R Guirlet
email: remy.guirlet@cea.fr

J L Schwob

O Meyer

S Vartanian

Absolute sensitivity calibration of an extreme ultraviolet spectrometer for tokamak measurements

Keywords: extreme ultraviolet, spectroscopy, tokamaks, absolute calibration

An extreme ultraviolet spectrometer installed on the Tore Supra tokamak has been calibrated in absolute units of brightness in the range 10-340 Å. This has been performed by means of a combination of techniques. The range 10-113 Å was absolutely calibrated by using an ultrasoft-X ray source emitting six spectral lines in this range. The calibration transfer to the range 113-182 Å was performed using the spectral line intensity branching ratio method.

The range 182-340 Å was calibrated thanks to radiative-collisional modelling of spectral line intensity ratios. The maximum sensitivity of the spectrometer was found to lie around 100 Å.

Around this wavelength, the sensitivity is fairly flat in a 80 Å wide interval. The spatial variations of sensitivity along the detector assembly were also measured. The observed trend is related to the quantum efficiency decrease as the angle of the incoming photon trajectories becomes more grazing.

Introduction

Extreme ultraviolet (EUV) spectroscopy is used extensively in various plasma physics research fields such as astrophysics and inertial and magnetic fusion. Its main interest resides in the detailed information it provides on the various species present in a plasma. It thus helps determine the qualitative composition of a plasma by the observation and identification of the spectral lines emitted by the ion species of the plasma. The density of the various emitting ions can also be deduced from spectroscopic measurements provided certain experimental conditions are fulfilled. One of them is that the spectral line intensities must be measured in absolute units. This necessitates that the spectroscopic instrument be calibrated in sensitivity.

A commonly used method is the so-called line intensity branching ratio method [1, 2].

It consists of selecting spectral line pairs emitted by the same ion from one given upper level to two different lower levels and comparing their measured intensity ratio with the theoretical one. For this purpose, usually the spectrometer to be calibrated includes a visible line of sight as close as possible to the EUV line of sight and connected to a visible spectrometer (for which an absolute calibration is relatively easy). One line of the pair is chosen in the visible range, and thus the sensitivity of the EUV spectrometer at the second line wavelength can be deduced. This method has been used already many years ago on the TA 2000 torus [3,4] and is still in use nowadays, for example at JET for the SPRED VUV spectrometer in the range 130-360 Å [START_REF] Lawson | Stamp and JET-EFDA contributors[END_REF]. Another way of calibrating an EUV spectrometer in absolute intensity units is to compare the spectrometer signals with those of an already absolutely calibrated instrument, as was done in [6] in the soft-X ray range.

In the present work, the Tore Supra tokamak is equipped with a high resolution, duomultichannel grazing incidence spectrometer [7] of the Schwob-Fraenkel type. Two interferometrically aligned, ruled, concave gratings are mounted permanently on the spectrometer. For most of the applications and in particular for the present measurements, a 600 g/mm grating blazed at 1.5° is used. It covers the 10-340 Å wavelength range. The spectrometer is supported by a mobile structure which allows to spatially scan the lower half of the plasma at a frequency 0.5 Hz.

Detection on this spectrometer is performed by means of two double microchannel plate (MCP) detector assemblies in chevron configuration mounted on two carriages moved independently along the materialised Rowland circle. The range of one detector is limited on one end by the shortest wavelength mechanically accessible and on the other end by the second detector assembly. It is thus called the 'short wavelength' (or SW) detector.

Conversely, the other assembly is limited by the SW detector and the longest wavelength mechanically accessible, hence its name: 'long wavelenth' (or LW) detector. The electrons produced in the microchannels by impact of the incident EUV photons are converted into visible photons by phosphor screens behind the MCPs and recorded by PDA (photodiode array) cameras (one for either MCP assembly). An example of a spectrum recorded on the LW detector is shown in Fig. 1. Figure 1: Spectrum recorded by the long wavelength detector with identification of the most prominent lines. This spectrometer is not built with a visible line of sight so we could not use the branching ratio method exactly as presented in [1]. For the short wavelength part of the accessible domain we have used a combination of methods which are reported in this article.

Section 2 describes the use of an ultrasoft-X ray source for absolute calibration in the 10-113 Å range. Section 3 describes the method used for calibration in the longer wavelength range, which combines the branching ratio method with a comparison of line intensity ratio measurements with collisional-radiative calculations, a method already used in [8]. Section 4 contains the results with a discussion on the uncertainties and a study of the spatial variation of the detector sensitivity. Section 5 presents a summary and conclusions. In the short wavelength range, an absolute calibration was performed in the spectroscopy laboratory with the help of a Manson Model 5 multi-anode ultrasoft-X ray source [START_REF] Manson | Manson model 5 ultrasoft-X ray calibration source[END_REF]. The set-up is sketched on Fig. 2. The source emits photons at a given wavelength (the so-called Kα line) by electron beam impact on targets (playing the role of anodes for the electrons) of various materials. A carousel of six targets allows to produce as many spectral lines between 9.9 and 113 Å (see Table 1).

Sensitivity calibration in

A gas flow proportional counter (GPC) is placed at 45° from the electron beam axis (a setup very similar to the one used in [10]) to monitor the photon emission which can be as high as 10 12 photons/(s.sr). The GPC is set up so that it has a 100% efficiency. In order to preserve its operating pressure, which is different from that in the source volume, a membrane In addition, we have used a grid filter (transmission T F = 0.108) to attenuate the GPC signal. The photon rate (in s -1 ) measured by the GPC is thus given by:

) ( ) ( ) ( λ λ λ i GPC F GPC m GPC N T T N × × = (1)
where N i GPC (λ) and N m GPC (λ) are the incident and measured photon rates respectively.

The spectrometer beam line is placed in a position symmetric to the GPC with respect to the electron beam to take advantage of the photon emission symmetry around the electron beam axis. The ratio of the photon rate incident on the spectrometer N sp i (λ) to the photon rate N i GPC (λ) incident on the GPC using a given target is equal to the solid angle ratio of the two detectors:

GPC sp i GPC i sp N N Ω Ω = ) ( ) ( λ λ (2)
Note here that N sp i (λ) represents the total number of photons within the whole spectral line width excluding the background in the same spectral interval.

The spectrometer sensitivity at wavelength λ is defined as the ratio of the measured count rate to the incident photon rate:

) ( ) ( ) ( λ λ λ η i sp m sp N N = (3)
where N sp m (λ) is the count rate measured by the spectrometer readout and acquisition system (expressed in counts/s in our setup). Due to the 100% efficiency of the gas counter and using

Eqs. 1 and 2, one has:

F GPC m GPC GPC sp i GPC GPC sp i sp T T N N N ) ( ) ( ) ( ) ( λ λ λ λ Ω Ω = Ω Ω =
and thus:

( ) sp GPC F CP m GPC m sp T T N N Ω Ω = ) ( / ) ( ) ( ) ( λ λ λ λ η (4)
The spectrometer sensitivity can thus be deduced from the geometric parameters of the setup, which are known, and the measurements of the detectors.

The tokamak plasma observed with the spectrometer is an extended light source. The measurement performed by the spectrometer is thus the radiance (also commonly called brightness) defined as:

( ) ( ) ∫ × = - dl l B ε π 1 4 [photons / (cm 2 sr s)] (5)
where ε (in cm -3 s -1 ), called emissivity, is the photon rate emitted by plasma unit volume in a given spectral line and l is the abscissa along the line of sight. The integral is performed over the whole line of sight path within the plasma. The quantity we aim at determining is the brightness calibration coefficient K(λ) defined by:

( ) ( ) ( ) λ λ λ m sp N K B × = (6)
over the whole wavelength range of the spectrometer. This quantity is crucial for plasma applications since it is needed to relate the measured quantity

( ) λ m sp
N with the density of the emitting ions. It can be obtained in the following manner. When a spectral line emitted in the plasma is observed, the incident photon rate is by definition of η(λ):

( ) ( ) ( ) λ η λ λ m sp i sp N N = (7)
The spectral line brightness is thus given by:

( ) ( ) ( ) ( ) sp m sp sp i sp S N S N B Ω × = Ω = ) ( ) ( λ η λ λ λ (8)
where (SΩ) sp is the spectrometer geometric etendue (here S is the entrance slit area). The brightness calibration coefficient is thus given by:

( ) ( ) ( ) sp S K Ω × = λ η λ 1 (9)
and is expressed in [photons/(s cm 2 sr)]/(counts/s).

Results and comparison with a previous calibration

The method exposed in the previous section has been applied to both the 'shorter wavelength'

(SW) and 'longer wavelength' (LW) detectors. The brightness calibration coefficient has been determined for the six wavelengths available with the calibration source. It is shown in Fig. 3.

As the LW detector cannot be positioned to observe wavelengths shorter than 77 Å, only the coefficient at 113 Å could be obtained by this method. Interestingly, it has almost the same value as for the SW detector at the same wavelength. This observation results from the fact that the two detectors are practically identical. It also denotes the accuracy of the interferometric alignment of the spectrometer [7] and of the mechanical positioning of the detectors along the Rowland circle to better than 25 µm. In the following we will thus not distinguish between the two detectors on the calibration curves. It can be seen from the slope of the calibration curve that on the short wavelength side the spectrometer sensitivity (proportional to 1/K) decreases with decreasing wavelength, which illustrates the difficulty to measure spectral line intensities below 10 Å with this 600g/mm gold coated ruled grating. The comparison of the latest calibration curve with the previous one shows that the various improvements to the spectrometer (use of two microchannel plates in chevron configuration for each detector assembly, installation of a new grating, better performance PDA camera) have enhanced the spectrometer sensitivity by about a factor 30 over the whole calibrated wavelength range except below about 20 Å. The latter feature is most likely due to the characteristics of the previous 600 l/mm holographic grating which was platinum coated, while the new grating is a ruled one and gold coated with a steeply decreasing efficiency toward the very short wavelengths below 15 Å.

As this new grating is not designed to suppress the higher diffraction orders, the ultrasoft X-ray source lines at 44.4 Å and 67 Å have also been observed in the second order and have been used for the calibration, as shown in Fig. 3. They show that the spectrometer sensitivity in the second order is poorer than in the first order, but only by a factor of 5 to 8.

We have actually observed intense spectral lines emitted by the tokamak plasma in as high an order as the 7 th or the 8 th . Notice that the second order calibration is almost the same for the SW and the LW detectors, another indication that the two detectors are practically identical.

Sensitivity calibration in the long wavelength range

Use of the branching ratio method

The mechanical design of the spectrometer presently equipped with two detector carriages sets a lower limit of about 77 Å to the spectral range accessible to the LW detector (this limit is actually reached when the SW detector carriage is itself positioned at the shortest possible wavelength position). The only line emitted by the ultrasoft X-ray calibration source above this limit, and thus the only available one for the LW detector calibration in the first order, is at 113 Å. Therefore, another method has to be used in order to calibrate the spectrometer up to its maximum wavelength, which reaches 340 Å with the routinely used 600 g/mm grating.

The first additional method we use here is the so-called branching ratio method [1, 2], which we will now describe briefly. The emissivity ratio of two spectral lines of a given ion emitted by transitions from the same upper level to two different lower levels depends only on atomic constants and not on the plasma conditions. In tokamak plasmas the emission is completely dominated by spontaneous decay (rather than collisional de-excitation) so that the ratio can be written as:

ik ij ik i ij i ik ij A A A n A n = = ε ε (10)
where n i is the population density of the upper level i and A ij and A ik are the Einstein coefficients for spontaneous decay from levels i to levels j and k respectively. This relation holds as long as neither spectral line is self-absorbed by the plasma, i.e. when the plasma optical thickness can be neglected, which is the case here since the impurity ion density is always far below the main plasma ion density of about 5×10 19 m -3 . The effect of radiation trapping on the line brightness has been calculated using a mean transmission factor approach [2, 11] and the predictions were confirmed by measurements on the TA2000 torus [4]. It was found that for an optical thickness of the plasma below 0.1, the self-absorption is less than 3.5%. It is thus negligble in the present experimental conditions. Using Eq. ( 5) it is easy to show that the same relation can be used for the brightness ratio B ij /B ik measured by a spectrometer along a line of sight through the plasma. The relation between the measured signal ratio and the brightness ratio can be deduced from Eqs. 6 and 10:

ik ij ik ij m ik ik m ij ij A A B B N K N K = = ) ( ) ( λ λ (11)
This leads to the relation:

ik ij m ij m ik ik ij A A N N K K = ) ( ) ( λ λ (12)
This relation shows that the ratio of calibration coefficients at two different wavelengths can be deduced from line intensity measurements, which can be performed using the tokamak plasma itself as a calibration source, and from Einstein coefficients, which are well known atomic constants in our case. This relation can thus be used for relative calibration for the two wavelengths λ ij and λ ik . This is particularly useful to determine the absolute calibration factor at either wavelength when it is already known at the other. As already said, the latter application is often used for VUV spectrometers using a visible spectrometer having the same line of sight [3,4,5].

As we did not have such a setup, we took advantage of the absolute calibration over the SW range described in the previous paragraph to calibrate the longer wavelength range by using spectral line pairs with one line below 113 Å (measured in absolute units with the SW detector) and the other at a wavelength to be calibrated above this value (measured with the LW detector). This procedure relies on the assumption that the two detectors have the same sensitivity at any given wavelength, an assumption supported by their identical design and by the identical absolute calibration coefficient found at 113 Å in Section 2.

In our case, the plasma emits few pairs of lines obeying the constraints imposed by the branching ratio method and the spectrometer wavelength coverage (two lines emitted from the same initial level of the same ion with a sufficient intensity, the wavelength of one between 10 and 113 Å, the other between 113 and 340 Å). Only two suitable pairs were found, emitted by Carbon, the dominant impurity in Tore Supra plasmas. They are shown in Table 3 This method provides invaluable information in that it allows to link the absolute calibration in the shorter wavelength range with the relative calibration in the longer wavelength range. Nevertheless it is clearly not sufficient to calibrate the whole longer wavelength range of the spectrometer coverage. A complementary method is presented below.

Collisional-radiative modelling of line intensity ratios

The results of the branching ratio method exposed in the previous paragraph do not depend on the experimental conditions such as the plasma parameters and their time evolution or the spectrometer line of sight geometry. However, as it has just been shown, there are in general very few pairs of spectral lines which can be used in a given experimental situation.

Relaxing the constraint of an identical upper level for the spectral line pairs used for the calibration, we find many groups of lines emitted by a given ion in the plasma within the relevant wavelength range. The drawback is that the relative intensities of the lines within a group depend not only on atomic physics but also on the plasma parameters. They can be calculated in the frame of a collisional-radiative model (CRM).

This calibration method, less accurate than the branching ratio method, has been applied on the SPRED VUV spectrometer at JET for the 360-980 Å range using spectral lines from mostly low ionisation stages [5]. In the present work, we aimed at calibrating a shorter wavelength range (130-340 Å) than at JET. We also wanted to avoid using spectral lines emitted near the plasma edge, where the plasma parameters are not so well known (in particular the electron temperature). For both these reasons we did not select very low ionisation stages, as can be seen on Table 4. In the collisional-radiative modelling, instead of expressing the line emissivity as a function of the population density of the initial level of the transition (as in Eq. 10), we use the total density n z of the emitting ion. The emissivity of a given line between levels i and j can be written as:

Emitter Wavelength (Å) Transition

) , ( e e ij z e ij T n PEC n n = ε , (13)
where n e and T e are the electron density and temperature respectively. The PEC ij quantity, called photon emission coefficient, is calculated with a collisional-radiative model (CRM). It depends in a complex way on the collisional and radiative atomic processes in the plasma, namely transitions between excited levels of the emitting ions, recombination onto and ionisation from excited levels. The PEC dependence on n e is generally weak and will be neglected here. In the present case the PEC values were obtained from the ADAS data and model [START_REF] Summers | Atomic Data and Analysis Structure User Manual[END_REF].

From Eq. 13 it can be deduced that the emissivity ratio of two lines ij and kl emitted by the same ion is equal to the PEC ratio. For the brightness, which is the quantity actually measured by the spectrometer, the situation is slightly more complex:

∫ ∫ = dl T PEC n n dl T PEC n n B B e kl z e e ij z e kl ij ) ( ) ( (14)
where the integration is done along the line of sight. The exact calculation requires that we know the spatial distribution of all quantities in the integrals, in particular the emitting ion density profile along the line of sight. The most accurate way to obtain this is from a dedicated transport study [13], a sophisticated and somewhat lengthy procedure. Instead, we make here the rougher assumption that the PECs do not depend on T e . This is verified in our case because the emitting layer of the selected ions in this study is very narrow. As an additional precaution, we have rejected lines with PECs depending strongly on the temperature in the T e range where the emitting ion is abundant (e.g. C V 40.3 Å, 1s 2 1 S 0 -

1s2p 1 P 1 o
). As a consequence, denoting T e em the electron temperature of the emitting layer, the measured brightness ratio will thus be approximately equal to the PEC ratio: Provided the calibration coefficient is known at one wavelength, say λ ij , the coefficient at the other wavelength λ kl can be obtained by using Eq. 15:

( ) ( ) ij kl m kl m ij ij kl PEC PEC N N K K λ λ = (17)
Comparing the calculated and measured C VI line brightness ratios, we have calculated the absolute calibration coefficients at 134.9 Å and 182.2 Å. Note that at 134.9 Å the Balmer β line is blended with the fourth order of the C VI Ly α line at 33.7 Å. In order to subtract the latter contribution it was necessary to estimate the grating efficiency in the fourth order. This was done by measuring the intensity of the well resolved C V 34.97 Å line in the first and fourth orders in identical pulses designed for the calibration described here (see next Section). This allowed us to deduce that the grating efficiency in the fourth order with respect to that in the first order is about 10% at this wavelength. The contribution of the fourth order C VI Ly α line to the measured 134.9 Å intensity was then calculated using the measured first order C VI Ly α line intensity and the fourth order efficiency. It was then subtracted from the measured intensity at 134.9 Å before the calibration coefficients were calculated.

Then we interpolate the calibration coefficient of the 150.1 Å line of the O VI group between the values at 134.9 Å and 182.2 Å. From there, we use Eq. 17 with the O VI line group to obtain the calibration coefficients at 129.9 Å, 173 Å and 184 Å. Then with the same hypothesis we obtain the 151.5 Å (O V group) calibration coefficient, and this allows us to obtain the calibration coefficient at the second wavelength of the O V group, 192.9 Å. With the same reasoning, we obtain the calibration coefficients at 192.0 Å and 255.1 Å (Fe XXIV group) and at the six wavelengths of the C IV group. It has been checked that the final result (the curve which will be fitted to the data points) remains within the error bars if the order in which the line groups are added is changed.

Results and uncertainties

Results

A series of identical, ohmic pulses have been performed to record the useful spectral line brightnesses (Tore Supra pulses TS#31512 to TS#31519). The plasmas are found to be very stationary and reproducible so there was no need to perform a multi-pulse statistical study of the line ratios. The spectrometer was used in its spatial scanning mode, which means that the whole spectrometer was rotated around a horizontal axis located in front of the apparatus. In this mode of operation, the lower half of the plasma (see Fig. 4) could be scanned at a period of 0.5 Hz. Both the spectral line shapes and the radial profiles were used to reject blended lines.

In the case of the Fe XXIV lines, observed to be blended in [START_REF] Lawson | Stamp and JET-EFDA contributors[END_REF], the analysis of the radial brightness profiles allows to distinguish them from blended light species lines.

The calibration coefficients obtained with this method have been added to the results obtained in Section 2.2. The overall calibration curve is shown in Fig. 5. It shows a broad minimum (corresponding to a maximum in sensitivity) around 100 Å over a range of about 70 Å. The spectrometer sensitivity decreases steeply on both sides, although in the long wavelength direction the slope tends to become lower. This indicates that with the same grating a modified spectrometer with a longer mechanical range for the detector would be sensitive enough to provide information over a broader wavelength range. This has been done

for the Schwob-Fraenkel spectrometer installed on the Berlin EBIT experiment [14, 15]. On the contrary, in the short wavelength direction the slope is steeper and steeper. This indicates that extending the mechanical range to shorter wavelengths would not provide additional useful information below 10 Å. Figure 5: Absolute brightness calibration in lab (solid line with ), calibration transfer using the branching ratio method ( ) and relative calibration using the CRM of line ratios with plasma (the symbols are explained on the figure). The grey dashed line is a spline among the points and is adopted as the final calibration curve.

Uncertainties

In the wavelength range absolutely calibrated with the ultrasoft-X ray source (9.9 -113 Å), the main uncertainty is that associated with the spectral line intensities measured with the spectrometer. It is mostly due to the uncertainty on the background estimate, which can be difficult for the weaker lines of the calibration source. The uncertainty on these intensities is at maximum 10% (it can be as low as 5% for the stronger lines). In addition, we estimate an uncertainty of 10% to take account of the geometric aperture uncertainty. The uncertainty on the proportional gas counter measurements is negligible compared to those associated with the spectrometer measurements. We have thus a global uncertainty of 20% for the calibration coefficients up to 113 Å.

For the calibration points using the branching ratio method, we must take into account the time fluctuations of the two spectral line intensities used for each point. These fluctuations are not negligible even during the stationary phase of the plasma. They are actually much larger than the statistical error (which is the square root of the time average signal if a Poisson distribution is assumed). The total uncertainty is thus estimated to 40% at 134.9 Å and 32% at 182.2 Å.

For the CRM calibration method, a part of the uncertainty associated with the reference line (at wavelength λ 0 ) of a given line group is determined from the time fluctuation of the measured signal as discussed in the previous paragraph. To this fluctuation uncertainty, an uncertainty of 30% is added, corresponding to the interpolation of this reference line between two already calibrated wavelengths. For any other line (wavelength λ) of the group, the uncertainty is deduced from Eq. 17:

) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( ) ( 0 0 0 0 0 0 λ λ λ λ λ λ λ λ λ λ λ λ m m m m N N N N PEC PEC PEC PEC K K K K ∆ + ∆ +         ∆ + ∆ = ∆ (18)
The relative uncertainties on the signals N m (λ) and N m (λ 0 ) are calculated from the time fluctuations of the measurements, as said above. The uncertainty on the PECs themselves is difficult to assess and not always available in the literature. It seems that a global value of 30% for all PEC ratios reflects satisfactorily both the accuracy of the atomic physics calculations and the residual PEC ratio dependence on (see above the discussion about

Eq. 15)

.

For a practical purpose, a curve has been fitted on the points in Fig. 5. The most satisfactory result was obtained with a spline. Below 120 Å the 20% uncertainty estimated for the absolute calibration points can be retained. Between 120 and 180 Å, where line intensity branching ratios were available, an uncertainty of about 35% is estimated. Above this wavelength, a value of 50% reflects satisfactorily the spreading and uncertainties of the relative calibration points. In this range, the uncertainty might be an underestimate of the actual uncertainty due to the use of the CRM, for which the uncertainties are not well known.

Spatial variations of the detector response

The tolerances of the spectrometer design and realisation are very tight, so that most mechanical pieces are positioned to less than 25 µm. Nevertheless, the response of the detector assembly along its length (i. e. along the wavelength direction) is not perfectly uniform. It can be due to several reasons such as the small inhomogeneities of the multichannel plate and phosphor screen responses, the transmission of the fiber optics bundle or the quantum efficiency dependence on the photon incidence angle on the MCP input face.

As the non-uniformity and the spatial variation of the detector response play a role in the estimate of the spectral line absolute brigthnesses, it has been measured for the LW assembly. The simplest way of doing this measurement is to select a spectral range containing well isolated spectral lines and perform several measurements, moving the detector by small position shifts between measurements in such a way that the spectral lines would strike different parts of the MCP.

Due to programme constraints, this method could not be applied in the spectroscopy laboratory. Therefore we have used the same series of identical discharges on the Tore Supra tokamak as for the calibration. During this series, the detectors were moved in a limited number of positions. As a result of this procedure, many spectral lines could be measured at a few positions on the detector. By comparing the spectrometer measurements of a given spectral line in the various positions and synthetising the results for all lines, we were able to deduce the non-uniformity and spatial variation of the detector assembly response. The list of the lines used for this procedure is given in The synthesis of all these measurements is presented on Fig. 6. The results show that the intensity response is a decreasing function of the spectral line position in the direction of increasing pixel number (corresponding to increasing wavelengths) on the MCP detector in the useful range (between pixels 70 and 900 for the LW detector). The measurements show that the response at both ends of the detector (below pixel 70 and above pixel 900) is substantially degraded with respect to the major part of the detector range. This is due to the fact that the size of the PDA is slightly larger than the fiber optics bundle size. One notices that the unuseful portion on the large pixel number extremity is wider than that on the small pixel number extremity. This indicates that the bundle is not perfectly centred on the photodiode array. Both ends of the detector have thus been excluded from the study.

A straight line has been fitted to the data and the correction factor curve thus obtained has been normalised so that it is 1 in the middle of the detector (pixel 512 here). The spreading of the points around a given position and wavelength in Fig. 6 indicates that the measurement fluctuations are dominant over the spatial inhomogeneities along the detector.

The response decrease along the detector seems to be mostly related to the varying response of the MCP with the photon incidence angle. Indeed it is known that the MCP quantum efficiency decreases as the incoming photon angle with the grating plane becomes more grazing.

In Fig. 6, the average slope for the group of lines around 130 Å does not show a significant difference with that for the group in the range 240-292 Å (it would correspond to a response difference of less than 3%). Therefore we can consider that the wavelength dependence of the detector response spatial variation can be neglected. As no data in the short (10-70 Å) wavelength range are available for this calibration campaign, the average decrease of Fig. 6 was used to correct all the line intensity measurements performed for the Manson source and the branching ratio methods (Figure 5 includes these corrections.) As the intensity response curve introduces a maximum correction of about 20%, which is small compared with the global uncertainty estimated in Section 4.2, it was not necessary to make this correction for the CRM calibration above 200 Å. 4). Dashed line: final correction factor.

Summary and conclusion

The grazing incidence spectrometer operated on Tore Supra with a 600g/mm grating blazed at 1.5° has been absolutely calibrated over most of its wavelength coverage, i. e. 9.9-312 Å. For the lower part of this domain (9.9-113 Å) we have used an ultrasoft-X ray source calibrated against a gas flow proportional counter set up with a 100% efficiency. For the rest of the wavelength domain we have used the branching ratio method for absolute calibration transfer and collisional-radiative modelling of line intensity ratios for relative calibration.

The results show that the spectrometer sensitivity has improved with respect to the previous setup thanks to the new grating and the double multichannel plates in chevron configuration. The spectrometer is most sensitive in the 50-200 Å range, with a steep decrease below 50 Å. On the long wavelength side the sensitivity decrease is not as steep. In fact, after the present calibration procedure we have exchanged the 600 g/mm grating with a 300 g/mm one and obtained useful measurements up to 680 Å.

The uncertainties have been calculated for each individual calibration wavelength. Due to the variety of methods used for the whole wavelength range, it is not straightforward to determine a precise global uncertainty. We estimate a 20% uncertainty below 120 Å, where direct absolute calibration was obtained with the ultrasoft-X ray source, and 35% in the range 120-180 Å where the line branching ratio method was used. In the range above 180 Å where only the relative calibration procedure (collisional-radiative modelling of line intensity ratios)

the short wavelength range 2 . 1

 21 Figure 2: Absolute calibration setup with the ultrasoft-X ray Manson source

  front of the counter as a separation from the source volume. The membrane transmission factor T GPC depends on the wavelength, as shown in

Figure 3 :

 3 Figure 3: Absolute brightness calibration coefficient as a function of wavelength. SW detector: (red and dashed line) previous calibration in the first order and (blue and solid line) latest calibration in the first and second orders. LW detector: (blue + and dasheddotted line) latest calibration in the first two orders.

Table 3 :

 3 . The calibration coefficients at 28.5 Å and 27.0 Å are calculated by a linear interpolation between the two closest calibration points obtained in Section 2, namely 23.7 Å and 31.6 Å. Pairs of spectral lines and theoretical intensity ratios which have been used for relative calibration of the spectrometer above 113 Å.

  An accurate determination of T e em would require either a full transport study, as already mentioned, or enough lines of sight to determine experimentally the position of the emission layer. The weak T e dependence requested from the PECs retained in this study allowed to estimate T e em witout loss of accuracy from the position of the emitting layers as calculated by a local ionisation balance calculation. Denoting again N ij m the measured signal and K(λ ij ) the corresponding calibration coefficient, one gets by definition of the calibration coefficient (Eq.

Figure 4 :

 4 Figure 4: Poloidal cross section (solid line) of the tokamak vessel, (dashed-dotted line) of the plasma last closed flux surface and (dashed line) of the extreme positions of the line of sight.

Figure 6 :

 6 Figure 6: Intensity response of the LW detector assembly as a function of the line position on the detector (measured in pixels). Each symbol represents a different spectral line (see list onTable4). Dashed line: final correction factor.

Table 1 :

 1 List

of emitting elements in the various targets and wavelengths of the corresponding spectral lines.

Table 2 .

 2

	Wavelength (Å) 9.9 23.7 31.6 44.4 67.0 113.0
	T GPC (%)	55 42	32	19	50	37

Table 2 :

 2 transmission factor of the membrane in front of the gas flow proportional counter

Table 4 :

 4 Spectral

lines used in the branching ratio method for absolute calibration transfer (in bold) and in the CRM line ratio method for relative calibration.

Table 5 .

 5

	Wavelength (Å) Emitter
	129.9	O VI
	132.9	Fe XXIII
	134.9	C VI 2-4 (+ Ly α 4 th order)
	135.8	Fe XXII
	238.5	O IV, C IV
	241.5	C V (40.3 Å 6 th order)
	244.9	C IV
	281.9	C V
	284.1	Fe XV
	289.2	C IV
	292.0, 291.3	Ni XVIII, C III

Table 5 :

 5 List

of spectral lines and corresponding emitters for the evaluation of the nonuniformity and spatial variation of the detector response.


Alaeddine Mihoub
email: alaeddine.mihoub@gipsa-lab.fr

Gérard Bailly

Christian Wolf

Frédéric Elisei

Graphical models for social behavior modeling in face-to face interaction

Keywords: Face-to-face interaction, Behavioral model, DBN, Structure learning, Multimodal generation

The goal of this paper is to model the coverbal behavior of a subject involved in face-to-face social interactions. For this end, we present a multimodal behavioral model based on a Dynamic Bayesian Network (DBN). The model was inferred from multimodal data of interacting dyads in a specific scenario designed to foster mutual attention and multimodal deixis of objects and places in a collaborative task. The challenge for this behavioral model is to generate coverbal actions (gaze, hand gestures) for the subject given his verbal productions, the current phase of the interaction and the perceived actions of the partner. In our work, the structure of the DBN was learned from data, which revealed an interesting causality graph describing precisely how verbal and coverbal human behaviors are coordinated during the studied interactions. Using this structure, DBN exhibits better performances compared to classical baseline models such as Hidden Markov Models (HMMs) and Hidden Semi-Markov Models (HSMMs). We outperform the baseline in both measures of performance, i.e. interaction unit recognition and behavior generation. DBN also reproduces more faithfully the coordination patterns between modalities observed in ground truth compared to the baseline models.

Introduction

Face-to-face communication is considered as one of the most basic and classic forms of communication in our daily life [START_REF] Otsuka | Conversation Scene Analysis [Social Sciences[END_REF]. Its apparent simplicity and intuitive use conceals a complex and sophisticated bidirectional multimodal phenomenon in which partners continually convey, perceive, interpret and react to the other person's verbal and co-verbal signals and displays [START_REF] Scherer | Perception markup language: towards a standardized representation of perceived nonverbal behaviors[END_REF]. Studies on human behavior have confirmed for instance that co-verbal cuessuch as body posture, arm/hand gestures, head movement, facial expressions, and eye gazestrongly participate in the encoding and decoding of linguistic, paralinguistic and non-linguistic information. Several researchers have notably claimed that these cues are largely involved in maintaining mutual attention and social glue [START_REF] Lakin | The Chameleon Effect as Social Glue: Evidence for the Evolutionary Significance of Nonconscious Mimicry[END_REF].

Human interactions are paced by multi-level perceptionaction loops [START_REF] Bailly | Boucles de perception-action et interaction face-àface[END_REF]. Thus, a multimodal behavioral model should be able to orchestrate this complex closed-loop system. In particular, the model is facing the complex task of predicting multimodal behavior given a scene analysis while monitoring the intended goals of the conversation. Our challenge in this paper is to build statistical multimodal behavioral models that are trained by exemplars of successful human-human (H/H) interactions i.e. that map perception to action. The end goal of this research is to build user-aware social robots that are able to engage efficient and believable face-to-face conversations with human partners. In this work, this problem is solved in a data driven way through a Dynamic Bayesian Network (DBN) whose graphical structure and its parameters are learned from observed training data. We will show that automatically learning the model's structure as well as parameters leads to faithful predictions of multimodal scores that reproduce how humans coordinate their own modalities (intra) and between each other (inter).

The paper is organized as follows: the next section briefly reviews the state-of-the art of multimodal behavior analysis and modeling. In section 3, we present our face-to-face interaction scenario, the experimental setting and the collected signals. In section 4, the DBN model is presented and the structure of intraframe and inter-frame dependencies is discussed. Two other models (HMMs/HSMMs) are used as baselines. In section 5, comparative performances of these models are given and discussed. We show that the DBN model outperforms the other statistical models both in terms of performance and reproduction of coordination patterns.

Related Work

This research is a part of the general field of Social Signal Processing (SSP) [START_REF] Vinciarelli | Bridging the Gap between Social Animal and Unsocial Machine: A Survey of Social Signal Processing[END_REF], a new emerging domain spanning research not only in signal and image processing but also in social and human science. In recent years, it is becoming an attractive research area and there is an increasing awareness about its technological and scientific challenges. SSP essentially deals with the analysis and synthesis of multimodal behavior in social interactions.

One of the goals of SSP is automatic conversation and scene analysis [START_REF] Gatica-Perez | Automatic nonverbal analysis of social interaction in small groups: A review[END_REF]. The challenge is here to retrieve high-level information such as cognitive activities (e.g. addressing, turn taking, backchannel), social emotions (e.g. happiness, anger, fear), social relations (e.g. roles) as well as social attitudes (e.g. degree of engagement or interest, dominance, personality) [START_REF] Vinciarelli | Bridging the Gap between Social Animal and Unsocial Machine: A Survey of Social Signal Processing[END_REF] from the exchanged signals. Several computational models have been proposed to cope with these problems. Pentland et al. [START_REF] Pentland | Human dynamics: computation for organizations[END_REF] have characterized face-to-face conversations using wearable sensors. They have built a computational model based on Coupled Hidden Markov Models (CHMMs) to describe interactions between two people and characterize their dynamics in order to estimate the success of the intended goals. [START_REF] Otsuka | Automatic inference of cross-modal nonverbal interactions in multiparty conversations: "who responds to whom, when, and how?" from gaze, head gestures, and utterances[END_REF] proposed a Dynamic Bayesian Network (DBN) to estimate addressing and turn taking ("who responds to whom and when?"). The DBN framework is composed of three layers. The first one perceives speech and head gestures, the second layer estimates gaze patterns while the third one estimates conversation regimes. The objective of Otsuka and colleagues is to evaluate the interaction between regimes and behaviors during multi-party conversations. For social affect detection, Petridis and Pantic [START_REF] Petridis | Audiovisual discrimination between laughter and speech[END_REF] presented an audiovisual approach to distinguish laughter from speech and showed that this approach outperforms the unimodal ones. The model uses a combination of AdaBoost and Neural Networks, where AdaBoost is used as a feature selector rather than a classifier. The model achieved a 86.9% recall rate with 76.7% precision. A Decision Tree is used in [START_REF] Banerjee | Using Simple Speech-Based Features to Detect the State of a Meeting and the Roles of the Meeting Participants[END_REF] for automatic role detection in multiparty conversations. Based mostly on acoustic features, the classifier assigns roles to each participant including effective participator, presenter, current information provider, and information consumer. In [START_REF] Jayagopi | Modeling dominance in group conversations using nonverbal activity cues[END_REF], Support Vectors Machines (SVM) have been used to rate each person's dominance in multiparty interactions. The results showed that, while audio modality remains the most relevant, visual cues contribute in improving the discriminative power of the classifier. More complete reviews on models and issues related to nonverbal analysis of social interaction can be found in (Gatica-Perez, 2009) [START_REF] Vinciarelli | Bridging the Gap between Social Animal and Unsocial Machine: A Survey of Social Signal Processing[END_REF].

The second scope of SSP is the generation of relevant social behavior. The behavioral models should here predict the most appropriate sequence of multimodal signals for conveying given linguistic, paralinguistic or non-linguistic information. One possible application is to integrate these models into social agents [START_REF] Kok | Integrating Backchannel Prediction Models into Embodied Conversational Agents[END_REF] to make them capable of displaying social actions, social emotions and social attitudes via an appropriate animation of their artificial bodies. Several models have proposed to model and synthesize human behavior. We here focus on data-driven approaches, which automatically infer the behavioral models from data using machine learning techniques. For instance, Morency et al. [START_REF] Morency | A probabilistic multimodal approach for predicting listener backchannels[END_REF] showed how sequential probabilistic models, i.e. HMMs (Hidden Markov Models) and CRFs (Conditional Random Fields) can directly estimate listener backchannels from a dataset of human-to-human interactions using multimodal output features of the speaker, in particular spoken words, prosody and eye gaze. They notably addressed the problem of automatically selecting relevant features and their optimal representation for probabilistic models. [START_REF] Lee | Modeling Speaker Behavior: A Comparison of Two Approaches[END_REF]) also opted for a probabilistic approach to predict speaker head nods and eyebrow movements for a virtual agent application. The authors explored different feature sets (syntactic features, dialog acts, paralinguistic features, etc.) and different learning algorithms, namely HMM, CRF and Latent-Dynamic CRF (LDCRF). Quantitative evaluation showed that the LDCRF models achieved the best performance, underlying the importance of learning the dynamics between different gesture classes and the orchestration of the gestures. In our previous work [START_REF] Mihoub | Modeling Perception-action Loops: Comparing Sequential Models with Frame-based Classifiers[END_REF], we proposed statistical models that, for a given interaction scenario (i.e. a sentence-repeating game), estimate the cognitive state of a subjectgiven his verbal activity and the multimodal behavior of his interlocutorand then generate his gaze. We showed that sequential models (HMMs) are better than frame-based classifiers (SVMs and decision trees) in both tasks. Moreover, Huang et al. [START_REF] Huang | Learning-based Modeling of Multimodal Behaviors for Humanlike Robots[END_REF] used Dynamic Bayesian Networks (DBNs) to model the coordination of speech, gaze, and gesture behaviors in narration. Given input speech features, the most probable coverbal behaviorgesture type and gaze targetwere computed. The evaluation of their model shows that this learning-based approach achieves similar performance compared to conventional rule-based approaches while reducing the effort involved in identifying hidden behavioral patterns. More generally, these learning approaches frequently use probabilistic graphical models because of their capacity to capture subtle covariations between modalities and coordination between multimodal events that often escape to human expertise. Other interesting properties of statistical models include their ability in discovering and exploiting hidden states and latent variables that are not directly observed. That is why, in this work, the proposed behavioral models are data-driven and confronted to multimodal observation spaces.

In the next section we describe the scenario we designed to collect multimodal data of H/H face to-face social interactions. This data is then used to train and compare statistical models of joint behaviors.

Face-to-face interaction

Scenario

The objective of the proposed face-to-face interaction is to collect multimodal behaviors observed in a collaborative task called "put that there" [START_REF] Bolt | Put-That-There": Voice and Gesture at the Graphics Interface[END_REF] involving an instructor and a manipulator. This tasksimple as it can appear at first sightis a very interesting benchmark for studying and learning human strategies used to maintain mutual attention and coordinate multimodal deixis towards objects and locations.

More concretely, the task consists in reproducing a particular arrangement of cubes. Each game involves an instructor and a manipulator, the latter following orders of the former. The objective of the statistical model is to learn and reproduce the instructor's behaviors. The long-term goal is to transfer this model to a humanoid robot that will instruct a human manipulator. Credible scenarios where the HRI leads robots to instruct human partners are not so uncommon: robots may serve as coaches for physical or mental training [START_REF] Fasola | A Socially Assistive Robot Exercise Coach for the Elderly[END_REF][START_REF] Görer | A Robotic Fitness Coach for the Elderly[END_REF] or rehabilitation, education [START_REF] Brown | The positive effects of verbal encouragement in mathematics education using a social robot[END_REF][START_REF] Fridin | Storytelling by a kindergarten social assistive robot: A tool for constructive learning in preschool education[END_REF] as well as instructors for gaming or shopping recommendation [START_REF] Shiomi | Recommendation Effects of a Social Robot for Advertisement-Use Context in a Shopping Mall[END_REF].

In our scenario, the instructor has to reproduce a target arrangement of cubes with the help of the manipulator who is the only agent allowed to touch and move the cubes. Conversely, the target arrangement is only known to the instructor. The instructor and the manipulator must therefore cooperate (i.e.; share knowledge and coordinate their sensory-motor capabilities) to perform this collaborative task. The game involves 16 cubes. Each cube is marked by a colored symbol drawn on its upper side, i.e. a unique combination of one symbol (square, cross, circle and dot) and one color (red, green, blue and black). The gaming table comprises three areas as shown in Fig. 1.a:

 A manipulator space where the 16 cubes are initially randomly positioned. This space is close to the manipulator.  A task space in the form of a 5x5 checkerboard where the target arrangement of the cubes must be reproduced.  A graphics tablet displaying the current target configuration, i.e. which cube to move from the manipulator space and its destination area in the task space. These instructions are only visible by the instructor. They are incrementally made available to the instructor each time he performs a hand gesture on the tablet's touchscreen after the manipulator has effectively achieved the previous move. To ensure independence of the input data, the software randomly distributes source and target positions of the cubes. At the start of each game, the task space is empty and a first target cube is designated to the instructor to be placed at the center of the chessboard. His goal is thus to identify it in the manipulator space and to ask the manipulator to grasp and place it in the right position of the task space. Although the game may be accomplished using verbal instructions only, the instructor is encouraged to intensively use co-verbal behaviors such as gaze, head movements and deictic gestures in order to lighten the cognitive load of the manipulator, avoid verbal repetitions and ease the identification of cubes and places (e.g. use rapid oscillations of index pointing to indicate absolute and relative positions). Subsequent positions are specified as relative positions with respect to a previously placed cube, i.e. "above", "below", "at the right" and "at the left" (see examples in

Experimental setting

The aim of this experimentation is to train a model that predicts the coverbal behavior of the instructor using only egocentric observations, which can then be used by a robot for the generation of its coverbal behavior. For that reason, the manipulator is not equipped with any sensors and the scene analysis is performed from the instructor's viewpoint. Conversely, motion of the instructor is captured by:  A Qualysis® Motion Capture system (MoCap). 5 Markers were placed on the helmet of the instructor to capture head movements and another 5 markers on his right hand and his index to get his pointing gestures. The MoCap system uses 4 infrared cameras, all facing the instructor.  A monocular Pertech® eyetracker, consisting of a headmounted eye camera and a scene camera. It delivers fixation data at 25Hz. The video of the scene camera (see Fig. 2) is also used for annotation and visual perception.  A head mounted microphone used to monitor the instructor's speech signal.

For the purpose of annotation and data verification, we also equipped the environment with a camera mounted on the ceiling in order to have access to the complete scene. A chronometer is also placed in the visual field of the ceiling and scene cameras in order to accurately tag and synchronize the different videos streams. Claps are also performed before and after each interaction in order to precisely synchronize audio and video.

Data and modeling

We recorded 30 games in which the instructor interacted with 3 different partners (10 games with each one). Each game consists in placing the first 10 cubes of one random arrangement. The mean duration of a single game is around 1 minute and 20 seconds (~2000 frames, 40ms per frame). To model our interaction, 5 discrete variables were annotated semiautomatically (see below):

 IU: interaction units. These are joint sub-tasks describing the sequential organization of an elementary interaction. We distinguish (and annotated) interest (manipulator's face / manipulator space / task space / cube / target location / reference cube / tablet / else). MP and FX have been annotated manually using Pertech scene video. SP is automatically transcribed by a speech recognition system. GT is annotated semi-automatically using the Qualysis signals and adjusted manually using Pertech scene video. Finally IU is manually annotated on the basis of gaze triggering events. The Elan software [START_REF] Sloetjes | Annotation by Category: ELAN and ISO DCR[END_REF] is used to edit the multimodal scores. Note that these multimodal scores are time-series of our 5 discrete variables sampled at 25Hz. These joint multimodal scores are used to infer a coverbal behavioral model for the instructor. This model should first estimate the sequence of IUs given verbal and perceived cues and secondly to trigger the appropriate co-verbal behaviors: onsets of GT and FX are supposed to trigger gesture controllers that will effectively perform the pointing gestures, respectively by hand/finger and head/eye, while taking into account contingent parameters such as the referent target location and size. Our behavioral models compute what to perform and when to do it. The gesture controllers finally compute how to do it with the available effectors of the avatar.

Actually, the data is organized into three streams:

 The input stream consists in "SP" and "MP"  The output stream consists in "GT" and "FX".  The interaction unit stream contains "IU".

Let us repeat that notions like "input" and "output" are always to be considered from the point of view of the instructor. The behavioral model (see Fig. 3) will estimate the joint IUs from the input stream and generate the optimal output stream that is turned into coverbal actions. Note that we are interested in synthesizing co-verbal cues, not speech; for this reason, the speech activity of the instructor is considered as an input observation. In the next section, we will present our proposed behavioral models.

Fig. 3. The model of joint behavior captures the interleaving multimodal behaviors of both interlocutors structured by joint interaction units (IU). It is further used to predict an output stream (GT & FX) given partial observation of the joint activity (SP & MP).

Behavioral models

In this section, we present the statistical behavioral models, which will first be trained on the joint input, interaction and output streams. Machine learning and statistical modeling are used to intrinsically associate actions and percepts given synchronized sensory-motor streams and to organize sequences of percepts and actions into so-called joint sensory-motor behaviors. Our first model is based on a Dynamic Bayesian Network [START_REF] Murphy | Dynamic bayesian networks: representation, inference and learning[END_REF].

DBN

A dynamic Bayesian network (DBN) is a probabilistic graphical model (PGM) that provides a compact representation of conditional independence relationships among stochastic processes [START_REF] Koller | Probabilistic Graphical Models: Principles and Techniques -Adaptive Computation and Machine Learning[END_REF]. DBNs generalize static Bayesian Nets (BNs) with a temporal extent by incorporating temporal dependencies among random variables. DBNs also generalize Hidden Markov Models (HMMs) and their variants, which can be seen as special cases. Because of their intuitive graphical presentation, the ability to deal with uncertainty and to model complex temporal relationships among variables, DBNs have been successfully applied to several domains. These characteristics make DBNs particularly attractive and useful in modeling the dynamics of multimodal behavior in face-to-face interactions [START_REF] Huang | Learning-based Modeling of Multimodal Behaviors for Humanlike Robots[END_REF]). An extensive review of PGMs and particularly DBNs (representation, learning, and inference) can be found in [START_REF] Koller | Probabilistic Graphical Models: Principles and Techniques -Adaptive Computation and Machine Learning[END_REF] and [START_REF] Murphy | Dynamic bayesian networks: representation, inference and learning[END_REF].

DBNs are directed acyclic graphs in which nodes represent random variables and edges represent conditional independencies. Semantically, an edge from a parent node X to a child node Y means that node X has influence over node Y. In some situations and depending on the application, this dependency structure may be given by an expert [START_REF] Leray | Binary Codes Capable of Correcting Deletions, Insertions and Reversals[END_REF]. If not, several methods have been introduced to learn the network's structure automatically from data. In our application, our DBN structure (see Fig. 4) has been totally learned from the data described in the previous section. The intra-slice structure is learnt using the K2 algorithm [START_REF] Cooper | A Bayesian method for the induction of probabilistic networks from data[END_REF]. The inter-slice structure is learned using the REVEAL algorithm [START_REF] Liang | Reveal, a general reverse engineering algorithm for inference of genetic network architectures[END_REF]. We employed the Bayes Net Toolbox [START_REF] Murphy | The Bayes Net Toolbox for MATLAB[END_REF] for training and inference. The reveal algorithm assumes no intra-slice arcs, the optimal set of parents (slice t) for each child node (slice t+1) is then calculated separately. The idea is to infer the connections between nodes from measures of mutual information between children and parents. For the K2 algorithm, each node has no parents initially. Then, according to a given order of examination of nodes, the algorithm incrementally adds a parent (with a maximum of four parents per node) if it improves significantly the score of the resulting structure. The adopted order was IU, MP, SP, GT, FX i.e. interaction unit in the first level and sensorimotor data in a lower level. The IU is considered at the highest level since it reflects the cognitive states that guide the sensorymotor behaviors [START_REF] Lee | The Rickel Gaze Model: A Window on the Mind of a Virtual Human[END_REF]. The resulting causality network (see Fig. 4) presents very interesting proprieties:

 The interaction units influence both perception and action streams (black arrows).  The instructor reacts to the manipulator actions (MP impacts SP, GT and FX) (blue arrows)  The speech activity (SP) of the instructor influences his coverbal behavior (GT and FX) (green arrows). This is consistent with co-verbal contingency [START_REF] Mcneill | Hand and Mind: What Gestures Reveal about Thought[END_REF].  Each random variable (slice t+1) is influenced by its history (slice t) (gray arrows)  Perception-Action loops can be easily identified by the following sequences of edges in the dependency graph:

HMM and HSMM

In order to compare the performance of the DBN model with a state-of-the-art baseline, we trained a second behavioral model based on HMMs. In this case, the conditional independence properties, i.e. the graphical structure of the model, are fixed and not learned. For each dyad, we model each interaction unit with a single Discrete Hidden Markov Model (DHMM) and the whole interaction with a global HMM, that chains all single models with a task-specific grammar. The hidden states of these HMMs model the perception-action loop by capturing joined behaviors. In fact, the observation vectors are composed of two parts: the first part contains the perceptual streams and the second part observes action streams. The "hidden" states are then intrinsically sensory-motor. At the training stage, all data are available while in testing only perceptual observations are available. For that reason, after training, two sub-models are extracted: a recognition model that will be responsible of estimating sensory-motor states from perceptual observations and a generation model that will generate actions from these estimated states. For more details, please refer to [START_REF] Mihoub | Social Behavior Modeling Based on Incremental Discrete Hidden Markov Models[END_REF].

A third model based on Hidden Semi-Markov Model (HSMM) is also tested. In fact, a major inconvenient of conventional HMMs is state duration modeling. Durations of hidden states implicitly follow a geometric distribution, which may be often inappropriate to adequately constrain the statespecific residence time. As an extension of the HMM, the HSMM explicitly models state durations [START_REF] Yu | Hidden semi-Markov models[END_REF]. The structure of the HSMM is similar to the HMM model. However, HSMM needs an additional parameter matrix corresponding to the duration probabilities of the different sensory-motor states. This matrix is learned from data. For more details, we refer to [START_REF] Mihoub | Learning multimodal behavioral models for face-to-face social interaction[END_REF]. In the next section we will show the DBN results and a comparison with HMMs/HSMMs is made.

Results & Discussion

The proposed models should be able to (1) estimate the interaction units from input observations (speech activity of the instructor / gestures of the manipulator); when the two partners cooperate, the sequential organization of the interaction units should ideally reflect the shared mental states of the conversation partners at that particular moment; (2) generate suitable actions (hand gestures and gaze fixations of the instructor) that reflect his current awareness of the evolution of the shared plan. The learned DBN model captures these relationships. In order to estimate an optimal output stream (in the DBN model sense) given an observed input stream, we used the junction tree algorithm [START_REF] Cowell | Probabilistic Networks and Expert Systems: Exact Computational Methods for Bayesian Networks[END_REF]. Its role is to perform offline estimation by computing the MPE (most probable explanation) of IU, GT and FX given the whole sequence of MP and SP. The junction tree algorithm gives an exact solution to this combinatorial problem, similar to the Viterbi algorithm used for aligning HMMs states with observations. For all models, 30-fold cross validation was applied. In this paper, we tackle the non-trivial problem of evaluating the similarity of two sequences. A direct frame-by-frame comparison is of course always possible. However, a simple example can illustrate the problems of this approach: if two sequences A and B are given, where B is a shifted version of A by a single frame, the direct matching may result in a large dissimilarity measure, despite the fact that these sequences have identical structures. We address these shortcomings by first aligning the sequences before calculating classification measures.

The Levenshtein distance [START_REF] Leray | Binary Codes Capable of Correcting Deletions, Insertions and Reversals[END_REF]) is adopted for the evaluation because it computes a warped distance between predicted and original signals, which is tolerant to small missalignments. In fact, the Levenshtein distance is a metric for measuring the difference between two sequences; it computes the minimum number of elementary operations (insertions, deletions and substitutions) required to change one sequence into the other. From this optimal alignment, recall, precision and their harmonic mean (the F-measure) can be directly computed. Note that elements of the sequence are frames i.e. one instant t in a DBN, HMM or HSMM corresponds to one 40ms frame. In this paper exact estimation rates are presented (Fig. 5) but we mainly compare the F-measures of the Levenshtein evaluation (Fig. 6), all these rates are given at the level of frames.

Rates comparison

A direct comparison between all models is shown in Fig. 5 and Fig. 6. For both figures, the estimation rates of the three models are largely higher than random rates, computed from the empirical distribution of the data. Thanks to its capacity to explicitly model state durations, the HSMM leads to better Levenshtein rates (Fig. 6) in IU recognition (79% vs. 72%) and gaze generation (69% vs. 60%) compared to the basic HMM. The DBN model outperforms significantly both models (95% of confidence level): 85% for IU estimation, 87% for gesture generation and 71% for gaze generation. The same finding is observed for exact evaluation rates (Fig. 5). This performance gap may be explained by the fact that the DBN interestingly authorizes direct dependency relations between input and output observations. On the contrary, in the HMM paradigm, there is no direct relationships between the input and output variables of the observation vector (MP,SP,GT,FX) which presents a significant limitation compared to general Dynamic Bayesian Networks. Note however that [START_REF] Bengio | Input-output HMMs for sequence processing[END_REF] have proposed so called Input/output HMMs that could partially solve the problem.

Coordination histograms

Beyond the comparison between prediction performances, we evaluated the capacity of each model to capture and reproduce the micro-coordination between multimodal streams (speech, deictic gesture and eye gaze). To this end, we here propose the concept of "coordination histograms". These histograms give a global picture of the coordination patterns between different modalities. They can be computed both on data from ground truth and predicted output streams. They are thus quite suitable for characterizing similarity between generated interaction patterns and real interaction patterns. In the following, we compare the coordination histograms computed for original data, output streams predicted by DBN, HMM and HSMM.

Let us recall that each modality is segmented into a certain number of discrete events e.g. GT has 5 events (rest, cube, etc.). A coordination histogram for each stream is computed as follows: for each event onset, we look for the nearest event onset of the other modalities (i.e. SP and FX) and calculate the time delay between these two events. We then tabulate these delays for all events into a histogram, called coordination histogram for that particular stream. A coordination histogram captures the global structure of the micro-coordination between one modality and the others given synchronous streams of discrete values. Let's consider the histogram in Fig. 7b, top row. The value of ~600 for the highest bin centered on value "0" indicates that, in the ground truth data, 600 events of type "GT" had the nearest neighboring "FX" or "SP" event in the range [-50ms,+50ms], which is the interval corresponding to the central histogram bin of 100ms. Similarly, we compute coordination histograms for SP and FX (see the first row of Fig. 7) for ground truth. Coordination histograms are also computed for streams generated by the statistical models: DBN (second row in Fig. 7), HMM (see third row of Fig. 7) and HSMM (last row of Fig. 7).

Kolmogorov-Sminov tests of normality (see Tab. 1) show that ground truth histograms are derived from a standard normal distribution (SP and FX). This finding illustrates that human behavior is paced by hidden patterns. For our models, only the FX coordination histogram of the DBN model verifies this property. When comparing histograms in Fig. 7, we can see that distributions of the DBN model are visually more similar to the ground truth distributions than the other models. In Tab. 2, we provide the chi-squared distances between the coordination histograms for data of ground truth and the three models. The smallest distances are those of the DBN model: besides having the best prediction rates, the DBN also model exhibits the most faithful behavior coordination among the proposed models.

Conclusions & Perspectives

In this paper, we introduce an original scenario for a face-toface collaborative task. The multimodal data collected on dyads involved in this task were used to train joint behavioral models based essentially on HMMs, HSMMs and DBNs. These models are trained to predict the face-to-face interaction units and to generate coverbal behaviors of a given subject given his verbal behavior and the observed behavior of his partner. The conditional structure between variables discovered by the Dynamic Bayesian Network evidences and assesses the complex relationships between the different modalities of the human behavior. As a result, DBN leads to better performances in both IU recognition and behavior generation. We further introduced the concept of a coordination histogram, which is a new method to evaluate the capability of behavioral models to faithfully reproduce natural coordination among his and others' modalities. The coordination histograms produced by DBN were the closest to ground truth histograms compared to HMM and HSMM.

The DBN has the best performance compared to HMM and HSMM, but there is still a gap to 100%. Part of this gap is certainly due to human variabilityoccurring even when subjects are performing such repetitive tasksand the consistency of semi-automatic labeling of events by human labelers. We also think that the DBN could be improved by considering latent variables, their durations and additional modalities such as head or body motion. Other models should also be considered such as Long Short-Term Memory (LSTM) networks.

The quest for objective performance should be complemented with subjective assessment of the entire generation process, including both planning by the present proposal and gestural controllers that will effectively perform the movements. In our future work, we plan to implement these models on our iCub robot, put the robot into a real face to-face interaction and get a subjective evaluation of the relevance of our models.

  Fig. 1.b & c).

  Fig. 1. (a) The gaming table. (b) Example of a game in progress, the indication displayed to the instructor should be transmitted to the manipulator in this way: "put the green cross at the right of the black dot". (c) The final target configuration.

Fig. 2 .

 2 Fig. 2. Example of an interaction, filmed by the scene camera mounted on the instructor's head.

Fig. 4 .

 4 Fig. 4. The learned structure of our DBN model (variables in gray circles are the variables to predict in the inference stage)

o

  MP  SP  MP (2 slices: t and t+1) o MP  GT  SP  MP (3 slices) o MP FX  GT SP  MP (4 slices)  There is a mutual influence between the modalities of instructor's behavior: o SP  GT  SP (green and red arrows) o SP  FX GT SP (green and red arrows) o GT  FX  GT (yellow and red arrows)

Fig. 5 .

 5 Fig. 5. Exact estimation rates for all models, the dashed line illustrates the random level.

Fig. 6 .

 6 Fig. 6. Levenshtein estimation rates for all models, the dashed line illustrates the random level.

  Fig. 7. Coordination histograms computed with a 100ms bin. (a) speech coordination with gesture and gaze (b) gesture coordination with speech and gaze (c) gaze coordination with speech and gesture.

  6 different IUs: o Get: get the instruction from the tablet o Seek: seek the cube that must be moved o Point: point the cube in the manipulator space o Indicate: indicate the position in the task space o Verify: verify the manipulation o Validate: validate and acknowledge the manipulation  MP: manipulator gestures. We distinguish between 5 values (rest / grasp / manipulate / end / none).

	 SP: instructor speech with 5 values (cube / preposition /
	reference cube / else / none).
	 GT: region of interest pointed by the instructor's index finger
	with 5 values (rest / cube / target location / reference cube /
	none).
	 FX: gaze fixations of the instructor; we distinguish 8 regions of

Acknowledgments

This research is financed by the Rhône-Alpes ARC6 research council and the ANR-14-CE27-0014 SOMBRERO.

Appendix

Synchronized videos, speech data and annotations used in this experiment are freely available under the item "Put-that-there" at http://www.gipsa-lab.fr/projet/SOMBRERO/data.html


Peter A Machonis
email: machonis@fiu.edu

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Introduction

In Natural Language Processing (NLP), there has been much recent interest concerning phrasal verbs and other multiword expressions [START_REF] Dehé | ParticleVerbs in English. Syntax, Information Structure and Intonation[END_REF][START_REF] Guenthner | Multi-lexemic expressions: an overview[END_REF][START_REF] Sag | Multiword Expressions: A Pain in the Neck for NLP[END_REF]. Transitive phrasal verbs for the most part exhibit a continuous and discontinuous form:

(1) We cleared up the problem

We cleared the problem up Furthermore, in the case of a pronominal direct object, only the discontinuous form is grammatical:

(2) We cleared it up *We cleared up it Linguists debate where and how to store these expressions in the lexicon, how to electronically identify discontinuous strings in a corpus, and if the underlying form should theoretically be considered the continuous or discontinuous one. However, one very practical problem for NLP remains: disambiguating lexically identical, but semantically different expressions. The difference in meaning is by and large determined by the nature of the object rather than the subject, as the following examples show:

(3) a. The mother picked up the children This study enlarges the systematic description of the most productive particle used in English phrasal verb constructions: up. The initial database, composed of 300 transitive occurrences of up, collected from The American Heritage Dictionary and Spears 1996, was expanded to over 700 occurrences with the help of [START_REF] Fraser | The Verb-particle Combination in English[END_REF] and two other phrasal verbs dictionaries: The Longman Phrasal Verbs Dictionary (2000) and The Cambridge International Dictionary of Phrasal Verbs (1997).

In this expansion, we also included some support verbs (e.g., throw, put) involving particle movement, such as:

(4) a. Since they may also be continuous or discontinuous, we integrated adverbials, or spatial particles [START_REF] Jackendoff | English Particle Constructions, the Lexicon, and the Autonomy of Syntax[END_REF], in our database, as well:

(5) Max (kicked + threw + tossed) up the ball Max (kicked + threw + tossed) the ball up (6) Mary flipped up the switch Mary flipped the switch up Finally, to highlight all possible ambiguity, we included what are often called prepositional verbs. These are similar to phrasal verbs, but they do not involve movement of the particle or preposition up, such as:

(7) a. Women make up [= comprise] 90% of the applicants, while men make up the rest b. *Women make 90% of the applicants up, while men make the rest up (8) a. The Florida Marlins rang up [= accomplish] 6 runs in the last inning b. *The Florida Marlins rang 6 runs up in the last inning

We also incorporated some reduced structures as well, but obvious prepositional phrases, such as:

(9) The hurricane chugged up the peninsula were not included in our data.

Compositionality and neutrality

The particle up appears to be often used as an intensifier or as an aspect marker, which changes the activity into one of accomplishment, and can be deleted in almost 40% of the cases examined. We refer to these as compositional 1 phrasal verbs, since in most cases they are clearly not frozen expressions, but rather regular verbs that can be modified with a particle:

(10) They drank up the soda They drank the soda up They drank the soda (11) Max heated up the water Max heated the water up Max heated the water Furthermore, 25% of the expressions listed exhibit neutrality [START_REF] Boons | La structure des phrases simples en français[END_REF] or the causative alternation [START_REF] Levin | English Verb Classes and Alternations: A Preliminary Investigation[END_REF]) such as:

(12)
We cleared up the problem The problem cleared up (13) Laura burned up the house The house burned up

In many cases, typically neutral verbs (e.g., burn, break, etc.), remain neutral when followed by the particle up:

(14)
The decision burned up Max [= make angry] Max burned up (15) The comic broke up the audience [= cause to laugh] The audience broke up This is not always the case, though:

(16)

The driver burned up the track [= travel at high speed] *The track burned up An unanticipated observation, however, was that a large number of transitive verbs that are typically not neutral, took on the property of neutral verbs when followed by up. For example, transitive verbs such as hike, line, and power are not generally classified as neutral verbs, but with the added particle they can become neutral: The engine powered up

Conversely, in a few cases, some typically neutral verbs did not accept the intransitive when the particle was added:

(19)
The cook boiled (E + up) the water The water was boiling (E + *up) (20)

The garlic smells (*E + up) the kitchen The kitchen smells (E + *up)

These exceptions confirm the necessity of listing each expression in lexicongrammar tables.

Lexicon-Grammar tables

Originally, we had divided the data into five separate tables, depending on whether the particle was optional and if the expression exhibited neutrality: For this study, however, we combined all the tables into one large database in order to consider the problem of ambiguity involving homonyms from different tables. As can be seen in the following sample tables, extracted from the general database, these various syntactic possibilities are indicated via transformations along with the nature of the subject and object. The transformations categorized include particle deletion, the causative (or neutral) alternation with particle, and the causative (or neutral) alternation without particle. Finally, semantic information in the form of a synonym is included.

In the final database of 721 up expressions, 64% are ambiguous. Of these ambiguous expressions, over 60% involve just two or three homonyms, such as crack up the audience [= make laugh] vs. crack up the car [= damage], whereas about 20% comprise four or five homonyms, such as bring up or burn up (cf. Tables 6 &7). But some include nine or ten cases, such as throw up (cf. Table 8), while the expression pick up has at least fourteen distinct meanings, as can be seen in Table 1, where a French translation is also provided to underscore the difficulties this presents to NLP.

Since phrasal verbs, like regular one-word verbs, can be ambiguous in the lexicon, explicit selectional restrictions and other semantic features are needed in our lexicon-grammar in order to distinguish the various uses of the same expression in NLP. In some cases, the selectional restrictions of the direct object, which were limited to the features of [+ human] and [-human] in this classification, seemed to suffice. But, since differences in meaning are most often determined by the nature of the object, we have recently begun to expand our categorization to describe the object more fully. Gaston [START_REF] Gross | Classes d'objets et description des verbes[END_REF][START_REF] Gross | Classes sémantiques et description des langues[END_REF] and other researchers at LLI (e.g., Le We started with the eight hyperclasses from Gross 1994: human, animal, plant, inanimate (concrete), inanimate (abstract), location, time, and event.

N 0 =: Nhum N 0 =: N-hum Verb Particle Example of N 1 N 1 =: Nhum N 1 =: N-hum Without particle N 1 V Part N 1 V Synonym French Translation + -
We then developed basic semantic classes as we sifted through our data of ambiguous phrasal verbs, such as beverage, body part, business, clothing, food, fuel, hobby/skill, information, machine, money, musical instrument, vehicle, and so forth, along with other semantic information, such as energy, false, hostile, list, undesirable, etc.

Let us start with some of the straightforward cases, i.e., those involving just two distinct meanings. Objects identified as only accepting [+ human] complements were simply marked as human under hyperclass. Likewise those only taking [-human] complements were merely labeled as concrete. In fact, some ambiguous pairs of phrasal verbs can be distinguished in this straightforward manner, as can be seen in Table 2. But this only happens in 16% of the cases examined: i.e., only 13 out of 83 pairs can be disambiguated in this fashion.

Next we looked at cases involving two homophonous phrasal verbs both requiring direct objects that are [-human]. Here we tried to hone in on the various groups of possible lexical items associated with each meaning. In some cases, the hyperclasses were sufficient to disambiguate; in others, semantic classes were necessary, as can be seen in Table 3. It is obvious that if we look at this on a continuum, the more free the expression, the more vague the semantic information can be, whereas, the more frozen the expression, the easier it is to define a limited semantic class of possible objects.

After that, we tried to distinguish cases where one expression accepts only [-human] complements and the other takes both [+ or -human], such as tune up, which can mean both "adjust engine" as well as "adjust musical pitch", as in Table 4. Again, more specific semantic features such as body part, drug, coin, and vehicle, along with the hyperclass helped to alleviate the ambiguity between the two separate connotations. In some cases, however, only pragmatics, a longer chunk of text, or the identification of an elision can resolve all ambiguity: Subsequently, we examined cases of ambiguity involving more than two distinct meanings. In some cases, hyperclasses in themselves were sufficient to disambiguate, as in Table 5. Even though the various meanings of brighten up are very closely connected, and perhaps might not be considered homophonous by all, we do observe divergent syntactic behavior, either in terms of transformations or selectional restrictions between the various shades of meaning. For other cases of ambiguity involving more than two meanings, a larger context is needed to fully distinguish these expressions. In these cases, we followed Le Pesant & Mathieu-Colas 1998 and introduced domains, along with hyperclasses and semantic classes, as seen in Table 6.

Semi-frozen vs. free expressions

There are many cases where the verb-particle combination along with the complement is indisputably idiomatic or frozen since only one complement is possible, as in live it up "party extravagantly" or where only a couple of complements are possible, as in pick up (speed + steam) "go faster". However, some phrasal verbs exist in very limited paradigms and might be construed as semi-idioms, whereas others accept a variety of complements and can be considered freer. For example, in Table 7, the first three cases have very limited domains -burn up the (raceway + speedway + track), burn up (energy + fat + calories), and burn up (fuel + gas + money) -while the last two meanings "destroy by fire" and "make angry" are less restricted as to possible complements, are able to be composed without the particle, and can be considered compositional. Finally, in Table 8, while the first case of "throw upwards" can be construed as compositional, accepting many possible complements and difficult to distinguish from some of the more idiomatic senses, the other eight cases can be clearly distinguished by semantic classes.

Conclusion

We conclude that subcategorization refinements, such as hyperclasses, semantic classes, and domains help mitigate ambiguity involving English phrasal verbs.

  [= stop for] b. The police picked up the drug dealer [= arrest] c. The student picked up a new language [= acquire/learn] d. The gentleman picked up the young lady [= make contact with] e. The editor picked up the errors [= notice] f. Anne picked up dinner [= buy]

(

  17) a. Max hiked the trail *The trail hiked b. The company hiked up gas prices [= increase] Gas prices hiked up (18) a. FPL powered the building *The building powered b. Max powered up the engine [= start]

(

  21) a. Max lifted up the patient [= raise the patient (literally, e.g., out of bed)] b. Max's good humor lifted up the patient [= increase (emotionally) the patient's spirits] (22) a. Ann decided to look up Max [= find Max's name in the telephone book] b. Ann decided to look up Max [= visit Max]

(

  23) a. The parents brought up the baby [= mention in a conversation] b. The parents brought up the baby [= raise / educate, as a child] c. The parents brought up the baby [= carry up to a specific location]

Table 1 . Ambigutity involving the phrasal verb pick up 3. Semantic distinctions: Hyperclasses, semantic classes, domains

 1

	pick up a new language -+ ---acquire / learn	apprendre
	+ -pick up the drug dealer + ----	arrest / take into custody	arrêter, placer en détention préventive
	+ -pick up dinner	-+ ---buy / acquire	acheter
	+ + pick up the debris	+ + ---	collect / lift / gather	ramasser, soulever
	+ + pick up the phone	-+ ---	answer phone / get messages	décrocher
			make contact
	+ -pick up the young lady + ----	with (sexual	draguer
			intentions)
	+ + pick up the error	-+ ---	notice	relever
			stop for
	+ + pick up the children	+ + ---	(passenger or	passer prendre
			item) / call for
	+ + pick up Max	+ ----	invigorate	remonter, améliorer
	+ -pick up the bedroom	-+ ---	clean	nettoyer
	+ -pick up the discussion -+ ---	continue	reprendre
	+ + pick up the award	-+ ---	win / earn	gagner
	+ + pick up the radio station -+ ---obtain signal	capter
	+ -pick up a cold	-+ ---	get an infectious disease	attraper

  [START_REF] Pesant | Introduction aux classes d'objets[END_REF] have previously introduced semantic factors or "classes d'objets" into linguistic data. Basically, arguments are classified according to semantic classes, which in turn correspond to semantic classes that predicates may take. Thus the meaning of a polysemous predicate can be automatically recognized in a text, if the arguments are also catalogued in this manner. But classifying each phrasal verb as accepting certain general hyperclasses or "traits" and more refined semantic classes or "classes d'objets" was so overwhelming for this initial study in ambiguity that we decided to see if a limited number of features associated with acceptable objects would suffice to mitigate the ambiguity with the phrasal verbs in question.

Table 4 . Disambiguation when object can be either [+ human] or [-human]

 4

	N 1 V	Synonym	Hyper-class	Semantic Class

V Synonym Hyper- class

						Semantic
						Class Domain
	+ + burn up	the track	-+ ---	travel at high speed	concrete roadway racing
	+ + burn up money -+ ---	use too much	concrete	money / fuel	spending
	+ -burn up calories -+ + --consume concrete energy exercise
	+ + burn up	the barn	+ + + + +	destroy by fire	human / concrete	location	fire
	+ + burn up Max	+ -+ + -	make angry	human human	emotion-al state

Table 7 . Disambiguation of burn up

 7

Semantic Class + + brighten up the day -+ + +make happier time -+ brighten up the room -+ + +make more attractive location + + brighten up Mary + --+ + make more cheerful human Here, in Table 6, the phrasal verb bring up translates into French as "accuser," "soulever," "élever," "vomir," or "apporter," depending on the domain or context.

Although it remains to be seen how we can precisely identify these domains by way of NLP programming, that information can nevertheless help disambiguate a sentence such as:

However, some uncertainty still remains, when the ambiguity involves subject commutation, as the following examples show: Expanding the selectional restrictions of the subject in the lexicon-grammar will clearly help solve the issue of ambiguity, but better defining context or domains is the only way to fully distinguish diverse meanings of lexically uniform phrasal verbs. Our data nevertheless underscore the importance of a lexicon-grammar approach to English phrasal verbs.

Note

1. We refer to these as compositional, since the particle can basically be viewed as an intensifier (beat up the kids), an aspect marker (boot up the computer), or an adverbial (drive up prices) that is added to the one-word verb. Some cases where the particle can be deleted, however, do involve idiomatic or non-compositional expressions, such as the following:

i. The administrator backed (up + E) the teacher [= support] ii. The situation was eating (up + E) Mary [= bother]

Summary -Disambiguating phrasal verbs

Like regular one-word verbs, verb-particle combinations or phrasal verbs can be ambiguous in the lexicon. This study examines ways to disambiguate by adding specific semantic features or "classes d'objets" to the lexicon-grammar, along with characteristic syntactic selectional restrictions. We first enlarged the systematic description of the most productive particle used in English phrasal verb constructions: up. The initial database, composed of 300 transitive and neutral occurrences of phrasal verbs with up was expanded, and in the final database of 721 up expressions, 64% were shown to be ambiguous. Of these ambiguous expressions, over 60% involve just two or three homonyms, such as crack up the audience [= make laugh] vs. crack up the car [= damage], while another 20% comprise four or five homonyms. The rest involve six or more homonyms, with the expression pick up having fourteen distinct meanings. Following Gaston [START_REF] Gross | Classes d'objets et description des verbes[END_REF][START_REF] Gross | Classes sémantiques et description des langues[END_REF], [START_REF] Pesant | Introduction aux classes d'objets[END_REF], and other researchers at LLI, we introduce hyperclasses, semantic classes, and domains to the object description of some of our data. These subcategorization refinements seem to help mitigate ambiguity and underscore the importance of a lexicon-grammar approach, which includes both syntactic and semantic information, to English phrasal verbs.

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