Jarmo Hietarinta
email: jarmo.hietarinta@utu.fi

Claude Viallet
email: claude.viallet@upmc.fr

Weak Lax pairs for lattice equations

We consider various 2D lattice equations and their integrability, from the point of view of 3D consistency, Lax pairs and Bäcklund transformations. We show that these concepts, which are associated with integrability, are not strictly equivalent. In the course of our analysis, we introduce a number of black and white lattice models, as well as variants of the functional Yang-Baxter equation.

Introduction

Recent progress in the description of integrable partial difference equations is to a great part due to the consistency approach [START_REF] Fw Nijhoff | On Discrete Painlevé Equations Associated with the Lattice KdV Systems and the Painlevé VI Equation[END_REF][START_REF] Nijhoff | The discrete and continuous Painlevé VI hierarchy and the Garnier systems[END_REF][START_REF] Bobenko | Integrable systems on quad-graphs[END_REF][START_REF] Adler | Classification of Integrable Equations on Quad-Graphs. The Consistency Approach[END_REF], in particular in the form of 3 dimensional Consistency-Around-a-Cube (CAC). One of the highlights of this approach is the immediate existence of a Lax pair and Bäcklund transforms (BT), which can be directly constructed from the "side-equations" of the cube [START_REF] Nijhoff | The discrete and continuous Painlevé VI hierarchy and the Garnier systems[END_REF][START_REF] Fw | Lax pair for the Adler (lattice Krichever-Novikov) system[END_REF]. One can say, in effect, that the set of side equations yields the BT and the Lax pair. One situation where side equations have been used effectively is in constructing soliton solutions to the lattice equations [START_REF] Atkinson | Seed and soliton solutions of Adler's lattice equation[END_REF][START_REF] Atkinson | Soliton solutions for Q3[END_REF][START_REF] Hietarinta | Soliton solutions for ABS lattice equations: II Casoratians and bilinearization[END_REF].

Originally it was assumed that on all faces of the cube the equations were the same in form, depending on the relevant corner variables (one component at each corner) and spectral parameters. Recently, 3D consistent sets have appeared, with different equations on the faces [START_REF] Adler | Discrete Nonlinear Hyperbolic Equations. Classification of Integrable Cases[END_REF][START_REF] Atkinson | Bäcklund transformations for integrable lattice equations[END_REF][START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF][START_REF] Levi | On a nonlinear integrable difference equation on the square[END_REF][START_REF] Boll | Classification of 3D consistent quad-equations[END_REF]. In this more general context it is of interest to take a closer look at the Lax pairs, Bäcklund transforms and consistency, and investigate what they are good for. It should be noted that in the context of partial differential equations the existence of trivial Lax pairs is well known [START_REF] Calogero | Lax pairs galore[END_REF] and similar examples have also been noted for some discrete equations (see [START_REF] Hay | Discrete Lax Pairs, Reductions and Hierarchies[END_REF], Chapt. 6).

We will first recall how consistency around the cube, existence of Lax pairs and Bäcklund transformations are intimately related for lattice maps on the square lattice given by multiaffine relations (sections 2 and 3). These considerations apply to the elementary cells, and are local. In section 4, we describe specific examples having the CAC property. We detail in particular the already known explicit forms of the equations and Lax pairs which we use in the rest of this paper. In particular, we find that in some cases the zero curvature condition (ZCC) yields two different equations that can be used to define rational evolution in the lattice. We then address the global problem of defining equations over the whole lattice, with the guideline given by the 3 dimensional structure coming from the CAC construction (section 5), and check integrability with the calculation of algebraic entropy. In section 6, we push the use of 2 × 2-matrix Lax pairs to its limits, by constructing discrete systems over a larger sub-lattice of the original lattice. This brings to the light interesting (integrable) structures related to a generalized form of the functional Yang-Baxter equations [START_REF] Hietarinta | Integrable lattices with vertex and bond variables[END_REF].

3D consistency, a reminder

The starting point is a regular 2D square lattice, with vertices labeled by integers n, m. Functions x n,m are associated to the vertices, and they are subject to a constraint at all elementary cells. This constraint is expressed by an equation Q(x n,m , x n+1,m , x n,m+1 , x n+1,m+1 ) = 0, assumed to be multi-affine in the four vertex variables. It should depend on all 4 vertex variables, and it should not factorize. It may also depend on some parameters. Sometimes the parameters can be associated to specific directions of the lattice, in which case they appear as "spectral parameters". To ease the notation, one usually denotes the running value x n,m by x n,m = x, and for neighboring values one only indicates the shifts: x n,m+1 = x 2 , or in 3D setting, x 1 = x n+1,m,k , x 113 = x n+2,m,k+1 etc.

For multidimensional consistency one needs to build a cube on top of a square and give equations on all six faces of the cube, see Figure 1, the bottom equation being the original one. using the left side equation, and x 23 using the back side equation. We may then calculate the final value x 123 in three different ways, using the front-, right-and top-equations, respectively. The equations are said to be Consistent-Around-a-Cube (CAC) if the three ways yield the same value for x 123 .

Note that it is also possible to check CAC with other initial values that allow full evolution, for example, x 3 , x, x 1 , x 12 .

Lax ≃ Bäcklund

The Lax/BT approaches differ from CAC in that only the side equations are used as input, while the top and bottom equations are supposed to be derived from them.

Construction of the Lax pair

The Lax pair for the bottom equation is constructed from the side equations by isolating the variables x 3 , x 13 , x 23 , x 123 , and writing the equations as: left:

x 13 x 3 c 1 (x 1 , x) + x 13 c 2 (x 1 , x) + x 3 c 3 (x 1 , x) + c 4 (x 1 , x) = 0, (1a) right x 123 x 23 c1 (x 12 , x 2 ) + x 123 c2 (x 12 , x 2 ) + x 23 c3 (x 12 , x 2 ) + c4 (x 12 , x 2 ) = 0, (1b) back x 23 x 3 b 1 (x 2 , x) + x 23 b 2 (x 2 , x) + x 3 b 3 (x 2 , x) + b 4 (x 2 , x) = 0, (1c) front
x 123 x 13 b1 (x 12 , x 1 ) + x 123 b2 (x 12 , x 1 ) + x 13 b3 (x 12 , x 1 ) + b4 (x 12 , x 1 ) = 0, .

The coefficient functions b i , bi , c i , ci will be affine linear in their arguments.

We now introduce the homogeneous coordinates f, g for x 3 and its shifts by

x 3 = f /g, x 23 = f 2 /g 2 , x 13 = f 1 /g 1 , x 123 = f 12 /g 12 .
This amounts to considering x 3 as belonging to the projective space CP 1 . We denote by ψ the pair

ψ = f g
which is defined up to a global factor. Equations (1) can then be written as

ψ 1 ≃ Lψ, (ψ 2 ) 1 ≃ Lψ 2 , ψ 2 ≃ M ψ, (ψ 1 ) 2 ≃ M (ψ 1 ),
where

L(x 1 , x) ≃ -c 3 (x 1 , x) -c 4 (x 1 , x) c 1 (x 1 , x) c 2 (x 1 , x) , M (x 2 , x) ≃ -b 3 (x 2 , x) -b 4 (x 2 , x) b 1 (x 2 , x) b 2 (x 2 , x) ,
and similarly for the bar-quantities. Since we are working in CP 1 all equalities are projective equalities, and as a reminder of this we use the symbol ≃ to indicate that two matrices are equivalent if their entries are proportional, in other words, L and M belong to P Gl(2, C).

The Lax matrices provide parallel transport of ψ along the bonds of the lattice. The zero curvature condition means that the parallel transport along any closed path on the lattice is trivial. It is necessary and sufficient to ensure that taking ψ from position (0, 0) to (1, 1) via the two routes (0, 0) → (0, 1) → (1, 1) and (0, 0) → (1, 0) → (1, 1) gives the same result:

(ψ 1 ) 2 ≃ (ψ 2 ) 1 , i.e., L(x 12 , x 2 )M (x 2 , x) ≃ M (x 12 , x 1 )L(x 1 , x). (2)
This matrix relation yields three scalar equations. 1 These equations are written in terms of the variables x, x 1 , x 2 , x 12 , and in order to satisfy the ZCC we must impose a constraint on these variables. In standard cases, this constraint will just be the bottom equation. Indeed, in integrable cases the three equations in (2) have a common factor. It may also happen that the ZCC is satisfied automatically, if the side equations are simple enough, or sometimes the common factor may factorize, yielding multiple choices. We will examine specific examples of this phenomenon below.

Direct approach: Bäcklund transformation

A Bäcklund transformation (BT) is generated by a set of equations E(X, Y ) = 0 on two sets of functions X and Y , such that eliminating one set of functions say X (resp. Y ) one gets an equations E(Y ) = 0 (resp. E ′ (X) = 0) on the other set (for details, see Proposition 4.1 in [START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF].)

For a 3D consistent set of equations the side equations provide a BT between the top and bottom equations. In order to derive the bottom equation from the side equations one proceeds as follows:

1. Solve x 13 from the left equation (1a).

2. Solve x 23 from the back equation (1c).

3. Solve x 123 from the front equation (1d). 4. After this the right equation (1b) can be written as x 2 3 R 2 + x 3 R 1 + R 0 = 0, where R i are polynomials in x, x 1 , x 2 , x 12 . The greatest common divisor (GCD) of R i (or one of its factors if it factorizes) will be the bottom equation.

One can find the following explicit forms for the R i :

R 2 = det c 1 0 b3 b1 0 b 1 c3 c1 c 3 0 b4 b2 0 b 3 c4 c2 , R 0 = det c 2 0 b3 b1 0 b 2 c3 c1 c 4 0 b4 b2 0 b 4 c4 c2 (3) R 1 = det c 2 0 b3 b1 0 b 1 c3 c1 c 4 0 b4 b2 0 b 3 c4 c2 + det c 1 0 b3 b1 0 b 2 c3 c1 c 3 0 b4 b2 0 b 4 c4 c2 . ( 4
)
That the Lax and the BT approaches yield the same equations can be seen as follows: Let us denote V := M L, U := LM , then the matrix elements of V, U are related to R i as follows (here subscripts indicate the matrix element):

U 21 U 11 - V 21 V 11 ≃ R 2 V 11 U 11 , U 22 U 12 - V 22 V 12 ≃ R 0 V 12 U 12 , (5)
U 21 V 12 U 11 V 11 - U 12 V 21 U 11 V 11 + U 22 U 11 - V 22 V 11 ≃ R 1 U 11 V 11 . (6)
Thus

U ≃ V iff R i = 0.
Of course one can equally well use the side equations to solve for the variables x 1 , x 2 , x 12 from the left-, back-, and front-equations, after which the right-equation will be a polynomial in x with coefficient depending on x 3 , x 13 , x 23 , x 123 , with their GCD yielding the top equation.

Examples

Linear side equations

As a first example we consider the case where all the side equations are linear, i.e., the left side equation is:

x 13 -x 1 -x 3 + x = 0 (7)
and we have the same equation with suitable subscript changes on the other vertical sides.

One then finds that neither the Lax nor the BT approach yields anything, The conditions are satisfied without reference to the bottom equation.

What about CAC? It will involve both the bottom and the top equations, so it should give some conditions. Indeed, if one tries CAC with [START_REF] Atkinson | Soliton solutions for Q3[END_REF] and a completely general multiaffine bottom and top equations, related by a shift (but with same parameters) one finds a consistent set with the bottom equation

a(x -x 1 )(x 2 -x 12 ) + b(x -x 2 )(x 1 -x 12 ) + c(x -x 1 -x 2 + x 12 ) + d = 0. ( 8
)
This is a combination of the lattice modified KdV equation (lmKdV) (aka Q1 in the ABS list [START_REF] Adler | Classification of Integrable Equations on Quad-Graphs. The Consistency Approach[END_REF]), and the linear equation.

A similar analysis can be done starting from the linearizable side equation

x 13 x = x 1 x 3 . (9)
The Lax matrix for this system is diagonal and the ZCC is automatically satisfied. From CAC analysis we find that ( 9) is compatible with the six parameter family of homogeneous bottom/top equations of degree 2

a 1 xx 1 + a 2 xx 2 + a 3 xx 12 + a 4 x 1 x 2 + a 5 x 1 x 12 + a 6 x 2 x 12 = 0. ( 10
)
We will examine the integrability of these equations in section (5.1).

H1

The lattice potential KdV (lpKdV), which describes the permutability property of continuous KdV, is a paradigm of integrable lattice equations (aka H1 in the ABS list [START_REF] Adler | Classification of Integrable Equations on Quad-Graphs. The Consistency Approach[END_REF]). For this system everything works well. [We will return to this model in a new context in section 6.2.] The model is given by H1

:= (x 1 -x 2 )(x -x 12 ) -p + q = 0. ( 11
)
After imposing this equation on the sides of the CAC cube, with suitable variable changes, i.e., left:

(x -x 13 )(x 1 -x 3 ) -(p -r) = 0, (12a) right: (x 2 -x 123 )(x 12 -x 23 ) -(p -r) = 0, (12b) back: (x -x 23 )(x 2 -x 3 ) -(q -r) = 0, (12c) front: (x 1 -x 123 )(x 12 -x 13 ) -(q -r) = 0, (12d)
one easily finds

R 2 = (x 12 -x) • H1, (13a) R 1 = [(x -x 12 )(x 1 + x 2 ) -α -β + 2γ] • H1, (13b) R 0 = [x 1 x 2 (x 12 -x) + (β -γ)x 1 + (α -γ)x 2 ] • H1, (13c)
with H1, as given in [START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF], as the GCD. Similarly by working on the bottom variables x, x 1 , x 2 , x 12 one obtains the 3-shifted H1 as the top equation.

The Lax matrices in this case are

L(x 1 , x) = x p -r -xx 1 1 -x 1 , M (x 2 , x) = x q -r -xx 2 1 -x 2 , (14)
and one easily finds that

M (x 12 , x 1 ) L(x 1 , x) -L(x 12 , x 2 ) M (x 2 , x) = H1 × 1 -(x 1 + x 2 ) 0 -1 .

H1 ǫ : a deformed version of H1

This is an asymmetric deformation of (12) [START_REF] Adler | Discrete Nonlinear Hyperbolic Equations. Classification of Integrable Cases[END_REF][START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF] left:

(x -x 13 )(x 1 -x 3 ) -(p -r)(1 + ǫxx 13 ) = 0, (15a) right: (x 2 -x 123 )(x 12 -x 23 ) -(p -r)(1 + ǫx 12 x 23 ) = 0, (15b) back: (x -x 23 )(x 2 -x 3 ) -(q -r)(1 + ǫxx 23 ) = 0, (15c) front: (x 1 -x 123 )(x 12 -x 13 ) -(q -r)(1 + ǫx 13 x 12 ) = 0. ( 15d
)
The BT or Lax computations give as GCD the bottom equation

(x -x 12 )(x 1 -x 2 ) -(p -q)(1 + ǫxx 12 ) = 0 (15e)
and similarly for the top equation we get

(x 3 -x 123 )(x 13 -x 23 ) -(p -q)(1 + ǫx 13 x 23 ) = 0. (15f)
If we draw a line connecting the corners appearing in the deformation term as a product, the lines form a tetrahedron inside the cube, see Figure 2.

t x 13 t x 3 t x 23 t x 12 t x t x 123 t x 1 t x 2 ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ✑ ❏ ❏ ❏ ❏ ❏ ❏ ❏ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✂ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ✥ ❍ ❍ ❍ ❍ ❍ ❍ ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ ❅ Figure 2:
The cube of H1e

The special thing about these equations is that the parallel sides are not obtained by shifts, but the shift must be accompanied by a 90 o rotation, as described in Figure 2. The fact that the parallel sides are not identical implies that the Lax matrices associated to parallel bonds come in two different forms. Letting

L(x 1 , x) = x + ǫ(p -r)x 1 p -r -xx 1 1 -x 1 , M (x 2 , x) = L| p→q, x 1 →x 2 , (16)
and

L ′ (x 1 , x) = x p -r -xx 1 1 -x 1 -ǫ(p -r)x , M ′ (x 2 , x) = L ′ | p→q, x 1 →x 2 , (17)
we have

M ′ (x 12 , x 1 ) L(x 1 , x) -L ′ (x 12 , x 2 ) M (x 2 , x) = (18e) × 1 -ǫx 1 x 2 -(x 1 + x 2 ) -ǫx 1 x 2 -1 + ǫx 1 x 2 .
Since we have two different parallel sides we can have two different bottom equations, one derived from M ′ (x 12 , x 1 ) L(x 1 , x) -L ′ (x 12 , x 2 ) M (x 2 , x) as above, the other possible choice being

M (x 12 , x 1 ) L ′ (x 1 , x) -L(x 12 , x 2 ) M ′ (x 2 , x) = (15e) × 1 -(x 1 + x 2 ) 0 -1 .
The totality of equations on this cube, obtained from the previous one with L ↔ L ′ etc actually corresponds to an inversion of the cube by

x ↔ x 123 , x 1 ↔ x 23 , x 2 ↔ x 13 , x 3 ↔ x 12 , which yields left: (x -x 13 )(x 1 -x 3 ) -(p -r)(1 + ǫx 1 x 3 ) = 0, (18a) right: (x 2 -x 123 )(x 12 -x 23 ) -(p -r)(1 + ǫx 2 x 123 ) = 0, (18b) back: (x -x 23 )(x 2 -x 3 ) -(q -r)(1 + ǫx 2 x 3 ) = 0, (18c) front: (x 1 -x 123 )(x 12 -x 13 ) -(q -r)(1 + ǫx 1 x 123 ) = 0, (18d) bottom: (x -x 12 )(x 1 -x 2 ) -(p -q)(1 + ǫx 1 x 2 ) = 0, (18e) top: (x 3 -x 123 )(x 13 -x 23 ) -(p -q)(1 + ǫx 3 x 123 ) = 0. ( 18f
)
These are also consistent. We thus have two kinds of cubes, one defined with [START_REF] Hay | Discrete Lax Pairs, Reductions and Hierarchies[END_REF], and one with [START_REF]Viallet Algebraic entropy for lattice equations[END_REF]. These cubes can be glued together: note that the 2-shift of (18a) is equal to (15b). In fact under the central reflection the diagonal lines in Figure 2 would change to the other diagonals.

We will return later to the question of gluing the cubes to fill the space.

Flipped H1 ǫ

This model was proposed in [START_REF] Boll | Classification of 3D consistent quad-equations[END_REF] (see Sec. 3.1, Case (ǫ, 0, 0, ǫ)). In that paper the model was given in a cube with flipped coordinates x 2 ↔ x 23 , x 1 ↔ x 13 . In the coordinates of Figure 1 the side equations of this model are given by left:

(x -x 1 )(x 13 -x 3 ) -(p -r)(1 + ǫxx 1 ) = 0, (19a) right:
(

x 2 -x 12 )(x 123 -x 23 ) -(p -r)(1 + ǫx 2 x 12 ) = 0, (19b) back: (x -x 2 )(x 23 -x 3 ) -(q -r)(1 + ǫxx 2 ) = 0, (19c) front: (x 1 -x 12 )(x 123 -x 13 ) -(q -r)(1 + ǫx 1 x 12 ) = 0. ( 19d
)
BT derivation of bottom and top-equations. Now computing the values of x 13 , x 23 , x 123 from left-, back-and right-equations, respectively, gives for the front equation an expression that does not contain x 3 at all. This expression factorizes into two factors and thus we could have two different bottom-equations:

bottom1 ǫxx 1 x 2 x 12 (1/x -1/x 1 -1/x 2 + 1/x 12 ) -x + x 1 + x 2 -x 12 = 0, (20a) bottom2 p(x -x 2 )(x 1 -x 12 ) + q(x -x 1 )(x 12 -x 2 ) + r(x -x 12 )(x 2 -x 1 ) = 0.(20b)
Similarly, working with the values at the bottom square we get two candidates for the top equations:

top1 x 3 -x 13 -x 23 + x 123 = 0, (21a) top2 p(x 3 -x 23 )(x 13 -x 123 ) + q(x 3 -x 13 )(x 123 -x 23 ) + r(x 3 -x 123 )(x 23 -x 13 ) +ǫ(p -q)(q -r)(r -p) = 0. ( 21b
)
Notice that in down2 and top2, there is an explicit dependence on r even though these are 2D equations. In fact, one should now consider r as a global parameter, although it was associated with the third dimension in the above derivation.

Performing the usual CAC computations with the given sides and different top and bottom equations reveals that the set of equations is consistent in two cases: with the pair (bottom1,top1), or with (bottom2,top2), which was given in [START_REF] Adler | Discrete Nonlinear Hyperbolic Equations. Classification of Integrable Cases[END_REF]. In other words, given the side equations [START_REF] Tremblay | Integrable lattice equations and their growth properties[END_REF] there are two consistent ways of completing the cube. Continuing further, we can also interpret the cube to provide a BT between the left and right equations. Indeed, if we do the above BT construction on the corners of the left side equation the result is identically zero with (bottom1,top1), while (bottom2,top2) produces the right-equation.

The Lax matrices. The standard procedure gives

L(x 1 , x) = 1 λ(p, x, x 1 ) 0 1 , M (x 2 , x) = 1 λ(q, x, x 2 ) 0 1 , λ(a, x, y) := (a -r)(1 + ǫxy) x -y (22)
Since the matrices are upper triangular the ZCC implies

Σ := λ(p, x 2 , x 12 ) + λ(q, x, x 2 ) -λ(q, x 1 , x 12 ) -λ(p, x, x 1 ) = 0. ( 23
)
Remarkably enough, the above sum factorize as

Σ = bottom1 • bottom2 /[(x -x 1 )(x -x 2 )(x 1 -x 12 )(x 2 -x 12 )].
Note that we can write (23) also in the form

Σ = (T -1)λ(p, x, x 1 ) -(S -1)λ(q, x, x 2 ) = 0,
where T is a shift in m and S a shift in n. This of course is in the form of a conservation law.

Filling the space with consistent cubes

So far we have only considered a single cube and its CAC/Lax/BT. But as the name indicates, lattice equations should be defined over the whole lattice. This brings further complications, for example with one cube we could freely do different Möbius transformations in each corner of a cube, but when the cube is part of lattice such seemingly innocuous actions will affect neighboring cubes as well and can destroy the lattice structure.

The rule is simple: cover the two dimensional lattice with consistent cubes, with the condition that adjacent vertical faces coincide exactly, that is to say their four corner values satisfy the same equation. This is expected to produce integrable lattice equations.

We will follow this guideline for various models mentioned before, and systematically check integrability of the lattice equations so obtained, by calculating their algebraic entropy [START_REF] Bellon | [END_REF][START_REF]Viallet Algebraic entropy for lattice equations[END_REF]: the vanishing of the entropy is a yes/no test which gives a clear cut separation between integrable and non integrable cases.

We may briefly recall how to calculate the entropy. The local equation determines an evolution, starting from initial conditions given for example on a diagonal staircase (lattice points of coordinates (m, n) with m + n = 0 or 1). The solution is then calculated on diagonals moving away from the diagonal of initial conditions, explicitly in terms of these initial conditions. The algebraic entropy is defined as the rate of growth of the degrees on these diagonals. Exponential growth is generic, and polynomial growth is characteristic of integrability, while linear growth is associated with linearizable equations [START_REF] Bellon | [END_REF][START_REF]Viallet Algebraic entropy for lattice equations[END_REF][START_REF] Tremblay | Integrable lattice equations and their growth properties[END_REF].

The exact shape of the diagonal line on which the initial values are given is not important. If one modifies this shape locally, the sequence of degrees will change, but not its asymptotic rate of growth. This should be kept in mind for some of the models studied below. For example one could very well change the initial diagonal (steps of height 1 and width 1) to a diagonal with bigger steps, for example with height 2 and width 2, as this will not affect the calculation of the entropy.

Equations consistent with linear sides

We can check the integrability of the two quad equations given in section (4.1). The first one, i.e., equation ( 8), leads to the sequence of degrees: Remark: Since it is integrable, it should also be consistent with a nontrivial set of sideequations, such that one can produce it via Lax/BT computations, but we will leave this open.

{d n } = 1, 2,
For the second equation of section (4.1), that is to say the general homogeneous relation (10) of degree 2, the result is different. We get the following sequence of degrees:

{d n } = 1, 2, 4, 9, 21, 50, 120, 289, 697 . . . which may be fitted with the generating function

g(s) = n d n s n = s 2 + s -1 (1 -s) (s 2 + 2 s -1) ( 24
)
indicating a non vanishing entropy ǫ = log(1 + √ 2), showing non-integrability. Thus even CAC is not sharp in this case. It was actually shown in [START_REF] Hietarinta | Searching for integrable lattice maps using factorization[END_REF] that the simple additional condition a 3 = a 4 , renders (9) integrable.

H1ǫ: Checkerboard lattice

We have already noted that in the H1ǫ model there are two different cubes related by inversion, and that these cubes can be glued together in a unique way, providing a blackwhite lattice. This problem has been discussed in detail in [START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF].

Since the gluing process is completely fixed and each cube has the CAC property it is expected that the composite lattice is integrable. We have calculated the sequence of degrees {d n } for the evolution defined by this model, with initial conditions on a diagonal as prescribed above. The outcome is the sequence [START_REF] Boll | Classification of 3D consistent quad-equations[END_REF]25,41,61,85,113,145,181,221, . . . fitted by the generating function

{d n } = 1, 5,
g(s) = n d n s n = (1 + s) 2 (1 -s) 3
The above sequence has quadratic growth. Thus the entropy is vanishing and the model is integrable.

Flipped H1ǫ: More black and white lattices

In the flipped H1ǫ case (Sec. 4.4), the side equations are the same, allowing simple gluing together of the cubes, but, as we saw in section (4.4), the side-equations are somewhat weak and allow two different compatible pairs of bottom/top equations. We may then cover the two dimensional lattice with consistent cubes, assigning either equation bottom1 (top1), which we call white, or equation bottom2(top2) which we call black to each elementary cell. This can be done in an arbitrary way if one just insists on having a compatible 3D structure of cubes over the 2D lattice. It is then natural to ask which of the configurations obtained in this way are integrable.

Let us consider periodic distributions. The lattice is divided into rectangular groups of cells of width h and height v. Within such a rectangle, a fixed assignment is made, and the pattern is repeated periodically in both directions. (A pattern with v = 1 and h = 1 gives a uni-colored assignment.)

Consider for example (h, v) = (2, 2). There are a priori 2 4 possible patterns of that size, but only 3 inequivalent ones which cannot be reduced to configurations having smaller periods (see Figure 3). The naming convention is to list the colors starting from the lower left corner onwards, denoting bottom1/top1 with 0, alias white, bottom2/top2 with 1, alias black. The equivalence of patterns comes from the fact that we have to look at the lattice globally. It is easy to see, for example, that in the case (h, v) = ( 2 Claim: Some of the distributions are integrable, and some are not. Although the pattern is 3D consistent, the Lax pair is weak and cannot precisely fix the bottom and top equations.

1 × 1 patterns (unicolor distributions). Both unicolor distributions (h, v) = (1, 1) have vanishing entropy. The purely white one is linear. The purely black one is non-trivially integrable, showing quadratic growth of the sequence of degrees

{d n } = 1, 2,
1 × 2 patterns. Both 1 × 2 patterns (h, v) = (1, 2) or (h, v) = (2, 1)
, that is to say alternating black and white stripes, are integrable, with quadratic growth of the degrees.

2 × 2 patterns. For (h, v) = (2, 2) we have different results for the different patterns in Figure 3.

• Both [1010] and [0100] are integrable, with quadratic growth of the degrees.

• The calculation of the degrees for [1011] yields the sequence

{d n } = 1,
This sequence if fitted by the rational generating function

g(s) = n d n s n = 1 -s 2 -2 s 3 + s 5 -s 6 -s 8 + s 9 (1 -s) (s + 1) (s 4 -2 s 3 -2 s + 1) (s 4 + 1) , (27)
and gives a non vanishing entropy ǫ = log(s) with s the largest root of s 4 -2 s 3 -2 s+1, approximately ǫ = log(2.29663).

Caveat: When computing sequences of degrees, one should in principle consider iterations of the whole pattern, but that tends to make the calculations heavier. For the sequence (26), this would mean considering only the subsequence formed by odd terms, leading to a growth given by the maximal root

τ of t 4 -4 t 3 -6 t 2 -4 t + 1. Of course τ = σ 2 .
2×3 patterns. We have examined all the period (2, 3) patterns. The various nonequivalent patterns are depicted in Figure 4.

The computations show that what matters is not just the proportion of black and white cells, but the actual conformation of the pattern. For example the period (2, 3) patterns [010110] and [001011] have an equal number of black and white cells. The first one is integrable (quadratic growth of the degrees) while the latter is not, as may be seen from the sequence:

{d n } = 1, 1, 2, 3, 5, 9, 19, 41, 84, 169, 329, 631, 1199, 2287, 4412, 8627, 17059, 33941, 67573, 134071, 264576, 519343, 1015531, 1982461, 3871597, 7574863, 14855790 . . .(28)
This sequence has exponential growth, but is not long enough to determine an exact value of the entropy. The approximate value is log(1.96).

Out of the 14 period (2, 3) nonequivalent patterns, we have one linear case (all white The following pictures show the aspect of two integrable cases and two non integrable ones.

Remark:

The entropy calculations for these patterns can be made equally well with the relations { white = bottom1, black=bottom2 } or with { white = top1, black=top2}. Both would give the same results.

From the above results, one may already conclude that random distributions are expected to be non-integrable. 6 Lax pair for a 2 × 2 sublattice

We will next push the Lax concept and ZCC to a 2 × 2 sublattice described in Figure 7. (Such sub-lattices have been discussed previously, e.g., in [START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF].) To determine the evolution we need 5 initial values, marked with black disks and expect to get values for the vertices at the open circles. Since the Lax matrices belong to P GL(2, C) the zero curvature conditions can provide at most three equations, and thus if everything works well the evolution is determined. It is also clear that this will not work for bigger sub-lattices as we would then need to provide more than 3 values.

Flipped H1ǫ

In the flipped H1ǫ case the Lax matrices were given in Eq. ( 22) Now using this on a 2 × 2 sub-lattice we get just one condition, namely λ(p, x 122 , x 1122 ) + λ(p, x 22 , x 122 ) + λ(q, x 2 , x 22 ) + λ(q, x, x 2 ) = λ(q, x 112 , x 1122 ) + λ(q, x 11 , x 112 ) + λ(p, x 1 , x 11 ) + λ(p, x, x 1 ).

From this one can in principle solve x 1122 in terms of the other variables. However, this equation does not determine the values for x 122 or x 112 and therefore these Lax matrices fail to give the evolution.

H1

For this basic model the Lax matrices were given in Eq. ( 14). Condition (29) leads to equations that have two rational solutions: The regular one

x 112 = x 1 + (p -q)(x 1 -x 2 ) (x 1 -x 2 )(x -x 11 ) -(p -q) , (30a)
x 122 = x 2 + (q -p)(x 2 -x 1 ) (x 2 -x 1 )(x -x 22 ) -(q -p) , (30b)
x 1122 = x + (p -q) (p -q)(x 11 + x 22 -2x) + 2(x -x 11 )(x -x 22 )(x 1 -x 2 ) (p -q) 2 -(x -x 11 )(x -x 22 )(x 1 -x 2 ) 2 , (30c)
and an exotic solution

x 1122 = x 11 + x 22 -x, (31a) x 122 = x 112 -x 1 + x 2 , (31b)
x 112 = x 1 - (x 1 -x 2 )[(p -r)(x -x 22 ) + (q -r)(x -x 11 )] (p -r)(x -x 22 ) -(q -r)(x -x 11 ) -(x -x 11 )(x -x 22 )(x 1 -x 2 ) , (31c)
The regular solution could also be obtained using the evolution on the original lattice, first solving for x 12 . As a consequence x 122 depends only on x, x 1 , x 2 , x 22 and x 112 only on x, x 1 , x 2 , x 11 . The exotic solution is different, as x 122 and x 112 both depend on all initial values. Furthermore, it depends on p -r and q -r, and not solely on p -q, as is the case for the regular solution.

We may view the variables x, x 11 , x 22 , x 1122 as associated to the vertices and x 1 , x 2 , x 112 , x 122 as associated to the bonds of the 2 × 2 sublattice.

In the algebraic entropy analysis the vertex variables are linear and for the bond variables we find the sequence of degrees 13, 28, 49, 76, 109, 148, 193, 244, 301, 364, 433, . . . (32) This sequence can be fitted with the generating function

{d n } = 1, 4,
ζ(s) = n d n s n = 1 + 4 s 2 + s (1 -s) 3 (33)
The sequence has quadratic growth, signaling integrability.

What it the nature of the exotic solution? Since the vertex variables have independent linear evolution we can solve the equation with x 2n,2m = F (n) + G(m). When this is substituted into the bond equations they give a non-autonomous generalization of a Yang-Baxter map: using the coarse grained indexing w

n,m = x 2n,2m , X n,m = x 2n+1,2m , Y n,m = x 2n,2m+1 , i.e., x 1 = X, x 2 = Y, x 112 = Y 1 , x 122 = X 2 we have Y 1 -X = P (X, Y ), X 2 -Y = P (X, Y ). ( 34a
)
The solution w = constant is not allowed and if either F or G is constant, P collapses to P = ±(x -y). In the generic case, denoting

f (n) := p -r F (n) -F (n + 1) , g(m) := q -r G(m) -G(m + 1) , we get P = (X -Y )[f (n) + g(m)] X -Y -f (n) + g(m) .
After the further translation

X → X + f (n) + T (n, m), Y → Y + g(n) + T (n, m), where T is a solution of T (n, m + 1) -T (n, m) = 2g(m), T (n + 1, m) -T (n, m) = 2f (n) we finally get P = f (n) 2 -g(m) 2 X -Y , (34b)
which is a non-autonomous version of the Adler map [START_REF] Adler | Recuttings of polygons[END_REF] (aka F V in the classification [START_REF] Adler | Geometry of YangBaxter Maps: pencils of conics and quadrirational mappings[END_REF]). The situation can be described by the following diagram:

standard solution ← ---H1 Lax for 2 × 2 sublattice ---→ exotic solution (31)

    H1 non-autonomous F V (34)

H3

The phenomenon described in the previous section is not generic. Indeed, applying the same coarse-graining to an arbitrary integrable quad-equation will lead to a system having only one rational solution (the regular one coming from the original lattice).

We have, however, found more examples where an exotic rational solution exists. Here is one, provided by the lattice modified KdV (lmKdV) (aka H3 δ=0 ). In that case the defining relations of the exotic solution are:

x 1122 x = x 11 x 22 , (35a) x 122 x 1 = x 112 x 2 , (35b) x 122 x 2 = x 112 x 1 = (q 2 x 22 -r 2 x)(x -x 11 )px 1 -(p 2 x 11 -r 2 x)(x -x 22 )qx 2 (r 2 x 22 -q 2 x)(x 11 -x)px 2 -(r 2 x 11 -p 2 x)(x 22 -x)qx 1 (35c)

In the algebraic entropy analysis the sequence of degrees for the vertex variables has linear growth as expected, while the sequence for the bonds is the same as for H1 (see above). Now the equation on the vertex variables (35a) can be solved with we obtain the bond equations in the form

X 2 Y = Y 1 X = (q 2 + r 2 -g(m))pX -(p 2 + r 2 -f (n))qY f (n)qX -g(m)pY , (36)
where

α(n) = λp 2 /[f (n)(f (n) -p 2 -r 2 )], β(n) = λq 2 /[g(n)(g(n) -q 2 -r 2 )].
This is nothing but a non-autonomous version of F III in the classification of [START_REF] Adler | Geometry of YangBaxter Maps: pencils of conics and quadrirational mappings[END_REF]. The diagram presented for H1 works also for H3(δ = 0).

We have found that this phenomenon occurs also for the lattice modified KdV and for the lattice Schwarzian KdV. We have examined in some detail the properties of the models defined in this way and we will present these results elsewhere [START_REF] Hietarinta | Integrable lattices with vertex and bond variables[END_REF].

Discussion

We have discussed the strength of the Lax pairs (or the zero curvature condition) and BT through various examples. We have found several cases where the ZCC does not uniquely determine the evolution but allows two possibilities. This happens, e.g., in the flipped H1ǫ model. If one then builds an infinite lattice by arbitrarily choosing for each cell one of the two allowed relations, the result is sometimes integrable and sometimes shows nonzero entropy.

If the ZCC is pushed to a 2 × 2 sublattice we get more examples where it is ambiguous and yields both the regular solution as well as an exotic one. The latter cannot be generated by some equation in the sublattice, because in the exotic solution the variables x 122 and x 112 depend on both x 11 and x 22 which is not possible using the equations on the elementary squares.

The equations we have obtained in this way can be interpreted as having vertex and edge variables: the variables with even number of indices live at the vertices while the ones with an odd number of indices live on the edges. The edge variables evolve as in a non-autonomous functional Yang-Baxter equation. For more details see [START_REF] Hietarinta | Integrable lattices with vertex and bond variables[END_REF].

x 2 Figure 1 :

 21 Figure 1: The consistency cube

, 2 )

 2 we have the equivalences [0100] ≃ [0010] ≃ [1000] ≃ [0001], [1011] ≃ [1101] ≃ [0111] ≃ [1110], and [1010] ≃ [0101] (checkerboard lattice). Moreover [0000] and [1111] have periods (1, 1), [0101] and [1010], [0011], [1100] have periods (2, 1) and (1, 2).

Figure 3 :

 3 Figure 3: The three inequivalent (2, 2) patterns.

Figure 4 :

 4 Figure 4: Nonequivalent period (2, 3) patterns.

  [000000]), eight integrable cases ( [010000], [010100], [110000], [011000], [010101], [010110], [111100], [111111]), and four non integrable ones ([110100], [001011], [110101], [111001]).

Figure 5 :

 5 Figure 5: Two integrable (2, 3) patterns.

Figure 6 :

 6 Figure 6: Two nonintegrable (2, 3) patterns.

x 2 F

 2 2n,2m = F (n)G(m), and if we introducef (n) := r (n + 1) -p 2 F (n) F (n + 1) -F (n) , g(m) := r 2 G(m + 1) -q 2 G(m) G(m + 1) -G(m) ,

  using the previously introduced notation. With the further scalingX(n, m) → p T (n, m) X(n, m)/f (n), Y (n, m) → q T (n, m) Y (n, m)/g(m),where T solvesT (n, m+1)/T (n, m) = (q 2 +r 2 -g(m))/g(m), T (n+1, m)/T (n, m) = (p 2 +r 2 -f (n))/f (n),

  [START_REF] Adler | Classification of Integrable Equations on Quad-Graphs. The Consistency Approach[END_REF][START_REF] Atkinson | Soliton solutions for Q3[END_REF][START_REF] Xenitidis | Symmetries and integrability of discrete equations defined on a black-white lattice[END_REF][START_REF] Hietarinta | Integrable lattices with vertex and bond variables[END_REF][START_REF] Adler | Geometry of YangBaxter Maps: pencils of conics and quadrirational mappings[END_REF] 29, 37, 46, 67, 79, . . . that is to say d n = 1 + (n 2 + n)/2. This quadratic growth confirms integrability.

  4, 7, 11, 16, 22, 29, 37, 46, 56, 67, 79, 92, 106, 121, 137, 154, 172 . . . (25)

  The 2 × 2 configuration. Values at black discs are initial data (x, x 1 , x 11 , x 2 , x 22 ), and values at open circles (x 112 , x 122 , x 1122 ) should be determined by the evolution. The zero curvature condition for the 2 × 2 sublattice is given by M (x 1122 ,x 112 ) M (x 112 , x 11 ) L(x 11 , x 1 ) L(x 1 , x) ≃ L(x 1122 , x 122 ) L(x 122 , x 22 ) M (x 22 , x 2 ) M (x 2 , x).

	L(x 122 , x 22 ) L(x 1122 , x 122 )
	t	❞	❞
	M (x 22 , x 2 )		M (x 1122 , x 112 )
	t		❞
	M (x 2 , x)		M (x 112 , x 11 )
	t	t L(x 1 , x) L(x 11 , x 1 )	t
	Figure 7: (29)

One could do the computations in some particular representative of the equivalence class, e.g., by requiring the matrices to be uni-modular. However this is not necessary, and may in fact be cumbersome, if it introduces square roots.

Acknowledgments

One of us (JH) was partially supported by the Ville de Paris through the program "Research in Paris 2010". Some of the computations were done using REDUCE [23].


Laurent Romary

Keywords: digital libraries & online journals, e-print archives, communication models, communication platforms, copyright issues, open archive initiative

The chapter tackles the role of scholarly publication in the research process (quality, preservation) and looks at the consequences of new information technologies in the organization of the scholarly communication ecology. It will then show how new technologies have had an impact on the scholarly communication process and made it depart from the traditional publishing environment. Developments will address new editorial processes, dissemination of new content and services, as well as the development of

Introduction

This chapter provides an overview of the various issues related to scientific information seen both from the point of view of the researcher, with his/her need to have access to and disseminate research results, and the research organisation, which has to define means to optimize the efficiency and visibility of the research it performs. Indeed, this chapter will provide some basic guidelines on the design of a scientific information policy that aims at the benefit of research itself.

Scientific information is considered here in the broad sense of the knowledge that a scientist acquires to carry out his/her research as well as the knowledge he/she produces, and then communicates, in the context of his/her research. This definition indeed reflects the extremely individual nature of scientific information, which relates to the capacity that researcher's results will be further used and quoted. From a wider perspective, scientific information can be defined as the knowledge that circulates within a scientific community as part of the research processes. As a consequence, defining a scientific information policy consists in optimising the scientist's information ecology, by providing the best access to existing knowledge, as well as the brightest dissemination to research productions and results.

Whereas the management of scientific information could be seen as mainly targeted to benefit the progress of science, there are some additional factors, which have to be kept in mind when trying to figure out how to organise the corresponding processes. First, managing scientific information is a kind of second-order activity, which comes, from an economical and organisational point of view, in complement, sometimes even in competition, with the actual support (in staff and equipment) that could be directly provided to research. Second, scientific information, being a tangible sign of scientific activity, is the first objective element that is taken into account when assessing the research activity of an individual, a research group, or a research organisation. As a consequence, scientific information management can seldom be considered as a pure technical activity and has often to be taken at a highly political level, whenever it impacts on the strategy of research performingbut also research fundingorganisations.

Because of the intrinsic complexity of the field of scientific management, we will focus along the following sections on specific aspects that may help the reader both to identify the current trend, but also to forge himself an idea on the future evolution of the domain. After characterising scientific information at large, we will thus cover successively the domains of scientific information acquisition, the complementary issue of publication repository and open access, digital edition and data management. We will end up this chapter by providing some insights on the infrastructures that are needed for developing further scientific information services and finally by outlining what we think may be the actual information based research environment of the future.

Characterizing scientific information

There are various types of scientific information and trying to cover them all in this chapter would amount to describing all scientific fields in details. Indeed, each speciality uses and generates its own types of information and requires, when designing a scientific information policy, distinguished attention. At this stage, we can identify two main classes of scientific information:

 Scientific publications, which are mainly written descriptions of ideas, methods and results seen from the point of view of a specific author or group of authors;  Data sets, which are acquired through the use of experimental or observational settings, as well as data production (simulations) or gathering methods such as surveys in the social sciences.

In this last category, we would integrate all the primary sources that are typically used in the humanities, either in the form of ordinary textual documents, or as specific physical artefacts (ethnographical objects, paintings, encryptions, etc.).

It is important to note here that not all types of scientific information are actually digital. In many domains, artefacts such as archaeological objects or natural components such as seeds or bacteriological samples have to be archived in specific repositories for researchers to observe or use them within experiments. Even if digital surrogates (images, scans, genomic descriptions) are often used to provide as precise a description as possible of them, they barely replace the actual physical source. In this respect, this chapter only refers to digital materials and their management for scientific purposes.

From the point of view of content, scientific information has some peculiarities that makes it differ slightly from other (possibly published) type of information:

 The relation to the author is in itself peculiar, since the content of a scholarly paper (as well as any commentary or even data) is essentially based on a personal creation, which has to be acknowledged, each time the corresponding content is being used by another party;  Contrary to works of arts, which would be covered by the preceding point, scientific information is also subject to evaluation by the community of research, either through the peer-review process [START_REF] Suls | The Air We Breathe: A Critical Look at Practices and Alternatives in the Peer-Review Process[END_REF], or simply by the way a research work is cited by peer colleagues;  Scientific results should be, at least theoretically, available in the long-term [START_REF] Dirk | OECD Principles and Guidelines for Access to Research Data from Public Funding Data[END_REF], since scientific knowledge can be seen as the cumulative contributions of elementary scientific results.

The combination of the three preceding points makes scientific knowledge build a network of trusted contributions, where no single piece can indeed be understood without an explicit reference to surrounding works.

Seen from a systemic perspective, scholarly communication processes have a very special characteristic that makes them differ from most of the types of business we may know of, namely in the relation that the business itself has with regards to the corresponding producers and customers. Indeed, researchers play a triple role in their relation to scientific information:

 As producers, since, by definition, scientific information, and in particular, publications, is the dissemination vector of research results;  As consumers, since in most domains, existing publications and data sets play the main role in the research process, both as testimony of the current state of art or even as direct input for the establishment of new results;  As quality controller of the scholarly communication process, by intervening at each stages where evaluation is to take place, be it to peer review a submitted paper or to assess the work of a research entity.

This intricate commitment of scholars in the scientific information workflow is actually made sustainable because in fine the scholar himself is rewarded from the fact that the process is actually as efficient as possible. One has to make sure that -good‖ research results are made available to the community, which in turn will useand quotethem, which will result in the scholar to gain more fame (as well as institutional recognition), and thus more facilities to carry out his own research. As stated in (Edlin and Rubinfeld 2004:130): -Authors are quite different from more traditional production inputs, since part of their compensation derives from reaching readers.‖ Finally, it is hardly possible to speak about scientific information without tackling, at least, some basic components of the underlying technologies. Even if our purpose here is mainly to ponder upon the workflows associated to scientific information, we will see along the coming pages the strategic orientations that must be taken in order to provide science with trustful environment. This notion of trust (applicable to scientists, institutions as well as the public at large) relies on the capacity of providing reliable digital object management environments, as well as putting these within a network of interoperable components, allowing a researcher to seamlessly access and use scientific information in the various forms that we have identified so far. As we shall see such technological environment should be pragmatically designed, so that they serve a wide community of users, from big research consortia down to individual researchers.

Acquiring scientific publication

The acquisition of scholarly content through subscriptions has been for many years the main duty of research libraries, together with the acquisition of scientific books. The journal market, seen from the point of view of the library, can be characterised by a high level of stability, due basically to two main factors: a) the attachment of scholars to their favourite information sources, in a context where conservatism is the main drive for publication and reading, and b) the natural tendency not to break paper collections within the library so that one can characterise the library through its portfolio of -journals‖. This overall stability has been further reflected in the subscription contracts negotiated between the libraries and the publishers (or subscription agents such as SWETS or EBSCO): from one year to another the evolution pressure on the actual portfolio is essentially based on the explicit request for new titles on the part of the researchers and the identification of discarded, or less consulted, journals on the part of the library.

This intrinsic conservatism of the subscription ecology has been one of the major factors that led to the so-called serial crisis in the eighties. This crisis is the result of an unfortunate dynamics2 by which publishers, taking benefit from their exclusive situation, raised the journal prices at a pace largely exceeding inflation, and libraries, facing their own financial constraints and the impossibility to cut down their core journal portfolios, focused their subscription needs on major publishers. After a few years, this crisis led, on the part of the publishers, to a quick concentration of production means, and, on the part of the libraries, to the impossibility to actually fulfil the needs of their academic communities.

In the following section, we will make an attempt at characterizing the post-serial crisis era, starting from an analysis of the notion of big deal, and exploring some possible trends to facilitate a quick and favourable evolution of the commercial scientific publication landscape.

A transitional model -Big Deals

In the nineties, the contractual setting for subscriptions changed dramatically, following a joint necessity for publishers to optimize negotiation efforts, and, for academic libraries, to try to compensate for the high increase in price that had characterized the preceding period. This has led to the so-called -Big Deals‖, which have been characterized by [START_REF] Edlin | Exclusion or Efficient Pricing: The -Big Deal‖ Bundling of Academic Journals[END_REF] as follows:

-in a typical Big Deal contract a library enters into a long-term arrangement to get access to a large electronic library of journals at a substantial discount in exchange for a promise not to cut print subscriptions (the prices of which will increase over time)‖

As a matter of fact, such Big Deals have quickly evolved in some countries from a rather localized setting, limited to a University for instance, to cover clusters of academic institutions that started to jointly negotiate subscription agreements with publishers. After several years of practices, we would like to provide the reader with a distanced analysis of the lessons to be learnt from such big deals and see how much they may contribute to an evolution of the publishing landscape.

As a whole, Big Deals have had quite a few positive effects on the library landscape. Without analysing the actual financial issues in details, we can analyse the benefits of Big Deals by seeing how much they contributed to provide more maturity and awareness about scientific information within academic institutions:

 Big Deals participated in the creation of real community of practice among research and education libraries, since librarians had a real opportunity to compare their needs, their relations to the scholarly communities, and also their budget capacities;  By establishing a point of focus on the relations between a given publisher and one or several institutions, they raised the political implication of academic management, but also of scientists themselves, in the decision making process;  They speeded up the process of moving to electronic content, since most Big Deals include a wide access to the corresponding publisher's catalogue, thus bringing up the necessity of identifying the actual needs related to online access (such as long-term accessibility and archiving, see below), and the underlying infrastructures (access portals) to be put together;  They forced academic libraries to think in-depth on the value for money that subscription schemes actually bring to institutions, in particular considering such factors as usage (hardly considered in the paper world), or budget consolidation when Big Deals would directly impact on the capacity to establish subscription contracts with smaller publishers not involved in Big Deal negotiations.

Still, these rather organisational benefits should not hide the core problems that Big Deals have brought with them, and which can be analysed along two main lines:

 Big Deals have introduced a highly conservative view on the subscription models between libraries and publishers. Indeed, the journal-based model, coming from the printed world, and the corresponding constraint imposed by publishers that turnovers should be preserved on the basis of the existing print subscription, have locked libraries into a system which give them no margin of manoeuvre in the management of library costs in the future;  Big Deals have also showed the weaknesses of academics in dealing with strategic negotiations and in particular the difficulty for libraries to be strong at the negotiation table . Recent examples of clashes during a Big Deal negotiation should not hide the fact that many contracts have been renewed without much improvement from one round of negotiation to another.

Considering all factors, and in particular the risk that Big Deals may contribute to fossilize the subscription landscape, it is important to see such models as transient ones and identify possible evolutions that may prevent a long-term dependency to publisher's requirements. First, libraries should not be left alone in negotiating large-scale and long-term agreements with publishers. Whereas they are essential in providing objective information about the existing needs and usage, negotiation teams should always integrate academic managers and scholars with in-depth knowledge about scientific information processes. Second, prior to any negotiation, global objectives should be set, at the benefit of scholarly work, not only in terms of financial benefits, but also in terms of additional benefits that the community may gain from a new contract. We will see in the coming sections how much in particular, the notions of archival and open access may impact on the actual subscription policy of an academic institution.

Towards new contractual schemes

The difficulties related to the current subscription system could easily be seen as a deadlock for most research organisations since it basically hampers any possibility to define a real strategy in the domain of scientific information at large. Indeed, by freezing part of the budget on fixed expenses, it prevents these organisations from both adapting the corresponding budget to their economical situations or their priorities, but also is a major hindrance to the design of new ways for scientific information to be seamlessly exchanged among the research communities, as would be needed for better and quicker scientific progress.

Still, even if we identify that there is a need for an in-depth evolution of the publishing environment in the scholarly world, we also ascertain that it can only be implemented through the exploration of a variety of new deals between research organisations and publishers. With this orientation in mind, we present in the following sections some possible actions that could be pursued to contribute to such an evolution. All of these have been already implemented and validated within organisations and we will try to draw prospective conclusions from the assessment that we will make for each of them.

Open access publishing and budget centralisation

The first move we would like to address here actually comes from the publishing sector, which has experimented in the recent years ways of offering open access content (Velterop 2003) on the basis of a payment that would not result from a subscription, but that would take place on the author's side (hence the expression of author-pays model). In this domain, one needs to make a clear distinction between opt-in schemes and native open access journals.

In the opt-in open access schemes, publishers (e.g. the Open Choice scheme by Springer) offer the possibility for an author to finance the full accessibility on the publisher's web site of the final version of his paper at the time of publication. Such schemes have several disadvantages. It creates a burden on the authors, who have to decide on (and finance) the online publication of their papers, one by one. It implements a double payment system in institutions which do have subscriptions to the corresponding journals, and as a consequence, prevent the institutions from getting an accurate overview of the budget they dedicate to publication material. All in all, we strongly recommend not to support such schemes and to clearly inform the scholars about their danger.

True open access journals (such as the PLoS3 portfolio or most of the titles from BMC) offer the author-pays model whereby authors must systematically pay publication fees to the corresponding publisher, but conversely no subscription is required to get access to the content. As opposed to opt-in schemes, there is here no risk of double payment and the situation is by far clearer for institutions that may centralise a specific budget made widely available to authors (thus reducing the administrative overhead). Still, such schemes (but the reverse arguments exist for the standard subscription scheme) present the dangers that it may become even more difficult to publish for institutions or countries with reduced means, and also that there may be free-riders, i.e. entities (in particular private firms) which benefit from the publication material, without contributing at all to the corresponding cost. Still, the capacity that open access journals offer to centralize the corresponding budget and thus to monitor the actual evolutions within and across research institutions worldwide encourages us to advocate the integration of open access journals within the scientific policies of academic institutions at large.

Making publishers' offer fit academic needs

Not only has the move from the traditional printed journal model to online delivery changed the capacity of scientists to quickly access information, it has also deeply modified the perception that academic institutions had of the management processes one should deploy for such information. This has resulted in identifying new requirementsand indeed new servicesthat the publishers should fulfil in conjunction with what would normally be associated with a subscription contract.

This section explores how such requirements can be contemplated, and possibly implemented, from the point of view of the content proper, i.e. how much an institution should claim to receive precise information from publishers, in order to go towards a better and more sovereign management of its own scientific information. We will indeed explore these issues in two stages, related to a) the acquisition and management of reliable meta-data and b) the various archiving levels that one may demand in the context of subscription schemes.

It is quite straightforward to understand why it is of strategic importance for an institution to have a good overview of its scientific production and consequently why managing reliable meta-data about publications is considered as a very sensitive issue. As it provides an insight on the quantity and quality of the actual publication activity of individuals as well as of institutions, such information is at the core of reporting activities, of researchers' assessment, as well as for any strategic planning endeavour. It is also of paramount importance that such metadata be both precise and accurate, since it should allow gaining insights into such a variety of publication features as the actual domains where research is produced, or the collaboration schemes that an organisation may have with other institutions or other countries for instance.

What is meant here by precise and accurate is the capacity for a database, and consequently for an interchange format, to provide metadata information where all elementary and meaningful pieces correspond to a specific field, associated with a precise semantic and mappable onto the most relevant international standards. This has an impact at three main levels of a bibliographical representation:

 In the description of publication information where article information (title, volume, issue, pagination, DOI, publication date) and journal information (title, ISSN) should allow for both a precise identification but also accurate description of the article;  In the representation of author data, where not only names should be finely represented (all name components should have their own fields), but also affiliations should be dealt with as precisely as possible;  In the production of basic content related information such as keywords, domain classifications or abstracts.

Whereas the first point is rather straightforward and usually dealt with quite well in various publication platforms, the second one is often underestimated. Still, precise author data and in particular affiliation represent a key aspect for the further exploitation of publication data, in particular in for the study of collaboration patterns [START_REF] Subramanyam | Bibliometric studies of research collaboration[END_REF]. For instance, being able to sort out papers by institutions, or to analyse the geographical patterns of copublication is part of the patterns that one wants to be able to identify out of a bibliographical database.

In the ideal case, there would be an excellent opportunity to compile such meta-data on the basis of the information available from publishers (at least for journal papers). However, as demonstrated in particular by the technical work within the European PEER project4 , scientific publishers have no coherent framework for such data and, in fact, some have difficulty to provide precise information concerning authors and their affiliation. It occurred also that publication repositories are not that in a better shape and the PEER project is the opportunity to demonstrate how much a standard-based approach (based on the customisation possibilities of the TEI5 ) could lead to a higher degree of interoperability [START_REF] Nancy | International standard for a linguistic annotation framework[END_REF]) between platforms.

If we were to make a move towards higher interoperability across platforms, the scenario contemplated here would be that any publication repository, whether public or private that contains precise and reliable chunks of information should be in the position to deliver them to complement the information that another repository would require. Whereas such a scenario may be extremely complex to implement across any kind of platform, in particular because of the heterogeneity of formats we have identified above, it is possible to contemplate the maintenance of a clearinghouse6 , which would at least serve the network of public publication repositories.

We should note here that the precision required for exchanging meta-data between publication repositories in such scenarios as the ones addressed here has nothing to do with the very shallow formats required by current harvesting processes, which, for instance, are part of protocol such as OAI-PMH [START_REF] Lagoze | The Open Archives Initiative: Building a low-barrier interoperability framework[END_REF]. Indeed, we anticipate an essential evolution of publication repositories, which, seen as trusted sources of information, will be able to provide, at any level of granularity, all the description attached to their digital content (see also [START_REF] Paul | The anatomy of a nanopublication Information[END_REF].

Beyond meta-data, it is also important to consider how much an institution can demand on the availability of the full publication content and identify how much we could globally make progress in this domain. The issue here is quite simple to state: the move from paper content to digital one has changed the relation between the customers and the content in two complementary ways:

 The move to digital content has deprived step-by-step academic libraries from their role of reference archive for scholarly content (Greenstein 2000);  Publishers have progressively taken up the management of the archival dimension of digital content, claiming that this content is always -accessible‖ from their own platforms, which would offer better technical facilities as well as all guaranties for a sustainable availability (Kling and McKim 1999).

These changes have created a strong dependency towards the commercial sector, with academic institutions only lately identifying the need to define a strategy in this domain. What indeed would we have is such and such publisher would disappear, or if a major conflict arises between the academic sector and the private one, where the former would lack authority towards the latter for sake of this dependency? Even if not central such a feeling has contributed to the open access movement, when scholars (and their institutions) identified that in the digital age content could, and indeed should, be pooled together in a coordinated manner.

In order to go towards a better management of published material by research institutions themselves, there is a need to act explicitly during the negotiation stage of subscription contracts. There are indeed three levels of requirements that could be identified in the domain of long-term access to publication:

 If the data is to be solely archived by the publisher, one should minimally require a perpetual access right to the material subscribed at a given period. Concretely, this is to guaranty that even if a contract with the publisher is interrupted, all journal content that has been paid for (new issues and backfiles) will remain accessible for the population that had benefitted from the initial agreement;  To guaranty a better independence from the publisher's services and secure the availability of subscribed material, one can introduce a clause allowing the institution (or the corresponding consortium) to host the content and deliver it through its own servers. Further archival copies should of course be needed to ensure continuous and long-term accessibility;  Finally, an institution can require that all the subscribed material that also corresponds to content authored by its researchers7 could also be uploaded in a designated publication repository, in keeping with the institution's open access policy.

These three levels actually impact on the general copyright scheme that should be associated to scholarly content. While we argue that the private sector has an essential role in providing core services, such as certification, in the scientific publishing workflow, new deals have to be set so that such services are never correlated with any kind of exclusive copyright transfer.

As can be understood, we try to argue here that academic institutions should strive towards the establishment of scientific information repositories where publication meta-data and content are pooled together within a sustainable and reliable environment. Such an orientation bears a quite natural technical side, but it should also be taken very seriously as a component of ongoing discussions with the private sector. At the highest level, and in particular in the context of national licence program, such evolutions have to be discussed with the same level of attention as budget or coverage issues.

General perspective

As a whole, we see there is a need for a real strategic view in the way we are to handle future commercial deals with the publishing sector at large. On the one hand, we need to identify means to make our budget more depending on the real need of research organisation rather than see it be determined by external interests. On the other hand, we need to identify the actual services that we require from publishers and negotiate with them the best value for money, considering also the services that we do not actually want from them. As we shall see from the following developments on research repositories, research performing organisations may want to achieve some of the functions that were so far externalized to the private sector, when these reflect a strategic interest for them.

Scientific information and open access -the role of publication repositories

Defining open access again?

The open access movement has gained in the recent years enough momentum and fame that one could believe that there is hardly any need to enter too much a discussion about its scope and objectives8 . Epitomized by the Berlin declaration 9 , the open access ideas reflect a tension between two opposite sets of forces:

 The necessity for the publishing business to keep its revenue, thus leading to everincreasing subscription budgets for the academic institutions;  The feeling that dissemination of scientific information in the digital age should be straightforward (i.e. without intermediaries) and fundamentally cheap.

With a sense that there is no clear way out of this situation, the open access movement is an echo to the feeling that academics should take action and devise their own means of disseminating their research papers. The so-called green way to open access is thus focussing on providing technical platforms10 and policy settings11 , for the self-archiving and free dissemination of scholarly papers. In a way, it is complementary, or even contributes, to the attempt outlined in the first part of our paper to define new collaboration schemes between the academic institutions and the commercial publishers.

Still, the green open access movement can be characterized by a quite narrow view on scholarly publishing and the angelic idea that researchers may just join the self-deposit movement by conviction or by being mandated. The situation is de facto more complex, and instead of making here a theoretical or comparative analysis 12 of the publication repository landscape, we would like to illustrate the various views that may exist upon a publication repository, by presenting the specific case of the Hyper Archive en Ligne (HAL) repository, which, across the years has become the reference environment for the French academic landscape.

A reference case -HAL

In the mid-nineties, Hyper Archive en Ligne (HAL) was put together by physicists who wanted to implement a mirror archive to the already long-standing ArXiv [START_REF] Ginsparg | First Steps Towards Electronic Research Communication[END_REF]. At that time, the main drive was to benefit from an independent platform that could have its own editorial policy, be independent from possible access problems to the United States and also be able to develop its own functionalities. With the support of the CNRS 13 , a service unit 14 was put together and a first implementation made operational within several months. The spirit of this first environment was mainly targeted towards pre-prints (stage 1), to favour an early dissemination of research results.

Step by step, the French physicist community, as well as mathematicians, got used to deposit their papers in HAL and in the mid-nineties, the repository gained momentum when the CNRS decided to promote it within other disciplines and adopt it as its main source of information to published material by its researchers 15 . At the same period, several research organisations in France, among them INRIA and INSERM 16 , decided to adopt HAL as a way to make concrete their adhesion to the Berlin declaration on Open Access 17 . This extension process led to a national agreement, signed in 2007, of most of the French research institutions, together with the national conference of French Universities to sign an agreement to work jointly on the further development and support of HAL.

As analysed in Armbruster and Romary ( 2010), the evolution quickly outlined above has set HAL as a publication repository that can hardly be reduced to the usual narrow concept of an institutional repository.

 It offers services to multiple research performing organisations such as CNRS, INSERM or INRIA, as well as universities. Each institution may have its specific portal through which their researchers may deposit and where all corresponding productions are visible. Still, any content is part of a single repository, thus allowing searches to be extended to the whole content;  It bears a strong multidisciplinary mood, either because of the disciplinary nature of some of the supporting institutions, or because specific communities have set their own portal, but also more generally, because it matches the cultures of various scholarly communities by both considering pre-prints or published material as its core input;  Is has reached a cross-institutional recognition which makes it be the default repository for Universities or research funding organisations 18 aiming at indentifying their research production.

All in all, and things being seen from the wider perspective of a national scientific information policy, HAL is providing a high level service, well integrated in the institutional landscape, for a very low budget through its highly centralized technical nature. Still, institutional recognition is, as we know, useless, if researchers themselves are not convinced that using the platform may bring some added value to their own work. It is thus worth observing why in such a community as computer science, and in particular within INRIA, HAL has gained such a fame and become part of the scientists' daily practice.

Publication repositories -the researcher's view

One immediate feedback that is received from colleagues using the HAL-INRIA portal on a regular basis is the high visibility that the corresponding papers receive immediately from most international search engines (hear -Google‖). Indeed the centralized management of the archive has made it feasible since years to maintain good working relationship with the corresponding technical teams and to tune the software interfaces to optimize the visibility.

From the point of view of the researcher, this is observed through the immediate high retrievability of a paper, as soon as relevant keywords for the corresponding field are typed in. This visibility can also be traced on the ranking of publication repositories produced by Webometrics (Björneborn and Peter Ingwersen 2004), which actually shows HAL and HAL INRIA as performing respectively on the platform and the institutional ranking.

The second important aspect, which is often mixed up with the traditional notion of institutional repository (cf. Armbruster and Romary 2010) is the specific institutional setting.

Indeed HAL provides specific institutions (or communities) with dedicated portals which allow them to deal with the publication archives in their own way, by adapting the graphical charter, adopting their own editorial policy for content, or building up their additional tools (e.g. connection to in-house reporting mechanisms). Such views allow both the institution and the researchers to actually feel at home within the HAL platform, while benefiting from all generic features and evolutions that are developed globally.

Last but not least, the wide acceptance of the HAL Platform within INRIA can also be a great deal attributed to the important editorial support provided by the library network, which systematically reviews all entries after authors make a deposit, or at times even help author to make batch deposits when necessary. By completing missing meta-data, correcting actual descriptions (bibliographical descriptions, spell-checking of abstracts), by directly interacting with authors in border-line cases (software documentation, management of anteriority) and finally ensuring that the most appropriate tools and interface are being put higher-up on the developers' agenda, the librarians convey a feeling of stability that encourages even more the researchers to see HAL-INRIA as a trustful archive.

Perspective: intelligence in the platform

The experience we can gain from observing such a platform has HAL let us take a real distance with some of the most polemic (and at time conservative views 19 ) on open access and anticipate on how much publication repositories can be made a tool at the service of science at large. Without anticipating on the wider vision we will outline at the end of the paper, we can try to make a short term project on the way we see publication archives provide even better services to researchers.

Indeed, and taking up the notion of ecology of publication repositories from (Romary and Armbruster 2010), we see that if we want to better integrate publication archives in the researcher's information ecology, we need to provide him with a variety of seamless services that will facilitate the deposit and further use of research articles. Such services would actually occur at various levels:

 At the deposit stage of a paper, one should relieve the depositor from typing in information that could be retrieved from other sources, or the paper itself. Typically, a good management of authors and associated affiliations, in particular in the context of usual co-authors is essential. In complement, automatic information extraction techniques 20 from textual content should allow to pre-fill most of the meta-data information required for a proper management of content in publication repositories;  We should work towards providing researchers with more capacities at managing their workspaces within publication repositories. They should be allowed to keep drafts unpublished, add collections of graphics or images, or even additional documents such as slides, posters or videos, which may come as natural complements to the paper itself;  As the dissemination level, it is essential to provide efficient tools for researchers to compile information from the repository, either as publication lists when preparing a paper or an institutional report, or to generate his web page or that of his research group.

In the current publication repository picture (cf. Armbruster and Romary 2010), such features are occasionally implemented, but there is a need for a concerted development that only a more centralized view on repositories may allow us to seize. Furthermore, institutions should clearly state how much they consider the issue of polling up publication data by redirecting all information gathering needs towards what is actually available there.

Dealing with research data and primary sources

In the continuity of the infrastructural work carried out for publication, the academic organisations are more and more turned into considering the importance of dealing with research data as part of their scientific information management duties. Indeed, as exemplified by the report issued to the European commission in October 2010 (Wood 2010), the management of data has become a key issue for the definition of new research funding programs and in particular for the establishment of digital research infrastructures. One of the key issues related to scientific data infrastructures is that of trust, in the sense that researchers may deposit and re-use scientific data with full confidence that these will be properly curated and preserved in the long run.

Characterising research data

The notion of research data is by far more fluid and heterogeneous as that of publication and shall deserve a specific attention. Contrary to publications, research data cannot be apprehended as a set of clearly identified objects. Data occur at various stage of the research process and may usually be seen at various levels of granularity, from elementary samples to large collections (or corpora). Quality is also an issue where part of the research activity is indeed dedicated to the selection and enrichment of primary data acquired from some equipment, or, as is the case in the humanities [START_REF] Romary | Stabilizing knowledge through standards -A perspective for the humanities[END_REF], directly selected from various cultural heritage sources.

the content, but also in order to allow an adequate citation of the work. More generally, scientific data have to be, even more than publications, associated with precise metadata (in the same way as what we have for publications with bibliographical data). Indeed, whereas one can contemplate the idea of retrieving the source of a paper while looking at it, there is hardly any chance that a collection of numbers may tell anything of its format and origin. The fear with scientific data is that, by not taking the adequate time to document it, researchers may create data cemeteries, which may prevent any further reuse.

From a strategic point of view such issues cannot be dealt with without academic institutions having a real data curation strategy, which complements the issues of data description outlined above with that of data selection. As a matter of fact, it becomes more and more impossible for some scientific fields to keep all the data they produce, since these would go by far beyond the IT capacities as we know them today. To take the most prominent examples, the new Large Hadron Collider at CERN 21 is planned to generate several peta-bytes per year, which in turn forces their technical infrastructure to be organized as a cascading network of computer nodes, where just filtered-out data is percolated down to the individual researchers.

Pooling data together -the core of the scientific data business

Beyond the local management of research data at the production locus proper, it is important to keep in mind that a major challenge for the further progress of research in many fields is the capacity for research entities to be able to pool together data assets in order not only to avoid duplication of work, but even more to combine complementary evidence to form a wide-coverage informational basis for a given field. This trend has been initiated several decades ago by domains such as astronomy 22 , which actually endowed themselves with various means to create networked or even joint databases of observational data (images, frequency range observations), but also of stellar objects and associated bibliographical references. To extend such trend in all fields of science, research communities, but also research organisations and governmental bodies should act in basically three directions:

 At the political level, there should be a strong incentive towards researchers so that they actually make the wide dissemination of data a standard component of their work. Such incentives may take the form of financial support, but also of effective recognition mechanisms for those who take actively part to this endeavour;  From a legal point of view, communities should identify the least damaging licensing frameworks so that scientific results are of course systematically attributed to their producers, but also no hindrance is made to the combination of information which would have contradictory legal status 23 ;  Finally, the compilation of data collections requires a strong technical coherence, to ensure in particular that data assets are made interoperable for joint queries and combined visualization or processing. This requires that scientific communities be 21 http://public.web.cern.ch/public/en/lhc/lhc-en.html 22 See Heck (2003) for an overview, but also [START_REF] Heintz | Automated data retrieval in astronomy[END_REF] to get an idea of the visionary mood of the astronomers in the early 80's.

23 When applicable, a basic creative commons CC-BY (http://creativecommons.org/licenses/by/3.0/), where the sole constraint is actually to guaranty the attribution of the work to its source may be considered as a baseline for such licences. Any additional constraints may then become a stumbling stone for the further pooling of information. For a wider discussion on this see [START_REF] Wilbanks | Introduction to Science Commons[END_REF] involved in standardisation activities24 to produce the appropriate requirements and guidelines for the representation of the data relevant for their field of activity.

As can be anticipated, the last point cannot be seen as a short-term endeavour. Each field has to identify its own requirements, link these with the existing international standards and make sure that the corresponding standards will evolve at the same pace as scientific discovery proper. As demonstrated in [START_REF] Romary | Stabilizing knowledge through standards -A perspective for the humanities[END_REF] for the general area of the humanities, such standardisation efforts (Gray et al. 2005) relate to the capacity to provide conceptual models for the corresponding data, so that these models are also independent of the contingencies of IT facilities at a given time.

6 Towards a "scholarly workbench"25 -a vision for the future of scientific information

In the previous sections, we scrutinized the ongoing evolutions of the scientific information processes, and delineated step by step a vision where institutions and scholars would take up the lead in making these changes facilitate the scholarly work. We saw in particular how much the categories of publication and data may deserve in the long run a similar treatment in a context where the separation between the two becomes less and less marked. In this context, we would like to end up our analysis by describing the way we would dream the researcher's workspace of the future, as a target object that we would try to reach when making strategic choices within our organisations. This virtual research space (or eSciSpace) would indeed apply for all types of scholarly activities from -hard‖ physical sciences to the study of primary sources in the humanities.

In the virtual research space scenario, we define a research asset as any piece of information that may be manipulated and further made public by a scholar in his working space. These may be pieces of text, data collections of all kinds, annotations to any research asset, or virtual research folders grouping together research assets in the course of the scholar's activity.

In his research workspace, the scholar manages all the stages of his scientific information activity, gathering initial evidence by importing data from external repositories, in the form of -publications‖ or as extractions of existing observations or documents provided by other scholars. Building up from this evidence, he compiles and organises his thoughts in the form of drafts or annotations directly linking to the other documents in his workspace, applying specific software to compute new features from his observations, and organize his thoughts by grouping meaningful sets of information in dedicated research folders.

Core services of the virtual research space

The virtual workspace outlined above resides on the availability of some basic services, which, not necessarily being specific to the scientific information domain, are mandatory to implement the target scenarios we anticipate. These essential services are the following ones:

 The researcher is automatically identified when connecting to his/her workspace, on the basis of a global authentication process. As a consequence, the various parameters of his/her research environment (affiliations, ongoing funded projects, co-workers) are available, so that the appropriate information can be attached easily to any research asset he/she manipulates;  His/her workspace allows him/her to create research folders of any kind where he/she can compile various objects (notes, data sets, links to external sources, as well as related persons and events as, e.g., meetings 26 );  Unique identifiers are provided for all objects in the workspace, which can serve as a stable reference for any further quotation or reuse;  A precise versioning system is at hand, which allows him to trace the evolution of any research assets and publish any version according to his will.  Last but not least, the scholar has full liability to select any of his research assets and give access rights to other individuals, groups of individuals or the public at large.

Community review and certification

In the perspective we want to defend here, the research workspace is also the locus where the validation of the research results takes place, opening up a whole range of new possibilities for a scholar to gain approval or recognition from his peers. Indeed, moving away from the highly focused peer-review process that we currently have for publications, the management of a research workspace combining written documents and data-sets, together with the capacity to provide various levels of visibility to any combination of these objects, allows one to anticipate a much broader community based validation of scholarly content. In the various possibilities we will describe below, the scholar always keeps the initiative to launch a certification process, but the capacity on his virtual workspace allows him actually receives the level of feedback he actually wants.

EGU [START_REF] Pöschl | Interactive journal concept for improved scientific publishing and quality assurance[END_REF], or the attempt at creating data journals27 for assessing the added value related to the compilation of reference data sets would naturally fit into this picture. Besides, the basically open nature of research workspace would facilitate the compilation of new types of evaluation metrics. For instance, usage statistics, coupled with information concerning the actual scholar, community of institution having used the research asset, would bring usage profiles by far more precise then any kind of citation metrics we have nowadays.

The library continuum

The problem addressed with this vision of a virtual research workspace is to help the scientist manage the documents he uses and produces in his research, as well as making him feel like he is in charge of his own virtual research library, where he can easily retrieve documents, but also disseminate them in isolation or as collections to students, colleagues, or the wide public. Indeed such a vision decentralizes completely the notion of a research library, which would move from a central physical place to a delocalized space in the -cloud‖ (Aschenbrenner et al. 2009). Still, we may not expect that scholars would take up all the necessary work related to the curation of their research assets, and comprising such a variety of tasks as technical integrity or adequate meta-data description. They will have to be supported, and this is part of the infrastructure by new types of documentary experts (eLibrarians, or more commonly digital curators) that will accompany them in their information based research activity.

Infrastructures for scientific information

As a word of conclusion, we should situate the conditions under which the evolutions, as well as dreams, outlined in this paper could actually be implemented. Indeed, most of the developments contemplated here, whether related to publication or research data, and comprising what we did not develop here in domains such as bibliometry or digital editions, require long-standing involvements of the corresponding institutions in the domain of scientific information management. Over the years, such an involvement, together with the corresponding investments, has taken the form of real eInfrastructures at the service of science. Such infrastructures have shaped differently depending on the country or the academic setting ranging from high-level coordination directorate (at CNRS) or as a continuation of a strong library setting (as at the University of Göttingen, see (Lossau 2004)), it has also often been embodied as autonomous units dedicated to the management of scientific information (as in the Max-Planck Society with the Max Planck Digital Library28 ). All these service or decision units have shown from our own experience that their efficiency and capacity to contribute to the strong dynamics of the field rely on a series of essential factors:

 Scientific digital libraries, since they already have a name (Berman et al. 2003), should be close enough to the research communities they have to serve in order to understand both their needs but also their practices in the domain of scientific information; why indeed offer for instance information portals to scholars who would prefer using search engines to find their information sources?  All the same, they should be constructed around a core of highly competent staff that masters such a wide range of skills as budget negotiation, IT development and

This paper has strongly benefit from close interactions with Norbert Lossau, director of the State and University Library of Göttingen.

[START_REF] Mccabe | Law serials pricing and mergers: A portfolio approach[END_REF] also demonstrates that mergers among publishers have also been a determining factor.

Cf. Brown et al. (2003)

The meta-data available from 12 publishers, comprising some of the major companies in the field, have been mapped onto one single standardized structure, in order to be pushed to a group of publication repositories in the context of a large-scale (green) open access experiment.

Text Encoding Initiative, www.tei-c.org

The PEER Depot, implemented in the context of the PEER project is an excellent example of such a clearing house.

Depending on the agreement, the coverage can be limited to corresponding authors or (like was the case of the agreement between the Max Planck Society and Springer in 2008) extended to any co-author of the publication.

See (Davis 2009) for an overview of the doxa on the subject.

http://oa.mpg.de/lang/en-uk/berlin-prozess/berliner-erklarung/

usually referred to as institutional repositories (cf.[START_REF] Lynch | Institutional Repositories: Essential Infrastructure For Scholarship In The Digital Age[END_REF], and the wider distance analysis in[START_REF] Romary | Beyond institutional repositories[END_REF]

in the form of deposit mandates (see[START_REF] Sale | The patchwork mandate[END_REF]

see Armbruster and Romary (2010) for such a global comparison.

See for instance[START_REF] Harnad | Gold Open Access Publishing Must Not Be Allowed to Retard the Progress of Green Open Access Self-Archiving[END_REF].

Scientific data bear many common features with publications. In essence, they require to be as neatly associated to the originated researcher or institution, as a warrant for the trustfulness of 20 See in particular the importance of machine learning techniques in this respect[START_REF] Lopez | GROBID: Combining Automatic Bibliographic Data Recognition and Term Extraction for Scholarship Publications Research and advanced Technology for Digital Libraries[END_REF]

See Ochsenbein et al. 2005 for an exemplary community endeavour.

This expression appeared in the initial work plan of the eSciDoc project in 2005 (www.escidoc.org/)[START_REF] Dreyer | eSciDoc a Scholarly Information and Communication Platform for the Max[END_REF]).

The baseline case is not that far from the current peer-review system, as we know it. It is based on the assumption that there exists certification entities associated to a specific topic, and which are articulated around a scientific committee. In this scenario, the scholar gathers research assets in a dedicated research folder and, when he considers the corresponding result to be worth it, he simply makes it accessible to the certification entity, asking for -peer review‖. If the evaluation is positive, the research asset receives a review certificate, which can be associated to any data feed related to it. Through this process, and according to the editorial policyas well as the scientific recognitionof the certification entity, the research asset becomes a -peer-reviewed‖ publication in the literal meaning of the term.On the opposite side of the spectrum, the scholar may not want to have an official certification process, but would like to receive a certain level of recognition of his results from a community. To this end, he can publicize a research asset and issue a targeted call for comment, which may range from selected colleagues to a wider scientific community. Such calls would transit through scholarly feeds or social networks to which the researcher subscribed. Feedbacks to the call take the form of commentaries, which may be posted in the commentators' research space and linked to the research asset. The collection of commentaries can in turn be used to derive a new version of his work or to assess the recognition of his scientific contribution within the community. This generalized process of certification incorporates various attempts at exploring new types of peer review in various research communities. Initiatives like open peer review from the 26 Part of the necessary infrastructure would resemble services such as those offered by Calenda (http://calenda.revues.org/) the French diary of events in the humanities(Dacos et al. 2006).

In a context where many data journals initiative are taking shape, we can only point to the quite visionary initiative from JISC: Overlay Journal Infrastructure for Meteorological Sciences (OJIMS)

www.mpdl.mpg.de

knowledge representation. Scholars alone may not always have the adequate sense of the complexity related to certain decisions;  Even more importantly, the scientific digital library should be closely related to the management of the corresponding academic institution, since from our experience, most strategic decisions in the domain of scientific information directly impact on the research environment of the institution;  Finally, scientific digital libraries should cover the various fields of scientific information management. If their scope is limited to such a narrow domain as the management of journal subscriptions, they will not be in the position of identifying the adequate tactic moves across the various fields of scientific information.

Considering the current scientific information landscape, it seems that we are not far from having such scientific digital libraries at hand. Various attempts in this direction are taking place and at the same time, we better see the role and evolution of such elementary building block as publication repositories. The work ahead of us is now to bring all this together in a more coherent way.

Armbruster