in the syntactic tree:

1. Elimination of dates (for example "The disappointing performance, on Sunday, October 9th, of Ségolène Royal" becomes "The disappointing performance of Ségolène Royal "), 2. Elimination of phrases directly juxtaposed to a past participle (for example "He chose, while he was still hesitating, to help him" becomes "He chose to help him"), 3. Elimination of the relative pronoun and the proposition introduced by it ("Its presence, which was not moreover wished, was noticed" becomes "Its presence was noticed ").

These three heuristics are crucial to obtain a coherent title. In this step, grammaticality4 and concision5 must be respected.

Finally, both sentences are segmented according to punctuation (points, commas, colons, brackets, interrogation marks, exclamation marks, and so forth6 ) and only segments containing a "auxiliary + past participle" pattern are preserved (cf. Fig. 1, step 1.d). Also, segments containing pronouns are not retained in the following steps to avoid problems related to referents7 .

In the following example, each step is indicated by a reference sending back to the global process presented in Figure 1:

Original text:
• Yet they truly believed in it. The disappointing performance, on Sunday, October 9th, of Ségolène Royal, amazed the French citizens. For months, they defended their candidate on the Web.

Treatments:

• (1.a) Yet they truly believed in it. The disappointing performance, on Sunday, October 9th, of Ségolène Royal, amazed the French citizens.

• (1.b) The disappointing performance, on Sunday, October 9th, of Ségolène Royal, amazed the French citizens.

• (1.c) The disappointing performance of Ségolène Royal, amazed the French citizens.

• (1.d) amazed the French citizens8 .

The following step enables to determine a relevant title from the result obtained at step 1.d.

Linguistic Treatment

The linguistic treatment of segments, present in those sentences retained in the previous section, is constituted by two stages aiming at nominalizing the "auxiliary + past participle" pattern. Here, the verbal basis is transformed into an action noun.

The first step consists in obtaining the infinitive of the verb to be nominalized from the past participle. Then, from the infinitive, possible nominalized forms are returned. Even if several linguistic studies propose classifications by families of suffixes, it is complex to process them automatically. The use of a lexicon is a good solution allowing to ensure a correct nominalized form.

Semantic Treatment

From past participle towards infinitive verb.

In step 1.b, segments of sentences containing the "auxiliary + past participle" syntactic pattern were extracted. For every past participle extracted, the endings of conjugation are eliminated, and only radicals are preserved (for example, "mangées" (eaten) becomes "mang" (eat) (cf. Fig. 1, step 2.a). Afterwards, every radical is associated with its infinitive verb using a lexicon9 built for that purpose from the data established by the parser SYGFRAN (cf. Fig. 1, step 2.b).

From infinitive verb towards the verb action. JeuxDeMots10 is a French serious game enabling the construction of a lexical network via a recreational activity proposed on the Web. The prototype was created in 2008 [START_REF] Mathieu Lafourcade | Making people play for lexical acquisition[END_REF]. Today, more than 238,000 terms and more than 1,200,000 relations constitute the network. This popular, evolutionary, and good quality network, possesses a satisfactory knowledge coverage. All in all, more than 40 types of relations were recorded in the network. One of them interests us more particularly: The relation called "verb action". This "action" is very interesting for obtaining a nominalized form, in particular for verbs having their structure modified during their nominalization (addition of suffix or prefix in particular). For example, we obtain "départ" (departure) from the infinitive "partir" (to leave)(cf. Fig. 1, step 2.c).

Let us note that several action names can exist for the same verb. For example, "annonce" (announcement) and "annonciation" (annunciation) are two actions of the verb "annoncer" (to announce). At this stage, all action names are preserved and will be considered in the next phase, consisting in nominalizing the candidates determined in the step before.

Morphosyntactic Treatment

The morphosyntactic processing aims at establishing rules that automatically transform a constituent into its nominalized form. The purpose is not to establish an exhaustive list of transformation rules but to assure a correct transformation.

To transpose the agents of a verb into a nominalized constituent, the French language makes a proficient use of prepositions. So when nominalizing "auxiliary + past participle" in order to connect it with its complement, the preposition "de" ("of") is mandatory11 . In English, although "X of Y" is an accepted pattern, the genitive form "Y('s) X" would be preferred. If the complement does not exist, the subject takes its place. In section 3.1, relative subordinate pronoun and subordinate clauses are eliminated because the information they convey is too secondary to be emphasized in a title. For example, "My cousin, who lives in Paris, moved" becomes "My cousin moved". So, according to the second rule, the nominalized form will be "Moving of my cousin" and not "Moving of my cousin who lives in Paris".

The third rule leads to titles with a very popular form in French newspapers. It is about contextualizing the information via the use of a proper noun. So, if in the treated constituent a single proper noun appears (easily locatable by the presence of a capital letter), the common noun can be put in connection with the nominalized past participle (without concluding that this common noun is an agent of the nominalized verb). This new rule produces titles with the following form: "Proper noun: verb action + Prep + Complement". For example, "Ségolène returned to Strasburg" becomes "Ségolène: Strasburg comeback". Section 3.2.1, pointed that several nominalized forms were possible for the same verb. So, the phase of linguistic treatment enables to determine a list of possible noun forms for every constituent. For example, if in step 1 we had "The restaurant Gazza, situated in a business area, announced a new price", rule 1 would transform this sentence into two candidates: "Gazza: New price announcement" and "Gazza: New price annunciation" (queer indeed!). The following phase consists in selecting the most relevant candidate.

Selecting a Title

The selection of the most relevant title relies on a Web validation (cf. Fig. 1, stage 3). A segment that frequently appears on the Web tends to be seen as:

(1) popular, (2) structurally sound. Thus, the frequency of appearance of n-grams on the Web (via the Google search engine) appears as a good indicator of the n-gram popularity/soundness [START_REF] Keller | Using the web to obtain frequencies for unseen bigrams[END_REF] . In our case, a n-gram is a segment of the nominalized constituent, constituted by the nominalized past participle (NPP) and by the preposition followed by the short complement (i.e. reduced to the common noun).

The benefit of this validation is double. On one hand, it backs up the connection between the NPP and the complement (or subject according to the rule of used transformation). On the other hand, it helps eliminating semantically incorrect or unpopular constituents (for example, "Winners' annunciation") to prefer those which are more popular on the Web (for example, "Winners' announcement")12 .

Discussion

Our automatic titling approach (NOMIT) proposes titles for journalistic articles containing a "auxiliary + past participle" form in at least one of its first two sentences. The rationale for such a method is not only conciseness, but also presentation: How to generate a heading inciting the reader to go further on. Of course, transformation rules such as those presented here, can be numerous and various, and depend on language, genre, and purpose. The basic purpose of this work is to provide a sort of a "proof of concept", in which relevant titles might be automatically shaped.

Evaluation of titles is a difficult and boring task. That is why we set up an online evaluation to share the amount of work. A call for participation was submitted in the French community of researchers (informatics, linguistics). Even if we do not know the information relative to every annotator (nationality, age, etc.), we think that a great majority of these annotators have a rather good level in French, to judge titles (this is confirmed by the well-writing of the collected definitions for "relevance" and "catchiness").

NOMIT has been evaluated according to two protocols. The first one consisted in a quantitative evaluation, stemming from an on-line user evaluation 13 . 103 people have participated to this evaluation. The second was an evaluation performed by 3 judges. This last one enables to compute the agreement inter-judges on the various criteria of the evaluation process. In both cases, the French daily paper Le Monde (1994) is used, thus avoiding any connection to the subjectivity of recent news personal analysis.

Quantitative Evaluation

Protocol Description

As previously seen, titles proposed by automatic methods cannot be automatically evaluated. So, an on-line evaluation was set up, opened to every person. The interest of such an evaluation is to compare the various methods of automatic titling (cf. section 2) according to several judgments. So, for every text proposed to the human judges, four titles were presented, each resulting from different methods of titling:

• NOMIT: Automatic Titling by Nominalizing.

• POSTIT: Based on the extraction of noun phrases to propose them as titles.

• CATIT: Based on the construction of short titles.

• Real Title (RT).

13 http://www.lirmm.fr/~lopez/Titrage_ general/evaluation_web2/ For every title, the user had to attribute one of the following labels: "relevant", "rather relevant", "irrelevant", "neutral". Also, the user had to estimate the catchiness, by choosing one of the following labels: "catchy", "not catchy", "neutral". Before beginning the evaluation, the user is asked about his/her own definition of a relevant title and of a catchy title (all in all, 314 definitions were collected). Globally, there is a popular consensus saying that a title is relevant if it is syntactically correct while reflecting the essential idea conveyed in the document. However, definitions of catchiness were less consensual. Here are some collected definitions:

1. A title is catchy if the words association is syntactically correct but semantically "surprising". However, a catchy title has to be close to the contents of the text.

2. A catchy title is a title which tempts the reader into going through the article.

3. A title which holds attention, a title which we remember, a funny title for example.

4. A title which is going to catch my attention because it corresponds to my expectations or my centers of personal interests.

5. A catchy title is a short and precise title.

The titled texts were distributed to the judges in a random way. Every title was estimated by a number of persons between 2 and 10. All in all, 103 persons participated in the evaluation of NOMIT.

Let p1 be the number of titles considered relevant, p2 the number of titles considered rather relevant, and let p3 be the number of titles considered irrelevant. Within the framework of this evaluation, it is considered that a title is relevant if p1 ≥ p3, and rather relevant if p2 ≥ p3.

A title is considered "catchy" if at least two judges considered it catchy.

Results

In spite of the weak number of titles estimated in this first evaluation, the significant number of judges helped obtaining representative results. In our experiments, 53 titles generated by the NOMIT approach were evaluated representing a total of 360 evaluations. These results were compared with the 200 titles generated with POSTIT,200 with CATIT,and 200 RT (653 titles and 8354 evaluations). Results (cf. Table 1) show that 83% of the titles proposed by NOMIT were seen as relevant or rather relevant, against 70% for the titles stemming from the POSTIT approach, and 37% for the titles stemming from CATIT. Besides, NOMIT determines titles appreciably more catchy than both POSTIT and CATIT. Concerning the real titles (RT), 87.8% were judged relevant and 80.5% were catchy, meaning that humans still perform better than automated techniques, but only slightly for the relevance criterion, and anyway, are not judged as perfect (reference is far from absolute!). 4.2 Agreement Inter-judges

Protocol Description

This evaluation is similar to the previous one (same Web interface). The main difference is that we retained the first 100 articles appeared in Le Monde 1994 which enables our approach to return a title. Three judges estimated the real title as well as the NOMIT title for each of the texts, that is, a total of 600 evaluations.

Results

Kappa coefficient (noted K) is a measure defined by [START_REF] Cohen | A coefficient of agreement for nominal scales[END_REF] calculating the agreement between several annotators. It is based on the rate of observed concordances (Po) and on the rate of random concordances (Pe). Here the Kappa coefficient estimates the agreement inter-judges about the relevance and of catchiness of NOMIT titles (cf. Tables 2 -4). Considering the results and according to (Landis and [START_REF] Landis | The measurement of observer agreement for categorical data[END_REF], judges seem to obtain an average concordance for the relevance of NOMIT titles. This can be justified by the fact that there is a consensus between the three judges about the definition of what is a relevant title (cf. Table 3). Approxi-mately 71% of the titles were considered relevant by three judges (cf. Table 2).

On the other hand, the three judges obtain a bad concordance regarding catchiness; a catchy title for the one, could not be catchy for the other one. This is perfectly coherent with the definitions given by the three judges:

1. A title is catchy if the association of the words is syntactically correct but semantically "surprising".

2. A catchy title is a title which drives you to read the article.

3. A catchy title is a title which holds attention of the reader and tempts him/her to read the concerned text .

So, people have judged catchiness according to syntax, the relation between semantics of the title and semantic of the text, or have evaluated catchiness according to personal interests. The notion of catchiness is based on these three criteria. So, we could not expect a strong agreement between the assessors concerning the catchy character of a title (cf. that our approach of automatic titling by nominalization is more adapted to short texts. We are extremely prudent concerning this interpretation because it is based on only 29 articles.

Conclusion

Automatic titling is a complex task because titles must be at once informative, catchy, and syntactically correct. Based on linguistic and semantic treatments, our approach determines titles among which approximately 80% were evaluated as relevant and more than 60% were qualified as catchy. Experiment and results discussion have pointed at the following liability: The value of Kappa, the inter-judges agreement coefficient, is very difficult to evaluate, mostly when catchiness is at stake. The main cause is that it depends on personal interests. It is thus necessary to ask the following question: Do we have to consider that a title is definitely catchy when at least one person judges it so? Otherwise, how many people at least? This is still an open question and needs to be further investigated. Also, some interesting extensions could be envisaged: The approach presented in this paper uses three rules of transformation based on the presence of an auxiliary followed by a past participle. The addition of new rules would enable a syntactic enrichment of the titles. So, it might be profitable to set up rules taking into account the presence of syntactical patterns (others than "auxiliary + past participle") to allow more texts to be titled by NOMIT.

Taking the punctuation of the end of sentences into account might also be a promising track. For example, "did it use an electric detonator?" would become "Use of an electric detonator?". It is an interesting point because the presence of a punctuation at the end of a title (in particular the exclamation or the interrogation) constitutes a catchy criterion.

Last, NOMIT is a method (easily reproducible in other languages, English in particular) that stepped out of preceding attempts in automatic headings generation (POSTIT, CATIT). Exploring syntactic patterns, as it does, means that increasing the amount of linguistic information in the process might lead to a reliable heading method. One of the perspectives can be to track the optimum point between the richness of involved information and processes, and the cost of the method. The incremental methodology followed from POSTIT to NOMIT tends to enhance the belief that parameters (i.e. length, shape, relevance, etc...) for an automatic heading procedure have to be studied and well defined, thus leading to a customized titling process.

Figure 1 :

 1 Figure 1: Global process of NOMIT

  Fig. 1, step 1.a) is limited to extracting the first two sentences of the text.

•

  Rule 1: Subject + Aux + PP + Complement => Verb action + (de) + Complement -Original sentence: Il a annoncé les gagnants (He announced the winners) -Radicalisation (2.a): Annonc -Infinitive (2.b): Annoncer -Actions associated to the infinitive (2.c): Annonce ; annonciation -Nominalization (2.d): Annonce des gagnants (Announcement of the winners or Winners' announcement ) ; annonciation des gagnants (Annunciation of the winners or Winners' annunciation) • Rule 2: Subject + Aux + PP => Action of the verb + (de) + Subject -Original sentence: Le président a démissionné (The president resigned) -Radicalisation (2.a): Démission -Infinitive (2.b): Démissionner -Actions associated to the infinitive (2.c): Démission (Resignation) -Nominalization (2.d): Démission du président (Resignation of the president or President's resignation)

•

  Rule 3: Subject + Aux + PP => Proper Noun: Verb action + (de) + Complement (if it exists only one proper noun in the subject) -Original sentence: Bon nombre de particuliers se sont précipités (rushed)aux guichets des banques pour souscrire à des PEL (Several individuals rushed to bank counters and subscribed to home-buying savings plans) -Radicalisation (2.a): Précipit -Infinitive (2.b): Précipiter -Action associated to the infinitive (2.c): Précipitation -Nominalization (2.d): PEL : précipitation aux guichets des banques (Home Buying Saving plans: Rush at Banks Counters)

Table 1 :

 1 Evaluation Results for POSTIT, CATIT, NOMIT, and RT (Real Titles).

	en %	Relevant Weak relevant Irrelevant Catchy Not catchy
	POSTIT 39.1	30.9	30	49.1	50.9
	CATIT	15.7	21.3	63	47.2	52.8
	NOMIT 60.3	22.4	17.2	53.4	46.6
	RT	71.4	16.4	12.3	80.5	19.5

Table 3 )

 3 .

	in %	Relevant Irrelevant Neutral Total
	Relevant	70.7	10.3	0.7	81.7
	Irrelevant	6.0	10.3	0.7	17.0
	Neutral	1.0	0.3	0.0	1.3
	Total	77.7	21.0	0.7	100.0

Table 2 :

 2 Contingency Matrix for NOMIT (relevance).

	in %	Catchy Not Catchy Neutral Total
	Catchy	13.3	7.7	0.0	21.0
	Not catchy	34.7	41.0	1.3	77.0
	Neutral	0.7	1.3	0.0	2.0
	Total	48.7	50.0	1.3	100.0

Table 3 :

 3 Contingency Matrix for NOMIT (catchiness).

	As a rough guide, short journalistic articles 14 ob-
	tain better results than long articles (93% are rele-
	vant in that case and 69% are catchy). It thus seems

Table 4 :

 4 Kappa average for relevance and catchiness of titles obtained with NOMIT.

the pattern features are tuned to French, but the same structure globally applies to English too.

3 governors of constituents considered as indispensable to the grammatical and semantic coherence of the

sentence4 The sentence must be well formed and must obey the lan-

guage grammar. 5 a pruned sentence has to contain the relevant information of the original sentence.

Points marking an abbreviation are not obviously taken into account in this step.

For example, the title "Disappointment of her partisans" would not be very informative because of the presence of "her" (unknown referent).

We shall see in the section 3.2.2 how, in some cases, it is possible to take into account the subject, i.e. Ségolène Royal in this example.

this lexicon contains 5,897 entries.

http://www.jeuxdemots.org

The preposition can be contracted if needed ("de le" = "du", "de les" = "des", and so forth.)

We do not here claim to select the most coherent constituents regarding the text. Since the main hypothesis underlying this study is that the first two sentences of the article contain the necessary and sufficient information to determine a relevant title, we consider implicitly obtaining nominalized constituents, that are relevant to the text

We consider that an article is short when its number of words is less than 100.


Cédric Lopez
email: lopez@lirmm.fr

Violaine Prince
email: prince@lirmm.fr

Mathieu Roche
email: mroche@lirmm.fr

Just Title It! (by an Online Application)

This paper deals with an application of automatic titling. The aim of such application is to attribute a title for a given text. So, our application relies on three very different automatic titling methods. The first one extracts relevant noun phrases for their use as a heading, the second one automatically constructs headings by selecting words appearing in the text, and, finally, the third one uses nominalization in order to propose informative and catchy titles. Experiments based on 1048 titles have shown that our methods provide relevant titles.

Introduction

The important amount of textual documents is in perpetual growth and requires robust applications. Automatic titling is an essential task for several applications: Automatic titling of e-mails without subjects, text generation, summarization, and so forth. Furthermore, a system able to title HTML documents and so, to respect one of the W3C standards about Web site accessibility, is quite useful. The titling process goal is to provide a relevant representation of a document content. It might use metaphors, humor, or emphasis, thus separating a titling task from a summarization process, proving the importance of the rhetorical status in both tasks.

This paper presents an original application consisting in titling all kinds of texts. For that purpose, our application offers three main methods. The first one (called POSTIT) extracts noun phrases to be used as headings, the second one (called CATIT) automatically builds titles by selecting words appearing in the text, and, finally, the third one (called NOMIT) uses nominalization in order to propose relevant titles. Morphologic and semantic treatments are applied to obtain titles close to real titles. In particular, titles have to respect two characteristics: Relevance and catchiness.

Text Titling Application

The application presented in this paper was developed with PHP, and it is available on the Web1 . It is based on several methods using Natural Language Processing (NLP) and Information Retrieval (IR) techniques. So, the input is a text and the output is a set of titles based on different kinds of strategies.

A single automatic titling method is not sufficient to title texts. Actually, it cannot respect diversity, noticed in real titles, which vary according to the writer's personal interests or/and his/her writing style. With the aim of getting closer to this variety, the user can choose the more relevant title according to his personal criteria among a list of titles automatically proposed by our system.

A few other applications have focused on titling: One of the most typical, (Banko, 2000), consists in generating coherent summaries that are shorter than a single sentence. These summaries are called "headlines". The main difficulty is to adjust the threshold (i.e, the headline length), in order to obtain syntactically correct titles. Whereas our methods create titles which are intrinsically correct, both syntactically and semantically.

In this section, we present the POSTIT, CATIT, and NOMIT methods. These three methods run in parallel, without interaction with each other. Three very different titles are thus determined for every text. For each of them, an example of the produced title is given on the following sample text: "In her speech, Mrs Merkel has promised concrete steps towards a fiscal union -in effect close integration of the tax-and-spend polices of individual eurozone countries, with Brussels imposing penalties on members that break the rules. [...]". Even if examples are in English, the application is actually in French (but easily reproducible in English). The POS tagging was performed by Sygfran [START_REF] Chauché | Un outil multidimensionnel de l'analyse du discours[END_REF].

2.1 POSTIT (Jin, 2001) implemented a set of title generation methods and evaluated them: The statistical approach based on the TF-IDF obtains the best results. In the same way, the POSTIT (Titling using Position and Statistical Information) method uses statistical information. Related works have shown that verbs are not as widely spread as nouns, named entities, and adjectives (Lopez, 2011a). Moreover, it was noticed that elements appearing in the title are often present in the body of the text [START_REF] Zajic | Automatic headline generation for newspaper stories[END_REF]. (Zhou and Hovy, 2003) supports this idea and shows that the covering rate of those words present in titles, is very high in the first sentences of a text. So, the main idea is to extract noun phrases from the text and to select the more relevant for its use as title. The POSTIT approach is composed of the following steps:

1. Candidate Sentence Determination. We assume that any text contains only a few relevant sentences for titling. The goal of this step consists in recognizing them. Statistical analysis shows that, very often, terms useful for titling are located in the first sentences of the text.

2. Extracting Candidate Noun Phrases for Titling. This step uses syntactical filters relying on the statistical studies previously led. For that purpose, texts are tagged with Sygfran. Our syntactical patterns allowing noun phrase extraction are also inspired from [START_REF] Daille | Study and implementation of combined techniques for automatic extraction of terminology. The Balancing Act: Combining Symbolic and Statistical Approaches to language[END_REF].

3. Selecting a Title. Last, candidate noun phrases (t) are ranked according to a score based on the use of TF-IDF and information about noun phrase position (N P P OS ) (see Lopez, 2011a). With λ = 0.5, this method obtains good results (see Formula 1).

N P score (t) = λ × N P P OS (t) + (1 -λ) × N P T F -IDF (t) (1)
Example of title with POSTIT: Concrete steps towards a fiscal union.

On one hand, this method proposes titles which are syntactically correct. But on the other hand, provided titles can not be considered as original. Next method, called CATIT, enables to generate more 'original' titles.

CATIT

CATIT (Automatic Construction of Titles) is an automatic process that constructs short titles. Titles have to show coherence with both the text and the Web, as well as with their dynamic context (Lopez, 2011b). This process is based on a global approach consisting in three main stages:

1. Generation of Candidates Titles. The purpose is to extract relevant nouns (using TF-IDF criterion) and adjectives (using TF criterion) from the text. Potential relevant couples (candidate titles) are built respecting the "Noun Adjective" and/or "Adjective Noun" syntactical patterns.

2. Coherence of Candidate Titles. Among the list of candidate titles, which ones are grammatically and semantically consistent ? The produced titles are supposed to be consistent with the text through the use of TF-IDF. To reinforce coherence, we set up a distance coefficient between a noun and an adjective which constitutes a new coherence criterion in candidate titles. Besides, the frequency of appearance of candidate titles on the Web (with Dice measure) is used in order to measure the dependence between the noun and the adjective composing a candidate title. This method thus automatically favors well-formed candidates.

Dynamic Contextualization of Candidate Titles.

To determine the most relevant candidate title, the text context is compared with the context in which these candidates are met on the Web. They are both modeled as vectors, according to Salton's vector model.

Example of title with CATIT: Fiscal penalties.

The automatic generation of titles is a complex task because titles have to be coherent, grammatically correct, informative, and catchy. These criteria are a brake in the generation of longer titles (being studied). That is why we suggest a new approach consisting in reformulating relevant phrases in order to determine informative and catchy "long" titles.

NOMIT

Based on statistical analysis, NOMIT (Nominalization for Titling) provides original titles relying on several rules to transform a verbal phrase in a noun phrase.

1. Extracting Candidates. First step consists in extracting segments of phrases which contain a past participle (in French). For example: In her speech, Mrs Merkel has promised "concrete steps towards a fiscal union"in effect close integration of the tax-andspend polices individual eurozone countries, with Brussels imposing penalties on members that break the rules.

2. Linguistic Treatment. The linguistic treatment of the segments retained in the previous step consists of two steps aiming at nominalizing the "auxiliary + past participle" form (very frequent in French). First step consists in associating a noun for each past participle. Second step uses transforming rules in order to obtain nominalized segments. For example: has promised ⇒ promise.

3. Selecting a Title. Selection of the most relevant title relies on a Web validation. The interest of this validation is double. On one hand, the objective is to validate the connection between the nominalized past participle and the complement. On the other hand, the interest is to eliminate incorrect semantic constituents or not popular ones (e.g., "annunciation of the winners "), to prefer those which are more popular on Web (e.g. , "announcement of the winners"). This method enables to obtain even more original titles than the previous one (i.e. CATIT). A positive aspect is that new transforming rules can be easily added in order to respect morphosyntactical patterns of real titles.

Evaluations

Protocol Description

An online evaluation has been set up, accessible to all people (cf. Figure 1)2 . The benefit of such evaluation is to compare different automatic methods according to several judgements. So, for each text proposed to the human user, several titles are presented, each one resulting from one of the automatic titling methods presented in this paper (POSTIT, CATIT, and NOMIT). Furthermore, random titles stemming from CATIT and POSTIT methods are evaluated (CATIT-R, and POSTIT-R), i.e., candidate titles built by our methods but not selected because of their bad score. The idea is to measure the efficiency of our ranking functions.

This evaluation is run on French articles stemming from the daily newspaper 'Le Monde'. We retained the first article published every day for the year 1994, up to a total of 200 journalistic articles. 190 people have participated to the online experiment, evaluating a total of 1048 titles. On average, every person has evaluated 41 titles. Every title has been evaluated by several people (between 2 and 10). The total number of obtained evaluations is 7764.

Results

Results of this evaluation indicate that the most adapted titling method for articles is NOMIT. This one enables to title 82.7% of texts in a relevant way (cf. Table 1). However, NOMIT does not determine titles for all the texts (in this evaluation, NOMIT determined a title for 58 texts). Indeed, if no past participle is present in the text, there is no title returned with this method. It is thus essential to consider the other methods which assure a title for every text. POSTIT enables to title 70% of texts in a relevant way. It is interesting to note that both gathered methods POSTIT and NOMIT provide at least one relevant title for 74 % of texts (cf. Also, let us note that our ranking functions are relevant since CATIT-R and POSTIT-R obtain weak results compared with CATIT and POSTIT.

Conclusions

In this paper, we have compared the efficiency of three methods using various techniques. POSTIT uses noun phrases extracted from the text, CATIT consists in constructing short titles, and NOMIT uses nominalization. We proposed three different methods to approach the real context. Two persons can propose different titles for the same text, depending on personal criteria and on its own interests. That is why automatic titling is a complex task as much as evaluation of catchiness which remains subjective. Evaluation shows that our application provides relevant titles for 81% of texts and catchy titles for 78 % of texts. These results are very encouraging because real titles obtain close results.

A future work will consist in taking into account a context defined by the user. For example, the generated titles could depend on a political context if the user chooses to select a given thread. Furthermore, an "extended" context, automatically determined from the user's choice, could enhance or refine user's desiderata.

A next work will consist in adapting this application for English.

Figure 1 :

 1 Figure 1: Screenshot of Automatic Titling Evaluation

Table 2 )

 2 . Finally, even if CATIT obtains a weak score, this method provides a relevant title where POSTIT and NOMIT are silent. So, these three gathered methods propose at least one relevant title for 81% of journalistic articles.Concerning catchiness, the three methods seem equivalent, proposing catchy titles for approximately 50% of texts. The three gathered methods propose at least one catchy title for 78% of texts. Real titles (RT) obtain close score (80.5%).

	%	POSTIT POSTIT-R CATIT CATIT-R NOMIT RT
	Very relevant (VR)	39.1	16.4	15.7	10.3	60.3	71.4
	Relevant (R)	30.9	22.3	21.3	14.5	22.4	16.4
	(VR) and (R)	70.0	38.7	37.0	24.8	82.7	87.8
	Not relevant	30.0	61.4	63.0	75.2	17.2	12.3
	Catchy	49.1	30.9	47.2	32.2	53.4	80.5
	Not catchy	50.9	69.1	52.8	67.8	46.6	19.5

Table 1 :

 1 Average scores of our application.

	%	POSTIT & NOMIT POSTIT & CATIT NOMIT & CATIT POSTIT, CATIT, & NOMIT
	(VR)	47	46	28	54
	(R) or (VR)	74	78	49	81
	Catchy	57	73	55	78

Table 2 :

 2 Results of gathered methods.

https://www2.lirmm.fr/ ˜lopez/Titrage_ general/

URL: http://www2.lirmm.fr/ ˜lopez/ Titrage_general/evaluation_web2/