Marc Louis

Maurice François
email: francois@lmt.ens-cachan.fr

Giuseppe Geymonat
email: geymonat@lmt.ens-cachan.fr

Yves Berthaud
email: berthaud@umrserv.inrets.fr

DETERMINATION OF THE SYMMETRIES OF AN EXPERIMENTALLY DETERMINED STIFFNESS TENSOR; APPLICATION TO ACOUSTIC MEASUREMENTS abbreviated title: "symmetries of a stiffness tensor experimentally obtained"

teaching and research institutions in France or abroad, or from public or private research centers.

Determination of the symmetries of an experimentally

determined stiffness tensor; application to acoustic measurements

Introduction

Basic problem: the material symmetries are unknown

This paper addresses a general problem: the knowledge of the symmetry class and the symmetry axis of a material whose stiffness tensor is obtained through different experimental techniques, either mechanical or acoustic. For most of the materials, the manufacturing process implies the material symmetry. However, the symmetry axis can be hardly known when the process is difficult to control: the growing direction of our monocrystal (made of the  phase of a nickel-based superalloy) is not precisely known, although the atomic disposition involves a cubic symmetry. In the case of geological materials the symmetry class is often unknown. No simplification is then available on the measurement of the stiffness tensor, the 21 constants have to be identified. This tensor has to be studied to point out the possible symmetry class of the material.

Measurement of the entire stiffness tensor

The first step is to determine the stiffness tensor of the material before analyzing the possible symmetries of this tensor. [START_REF] Hayes | A simple statical approach to the measurement of the elastic constants in anisotropic media[END_REF] has solved the theoretical problem of the determination of the stiffness tensor C even if the material symmetry is unknown. The proposed mechanical tests appear to be difficult to perform. Six classic tensile tests in six independent directions [START_REF] François | Détermination des symétries matérielles de matériaux anisotropes[END_REF] are also able to give C once the strains in different directions are measured for each test. This later method implies a tedious machining and off-axis mechanical tests that are always difficult to perform [START_REF] Boehler | A new direct testing machine for anisotropic material[END_REF]. In the particular case of a priori known symmetries the identification of the symmetric tensor Cs is easily done (up to orthotropy) with various tensile specimens machined with respect to the symmetries of the material. The ultrasonic measurements are used for biological [START_REF] Van Bursirk | A theory of acoustic measurement of the elastic constants of a general anisotropic solid[END_REF] or geological [START_REF] Harder | Inversion of Phase Velocity for the Anisotropic Elastic Tensor[END_REF] materials because they are the only method that allows the measurement of the elastic properties on very small specimens. The transducers are directly stuck on parallel faces of the sample. This is called the direct contact method. The direction of the propagation of the ultrasonic waves is then fixed by the geometry of the specimen. To avoid the problem of coupling between the transducer and the material and to examine various directions of propagation, the immersion method, in which transducers are sending the waves to the sample through immobile water, is preferred for plate-shaped composite materials (Castagnède et al., 1990) Combined with digital signal processing, this technique ensures a high accuracy of the measurement of the velocity and involves continuously varying directions of the wave propagation as the plate is rotated. This method has been fully developed and is practically able to give stiffness tensors up to orthotropy either in the case of exactly aligned specimen or non aligned specimen [START_REF] Auld | Evaluation de la matrice d'élasticité des composites orthotropes par propagation ultrasonore en dehors des plans de symétrie[END_REF][START_REF] Chu | On the determination of orthotropic material moduli from ultrasonic velocity data in nonsymmetry planes[END_REF] but does not seem to have yet been applied to a real triclinic material. The direct contact method has been retained in our experiments on small specimens. This technique allows the determination of the raw stiffness tensor Co in the base Bo linked to the specimen. The expression raw stiffness tensor refers to a tensor that is perturbed by errors due to uncertainties of the measurements, to a possible non homogeneity of the tested specimen.

Quasi symmetries: indicators and visualization

At this step we suppose a raw stiffness tensor Co determined by some experimental method in the specimen's base Bo, for example the acoustical method. The 6x6 Voigt's representation table of Co does not exhibit generally the symmetry of the stiffness tensor as the base Bo has no relation with the (unknown) possible principal directions of the material. Furthermore the raw tensor Co is perturbed by experimental errors. It has generally no exact symmetry (triclinic) but may be close to a symetry level (in this case we say that it has a quasi symmetry ). This forbids (or makes complex) the use of classical indicators like the contractions C ijkk and C ikkj [START_REF] Jaric | On the condition for the existance of a plane of symmetry for anisotropic material[END_REF] of a stiffness tensor C. In order to have a qualitative information on the quasi symmetries of Co, we developed a map based on the crystallographic pole figures. These maps represent, on a colored scale, the relative discrepancy between Co and its symmetric according to the plane of normal r. The "spots" or "lines" indicate the normals of the planes for which Co is close to be monoclinic. Their number and their relative position reveal the level(s) of symmetry(ies) Co is close to. For example, we will see that the monocrystal exhibits clearly nine spots corresponding to the cubic symmetry although the tensor is stricto sensu triclinic.

The nearest symmetric stiffness tensor

Once a symmetry class is chosen using the above pole figure for the stiffness tensor we have to compute the symmetric tensor Cs belonging to the chosen class of symmetry and that is the nearest to the raw tensor Co. The natural base Bs is the base for which the tensor Cs has the classical form in the 6x6 Voigt matricial representation. One way to find Cs and Bs is to look for the base B that minimizes a function deduced from the classical relations between the components of the tensor that allow the Voigt's representation [START_REF] Arts | A study of general anisotropic elasticity in rocks by wave propagation[END_REF]. The choice of such minimization functions remains arbitrary and leads to non-intrinsic functions. We propose an intrinsic function that creates from Co and the arbitrary base B a tensor Cb which has the chosen symmetry group G. This function calculates the average of Co on its orbit according to G B related to the base B. The natural symmetry base Bs is the one for which the relative discrepancy D(B) between Cb and Co is minimum. Then Cb is Cs, the nearest (to Co) symmetric stiffness tensor and D(Bs) can be called the distance from Co to Cs; in other words the distance to the symmetry group G. This knowledge can be useful in other cases than the basic problem described above. We can imagine, for example, the simplified resolution of some mechanical problems while using a tensor of a higher symmetry group (fewer independent components), with some acceptable error.

Acoustic measurements

Description of a direct contact measurement

The propagation of acoustic waves in solid media is mainly described by the acoustic or Cristoffel's tensor  [START_REF] Auld | Evaluation de la matrice d'élasticité des composites orthotropes par propagation ultrasonore en dehors des plans de symétrie[END_REF]. It is linked to the unknown stiffness tensor C and for a given direction n of the wave propagation by the following relation:

(n) = n.C.n
(1) This symmetric second order tensor (n) can be written in a diagonal form. Each eigenvector (at least three) represents a direction of vibration of the particles u i , and each corresponding eigenvalue represents the product V i ) 2 where  is the mass density, and V i the velocity of the body wave polarized in the direction u i . The direction u 1 , the closest to the propagation direction n, is called the quasi-longitudinal wave and the two others, u 2,3 , the quasi-transverse waves. This allows us to write (n) in the following different form (where "" represents the tensorial product):

(n) =  i=1 3 (V i ) 2 u i u i (2a)
Let us call m the direction of the vibration (polarization vector) of both the ultrasonic transducers: the emitter and the receiver. They are stuck on two parallel faces of the specimen. In the case of transverse emission m is in the plane orthogonal to n and the transducers are coupled by a rod (Figure 1). In the case of longitudinal emission m is equal to n. The generated wave polarized in the direction m is decomposed in the material in the three directions u i (with a displacement proportional to the scalar product u i .m) allowed by the material and each wave propagates at the velocity V i . As these waves reach successively the receiver the displacement measured by the receiver is given by u i .m. The measure (supposing that the transducer has a linear response) is then proportional to (u i .m) 2 . This allows the operator, when using transverse transducers (m.n=0), to measure the polarization angle  ^ i from the direction X 3 to the direction X 2 in the set-up coordinates X i (X 1 is equal to the direction of propagation n) (Figure 1), while searching for the maximum of received signal, i.e. when u i .m is maximum (Figure 2). Pratically this is not possible for the quasi-longitudinal wave as u 1 .n is close to 1, u 1 .m is close to 0 and too weak to be measured:  ^ 1 cannot be measured with our equipment.

Figure 2: measurement of the polarization  ^  with transversal transducers.

For each direction n, the three wave speeds V ^ i and the two polarization  ^  angles (with  = 2, 3) of the quasi-transverse waves are finally measured. In this ideal case the measure is called a complete measure. The two deflection angles   between the plane n  (orthogonal to n) and u  (Figure 2) remain unknown. For each direction n we can define the measured acoustic tensor  ^(n) equal to:

 ^(n) =  i=1 3  ^(V ^i) 2 u ^i u ^i(2b)
All the measured values of a quantity x are denoted by x ^ . The tensor  ^ should be equal to  (eqn 1) if the measured values  ^ , V ^ i and u ^ i were exact. For each measurement along the direction n we have five experimental values (V ^ i and  ^  ) and two additional unknowns (  ). Then the determination of the 21 values of the unknown stiffness tensor requires at least 7 different directions n (in case of complete measurements).

The specimen and the measures equipment

The geometry of the specimen is a compromise between simple machining, high number of faces and small specimen. It has here 13 pairs of parallel faces (Figure 3). This will give redundant data (we have seen that the minimum is 7). This redundancy will reduce the effect of the experimental errors, through a minimization scheme. The equidistant faces are cut orthogonal to the three vectors x o1 , x o2 , x o3 of the specimen's base Bo, to its bisectors, and the same after a rotation along x o2 (Table 1). We used 5 MHz "Panametrics" transducers with a 12 mm diameter and a "Saphir" card integrated in a PC computer. Software has been developed to measure the velocities (using an intercorrelation technique) and the directions 

^  . face A B C I J K L M N     normal's 1 0 0 0 1/ 2 1/ 2 0 -1/ 2 -1/ 2 1/2 -1/2 -1/2 1/2 coordinate s 0 1 0 1/ 2 0 1/ 2 1/ 2 0 1/ 2 1/ 2 1/ 2 1/ 2 1/ 2 in Bo 0 0 1 1/ 2 1/ 2 0 -1/ 2 1/ 2 0 1/2 1/2 -1/2 -1/2 X 2 B C A A-L -B -C-N -A-I -B C-K -M- J- M- -J-
Table 1: position of the specimen's faces.

practical experimentation

Table 2 gives the values of the velocities V i and of the angles  ^  for all the faces of the superalloy specimen. The distance between two parallel faces is 18.5 mm. The data given (Table 2) have been obtained after three measurements (under the same conditions) on the same specimen. This allows us to evaluate the uncertainty of the experimental procedure. The accuracy of the velocity measurement can be estimated to ± 3% and to be about ± 5° for the angle. We can remark that the values given for the faces A, C,  and are uncertain because the signal was weak and distorted. They will be removed from the set of data. As a consequence it is possible to have either complete measurement (faces B, I , J, K, L, M and N for example) or incomplete measurement if the other faces are also considered to get more experimental data. The following two sections will deal with the case of complete and incomplete measurements.

face A B C I J K L M N     V ^ 1 (m/

Discrepancy tensor and minimization function J

The basic idea is to find the set of components of Co that makes every acoustic tensor (n) (eqn 1) as close as possible to every experimental acoustic tensor  ^(n) (eqn 2b) . For every measure (for every n) we define the function j(n) from the Euclidean norm of the discrepancy between (n) and  ^(n) :

j(n) = 1 2 ((n) - ^(n)) 2 (3)

minimization strategy

The "best" raw tensor Co (of every C) and the best deflection angles   are those that minimize the sum J of j over the set of different directions n with complete measurements. As the two sets of variables (the components of C and the deflection angles   ) have a completely different role, we chose to use an iterative process: the minimisation will be done alternately on each set. The first step is relative to the components of C, while the deflection angles   are set at zero at the beginning of the iterative procedure (this is the value corresponding to an isotropic tensor).

minimization of J with respect to the components C ijkl

The condition for J to be a minimum with respect to the components of C is the nullity of the following gradient:

∂j(n) ∂C = n  (n.C.n)  n - i=1 3  ^(V ^i) 2 n u ^i u ^i n (4)
The measured  ^  and the unknown   define u ^  but not u ^ 1 . This vector u ^ 1 is assumed to be orthogonal to u ^ 2 and u ^ 3 as required for exact measurements1 . The classic symmetries of C are guaranteed by 60 Lagrangian multipliers  m . We show the first of these terms

 1 (C 1112 -C 1121 ) = 0 (5)
The 81 equations ( 4) and the 60 equations ( 5) are disposed in a matrix form A.X = B in which the  m and the C ijkl are stored in the "vector" X, their multipliers in A and the second members of equations (4) in B . This linear matricial system is directly and quickly resolved, giving the best components C ijkl of C for the given deflection angles   .

minimization of each j with respect to the deflection angles   We now have to minimize J with respect to the deflection angles   , with C fixed. As the   (n) play an independent role in each j(n), we can minimize independently each j(n) with respect to the two deflection angles. The gradient of j with respect to the deflection angles   is given by the following equations (in which "" represents the vectorial product):

∂j(n) ∂  = -((n) - ^(n) ) :  i=1 3  ^(V ^i) 2 (u ^i ∂u ^i ∂  + ∂u ^i ∂  u ^i) (6) with ∂u ^ ∂  =   (-sin  m  + cos  n) (7)
and ∂u ^1

∂  = v  -u ^ 1 (v  .u ^ 1 ) (8) with v  =       ∂(u ^2 u ^3) ∂  ||u ^2 u ^3|| (9)
The knowledge of this gradient allows us to solve this non-linear problem through a B.F.G.S. [START_REF] Burlish | Optimal determination of the elastic constants of composite materials from ultrasonic wave-speed measurements[END_REF] method. convergence -stopping criteria Two criteria are retained for stopping the calculation. A first test is done on the value of J which can be zero if the measurements are simulated ones, and the second involves the rate of convergence. This rate commonly tends to 10 -2 after ten iterations. practical procedure One can compute the values of the speeds and of the polarizations given by this stiffness tensor Co and compare these values to the experimental ones. This may be useful to check doubtful measurements. The energy velocities are also computed to distinguish the waves that cannot reach the receiver without parasite reflection. This is the case for a strong anisotropy and for measurement direction n that are far from the symmetry axis. In such a case the corresponding measures are removed. Sometimes the received signal may be too weak to distinguish clearly a shear wave or to obtain its angle  ^  . In these cases the set of measurements is incomplete.

Incomplete measurements

Let us suppose that the speed V ^ k (and of course, if it corresponds to a transverse wave, the direction m k ) has not been detected or corresponds to very doubtful data (see Table 2). This situation is more realistic especially with natural material (biology, geology).

We introduce the component L ij from the components of ( - ^ ) in the base u ^ i u ^j (i, j ≠ k). 10) We now define the new function h replacing j by: h

L ij = (u ^ i n) : C : (nu ^j ) - ij  ^(V ^i) 2 (
(n) = 1 2  i,j knowns L 2 ij ( 11
)
This definition is similar to that of j (equation 3) if the u ^ i are orthogonal. The global minimization function J has to be the sum of all the functions j(n) corresponding to complete measures and all the functions h(n) corresponding to incomplete ones. This theory cannot work for a measurement in which two speeds are not known. If the unknown polarization is quasi transverse, e.g.  = 3, a polarization angle  ^ 3 is missing and forbids us to calculate the quasi-longitudinal direction of vibration u ^ 1 as before (orthogonal to u ^ 2 and u ^ 3 ). We know that the u ^ i have to be an orthonormed base. This is written:

sin 2 sin 3 + cos 2 cos 3 cos( ^ 2 - ^ 3 ) = 0 (12)
Given the variables  2 and  3 , this condition gives two solutions for  ^ 3 (so for u ^ 3 ); one of them is good (gives the lowest value for j). The gradient of h(n) with respect to C is given by:

∂h(n) ∂C =  i,j known L ij nu ^i u ^j n ( 13
)
Its structure is still linear with respect to the C ijkl and allows us to complete the matricial direct resolution described above. The gradient with respect to the variables   allowing a B.F.G.S. resolution is given by

∂h(n) ∂  =  i,j known L ij (C :: (n ∂u ^i ∂  u ^j n + nu ^i  ∂u ^j ∂  n)) (14)
We detail here the derivatives of u ^ i . If the unknown polarization corresponds to the quasi-longitudinal wave the calculation remains the same as before (eqn 7, 8, 9). If the unknown polarization corresponds to the quasi-transverse wave u ^ 3 , the derivative ∂u ^ 2 /∂ 2 is calculated as before (equation 7), but u ^ 1 and its derivative now depend on the value of  ^ 3 itself dependent on  3 (equation 12). We have, in this case:

∂u ^1 ∂ 2 = -sin 2 m ^ 2 u ^3 + cos 2 nu ^3 (15) ∂u ^1 ∂ 3 = -sin 3 u ^ 2 m ^3 + cos 3 u ^ 2 n + ± tan 2 cos 3 1 1-tan 2  2 tan 2  3 [ ] cos 2 cos 3 cos( ^3- ^2) n -sin 2 m ^3 (16)
The value of ± is given by the choice of the best  ^ 3 described before (equation 12 From the above measurements (Table 2), we obtained the following raw stiffness tensor Co for our superalloy specimen (Table 3). The components of this tensor are given in GPa and in the base attached to the specimen. One can also point out that some components are negative. This is admissible once the eigenvalues of this tensor are positives which is true in this case. As said, these matrices (written under Voigt's convention) do not reveal the possible nature of the symmetry of Co; this tensor looks triclinic. As expressed in Bo, Co cannot, at this step, be compared to the stiffness tensor measured by the micro-hardness method (Table 4) expressed in the natural symmetry base Bs related to the lattice. 3. Visualization of the quasi-symmetries: pole figures

principle

Let Co be a "raw" stiffness tensor determined by any experimental method, e.g., the acoustical one presented before. As said in the introduction, this tensor is generally triclinic (without symmetries) due to experimental errors and expressed in the randomly chosen specimen's base Bo. The pole figures classically used in crystallography represent the elements of the symmetry group G. Each symmetry level (of the eight possible [START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]) has a different set of symmetry planes (Figure 4). Plotting the symmetry planes will allow us to distinguish the symmetry level. Let us introduce the discrepancy function d(Co, r):

d(Co, r) = | | | | Co -S[r  ](Co) | | | | Co ( 17
)
In this expression S[r  ](Co) represents the stiffness tensor, symmetrical to Co with respect to the plane r  , orthogonal to r (see eqn 17a,b in the appendix)2 . The norm is taken as the Euclidian one (see eqn 17c in the appendix). The distance d is, of course, null if r  is a symmetry plane for Co. As said, Co is here generally triclinic but may be "close" to belonging to a higher symmetry group. In this case, some directions r will be such that d(Co,r) has a "low" value. Let us now plot d(Co,r) for each r of the half space; we obtain the pole figure of symmetry planes. We can see (Figures 5 and6) some of these pole figures. The x o3 axis is the normal to sheet plane, x o1 is on the right hand, and x o2 is upwards. To each "spot" corresponds a plane of "quasi-symmetry". We recall here, for an easier interpretation, the shape of pole figures in the case of the following quasi-symmetries (although this can be read on Figure 4): page 10 -triclinic: no spots monoclinic: one spot trigonal: three spots (coplanar, at 120°) -transverse isotropic: one band (infinity of coplanar normals) and one spot (orthogonal) -orthotropic: three spots (the normals are orthogonal each other) -tetragonal: five spots (four coplanar normals at 45° and one orthogonal) -cubic: nine spots (normals of nine cube's symmetry planes) -isotropic: all the map is black Figure 4: symmetry planes for each symmetry level.

Examples

A brief analysis of Figure 5 reveals the cubic nature of our monocrystal. We can clearly distinguish the nine spots. The cubic symmetry is however non exact, as the value 0 is nowhere reached for d(Co, r). This cubic symmetry is that of the crystal's atomic structure and we can remark that the x 03 axis of the specimen is 6 degrees apart from the symmetry axis of the crystal3 . When the measurements provide less accuracy, the pole figure is not very contrasted and as a consequence different levels of symmetry are possible. We can see that on the pole figure obained from a stifness tensor Co measured on an oak specimen (Figure 6). At a first sight transverse isotropy appears (horizontal zone). A closer examination also shows two spots in this zone that reveal a tendency to orthotropy. The ultrasonic measurements are less accurate than those of the monocrystal as the material has some important heterogeneity. The minimum value of d(Co,r) can be an indicator of the measurements' precision if the material is assumed to have some symmetry.

Computation of the nearest symmetric stiffness tensor

The last example reveals that a more precise definition of the "distance" between the raw stiffness tensor and the different possible symmetries is necessary for the engineer to choose the most appropriate symmetry level. Furthermore it is necessary to compute the nearest (to Co) stiffness tensor Cs that belongs to this class of symmetry and its associated natural base Bs (in which Cs has the classic matricial Voigt's expression).

general principle

The chosen symmetry for the studied material has a symmetry group G. This group is a subgroup of the orthogonal group O(3) but, as all the (fourth-rank) stiffness tensors have the punctual symmetry -I, one can consider G as a subgroup of SO(3) without loss of information. Most of the notations in the present paper are the ones used by [START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]. (20) This minimum is numerically found by a simplex [START_REF] Faurre | Analyse numérique[END_REF] method that determines three positioning Eulerian angles. One can remark that this distance does not depend on the arbitrary choice of Bo as the norm above is invariant relative to the choice of the base. The natural base Bs is the argument of the previous minimum: Ds = D(Bs) (20) And the nearest stiffness tensor Cs can now be given as the average of Co on its orbit according to G Bs :

Cs = < G Bs o Co > (21)

symmetry groups of stiffness tensors

In this section we detail the symmetry group for each symmetry level possible for a stiffness tensor [START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]. As said, we only take into account the elements of SO(3). triclinic In the case of the triclinic symmetry, the symmetry group G is reduced to the identity {I}. The distance D is of course zero and the base Bs is undefined. symmetries based on D n We consider as symmetry group G B the dihedral group D n : in the orthonormed base B=(i, j, k), D n is generated by Z n (a cyclic subgroup with n elements, generated by the rotations Q(k, 2/n) about z of an angle 2/n) and the rotation Q(i, ). D n has 2n elements. The value of n decides (eqn 18 & 21) of the symmetry class of Cb and, of course, Cs. We have:

- n  {1, 2} Cb is monoclinic - n  {3, 6} Cb is trigonal - n  {4} Cb is orthotropic - n  {5,7,9,...,} Cb is transverse isotropic - n  {8}
Cb is tetragonal In order to clarify this calculation, Figure 7 illustrates how we can obtain a trigonal tensor Cb when calculating the average of D 3 oCo. The result for the transverse isotropy is justified as a stiffness tensor cannot have these symmetry groups D n (see theorem 1, [START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]). The symmetry group obtained is the transverse isotropy as it contains D n . cubic The symmetry group G B of cubic stiffness tensors is O. It is generated, in the base B=(i, j, k), by the dihedral group D 4 (defined above) and the rotations Q(i+j+k, 2/3). It has 24 elements. isotropic In this case the symmetry group G B of isotropic stiffness tensors is SO(3). As this group has an infinite number of elements, this result cannot give directly the nearest stiffness tensor Cs. We propose here two ways to reach the isotropic symmetry. The first possibility is to observe that O is a maximal subgroup of SO(3). That means that SO(3) is generated by O and every subgroup S not included in O. This method gives an isotropic stiffness tensor Cs. The second method proposed here is to take as G B the symmetry group of the dodecahedron I . It has 60 elements in the following rotations: the rotations Q(n i , 2/5) around the 12 normals of the faces n i , the rotations Q(c j , 2/3) around the 12 corners c j and the rotations Q(e k , 2/2) around the 30 edges e k . It can be understood that as the stiffness tensor C cannot have the dodechedral symmetry (Theorem 1, [START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]), the following group is SO(3) himself. The result is, of course, independent of the choice of the position of B (i.e. the position of the dodecahedron or it's conjugated dodecahedron).

exemple

The stiffness tensor Co measured from the superalloy measurements (Table 3) is now considered. The Table 5 gives the distance Ds to each level of symmetry. We can notice that Co is really close to the left branch of the tree (the "orthotropic branch"); on the contrary, the "trigonal branch" is far from Co. It is obvious that the order relation between the symmetry levels has to be respected. Practically this requires avoiding local minima while searching for the base Bs (eqn 20); the position of base B is first manually set close to the real minima (using the pole figures of symmetry plane). For low level symmetries it is generally necessary to try many combinations before finding the absolute minima.

isotropic Comparing the distance from Co to each symmetry level of the left branch leads us to notice that Co is only 2.4% further to the cubic symmetry than to the orthotropic symmetry. The high level (only three independant constants) cubic symmetry appears, without any other choice constraints, to be the "right" symmetry level for this material. The nearest cubic tensor Cs is given Table 4. The monocrystal has a cubic lattice and X-ray diffraction measurements allows us to validate the obtained symmetry and position of the base B. Furthermore, every Cs can be compared to data from mechanical tests made using microhardness tests [START_REF] Espié | Étude expérimentale et modélisation numérique du comportement mécanique de monocristaux de superalliage[END_REF]. They allow the measurement of the stiffness tensor especially on small specimens by using load-unload paths. These measurements have been done with the hypothesis that the stiffness tensor has a cubic symmetry related to the corresponding symmetry of the microstructure. The values obtained in the two cases are different but are close to be proportionnal (Table 4). This is probably due to the difficulty of performing mechanical tests on these materials that exhibit some microplasticity even for low strains.

Conclusion

We propose in this paper a complete method able to provide the entire stiffness tensor of an unknown elastic material and the full analysis of this tensor. The measurement and the analysis can be used separately as many methods are now able to give the raw stiffness tensor. Our proposed ultrasonic method is therefore easy and seems reliable for homogeneous materials. The experimental set-up is very simple as a pair of transducers, a card plugged in PC, a software are sufficient to perform the measurements. A possible extension of this work concerns the measurements of induced anisotropy, for example due to damage. The planes symmetry pole figures are, in our opinion, a straightforward visualisation of the symmetry level of the complex elements that are the stiffness tensors. Their application may be extended to other tensors (different levels, or with different indicial symmetries). Finally, the presented computation of the nearest stiffness tensor Cs gives a powerful, complete and fast analysis of the stiffness tensor. Some interesting mathematical developments will be possible in the case of isotropic symmetry generated by the symmetry group of the dodecahedron. The concept of distance to a symmetry group leads to some surpises: in the case of our oak specimen, one can consider it, without any great loss of information, as transverse isotropic (only 5 constants) instead of the classic orthotropic symmetry level (9 constants) that is commonly used for woods.

Figure 1 :

 1 Figure 1: experimental set-up for acoustical measurements.

Figure 3 :

 3 Figure 3: 26-faces oak specimen.

  nearest cubic tensor Cs for the monocrystal (GPa). Values in italic are obtained from microhardness tests.

Figure 5 :

 5 Figure 5: pole figure of symmetry planes obtained from the superalloy's raw stifness tensor Co

Figure 7 :

 7 Figure 7: representation of the construction of a trigonal tensor Cb from a triclinic tensor Co. Let G B be a symmetry group G located by an orthonormed base B (in comparison with the specimen's base Bo). The raw stiffness tensor Co is a priori triclinic. We now define the orbit G B o Co as the collection of all the transformations of Co by the elements of G B . The average <G B o Co> of this orbit has, of course, G B as symmetry group. Let us call Cb such an average 4 , which is the nearest to Co stiffness tensor, having G B as symmetry group: Cb = < G B o Co > (18) We now can define a distance between Cb and Co. The following one has the same definition as d(Co, r) (eqn 17) when G is the symmetry group of the monoclinic symmetry:D(B) = || Co -< G B o Co > || || Co || (19)Then, the distance Ds from Co to the considered symmetry group G can be defined as the minimum of the distance D(B) when B varies: Ds = min B (D(B)) (20) This minimum is numerically found by a simplex[START_REF] Faurre | Analyse numérique[END_REF] method that determines three positioning Eulerian angles. One can remark that this distance does not depend on the arbitrary choice of Bo as the norm above is invariant relative to the choice of the base. The natural base Bs is the argument of the previous minimum: Ds = D(Bs) (20) And the nearest stiffness tensor Cs can now be given as the average of Co on its orbit according to G Bs :Cs = < G Bs o Co > (21)4.2. symmetry groups of stiffness tensorsIn this section we detail the symmetry group for each symmetry level possible for a stiffness tensor[START_REF] Forte | Symmetry classes for Elasticity Tensors[END_REF]. As said, we only take into account the elements of SO(3). triclinic In the case of the triclinic symmetry, the symmetry group G is reduced to the identity {I}. The distance D is of course zero and the base Bs is undefined.symmetries based on D nWe consider as symmetry group G B the dihedral group D n : in the orthonormed base B=(i, j, k), D n is generated by Z n (a cyclic subgroup with n elements, generated by the rotations Q(k, 2/n) about z of an angle 2/n) and the rotation Q(i, ). D n has 2n

Table 2 :

 2 acoustical measurements for the monocrystal. The * indicates doubtful data.

	s) 5437 5316 6131 6098 6066 6098 6151 6066 6165 6275 6244 6296 6307 ^ 2 (m/s) 3826 3863 3867 3918 3826 3840 3959 3863 3955 3615* 3615* 3676 2712 V  ^ 2 (d ) 0 0 115 115 165 110 125 175 135 130 130 145 37* V ^ 3 (m/s) 1869* 3863 1815* 2237 2143 2212 2134 2154 2244 2674 2396 2460* 3615  ^ 3 90 90 25* 25 69 35 35 85 37 45 35* 55* 145*
	(d	)

Table 3 :

 3 ). raw tensor Co obtained for the monocrystal (GPa).

	practical results
	243 136 135 22 52 -17
	136 239 137 -28 11 16
	135 137 233 29 -49 3
	22 -28 29 133 -10 -4
	52 11	49 -10 119 -2
	-17 16 3	-4 -2 130 Bo

Table 5 :

 5 distance from the raw stiffness tensor Co to each symmetry level

			34.6 %
	cubic	10.5 %	transverse	21.8 %
	tetragonal 9.9 %	i t i
	orthotropic 8.1 %	trigonal	21.3 %
		monoclinic 4.2 %
		triclinic	0 %

Even if u ^

and u ^

are not exactly orthogonal at this step of the calculation.

Remark: the computation is about 10 time faster while using the Bond's matrices[1]

x 03 is the axis of the cylinder (before machining the specimen), but x 01 and x 02 are randomly chosen.

It can be noticed that, as B is positionning the symmetry group G B , Cb can generally not be obtained from a rotation of another Cb' of this average in comparison to another base B'.

Appendix: Cartesian notation with indices

If not specified, the convention summation follows on indices.  ij is the Kronekker symbol and  ijk the direct permutation symbol.


Aisling Healy
email: ais.healy@gmail.comeric.verdier@univmed.fr

Eric Verdier

"Theory and Evidence in European Educational Research" Symposium "Knowledge and policy in the education sector in Europe" Network 23. Policy Studies and Politics of Education`

Knowledge systems and vocational training policy in the regions

In so doing, the government reasserted its 'determination' to anticipate in order to take action (not without echoes of the Keynesian state inseparable from national statistics), but this was done in a way which remained compatible with the emergence of a decentralised state: by establishing a framework rather than laying down rules. A circular dated 16 February 1988 thus gave the OREFs a common goal -developing diagnostic and forecasting tools to be shared by the regional actors [START_REF] Bertrand | L'expertise en région : entre légitimité de la connaissance et utilité pour l'action[END_REF]) -but the definition of the specific institutional form and methods was left up to the observatories themselves. Each French region thus came to choose the kind of information produced and the ways of using it in the context of regional employment and training policies [START_REF] Pascaud | Bilan des observatoires régionaux de l'emploi et de la formation -OREF[END_REF]).

In the two regions under consideration here, the initiatives were quite distinct: in Rhône-Alpes, they took the form of an association, and in PACA, that of a structure within the Regional Council, although this was funded through the State-Region Planning contract. The implication of the OREFs in the specific regional histories of the training-employment relationship was all the more profound because the 1988 circular pragmatically tied their creation to the 'multi-annual contractualisation' of public policy (cf. Gaudin 1999), as well as the 'continuity of the transfer of authority over initial and continuing education and training to the Regional Councils [START_REF] Brochier | Les observatoires régionaux de l'emploi et de la formation[END_REF]. These two observatories have thus been studied here from a socio-historical perspective (Thelan) in order to bring out the configurations of regional actors taking part in their creation and subsequent development. To what extent do interactions between those involved in the fields of employment and training (i.e., between organised 'interest groups' including the devolved state services, local authorities, social partners etc.) have an impact on the modes of production and use of the information produced and mobilised by the two OREFs under study? In the following presentation, we shall examine the changing content of the tools these OREFs develop in relation to the 'mandates' they take on and the autonomy they acquire in view of (possibly) gaining the status of expert institutions. Our hypothesis is that the statistical apparatus (Lascoumes and Le Galès 2005) of the regional trainingemployment relationship depends on an institutionalisation over the medium term, marked by technical innovations, the 'sedimentation' of numerous tools and the restructuring of their uses. Ultimately, we would maintain that the histories of these two observatories entail successive compromises between the heritage of the French-style 'planning state' of the 1960s and 1970s [START_REF] Tanguy | La mise en équivalence de la formation avec l'emploi dans les 4e et 5e Plans (1962-1970)[END_REF] and the emergence of territorial expertise networks in the context of a decentralised state (Desrosières 1997). To shed light on these regional encounters between two statistics systems -training and employment -we shall examine the production of these observatories in terms of three subject fields: sectors and occupations, territories and individual pathways.

More broadly, our approach is based on an analytical framework which considers the regulation of public policy as the resultant of interactions between three determinant elements, namely institutions, ideas and interest groups -'the 3i' (Théret 2000). 3 The OREFs redefine their missions and activities in response to this interplay, while periodically coming up against difficulties of a technical, organisational or political nature. The periodisation varies somewhat between the two OREFs, but not enough to warrant separate treatments; we shall thus deal with each period in terms of both OREFs.

Box 1 Approach and methods of investigation

This interregional comparison draws on a study which is part of a larger programme on 'Measurement Policies' supported by France's National Research Agency (ANR) and co-ordinated by Romuald Normand ('Education and Policies' mixed research unit, INRP and Université de Lyon 2), in relation with Jean-Louis Derouet (idem) and Martine Mespoulet (Université de Nantes). Three types of sources are used: transcriptions of semi-structured interviews lasting an average of two hours, both official and internal written documents and, less frequently, observation notes. The interviews were conducted with OREF staff but also members of the Regional Councils, the devolved state services (notably the local education authorities), other bodies producing expert information on employment and training in the regions (e.g., the regional INSEE offices) and the social partners. With regard to the written sources, we would like to thank the staff of the two OREFs and the training and employment departments of the PACA and Rhône-Alpes Regional Councils, who kindly gave us access to their archives.

FIRST PERIOD: THE FOUNDING, OR THE IMPRINT OF THE ORIGINAL CONTEXTS

Both OREFs have had to interact with state and regional institutions, but their activities got underway in very different social and political contexts. And the latter have subsequently been shaped by the OREFs' own statistical production, which defines the 3 The term 'regulation' is used here in the sense of the definition provided by Jean-Pierre Gaudin: 'The notion of regulation designates . . . the way of codifying legitimate rules or reconstructing them. This immediately brings to mind the corpus of legal decisions. But the idea of regulation has led more broadly to considering the elaboration of the rules as well, namely the social adjustments and compromises which make them acceptable'. L'action publique, sociologie et politique (Paris: Presses de Sciences Po-Dalloz, 2004), p. 193. regional social situation as much as it reflects it (Desrosières, ibid.). Beyond a common partisan affiliation, the two regional executives have partly shaped their respective observatories to correspond to dissimilar political and social structures even if, in technical terms, they have privileged the same subject area, namely the activity sector.

The Regional Observatory on Occupations (ORM), phase 1: corporatism in the Provence-Alpes-Côte d'Azur (PACA) region (1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996) In 1986 the ORM recruited its first senior researcher, with funding from the state, and took its place within the Regional Council. The latter favoured collaborations with the Regional Employers' Union (UPR) in order to gain better knowledge of employers' hiring decisions. The observatory's first activities ('workshops') thus aimed at determining the workforce training 'needs' of such and such a sector on the basis of demands coming from the legitimate representatives of the occupational branch(es), namely the company heads. The term used, 'occupations' (métiers), reflected a specific way of approaching the employmenttraining relationship, mainly from the standpoint of the (very) small enterprises, while the infra-regional territories were ignored. This approach was rooted in a political conception of training reduced to the acquisition of skills associated with occupations in the traditional, craft sense of the term. The Regional Council, headed by a majority composed of the classical right-wing political parties but also the far-right Front National (from 1986 to 1992), strongly promoted the development of apprenticeship leading to the traditional CAP (certificat d'aptitude professionelle, vocational aptitude certificate), notwithstanding the fact that the vocational baccalauréats had just been created. This socio-political configuration was not without impact on the kind of instruments favoured: direct surveys of (small) employers in order to obtain information about their short-and medium-term needs and adapt the training programmes, and especially apprenticeship, to them as closely as possible. That said, the members of the observatory, backed up by state structures (DRTEFP, Regional Department of Labour, Employment and Vocational Training), subsequently singled out the technical limitations of this approach and re-legitimated studies based on official statistics.

The Rhône-Alpes Regional Observatory on Employment and Training (OREFRA), phase 1: a planning-oriented approach within the context of regional neo-corporatism (1988)(1989)(1990)(1991)(1992)(1993)(1994)(1995)(1996)(1997)(1998) At the time of its creation, the OREFRA sought to assume the role of an expert institution in the 'Super-Planner' style by quickly producing broad statistical overviews of the training-employment relationship in the line of earlier studies by the Planning Commission and INSEE [START_REF] Affichard | Bilan de l'emploi par profession[END_REF]. This model was inspired by several factors: the skills and experience of the OREFRA's first director (who came from the statistics department of the Lyons education authority); the economic situation in the Rhône-Alpes region, which, since it was fairly representative of the national economy, favoured the regional adaptation of tools for 'French-style' planning of the training-employment relationship; and the availability of a 'Human Resources Databank' (BDRH) combining skills and activity sectors, which thus ensured the technical feasibility of this industry-based approach to the training-employment relationship.

This planning orientation is reflected in the OREFRA's proposal to the social actors, made at the beginning of the 1990s, for the development of a common language which would facilitate their dialogue and co-operation. After numerous exchanges with representatives of the occupational branches, this language came to be based on a classification of occupational families associating training fields and employment specialisations. Such a substantive link reinforced the OREFRA's capacity for innovation, which was legitimated in turn by the fact that the results were appropriated by the economic and social actors as well. The focus on occupational families was validated at national level by INSEE and the ANPE (National Employment Agency), as well as Céreq (Centre for Research on Education, Training and Employment) and the state-run education system. Through its database, the Observatory was quickly able to produce sector-based assessments of skills and, according to one of its members, as this activity became routine, it allowed 'the OREF to remain autonomous (with its own research programme) while meeting specific outside requests without any considerable increase in its means'. This technical capacity is significant within a regional political configuration which, in the area of vocational training, is an adaptation of traditional French-style tripartism: trade unions, employers' organisations and the state (cf. Mériaux 1999). It is all the more valid to qualify this regional version as neo-corporatist (Schmitter and Lembruch 1979) given the outstanding quality of the social dialogue in the Rhône-Alpes region, which in this particular case led to creating the OREFRA in the form of an association including the two public authorities as well as the social partners. The assessments it produced by sector and/or occupational families easily allowed it to remain in phase with the political initiatives taken by the Regional Council from 1986 on. Within the framework of the first State-Region Planning Contract, the regional executive did its best to develop so-called 'co-operative' apprenticeship with work contracts, in the vocational and technical high schools as well as the polytechnics, through the creation of 'apprentice training centres without walls' run by the occupational branches at regional level (for a critical analysis, see [START_REF] Brochier | Les observatoires régionaux de l'emploi et de la formation[END_REF]). This institutional experience, along with the pioneering work on occupational families, indicates the force of the innovative, experimental stance assumed early on by the Rhône-Alpes Regional Council [START_REF] Millon | L'imbrication des pouvoirs, limite pour la démocratie[END_REF]) and adopted under the council's impetus by many regional actors (see [START_REF] Jouve | La Région, laboratoire politique[END_REF].

SECOND PERIOD: CONVERGENCE TOWARDS A REGIONALISED NEO-CORPORATIST

REGULATION?

Since 1993, the regions' privileged instrument has been the Regional Development Plan for Youth Vocational Training (PRDFPJ), which was extended to adult training in 2002. Its elaboration, piloted by the Regional Council, was based on a particularly complex tangle of concertations and negotiations. Defining the rules of the game at regional level never depends on the wishes of the Regional Council alone but results from multiple interactions with the economic and social 'partners' (industry-wide and in the occupational branches), the other territorial authorities, state representatives and even the European level, given the funding it is likely to contribute (Verdier and Vion 2005).

Since 1987 -even before the creation of the PRDFs -it has been possible for the regions, the state and the occupational branches to sign territorial objectives contracts with the idea of making a segmented training supply more coherent. As of 1993, this sector-based approach became crucial for harmonising the different training streams through a group of occupational branch contracts within the framework of the regional development plan. This new institutional context enhanced the status of the OREF's missions in two respects. First, given the social partners' relative weakness at regional level [START_REF] Jobert | Les espaces de la négociation collective, branches et territoires[END_REF], making shared knowledge available, in the form of sector-based diagnostics of the trainingemployment relationship, emerged as an indispensable resource for a developing social dialogue. In addition, the basic rules of these observatories, in the Rhône-Alpes case at least, reflected or anticipated the spirit of the joint regulation then in question. For the PRDFs advocating the shift from a supply-driven training logic towards the primacy of demand, however, the sector-based framework could not suffice: the heterogeneousness of the regional spaces themselves and the assertion of territorial identities around development plans, notably with the emergence of new actors such as the 'localities' (pays) and communities of municipalities (communautés de communes), called for increasing expertise on the 'territories of training and employment'. In addition, the PRDFs' call for the collective regulation of training measures which had until then been strictly compartmentalised, such as school-based initial vocational training and apprenticeship, was gradually defining issues in terms of individual training pathways, labour-market entry and occupational mobility. Briefly stated, every PRDF was positioned in relation to three possible themes: occupational branches, territories and individuals, each of which amounted to the expression of a kind of demand with regard to training supplies. In practice, a regional standard has always expressed a subtle combination of these three approaches.

ORM, phase 2: supporting sector-based and territorial regulations and asserting its autonomy (1996)(1997)(1998)(1999)(2000)(2001)(2002)(2003)(2004) As of 1997, the ORM received a new institutional structure in the form of an association whose board of directors was composed of representatives of the state, the region and the social partners, all of whom were also involved in the elaboration and implementation of the PRDF. From that time on, the ORM did its best to become a recognised participant in regional expertise on employment and training. For its new director, this search for legitimacy constituted the best possible protection against the inevitable risks of political changeovers and the regular reappraisal of contracts between the region and the state. While the employers' organisations had been dominent until then, the arrival of the trade-union representative at the head of the board of directors shifted the balance. In such a context, the technical approach to the training-employment relationship could only make sense if knowledge production fed the dynamics of concertation.

Notwithstanding pious declarations about the virtues of co-operation, the ORM remained confronted by institutional uncertainties arising from various circumstances:

-The state's commitments were subject to instability because of new transfers of authority to the region, as wells as the double representation of the central government (Ministries of Labour and Education, with the latter further divided into two local education authorities);

-The 'social overhaul' project promoted by the French employers' confederation (MEDEF) at the end of the 1990s strained relations between employers and some trade unions;

-Because of the considerable weakness of its capacities for internal expertise, the Regional Council was tempted to make the ORM its own instrument.

In such a context, the regional observatory reinforced its institutional legitimacy through three main strategies: developing its capacities to analyse the training-employment relationship in the PACA region; systematically undertaking partnerships; and relying on locally available scientific expertise, all of which served to elaborate policy guidelines common to the different actors. The stakes were considerable, moreover, because at the end of the 1990s, as a member of the ORM has indicated, 'unlike certain OREFs of the same generation, this one did not equip itself with a major "statistical database" system' (Vial 2004).

Relying on national and academic expertise

Based in Marseilles since autumn 1992, the Centre d'études et de recherché sur les qualifications (Céreq), a national public institution responsible for the analysis of the training-employment relationship, has increasingly played the role of 'mentor' to the ORM. This situation is connected to the involvement of Céreq's administration in the definition of the PACA's first PRDF in the mid 1990s, at a time when the expertise capacities of the OREF in its first phase proved insufficient relative to the technical demands created by the region's new responsibilities. This episode considerably reinforced the observatory, in both institutional and technical terms. The new line was symbolised by the appointment of a highly recognised Céreq researcher as the ORM's director. The ties maintained with his 'parent institution' favoured periodic transfers of experience and technical support. This was particularly crucial in a phase where the observatory was seeking to significantly expand its scope.

An advisory board was also set up; composed of specialists in the trainingemployment relationship, notably academics and researchers from the Aix-Marseilles education and research cluster. The board was intended to mediate between requests formulated by political and social actors and the canons of sociological and economics research. Its president, the former director of the research laboratory hosting Céreq's associated centre for the PACA region, is quite clear about the aim of this mediation: 'Contrary to appearances and any temptation to set one's mind at ease, the figures do not speak for themselves. Their value is established by the questions raised and the hypotheses advanced as a result. It is this work alone -the so-called 'problematising'which lets us make the figures 'speak', intelligently and usefully'. 4 Created in 1997, this board has played a key role in the definition and legitimisation of the ORM's activities; it provides the observatory's administration with an essential resource for dealing with institutional backers, namely legitimate knowledge.

Technical partnerships as a working rule

Its ambition to cover the major part of the regional space has encouraged the ORM to develop co-operative ventures. The best way of eliminating hesitations about the observatory's application of its technical capacities to additional research fields has precisely been to associate institutions and experts already interested in the study to be carried out. Covering a broad field within a limited time period, moreover, has required other collaborations, in the form of co-contracting, subcontracting or delegation. The recourse to partnerships thus became a necessity at the different stages of the ORM's activities:

-Constituting the database called for continuous concertation with the main producers of statistical sources such as INSEE, the local education authorities, the different units of the regional public employment office and others.

-In the production of studies and reports: the ORM's partners were associated upstream in the choice of topics to be treated and the use of the sources; technical montages associated other public contributors, such as Céreq's associated regional centre, or private ones, such as consulting firms.

-At the publication stage: joint writing and publishing of the findings were frequent in the different communications media.

Legitimisation through the 'industrialisation' of diagnostic capacities

The ORM set up a system -intended to be exhaustive -for covering four main aspects of the training-employment relationship: economic activity sectors, qualifications, territories and training-supply mechanisms. The commitment to exhaustiveness stemmed from the desire to anticipate actors' demands for information and even more, to help in constructing it.

The idea was thus to make its technical pre-eminence into a kind of institutional visibility capable of increasing its autonomy for defining its work programme and thus allowing it devote time to innovative activities intended to reinforce its legitimacy.

With the advisory board's ongoing assistance, this recognition was acquired through a subtle process combining constant prudence -making no pretence of monopoly -with the clarity of a dual role as an efficient provider on the statistical diagnostic 'market' and a forum for debate about good practices in the study of the training-employment relationship. Two areas of research are emblematic of this institutional trajectory; one has been strategic from the outset -the activity sectors -while the other was emerging -the regions. A technical prerequisite for achieving this ambition was the acquisition of reliable datasets which were as comprehensive as possible at a time when other observatories were already updating their data, to 'broaden the field of observation and experiment with new methodological approaches' (Vial 2004, p. 10). Through its innovative use of management software, the ORM had caught up by 2001, and with a greatly enlarged staff -four people in 1997, nearly a dozen at the beginning of the next decade -its accomplishments managed to equal its ambitions.

The sector-based approach: a tool for negotiation

The basic tool -the ORM's sector-based model -included indicators describing the number of jobs in each activity by skills level, age, gender, education and training level, conditions of employment and their weight in the employment areas. This tool was inseparable from an explicit desire to facilitate the 'dialogue between representatives of the occupational branches, the authorised joint collection bodies (OPCAs), the joint employmenttraining commissions and public authorities' by constituting a 'standard for setting up forward-looking observatories on occupations and skills at national or regional level'.

In fact, rather than seeking a monopoly, the ORM offered several kinds of help to occupational branches seeking to create regional observatories: provision of data on activity sectors, occupations and training programmes, methodological support, organisation of meetings between branches desiring to benefit from shared experiences and address industrywide questions together. This technical partnership was aimed at maintaining coherence between the different sector-based forecasts by drawing on shared methodological guidelines. Paradoxically, the increased number of branch mechanisms has promoted the ORM's role as co-ordinating body. In addition, the growing mobility of wage-earners, and in particular the instability of the youth labour force, provides a de facto incentive for a regional, cross-sector approach. 'We know, for example, that young people are disappearing into other occupational branches; we'd like to have more detailed information on where they're going and -why not? -see if we can arrive at labour transfers' (branch representative).

The territorial approach as an alternative to 'matching' Since the appointment of a director coming from Céreq, the ORM has been a hotbed of criticism addressed at the 'training-employment match' approach. Such criticism bears at once on the qualitative aspect of such a logic, aimed at 'matching' training and employment contents, and its quantitative aspect, which advocates strict control of the flows of those trained in function of labour demands. The development of a credible alternative proved difficult, however. As the decentralisation of training policies advanced, 'the growing social demand confronting training-employment expertise at territorial level' became a key issue (Vial 2004). In this respect, developing a 'territorial approach' was promising: it began with the identification of the 'skills-related issues within a labour-market area, an administrative département or region, or any other geographical area' (ibid.). On this basis, the break with matching involved taking into account a path dependency proper to each territory studied: the quality of the living environment (which thus gives rise to positive migratory flows) and the proportion of seasonal jobs (the quality of which partly determines that of the tourism services) but also the 'attachment to the territory', which exerts a sharp influence on individual mobility zones. The production of territorial diagnostics (for each of the 22 employment areas) was aimed at meeting this demand for analysis.

The creation of such 'information coverage' was not free of tensions, notably with actors possessing recognised expertise capacities. Thus, in a sector as important for this region as construction and public works, most of the preliminary expertise for the 2004 tripartite branch agreement was ultimately carried out, under the aegis of the employers' associations, by a consortium of public and private actors, although the ORM had proposed its candidacy with the backing of the Regional Council (Mériaux and Verdier 2006). Going beyond the sole activity of observation or the questionable recording of the companies' skills 'needs' allowed the ORM to improve its relations with INSEE's regional department: after a long period of cultural and technical distance, the two structures have come to be governed by the complementarity of their positions. This has been possible because of the technical quality of the partnerships, especially in the area of the analysis of occupational mobility, and in the resulting success of emblematic operations. The ORM's gradual winning of institutional legitimacy was thus fed by the constant expansion of its capacities for intervention, in both quantitative and qualitative terms, combining highly detailed territorial investigation of local specificities with the use of employment and training zoning coming from national statisticsor in other words, a compromise (albeit an unstable one) between the industrialisation of its activity and networking (see Desrosières 1997).

OREFRA, phase 2: disillusionment with the regulation of interest groups through 'ideas' (1996-2000)

The OREFRA gradually came to be organised in a network structure:

in the course of the methodological innovations it promoted, the OREFRA made the rigorous choice of setting up an 'epistemological community' (along with other OREFs and the statistics departments of the different ministries involved with the employment-training relationship), which is to say, a community developing a pragmatic approach to the training-employment relationship outside of matching;

in phase with a specific configuration of political and social actors involved in a neocorporatist type of regulation, it promoted the creation of a community of practices (diagnostics and forecasts).

Reinforcing its autonomy through innovations in methodology

At the instigation of its director, the OREFRA, in co-operation with Céreq's associated regional centre, processed an extension of Céreq's 'Génération '98' survey representing the school-to-work transition in the Rhône-Alpes region. Counter to the advice of the occupational branches, moreover, the observatory also undertook the development of a forecasting tool focused on the impact of demographic changes between 2000 and 2020. This extremely macro-economic study gained legitimacy through the support of the DRTEFP's 'Studies-Forecasting-Assessment-Statistics' Unit (SEPES), INSEE and the Ministry of Education's Forecasting Department (DEP). Nonetheless, the observatory's success in the technical domain, which was also closely associated with the director himself, had the disadvantage of giving the social actors the impression that the regional observatory was above all a research body, removed from their 'commonplace' preoccupations of the moment.

Ideas too disconnected from the regulation of interest groups?

Beginning in the mid 1990s, however, the OREFRA also became involved in the introduction of the objectives contracts between state, region and occupational branches which were focused on training provision. In Rhône-Alpes, this procedure was based on the prior completion of branch-level Forecasting Studies Contracts (CEP). Through the efforts of the OREFRA, responsible for co-ordinating and running these forecasting activities, the Rhône-Alpes region funded forecasting diagnostics, as attested by the many sector-based CEPs (14 over the period of the 2 planning contracts; cf. the assessment study by the Geste and Amnyos consulting firms [2004]). This forecasting approach undeniably helped to mobilise the social partners and public authorities around a broader vision of the employmenttraining issues. Developing shared guidelines could not replace action, however, and the forecasting exercise proved unable to generate an operational vision through the Objectives Contracts. Before 2000, when the procedures were reevaluated, only one objectives contract had been signed, and in addition, it did not lead to any action plan. There are several interrelated reasons for these failed expectations:

-From an analytical standpoint, in most of the CEPs (with the exception of metallurgy, textiles and agriculture), the economic diagnostic was limited to an analysis of the productive fabric (number of companies, size, location) and salaried employees, while the approach to the markets, which is crucial for employment and skills forecasts, remained rather sketchy.

-Many branches were still badly structured and equipped; as a result, the state and the region lacked negotiating partners who were independent of the national representatives.

-The way the region was organised did not permit the reconciliation of the economic logic of assistance to companies on the one hand and the employment-training logic of the CEPs and objectives contracts on the other.

Nonetheless, the assessment of these contract-based approaches brought out two more positive elements which were to have an impact on the OREFRA's subsequent trajectory:

-The virtue of the territory: the most convincing CEPs were the most territorial, such as that of Courchevel, which suggested that the local level facilitated a global appreciation of both economic and employment-training approaches. This conclusion echoed the region's decision to set up Territorial Employment-Training Committees (CTEF).

-The quality of the social dialogue: for many CEP stakeholders, contractualisation allowed them to 'get beyond concertation as a pretext'. The collective learning process laid the foundations for the creation of a public interest group (GIP) intended to federate all the guidance networks, including the observatory.

This tension offers a good illustration of the distance between the sector-based logic of the Keynesian welfare state and the network architecture of the polycentric 'neoliberal' state already signalled by Desrosières (2003).

THIRD PERIOD: A SHARED OUTLOOK WITH RADICALLY DIFFERENT ORGANISATIONAL CHOICES (2003 -)

In terms of their action programmes for 2008 and 2009, the two OREFs seem to have fairly similar briefs. But since 2003-2004, these observatories have undergone significant transformations, owing to sharp path dependency relative to their previous trajectories. It is nonetheless possible to identify some common features which reflect economic and social changes extending far beyond the borders of the two regions concerned. These have tended to reconfigure expertise mechanisms around (1) questions focused on education, training and employment pathways and ( 2) practices for assisting actors in the training-employment relationship to define their projects so as to make the expertise activity more effective.

Box 2 The missions of the two observatories (as of 2008)

The ORM's responsibility for research and decision support is divided into different briefs:

Data collection: organisation of a regional employment-training database on the basis of co-operation agreements with the departments and bodies producing the information;

Studies: carrying out studies, commissioning studies from outside providers, assisting administrations and partners in the elaboration of terms and conditions;

Diagnostic and assessment: preparation and provision of diagnostic reports and assessment tools;

Organisation: participation in exchanges between administrations and concertations with social partners, technical organisation of partnerships, presentation of findings to decision-makers; Publication: dissemination of regional studies in the 'employment-training' and 'equal opportunity' fields.

The OREFRA's mission involves 'anticipating the consequences of economic transformations and changes in jobs and skills in the activity sectors; continuing to structure the employment and training information systems in view of the regional supervision of the training supply in accordance with the PRDF; providing the territories with tools and methods for analysing the training-employment relationship. Contributing to shared knowledge about training/job entry/occupational mobility trajectories. . . . The implementation of this mission takes place along the following lines: assuming technical leadership . . . Playing a role of assembler. . . . Providing technical support. . . Ensuring the dissemination of the research. . . .'

OREFRA, phase 3: the 'invisible' co-ordinator of public-policy networks

At first glance, the changes have been radical: 'The OREFRA has disappeared, so to speak. It doesn't even exist any more! The PRDF experts are the social partners or those who are active in the field. The OREFRA people are go-betweens and organisers' (PDRF official). In 2004, the OREFRA became a technical component within a new structure, the Rhône-Alpes Guidance Centre (PRAO), a public-interest group (GIP) jointly set up by the actors of the regional tripartite system, the region -the prime mover in this case -the state and the social partners (who obtained the status of founding stakeholders on the same footing as the public authorities). This agreement attests to a shared determination to federate the numerous public or joint structures which contribute to educational and vocational guidance. The idea was to counter a strong trend towards a logic of 'organised anarchy' (Cohen, March and Olsen, 1972) rendering public policy unintelligible; the region thus made the new structure an instrument for legitimating its own activity. This network, which in turn federates twenty-one 'guidance networks and units', reflects a major line of regional policy, namely support for the construction of individual career paths through 'lifelong guidance' [START_REF] Cesr Rhône | L'espace régional comme espace de dialogue et de négociation sociale[END_REF]) so as to make the itineraries more stable in the long run. This reorganisation was aimed at providing operational services to the actors of the training-employment relationship: 'relevant, readable information' for guidance professionals and 'support for decision-makers', notably within the context of the implementation of the new PRDF -the reason behind the OREFRA's participation. In addition, it was intended to broaden access to the accreditation of prior and experiential learning (validation des acquis de l'expérience, VAE, in French) and ultimately, to reach the general public. In fact, the institutional dismantling of the OREFRA has entailed neither the disappearance of this activity cluster nor a reduction of its capacities for action. The OREFRA, which provides assistance in the use of the statistical files, now develops its studies with the idea of improving the stakeholders' know-how. The presentation of the databases, whether they are territorial, sector-based or focused on labour-market entry, always highlight the meaningful use which guidance professionals can make of them. The question, however, is whether this overlapping between the information functions of those involved in labourmarket entry and an expertise mission prior to public decision-making actually produces a better linkage between knowledge and action.

Territorial instrumentation for clarifying individual and collective choices

The creation of the PRAO reflects a shift in regional policy on employment and training. Without overlooking the occupational branches, the regional public policy guideline places more emphasis on the building of individual career paths. Among the three key lines, the 'overhauling of the Rhône-Alpes PRDF' emphasises 'territorialisation for greater efficiency and coherence of regional action' and stresses that 'the relevance of the interventions depends on the quality of the analysis of the issues to be addressed' and not only the classic 'mobilisation of the actors'. In this context, the PRAO-OREFRA has developed a highly detailed, functional approach to the territories: at the level of the twenty-seven areas within the region (as well as each of the administrative départements and the region itself), the database is structured around concrete questions aimed at allowing users to develop their own diagnostics. 5 This combining of sectors, territories and occupations serves to bring out prospects for individuals. Addressed above all to local groups of actors, this setup formulates the results for a given territory in terms such as these: 'The training potential is inferior to employment needs because [of] recruitment difficulties and high opportunity indicator / The training potential seems balanced relative to employment (analysis to be further refined by training programme)'. But insofar as appropriate information sources do not exist at regional level, the regional guideline's increasing focus on individual support during labour-market entry calls for new methodological and statistical innovations in the short and medium term.

Increasing autonomy for the research function

The OREF mission within the PRAO has been extending its earlier studies in order to test an alternative to the job-matching approach. Without rejecting the idea of matching from the outset, the OREF put it to the test with a sophisticated statistical setup based on INSEE's Employment survey. A first study, published in 2005, analysed the connections between the young people's diplomas and their occupation five years later. Briefly stated, it showed that one-third of the young people worked in the occupational field 'targeted' by their training field, one-third in a related activity and one-third in an entirely different occupational field. 6At the end of 2007, a new study measured the degree of occupational mobility (each year, 13 % of the labour force, at national level and in the Rhône-Alpes region alike, change 'occupations', with considerable variations by age, diploma and gender). It also proposed a typology of occupation changes for eighty-four occupational families; this was based on three main categories of variables: mobility rates, career paths and the weight of promotions in occupational mobility [START_REF] Longin | La mobilité professionnelle des adultes : les changements de métier[END_REF]. For the authors, these findings confirm the conclusion already advanced in 2005: 'The training-employment relationship has undergone profound changes over the past twenty years for both economic and societal reasons. The classic concept of "matching" training and employment is no longer relevant, apart from professions where entry is controlled (e.g., doctors) or subject to a competitive entrance examination (e.g. teachers). The training-employment relationship seems to be taking a new form: the "transferability of competences"'. 7 These findings are rooted in the OREFRA's cognitive evolution, as personified by the founding director, who held the post from 1991 to 2007: on the one hand, these are national studies which are thus aimed at general validity; on the other, they have been carried out within an expertise network associating national and regional actors. The drawback of this national recognition of the quality of the studies, however, is an underinvestment in the tools which come closest to the analyses of the training-employment relationship carried out by the Rhône-Alpes actors. In the words of one PRAO staff member, 'The OREFRA is less of a trail-blazer now because it consistently reproduces the same data (from information provided by the Assedics [organisations in charge of unemployment payments] and so on', with the result that its involvement in the preparation of preliminary diagnostics for regional policy negotiations has declined.

The weakening of a historic asset: expertise in the service of regulating contract-based public policy

Since it has become an expertise structure within a GIP, the observatory's main role has been that of facilitating regional public action (see Salais 1998): it helps to organise meetings of the PRDF's policymaking and technical structures (Steering committee, working group on Publics and Training, working group on Pathways, working group on Economic sectors, working group on Territorial logics). 8 Similarly, while continuing to oversee the preparation of forecasting studies contracts (CEP) -notably for the occupational branches -it also draws up objectives contracts, with the aim of improving the link between knowledge and action, as recommended in the evaluation of these procedures carried out in 2005 (Amnyos Geste). The discussion process is as important as the subjects of the regulation process itself: 'What's involved is setting the pace, stimulating a negotiating dynamics by creating the conditions for regular, productive meetings between the partners' (member of the PRAO's board of directors representing the state).

The different interest groups are thus explicitly brought in line on the basis of regulation through expertise, which sets out the appropriate framework for a step-by-step approach to the medium-term problems revealed by the experts' diagnostics. This process explains the OREFRA's active, ongoing 'mission', from the diagnostic to the assessment of public policy contracts in the area of employment and training. The challenge is considerable, given that only seven objectives contracts have been signed in the occupational branches, compared to sixteen forecasting studies contracts. There is still a certain gap between the undeniable ability to generate debate and the difficulties of bringing the contractualisation process to completion, namely the determination of an effective plan of action. An approach which aims to link training, employment and economic development clearly comes up against serious institutional obstacles: within the Regional Council alone, such a project requires coordination between five departments, and thus five directors.

Such difficulties are perhaps one of the causes of the partial failure of the objectives contracts reform undertaken at the beginning of this decade. For the time being, the region's desire to introduce a single contract signed by all the actors -economic development, employment and training -has met with the refusal of the employers' organisations to sign joint agreements in the economic domain with the trade unions. That being the case, the OREF has left the field open for other institutional initiatives, such as the Observatory on Economic Changes, set up in November 2004 by the regional prefect, the president of the 7 Les liens entre diplômes et métiers. Une nouvelle lecture de la relation formation-emploi. Ministry of Education, Rhône-Alpes prefecture, Rhône-Alpes Regional Council and social partners, September 2004, p. 1. 8 Cf. www.prao.org.

Regional Council and the interministerial representative for economic transformations (MIME). Even if this partnership is ultimately not very efficient, it suggests that the OREFRA-PRAO approaches are not necessarily the most suitable for analysing the substantive issues of the crisis. More than ever before, it is necessary to adapt information sources and diagnostics to the increasingly fluid perimeters of economic problems and initiatives, such as the competitiveness clusters, but these all correspond less and less to the approach through occupational branches which accounts for a considerable share of the OREFRA's expertise and legitimacy.

ORM, phase 3: technical legitimacy and support for actors

The ORM has focused on the transformations of the training-employment-work relationship in terms of four processes: access to skills, job entry, changes in occupations and activity sectors, local development. On that basis, it has identified key issues for the regional employment and training actors to analyse. In 2008, these included precariousness, intermediate skills and occupational mobilities. In 2009, the observatory recommended labour-market pathways and transitions, as well as a procedural adaptation -in response to the crisis -aimed at reinforcing a twofold capacity for anticipating social transformations at regional level and reacting to the most acute social problems. In these different subject areas, moreover, the ORM now presents itself as the guardian of good procedures intended to define relevant questions for regional public policy: it is thus becoming the legitimate arena for discussion of all studies and surveys envisioned in the area of the training-employment relationship. It is also confirming a 'strategic turning point' which had gradually been getting underway in previous years. This involves the definition of protocols for providing actors with support in their different areas of intervention: territorial, sectoral or proper to one or several occupational groups. In sum, the ORM is constructing its present and future position as an 'expert services platform', with the participation and, if possible, the involvement of the institutional actors.

The emergence of pathways as the thematic priority

Apart from studies on the youth transition, the ORM has published little research dealing with occupational mobility. The most significant dates from November 2007, moreover, and appeared in the monthly newsletter of INSEE's Regional Department, Sud INSEE l'essentiel, under the title 'Occupational mobility: frequent but not always profitable'. The circumstances of this publication reflect the ORM's institutional position: in keeping with its role as 'assembler' and driving force, it legitimates itself through technical partnerships and above all, does not assume the role of advocate. In terms of content, while addressing the question of mobilities, this study refines one of the ORM's classic subject entries, that of business practices, combined with socioprofessional groups. The analysis of individual transition pathways functions as a pertinent indicator of the characteristic sectoral and occupational dynamics, combined with age and gender.

In future, the pathways themselves will occupy a growing place in the ORM's activity, beginning in 2009 with the processing of a regional extension of Céreq's Generation 2004 survey. Going further in this direction will probably require critical reflection on the sources of regional statistics: who is to provide them and with what legitimacy? The question is open.

Defining regional policy issues on the basis of 'good studies'

The two cases which follow are emblematic of the ORM's position. One concerns a labour-force category marked by job precariousness, the other, a sector marked by the issue of intermediate skills. The former, a study on seasonal employees in the tourism sector, was commissioned by the Regional Department of Labour, Employment and Vocational Training (DRTEFP), two of its counterparts at département level (DDTEFP) and the ORM. Carried out by a consulting firm, it was published in the form of a summary written by a researcher at the observatory [START_REF] Boyer | Les saisonniers du tourisme : quel devenir ?[END_REF]. With a view to linking research and public policy, the conclusions of the report take the form of recommendations (to cite only one example: 'The public authorities, with the assistance of the employers' representatives, could encourage the pooling of certain actions, notably for small enterprises, in order to improve the structuring of career pathways').

The second study, on the metalworking industry, was similarly aimed at connecting analysis and the elaboration of action plans. Subcontracted to the sector itself and a consulting firm, it was closely supervised by a technical committee -led by the ORM -which defined the objectives and the survey approach, insofar as its members drew up the 'interview guidelines [which] established the main lines of the questions to be posed'. This qualitative approach used data from three regional sources. 9 The observations bring out a sharp disparity between, on the one hand, 'the ideal profile of the person who would be recruited immediately by the metalworking companies . . . someone who is motivated, competent in the field of mechanical production. . . ' and on the other, the fact that 'the experienced persons competent in mechanical production are rare because they are sought by everyone; there are no longer enough graduates to meet the needs; . . . there seems to be a lack of motivation in a sector which doesn't really attract young people' (p. 73). The recommendations as a whole were intended to assist in the creation of a guideline for collective action aimed at anticipating the risk of a shortage of the human resources necessary for the companies' development. Among others, we may cite, 'Carrying out skills diagnostics for each company' (ibid. p. 76) in order to involve the latter in a training effort ultimately intended to 'Create a specific metalworking pool managed by the companies' (p.

Obtaining 'missions' in order to consolidate a reputation

Since the beginning of the decade, the ORM has established itself as an expert in the observation of categories targeted by public policy: the disabled (with the Fund for the Labour-Market Entry of Disabled Persons, AGEFIPH), young people (with the Regional Department for Youth and Sports, DRJS) and so on. It should be noted that these new activities most often take place within institutional partnerships which are prominently indicated in all the participants' publications and public-elations materials: working with others and for others is a kind of implicit doctrine which motivates the observatory's studies in a field that has become a priority in its own right and one that has in recent years, moreover, accounted for a rapid increase in staff size (16 persons at present).

Support services for anticipating and transmitting

In the context of an analysis of the territorial governance of employment and training, the ORM is making every effort to develop qualitative approaches for services intended to help public and private actors to define and implement their interventions. In the area of occupational skills, this constitutes a significant change for its researchers, who made little use of qualitative approaches in the past. Such an orientation calls for considerable development of ties with other research activities, well beyond the inclusion of professors and researchers on its advisory board as has been the case for the past eleven years.

The preparatory study for the first regional plan for health and social services training programmes (which came under the responsibility of the regions in 2004) tests an approachrather than a method -which would clearly define the employment-training relationship independently of any idea of matching. The preliminary diagnostic, conceived as a cross between a 'statistical inventory and exchanges between partners in order to arrive at a shared understanding of the phenomena involved', gave rise to the development of a 'collective work tool'. The underlying aim is to get to actors to take into account the elements influencing the definition of the work activity, such as the nature of the demand for healthcare or social services, especially in view of changes in family lifestyles. A much more general conclusion deals with 'observation skill': 'Observation skill has to be enriched with that of mediating between the experts who analyse training programmes, whatever these are, and the final decision-makers, in order to increase the pooling of training and employment networks on the territory' (Vial 2007, p. 4). The knowledge thus produced is no longer a simple addendum to regulation but rather, its mainstay.

Conclusion

Within the context of a considerably expanded decentralisation of training in the course of their two decades of activity, the two OREFs have undergone profound changes. They have evolved from the model of the descriptive statistical report bringing together information on a single theme (i.e., an occupational branch or group, a territory) drawn from varied sources with little coordination, to that of the diagnostic bringing out strategic issues and leading to public-policy recommendations. These practices essentially draw on standardised statistical sources provided by INSEE and the ministerial statistics departments in the regions. The observatory's distinctive role is precisely to give particular meaning to the information thus placed in perspective in order to explain or make known regional and local issues. At present, a new stage seems to be getting underway. It no longer suffices to prepare reports; it is necessary to accompany them with services permitting users to make use of these statistical 'products' in such a way that they give meaning to the local actors' policies. The development of this link between the specific features of the project areas on the one hand and the general values conveyed by standardised statistics on the other entails a compromise between a dialogue based on proximity and possibilities for more far-ranging comparison. In other words, the ability to combine the use of official statistics and specific advice. The efficiency of this multidimensional service is determinant for establishing the observatories' lasting institutional legitimacy. Such an evolution calls for several initiatives:

-The first is paradigmatic: it consists of escaping (by means other than simple denunciation) the hold of the planning model based on matching [START_REF] Affichard | Nomenclatures de formation et pratiques de classement[END_REF], which tends to be perpetuated by the observatories' classic base, namely the industrial sectors (how to meet the needs of the companies concerned?). Two subject fields are drawn upon: territories and individual pathways. To a greater or lesser degree, both are aimed at developing an approach based on the prevention of employment risks, tied to economic changes in one case and to interruptions in individual pathways in the other;

-The second is technological: it entails the users' involvement in the functioning of the database so that they construct a diagnostic based in part on their own observations from experience;

-The third is procedural: legitimate directions are determined not by prior instruction or acceptance of outside knowledge but by recourse to collective debate on both the validity of the projected studies or surveys and their conclusions. 10

The ultimate impact of these approaches remains quite uncertain: Are the forums sufficiently open to the diversity of the actors? Isn't the pluralism largely confined, on the one hand, to the branch-level social partners and, on the other, to ,public actors who are often edgy about their prerogatives, for lack of sufficient confidence about their respective spheres of authority? The weight of neo-corporatism remains great, given its foothold in the joint approaches associated with the occupational branches. In addition, combining the issues proper to the training-employment relationship with preoccupations stemming from economic development will call for confronting major technical problems, in other words, the reconciling of standard statistics and the other, ad-hoc statistics required by bodies with specific parameters, such as those of a competitiveness cluster or a development project initiated by a community of municipalities (see Desrosières 2008c). Is there any solution other than the creation of a supply of statistical services sufficiently flexible to correspond to the time frames of the territorial or local projects? How might these providers and the official statisticians be connected? And last of all, can a single body respond to these different questions over time?

In spite of their common features, the paths taken by the two observatories are considerably different. In the case of the ORM, the original issue was getting away from the corporatist model, which was tied to a particular political situation. The second stage permitted the development of an ability to provide standardised information about the employment-training relationship and thus gain at least partial freedom from the ascendancy of the demand, through the development of a diagnostic capacity by territories, occupational branches and socioprofessional groups. For the time being, however, this observatory has little involvement in the regulation of regional policy, although it does exert some influence. The exteriority of its expertise provision places it in a legitimate position to organise discussion forums around all the projected regional studies and surveys on employment and training. This ability to provide methodological support for the actors in the analyses preceding decisions is a major resource which, should its success be confirmed, would give it the status of an expertise institution of indisputable legitimacy. From this standpoint, the OREFRA's longstanding involvement in the regulation of regional public policy would seem to make it an essential technical actor in every partnership. Today it seems weakened by a growing distance between a simple information function as a department of the regional guidance centre and the innovative studies which have more impact at national level than regionally. Will this institutionalisation of the observatory be reinforced now that the PRAO is supposed to address itself to a 'general public' composed of private individuals and employers?

5' 1 .

 1 What is the present spectrum of jobs in your area, by activity sector and occupational field ? 2. What are the principal activities ? 3. How are jobs evolving ? 5. What are the occupational fields where recruitment is difficult ? 6. What are the exit flows from training : school based, apprenticeships, continuing training for young people or adults ? 7. Are training flows adapted to the needs of the job area? 8. What are the possible job opportunities for the individual's training plan ?' (see the PRAO site at www.prao.org).

  77), notably by setting up what are known as Employers' Groups for Job Entry and Skilling (GEIQ) or Local Hiring-Training Units (CLEF).

Michel Arliaud, speech at the ORM General Assembly of 14 March 2003, p. 1.

See 'Liens formations-métiers, regards croisés' (Perspectives on training-occupation connections). Les Dossiers de la Direction de l'évaluation et de la prospective no. 158, Ministry ofEducation, Paris, 2005.