Saïd Benachour
email: benachou@iecn.u-nancy.fr

Grzegorz Karch
email: karch@math.uni.wroc.pl

Philippe Laurenc ¸ot

Convection-diffusion equations 1

The large time behavior of zero-mass solutions to the Cauchy problem for the convectiondiffusion equation u t -u xx + (|u| q ) x = 0, u(x, 0) = u 0 (x) is studied when q > 1 and the initial datum u 0 belongs to L 1 (R, (1 + |x|) dx) and satisfies R u 0 (x) dx = 0. We provide conditions on the size, and shape of the initial datum u 0 as well as on the exponent q > 1 such that the large time asymptotics of solutions is given either by the derivative of the Gauss-Weierstrass kernel, or by a self-similar solution of the equation, or by hyperbolic N -waves.

Comportement asymptotique des solutions d'équations de convection-diffusion

Résumé. Le comportement asymptotique des solutions de masse nulle du problème de Cauchy pour l'équation de convection-diffusion u t -u xx + (|u| q ) x = 0, u(x, 0) = u 0 (x) est étudié lorsque q > 1 et la donnée initiale u 0 appartient à L 1 (R, (1+|x|) dx) et satisfait R u 0 (x) dx = 0. Nous donnons des conditions sur l'amplitude et la forme de la donnée initiale u 0 et sur l'exposant q > 1 sous lesquelles le comportement asymptotique des solutions est décrit par la dérivée première du noyau de Gauss-Weierstrass, ou par une solution auto-similaire de l'équation, ou par une N -onde hyperbolique.

Version française abrégée

Nous étudions le comportement asymptotique, lorsque t → ∞, des solutions de masse nulle du problème de Cauchy pour l'équation de convection-diffusion (1)- [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption. II -Uniqueness[END_REF]. Il est clair que cette équation met en jeu une compétition entre le terme de diffusion u xx et le terme de convection non linéaire (|u| q ) x , et le but de notre étude est de déterminer lequel de ces deux termes devient prépondérant lorsque t → ∞. Lorsque la masse totale M = R u 0 (x) dx = 0, ce problème a été considéré en particulier dans [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF][START_REF] Escobedo | Asymptotic behavior and source-type solutions for a diffusion-convection equation[END_REF][START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF]. Lorsque M = 0, les résultats de [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF][START_REF] Escobedo | Asymptotic behavior and source-type solutions for a diffusion-convection equation[END_REF][START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF] se traduisent seulement par la convergence de u(t) vers zéro dans L 1 (R). Nous présentons, dans cette note, des résultats plus précis pour certaines classes de données initiales. En effet, nous exhibons le premier terme dans le développement asymptotique des solutions de (1)-(2) selon les valeurs du paramètre q > 1 et le signe (et éventuellement la taille) de la primitive de la donnée initiale u 0 .

Nous supposons que u 0 vérifie (3) et désignons par u la solution correspondante de (1)- [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption. II -Uniqueness[END_REF]. Signalons dès à présent que notre approche est basée sur l'étude de l'équation de Hamilton-Jacobi diffusive ( 7)- [START_REF] Escobedo | Asymptotic behavior and source-type solutions for a diffusion-convection equation[END_REF] qui est naturellement associée à (1)- [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption. II -Uniqueness[END_REF]. En effet, la primitive U de u, définie par (6), est solution de ( 7)- [START_REF] Escobedo | Asymptotic behavior and source-type solutions for a diffusion-convection equation[END_REF].

En premier lieu, nous étudions le cas où la diffusion régit le comportement en temps grands.

Théorème 1 Supposons que l'une des trois conditions suivantes soit vérifiée : (i)

U 0 ≥ 0 et q > 3/2, (ii) U 0 ≤ 0 et q ≥ 2, ou (iii) U 0 ≤ 0, q ∈ (3/2, 2) et u 0 satisfait (9). Alors, u ∈ L q (R × (0, ∞)) et lim t→∞ t (1-1/p)/2+1/2 u(t) -I ∞ G x (t) p = 0 , p ∈ [1, ∞] ,
où I ∞ est un réel non nul défini par [START_REF] Gilding | The Cauchy problem for u t = ∆u + |∇u| q[END_REF] et G est la solution fondamentale de l'équation de la chaleur.

Considérons ensuite le cas où U 0 ≥ 0 et q ∈ (1, 3/2). L'influence des effets convectifs et diffusifs s'équilibre lorsque t → ∞ et on a le résultat suivant : Théorème 2 Si q ∈ (1, 3/2) et U 0 ≥ 0 vérifie la condition de croissance [START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF], alors

lim t→∞ t (1-1/p)/2+a/2 u(t) -W x (t) p = 0 , p ∈ [1, ∞] ,
où a := (2 -q)/(q -1) et W désigne la solution très singulière de [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF].

Enfin, nous identifions une classe de données initiales u 0 pour lesquelles le comportement en temps grands est régi par la convection.

Théorème 3 Supposons que q ∈ (1, 2) et que U 0 ≤ 0 vérifie [START_REF] Smoller | Shock waves and reaction-diffusion equations[END_REF]. Alors lim t→∞ t (1-1/p)/q u(t) -N σ,σ (t) p = 0 , p ∈ [1, ∞) , où σ est le réel strictement positif défini par (15) et N σ,σ est la N -onde hyperbolique définie par [START_REF] Ben-Artzi | Decay of mass for a semilinear parabolic equation[END_REF].

Lorsque q ∈ (1, 4/(1 + √ 3)), le Théorème 3 est vrai sans la condition de taille (14) sur u 0 et nous conjecturons qu'il reste valable sans cette condition pour tout q ∈ (1, 3/2).

On notera que, lorsque q ∈ (3/2, 2) et selon la taille de la donnée initiale, on peut observer aussi bien un comportement asymptotique où la diffusion domine qu'un comportement où la convection est prépondérante. De plus, il existe des solutions pour lesquelles les deux effets se compensent [START_REF] Ben-Artzi | The local theory for viscous Hamilton-Jacobi equations in Lebesgue spaces[END_REF].

Les preuves des résultats présentés ici, ainsi que des extensions en dimension supérieure, font l'objet de l'article [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF].

Introduction

The large time behavior of zero-mass solutions to the Cauchy problem

u t -u xx + (|u| q ) x = 0, x ∈ R , t > 0 , (1) u(x, 0) = u 0 (x), x ∈ R , (2)
is investigated when q > 1, under the main assumption

u 0 ∈ L 1 (R, (1 + |x|) dx) ∩ W 1,∞ (R) , u 0 ≡ 0 and R u 0 (x) dx = 0 . (3)
The equation ( 1) includes two competing effects, namely the diffusion u xx and the nonlinear convection (|u| q ) x , and the main issue in the study of the large time asymptotics is to figure out whether one of these effects dominates for large times. For integrable initial data with non-zero mass, i.e.,

u 0 ∈ L 1 (R) and R u 0 (x) dx = M = 0 ,
this question has already been investigated and the outcome may be summarized as follows: if q > 2, the large time dynamics is dominated by the diffusion and u behaves as the fundamental (or source-type) solution M G to the linear heat equation with G(x, t) = (4πt) -n/2 exp(-|x| 2 /(4t)) for (x, t) ∈ R × (0, ∞), see, e.g., [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF]. If q ∈ (1, 2) and either u 0 ≥ 0 (or u 0 ≤ 0) [START_REF] Escobedo | Asymptotic behavior and source-type solutions for a diffusion-convection equation[END_REF] or

inf x∈R x -∞
u 0 (y) dy ≤ 0 (4) [START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF], the convection term is preponderant for large times and there is σ ∈ R such that u behaves as the N -wave solution N σ,σ+M to the nonlinear conservation law z t + (|z| q ) x = 0. Moreover, σ = 0 if u 0 ≥ 0, σ = -M if u 0 ≤ 0 and σ ≥ 0 under the assumption (4). Recall that the N -wave solution N α,β is given explicitly by

N α,β (x, t) =        sign x • |x| qt 1/(q-1) , -q α q -1 (q-1)/q ≤ x t 1/q ≤ q β q -1 1/(q-1) , 0 otherwise , (5)
for α ≥ 0 and β ≥ 0 (see, e.g., [START_REF] Smoller | Shock waves and reaction-diffusion equations[END_REF]). When q = 2, there is a balance between the diffusive and convective terms and u behaves as the unique self-similar source-type solution S M to (1), that is, S M is the unique solution to [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF] with initial datum M δ [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF].

The previous results remain of course valid when M = 0. However, when q ≥ 2, they reduce to the convergence of u(t) to zero in L 1 (R), while if q ∈ (1, 2) and ( 4) is fulfilled, the possibility that σ = 0 is not excluded in [START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF]. Obtaining non-vanishing intermediate asymptotics in the zero-mass case thus seems to be more delicate, and is the purpose of this note. On the one hand, we identify conditions under which the constant σ defined previously does not vanish, thus leading to a truly hyperbolic large time behavior. On the other hand, we complete the study performed in [START_REF] Karch | On zero mass solutions of viscous conservation laws[END_REF] where conditions on the initial data u 0 are found for which the diffusion still plays a role in the large time asymptotics. Indeed, under the assumption that there is β ∈ (0, 1) such that sup t≥0 t β/2 e t∆ u 0 1 < ∞ if q ≥ 2 and sup t≥0 t β/2 e t∆ u 0 1 is sufficiently small for q ∈ (1+1/(1+β), 2), the large time asymptotics is dominated by the diffusive term and the asymptotics of solutions to (1)-( 2) is described by self-similar solutions to the heat equation [START_REF] Karch | On zero mass solutions of viscous conservation laws[END_REF]. A balance between diffusion and convection is also observed in [START_REF] Karch | On zero mass solutions of viscous conservation laws[END_REF] in the critical case q = 1 + 1/(1 + β) and, for suitably small initial data, the asymptotics of solutions to (1)-( 2) is described by a new class of self-similar solutions to [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF]. ¿From now on, we assume that u 0 fulfils (3). We denote by u = u(x, t) the corresponding solution to (1)-( 2) and set

U (x, t) = x -∞ u(y, t) dy = - ∞ x u(y, t) dy , (6)
the second inequality being true since the integral of u(t) over R vanishes for each t ≥ 0 by [START_REF] Benachour | Global solutions to viscous Hamilton-Jacobi equations with irregular initial data[END_REF]. Owing to (3), it is easy to see that

U 0 := U (0) belongs to L 1 (R) ∩ L ∞ (R) with R U 0 (x) dx = - R xu 0 (x) dx ,
and it readily follows from (1) that U is a solution to the viscous Hamilton-Jacobi equation

U t -U xx + |U x | q = 0, x ∈ R, t > 0, (7) U (x, 0) = U 0 (x), x ∈ R . ( 8
)
This observation is the basis of our approach towards the study of the large time behavior of zero-mass solutions to (1)-( 2), since we will actually investigate the large time dynamics of U and then deduce corresponding results for u.

Diffusion-dominated case

We begin with the case when the diffusive term is preponderant for large times.

Theorem 1 Assume that u 0 fulfils (3) and that one of the following assertions hold true:

(i) U 0 ≥ 0 and q > 3/2, (ii) U 0 ≤ 0 and q ≥ 2, (iii) U 0 ≤ 0, q ∈ (3/2, 2), and

R xu 0 (x) dx u 0 2q-3 ∞ is sufficiently small. (9)
Then, u ∈ L q (R × (0, ∞)), the constant I ∞ defined by

I ∞ := -lim t→∞ R xu(x, t) dx = - R xu 0 (x) dx - ∞ 0 R |u(x, s)| q dx ds (10) is well-defined with I ∞ > 0 if U 0 ≥ 0 and I ∞ < 0 if U 0 ≤ 0, and
lim t→∞ t (1-1/p)/2+1/2 u(t) -I ∞ G x (t) p = 0 for every p ∈ [1, ∞] . (11)
A result similar to Theorem 1 is also valid for U [1, Theorems 2.1 & 2.3]. The proof of Theorem 1 splits in two steps: first, the fact that u ∈ L q (R × (0, ∞)) and I ∞ ∈ R \ {0} under the assumptions of Theorem 1 follows from [START_REF] Benachour | Global solutions to viscous Hamilton-Jacobi equations with irregular initial data[END_REF][START_REF] Ben-Artzi | Decay of mass for a semilinear parabolic equation[END_REF] in the case (i) and [START_REF] Ph | Souplet On the growth of mass for a viscous Hamilton-Jacobi equation[END_REF] in the case (ii) and (iii). Next, the proof of ( 11) and its analogue for U relies on the representation of U by the Duhamel formula and L ∞ -and L q -estimates on ∂ x U = u established in [START_REF] Benachour | Global solutions to viscous Hamilton-Jacobi equations with irregular initial data[END_REF][START_REF] Gilding | The Cauchy problem for u t = ∆u + |∇u| q[END_REF] and [START_REF] Ph | Souplet On the growth of mass for a viscous Hamilton-Jacobi equation[END_REF], respectively, from which the estimates

sup t>0 t 1/2 u(t) 1 + sup t>0 {t u(t) ∞ } < ∞
follow. Classical properties of the heat semi-group e t∆ then allow us to complete the proof of Theorem 1.

Convergence towards very singular solutions

Our next theorem is devoted to the case q ∈ (1, 3/2) and U 0 ≥ 0 where there is a balance between the diffusive and convective effects, and a particular self-similar solution of (1) appears in the large time asymptotics.

Theorem 2 Suppose that u 0 fulfils (3). If q ∈ (1, 3/2) and U 0 is nonnegative and satisfies

lim |x|→∞ |x| a U 0 (x) = 0 with a = 2 -q q -1 , (12)
then lim t→∞ t (1-1/p)/2+a/2 u(t) -W x (t) p = 0 (13)

for every p ∈ [1, ∞],
where W is the very singular solution to [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF] and enjoys the self-similarity property

W (x, t) = t -a/2 W (xt -1/2 , 1) for (x, t) ∈ R × (0, ∞).
Note that a > 1 for q < 3/2, hence the convergence rate towards the self-similar profile in ( 13) is faster than the rate in [START_REF] Karch | On zero mass solutions of viscous conservation laws[END_REF].

We recall that a very singular solution W to ( 7) is a classical solution to [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF] in R × (0, ∞) which has a singular behavior as t → 0, namely lim t→0 {|x|≥r} W (x, t) dx = 0 and lim t→0 {|x|≤r} W (x, t) dx = ∞ for each r > 0. The existence and uniqueness of the very singular solution to [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF] are established in [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption. II -Uniqueness[END_REF][START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption I. Existence[END_REF]. The proof of Theorem 2 relies on a rescaling method together with some estimates from [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption I. Existence[END_REF]. More precisely, introducing the sequence of rescaled functions U k (x, t) := k a U (kx, k 2 t), k ≥ 1, an easy computation shows that U k is a solution to [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF] while it follows from [START_REF] Benachour | Very singular solutions to a nonlinear parabolic equation with absorption I. Existence[END_REF] that sup t>0 t (a-1)/2 u(t) 1 + t a/2 U (t) ∞ + t (a+1)/2 u(t) ∞ < ∞ .

Owing to these estimates, one can show that a subsequence of (U k ) converges towards W in L p (R) for every p ∈ [1, ∞]. The uniqueness of the very singular solution to [START_REF] Escobedo | Large time behavior for convection-diffusion equations in R N[END_REF] and the use of the Duhamel representation formula allow to extend the previous convergence to the whole sequence (U k ) and also to its first derivative, thus completing the proof of Theorem 2.

Hyperbolic-dominated case

We end up with the case when the large time behavior is ruled by the convection term and is given by self-similar solutions to the nonlinear conservation law z t + (|z| q ) x = 0. Theorem 3 Consider q ∈ (1, 2). Assume that u 0 fulfils (3) and that U 0 is non-positive and such that

U 0 ∞ u 0,x 1-2/q ∞ is sufficiently large. ( 14
) Then σ := lim t→∞ u(t) ∞ ∈ (0, ∞) (15)
and lim t→∞ t (1-1/p)/q u(t) -N σ,σ (t) p = 0 (16) for every p ∈ [1, ∞), N σ,σ being the N -wave solution to z t + (|z| q ) x = 0 defined by [START_REF] Ben-Artzi | Decay of mass for a semilinear parabolic equation[END_REF].

In addition, if q ∈ (1, 4/(1 + √ 3)), the previous result is valid without the condition ( 14) on u 0 .

As a consequence of Theorems 1 and 3, we realize that, when q ∈ (3/2, 2), both diffusion-dominated and hyperbolic-dominated large time behaviors are possible, according to the size of u 0 . In addition, when q ∈ (3/2, 2), there are non-positive initial data for which the large time behavior is governed by a balance beween the diffusive and convective effects: indeed, self-similar solutions to (7) of the form t -(2-q)/(2(q-1)) V (|x|t -1/2 ) are constructed in [START_REF] Ben-Artzi | The local theory for viscous Hamilton-Jacobi equations in Lebesgue spaces[END_REF] and V and its derivatives are smooth and decay exponentially as |x| → ∞.

The main step of the proof of Theorem 3 is to show (15). For that purpose, we use the unilateral estimate U xx (x, t) = u x (x, t) ≤ min u 0,x ∞ , C(q) U 0

(2-q)/q ∞ t -2/q . (17) This inequality can be seen as a weak form of the Oleinik gradient estimate for scalar conservation laws and is also derived in [START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF] (see also [START_REF] Feireisl | The L 1 -stability of constant states of degenerate convection-diffusion equations[END_REF] for related estimates). We however establish a version of (17) in a multi-dimensional setting involving the Hessian matrix of U [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF]. The proof of (17) follows from (1) by the maximum principle and the L ∞ -estimate u(t) ∞ ≤ C(q) U 0 1/q ∞ t -1/q [START_REF] Benachour | Global solutions to viscous Hamilton-Jacobi equations with irregular initial data[END_REF][START_REF] Gilding | The Cauchy problem for u t = ∆u + |∇u| q[END_REF]. Once (15) is established, the proof of ( 16) is performed by a classical rescaling method [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF][START_REF] Kim | An Oleinik type estimate for a convection-diffusion equation and convergence to N -waves[END_REF].

Remark 1. (a) Though the conditions ( 9) and ( 14) do not involve the same quantities, it can be shown by an application of Gagliardo-Nirenberg inequalities that, if ( 9) is fulfilled, the quantity involved in ( 14) is also small. (b) We believe that the condition ( 14) is not necessary when q ∈ (1, 3/2) for Theorem 3 to hold true but have only been able to prove it for 1 < q < 4/(1 + √ 3) < 3/2.

The proofs of the results presented in this note, together with their extension to higher space dimensions are to be found in [START_REF] Benachour | Asymptotic profiles of solutions to viscous Hamilton-Jacobi equations[END_REF].

Acknowledgements. Partial support from the KBN grant 2/P03A/002/24, the POLONIUM project ÉGIDE-KBN No. 05643SE, and the EU contract HYKE No. HPRN-CT-2002-00282, is gratefully ackowledged.


Daugeard Marion
email: marion.daugeard@sorbonne-nouvelle.fr

Isabelle Tritsch
email: isabelle.tritsch@gmail.com

D E Mello-Thery

Neli Aparecida

Thery Hervé

Vincent Dubreuil
email: vincent.dubreuil@univ-rennes2.fr

Arvor Damien
email: damien.arvor@univ-rennes2.fr

Combining socio-economic development with environmental governance in the Brazilian Amazon: The Mato Grosso agricultural frontier

Keywords: Brazilian Amazon, Mato Grosso, agricultural frontier, public policies, environmental governance

Agricultural landscapes of the Southern Brazilian Amazon are the result of eighty years of governmental policies to install a powerful agricultural sector. Yet, this rapid expansion raised important environmental considerations especially with regard to deforestation. The agricultural frontier is thus now facing a huge challenge: to combine socio-economic development with environmental conservation in a context of frontier expansion. Based on a conceptual model of the agricultural frontier, we review historical changes in environmental and development policies in the Brazilian state of Mato Grosso and emphasize their ambivalent trend to both encourage and control the progress of the frontier. We then extend this model with an integration stage where environmental governance and economic development evolve from competing to complementary concepts. At this stage, the efforts to slow down deforestation are accompanied with programs to promote new agricultural practices and support industrialization. Finally, we put into perspective this recent evolution with regards to the underlying reasons for changing the agricultural model, thus considering the agricultural frontier to be at a tipping point where first positive results need to be confirmed in spite of an unstable economic and political situation.

Introduction

Brazil has long been blamed for the severe damage caused by the rapid progress of its agricultural frontier to natural resources and especially to Amazon rainforests and savannahs [START_REF] Fearnside | Soybean cultivation as a threat to the environment in Brazil[END_REF]Laurance et al. 2001;[START_REF] Morton | Cropland expansion changes deforestation dynamics in the southern Brazilian Amazon[END_REF]). As a consequence, for more than a decade, Brazilian policies have faced a huge challenge, that of combining socio-economic development and environmental conservation in a context of frontier expansion. The agricultural frontier now appears to be at a tipping point and efforts are underway to establish effective environmental governance without hampering agricultural development. The spectacular 90 per cent decline in annual deforestation since 2005 [START_REF] Heckenberger | Amazonia 1492: Pristine Forest or Cultural Parkland?[END_REF]) through (i) the decoupling of agricultural expansion and deforestation [START_REF] Gollnow | Policy change, land use, and agriculture: The case of soy production and cattle ranching in Brazil, 2001-2012[END_REF][START_REF] Macedo | Decoupling of deforestation and soy production in the southern Amazon during the late 2000s[END_REF]) and (ii) the adoption of new agricultural practices to reduce pressure on forests (Arvor et al. 2012;[START_REF] Gil | Adoption and development of integrated croplivestock-forestry systems in Mato Grosso, Brazil[END_REF] is the major achievement of this new agro-environmental governance model.

As Brazil is now regarded as one of the few countries to achieve its transition to a major economic power without destroying most of its forests [START_REF] Davidson | The Amazon basin in transition[END_REF], it is important to analyse the past evolution of environmental and development policies that led to the present optimistic expectations of land use sustainability at the agricultural frontier in the Brazilian Amazon [START_REF] Galford | Prospects for land-use sustainability on the agricultural frontier of the Brazilian Amazon[END_REF]. As a complement to recent studies focused on major policy changes in the last decade to explain the recent land use dynamics [START_REF] Gibbs | Brazil's Soy Moratorium[END_REF][START_REF] Nepstad | Slowing Amazon deforestation through public policy and interventions in beef and soy supply chains[END_REF], our objective is to review the long term policies that shaped the Amazon agricultural frontier. In this regard, we focused our analysis on the state of Mato Grosso, where the trade-offs between development and conservation are exacerbated by the extent and rapidity of land use changes, the economic importance of the agricultural sector and the social and cultural differences between main stakeholders. To this end, we use the frontier model proposed by [START_REF] Defries | Land-use choices: balancing human needs and ecosystem function[END_REF] and evidence the emergence of an additional stage where environmental governance and economic development evolve from competing to complementary concepts.

Environmental and development policies on the Mato Grosso soybean agricultural frontier

The state of Mato Grosso (906,000 km²) is located in the southern part of the Legal Amazon (the part of Brazil's territory recognized as Amazonia by law, fig. 1). It is characterized by the presence of an active pioneer frontier that raises important social and environmental concerns.

The frontier concept has long been studied in geography, especially in the United States [START_REF] Turner | The Frontier in American History[END_REF] and Brazil [START_REF] Becker | Signification actuelle de la frontière: une interprétation géopolitique à partir du cas de l'Amazonie brésilienne[END_REF][START_REF] Droulers | Amazonie: la fin d'une frontière?[END_REF][START_REF] Léna | Aspects de la frontière amazonienne[END_REF][START_REF] Monbeig | Pionniers et planteurs de São Paulo[END_REF][START_REF] Théry | Franges pionnières d'hier et d'aujourd'hui[END_REF]. Pioneer frontiers are characterized by a mosaic of landscapes that are reflected in the wide range of spatial occupation models (Arvor et al. 2012;[START_REF] Dubreuil | Paysages et fronts pionniers amazoniens sous le regard des satellites: l'exemple du Mato Grosso[END_REF]). In agreement with that view, [START_REF] Defries | Land-use choices: balancing human needs and ecosystem function[END_REF] and [START_REF] Foley | Global Consequences of Land Use[END_REF] suggested understanding and modelling such frontiers using landscape analysis. These authors state that changes in the pioneer frontier take place in five successive stages, which can be defined by specific land use transitions (fig. 2). The pre-settlement stage describes the original stage in a territory before the pioneer frontier begins to evolve. Landscapes are dominated by wildlands.

The second stage, the occupation stage, begins with the arrival of the first settlers who start to clear the wildland (usually for timber or subsistence agriculture), whose area consequently decreases. The third stage, the consolidation stage, begins when small scale farms are replaced by large scale farms that cultivate commodities for sale on national and international markets. This process of agricultural expansion is hindered when access to new lands for expansion becomes too costly. In this case, farmers need to intensify their agricultural practices to ensure they can continue to develop. This is the intensification stage (fourth stage). The intensive stage is characterized by a large proportion of the agricultural area cultivated using intensive practices. In parallel, the development of profitable agriculture attracts new migrants and the towns grow bigger. As the population becomes urbanized, new considerations regarding environment and quality of life appear, allowing the emergence of new protected areas. Although this model appears to be linear, it is noteworthy that the frontier does not change constantly, either in space, or in time. Transition dynamics are both multiple and reversible, and the progress of the demographic and economic occupation of the territory is variable [START_REF] Lambin | Land use transitions: Socio-ecological feedback versus socio-economic change[END_REF]. One should thus keep in mind that: (i) land use transitions between the stages of the pioneer frontier are not unidirectional, that is a cultivated area can be abandoned and regenerate secondary forest (see the forest transition concept; [START_REF] Barbier | The forest transition: Towards a more comprehensive theoretical framework[END_REF][START_REF] Mather | The forest transition: a theoretical basis[END_REF][START_REF] Rudel | Forest transitions: An introduction[END_REF] or intensive practices may be abandoned due to financial restrictions; (ii) not all the stages of the pioneer frontier may affect a given territory, for example one would not expect protected areas to ever be cleared; (iii) the duration of each stage may vary depending on the location and the period. For instance, the entire process of transition from wildlands to intensive agriculture took thousands of years in Europe, whereas it is expected to last only a few decades in recently colonized areas like Amazonia [START_REF] Defries | Land-use choices: balancing human needs and ecosystem function[END_REF]). In the following sub-sections, we apply the model proposed by [START_REF] Defries | Land-use choices: balancing human needs and ecosystem function[END_REF] as a conceptual framework to analyse the evolution of development and environmental policies in each of the five stages of the pioneer frontier in the specific case of Mato Grosso.

Pre-settlement stage

Before first European settlers arrived in Mato Grosso, the territory was inhabited by indigenous populations (today, there are around 42,538 indigenous people which equals 1,4% of the total population of the state). At this time, the primitive vegetation, either Brazilian savannah (Cerrado), Pantanal or Amazonian forest, was largely preserved although largescale transformation of landscapes had already taken place in places now considered to be pristine [START_REF] Barlow | How pristine are tropical forests? An ecological perspective on the pre-Columbian human footprint in Amazonia and implications for contemporary conservation[END_REF][START_REF] Heckenberger | Amazonia 1492: Pristine Forest or Cultural Parkland?[END_REF][START_REF] Willis | How "Virgin" Is Virgin Rainforest?[END_REF]). The settlement of Mato Grosso by non-indigenous populations began in the southern regions of the state (based on current boundaries). The bandeirantes moved to Mato Grosso in the 17 th century to ranch or mine gold, and to capture indigenous inhabitants to be sold as slaves in other areas such as São Paulo. In the 18 th century, during peak gold mining activity, a few towns were created including Diamantino (whose name comes straight from diamond mining) and the capital of Mato Grosso, Cuiabá, which, for a while, was the third biggest city in Brazil [START_REF] Nédélec | Modélisation de la colonisation agricole et de la déforestation dans le nord du Mato Grosso: approche multiscalaire par télédétection[END_REF][START_REF] Siqueira | História de Mato Grosso: da ancestralidade aos dias atuais[END_REF]).

Occupation stage

Although a few settlements had already started to practice agriculture and ranching in the southern regions of the state in the 18 th century, the spatial occupation of Mato Grosso really began in the 1930s with the first governmental colonization programs in Amazonia. These programs were based on a development oriented (desenvolvimentista) model that remained unquestioned until the mid-1980s [START_REF] Drummond | Brazilian Environmental Laws and Policies, 1934-2002: A Critical Overview[END_REF]. In 1937, the authoritarian federal government led by President Getúlio Vargas (1934-1945and 1951-1954) presented a plan to conquer the Amazon basin: the 'March towards the West' (Marcha para o Oeste). There were two main reasons for implementing this plan: 1) to ensure national sovereignty in this distant region, and 2) the United States policy of helping Brazil to expand rubber production in the Amazon during the Second World War [START_REF] Droulers | Amazonie: la fin d'une frontière?[END_REF]. The plan led to the first occupations of the Cerrado biome in the states of Mato Grosso, Goiás and Paraná [START_REF] Droulers | Brésil: une géohistoire[END_REF]. After the Second World War, the new democratic Brazilian government continued to encourage development in the Cerrado and the Amazon basin. The "Legal Amazon" was created in 1953 and financial incentives were offered to attract people there. After 1956, President Kubitschek (1956-1961), who wanted to force Brazil to make 50 years of progress in five [START_REF] Summers | The Post-frontier: Land use and social change in the Brazilian Amazon[END_REF], reinforced the process by the building major infrastructure, including the new Brazilian capital, Brasília (1960), and main roads such as the highways linking Brasilia to Belém (the BR-010, built in 1960) and Cuiabá to Porto Velho (the BR-364, built in 1964). The latter road, which made it possible to cross Mato Grosso from east to west, reinforced the occupation process in the southern part of the state.

The expensive projects proposed at this time were criticized for encouraging inflation and reducing the influence of large-scale property owners [START_REF] Droulers | Brésil: une géohistoire[END_REF][START_REF] Théry | Le Brésil[END_REF]. In 1964, the government was replaced by a military government that remained in power for 20 years, and alternately encouraged colonization by small-scale and large-scale property owners. The Superintendent for the Development of Amazonia (SUDAM) was created in 1966 to manage the 'Operation Amazonia' program aimed at developing, occupying and integrating the Brazilian Amazon in the national economy [START_REF] Banerjee | Toward a Policy of Sustainable Forest Management in Brazil: A Historical Analysis[END_REF]. This program continued with the launch of the National Integration Plan (Portuguese acronym PIN) in 1970, which included an agrarian reform (famous for its slogan: land without men for men without land, terra sem homens para homens sem terra). This reform was led by the newly created National Institute for Colonization and Agrarian Reform (Portuguese acronym INCRA), which encouraged small farmers to migrate to the Amazon [START_REF] Droulers | L'Amazonie[END_REF][START_REF] Tritsch | Population densities and deforestation in the Brazilian Amazon: New insights on the current human settlement patterns[END_REF]. New trans-Amazonian roads were built including the BR-230 (1972) from Cabeledo (state of Paraíba) to Labrea (state of Amazonas), the BR-319 (1973) from Porto Velho to Manaus, the BR-174 (1974) from Manaus to Boa Vista to support the expected migrations.

The north-south BR-163 road linking Cuiabá to the Amazon River harbour of Santarém in the state of Pará was built in 1973 and allowed the occupation of the most northern regions of Mato Grosso.

Consolidation stage

Despite the important projects and the many infrastructures built in the territory by the government, colonization of public land by small-scale farmers did not reach the projected [START_REF] Mahar | Policies affecting land use in the Brazilian Amazon[END_REF]). In Mato Grosso, 33 private colonization companies purchased cheap public land (terras devolutas) from the government of the state or from the federal government in order to set up 88 colonization projects that served as a basis for the development of agricultural activities [START_REF] Nédélec | Modélisation de la colonisation agricole et de la déforestation dans le nord du Mato Grosso: approche multiscalaire par télédétection[END_REF][START_REF] Siqueira | História de Mato Grosso: da ancestralidade aos dias atuais[END_REF]). The occupation of Mato Grosso was thus consolidated through the implementation of a number of isolated spatially-distributed projects, confirming that the progress of the pioneer frontier is made of "breaks and jumps". After the end of the military government in 1984, economics gained the upper hand over geopolitics. Powerful mechanized agriculture was encouraged by policies that limited taxes on land and on agricultural income, favoured large-scale land allocations, and facilitated access to credit [START_REF] Binswanger | Brazilian policies that encourage deforestation in the Amazon[END_REF]. In Mato Grosso, these policies attracted farmers with capital who were interested in the agricultural potential of the large plains [START_REF] Jepson | Private agricultural colonization on a Brazilian frontier, 1970-1980[END_REF]). These farmers mostly came from the southern regions of Brazil (Rio Grande do Sul, Santa Catarina, Paraná), where they had experience in soybean cultivation. Soybean production started in Mato Grosso at that time, and its expansion (from 1.5 million to 8.9 million hectares between 1990 and 2015, fig.

3) relied on favourable politic and economic conditions. In 1994, the government introduced the Plano Real, which reduced inflation and triggered a domestic boom in demand, attracted multinational companies and led to a positive rate of exchange between the Real and the US Dollar which, in turn, led to high soybean prices in Brazil (Valdes 2006) (fig. 4). A few years later (1996), the outbreak of bovine spongiform encephalopathy (BSE) in Europe led to a dramatic increase in the demand for Brazilian soybean scrap since it was the only country where non-GMO soybean was being produced [START_REF] Elferink | Does the Amazon suffer from BSE prevention? Agriculture[END_REF]. Overall, the rapid rise of China's economy implied large demands for agricultural commodities [START_REF] Fearnside | Amazonian forest loss and the long reach of China's influence[END_REF]).

As a consequence, the soybean complex (raw soybean, soy oil and meals) gained into importance at national level so that, in 2016, it represented 37.1% of all exportations of the Brazilian agribusiness sector. It generated more than 28 billion US$ (2015), from which 15 billion originated from exports to China. Soybean is now the first product exported by Brazil and China is its first purchaser (MAPA 2016). Finally, it is worth mentioning that other crops including corn, cotton and sugar cane, were also cultivated.

Intensification stage

As cropped areas expanded, yields also increased rapidly (fig. 3) and Mato Grosso became the main agricultural state in Brazil (28.5 per cent of national soybean production in 2015; IBGE 2016). This increase was strongly encouraged by federal policies. First, since the 1980s, the government encouraged the Brazilian Agricultural Research Corporation (Portuguese acronym EMBRAPA) to develop new varieties adapted to tropical conditions in order to make soybean expansion possible in the Amazon [START_REF] Bertrand | L'avancée fulgurante du complexe soja dans le Mato Grosso : facteurs clés et limites prévisibles[END_REF]). The intensification process continued in the 2000s with the adoption of intensive practices such as double cropping systems (soybean followed by corn or cotton) promoted by national and regional research institutes. Second, a number of multi-annual federal plans (Brasil em Ação, 1996-1999;Avança Brasil, 2000[START_REF] Heckenberger | Amazonia 1492: Pristine Forest or Cultural Parkland?[END_REF]Brasil de todos, 2004Brasil de todos, -2007;;Plano Plurianual, 2008[START_REF] Tnc | Agronegócio e sustentabilidade: Lucas do Rio Verde Legal[END_REF]Plano Mais Brasil, 2012-2015) envisaged continuing investment in huge infrastructure projects aimed at reducing the cost of transport and energy (the planned asphalting of the BR-163 in the state of Pará is one such strategy). These plans were in response to increasing soybean production costs mainly due to Asian rust disease and to the high variability of the Dollar-Real exchange rates. In 2006, production costs exceeded the price paid for soybean (fig. 4), and soybean production areas decreased (fig. 3), illustrating the fact that the agricultural frontier can slow down or even stop, at least temporarily.

While the main political preoccupation was constructing the necessary infrastructure to enable export of agricultural commodities, environmental protection efforts were limited to a few international and federal programs including PPG7 (Pilot Program for the Conservation of Brazilian Rainforests), PNMA-I and -II (Política Nacional do Meio Ambiente I e II). In Mato Grosso, the state government launched the PRODEAGRO (Programa de Desenvolvimento Agroambiental) program in 1992 and the SLAPR system (Sistema de Licenciamento Ambiental de Propriedades Rurais) in 2000 to ensure environmental registration of rural properties. At that time, Mato Grosso was the first Brazilian state to implement such a system but its efficiency has subsequently been proven to be limited [START_REF] Azevedo | O perfil dos desmatamentos em Mato Grosso, após implementação do licenciamento ambiental em propriedades rurais[END_REF]).

Lula's government then adopted the 'Sustainable Amazon Plan' (PAS -Plano Amazônia Sustentável) as an environmental strategy designed for the Legal Amazon. Originally established as a specific part of the Avança Brasil (2000)(2001)(2002)(2003) plan, it became the main project of the Environment Ministry, prioritizing transversal efforts across the Amazon.

However, in Mato Grosso, the intensification process remained a priority, and the implementation of the environmental plan consequently increased tensions between producers and environmentalists. As a result, the environmental initiatives made no significant progress and deforestation and agricultural intensification continued to increase, and the state of Mato Grosso only integrated the PAS in 2006.

Intensive stage

Although crop expansion (land occupation and consolidation stages) and intensification processes (intensification stage) are still ongoing preoccupations in Mato Grosso, it is worth noting that recent decades have also been characterized by urbanization and the creation of new protected areas, which according to the theory of DeFries et al. ( 2004) (fig. 2), are indicators of the final intensive stage. In Mato Grosso, official statistics from (IBGE 2016) show that the urban population has increased dramatically since the 1970s (from 239,524 inhabitants in 1980 to 2,482,801 inhabitants in 2010; fig. 6) while the rural population remained nearly constant over the same period (552,321 inhabitants, i.e. 82 per cent of the population is urban). As such, the deforestation in Mato Grosso is considered as de-linked from migration [START_REF] Perz | Population, Land Use and Deforestation in the Pan Amazon Basin: a Comparison of Brazil, Bolivia, Colombia, Ecuador, Perú and Venezuela[END_REF]). In the meanwhile, a more environmentally aware and more organized civil society emerged, which affected new positive regulations in the Brazilian environmental laws and policies as part of an ecological modernization process [START_REF] Drummond | Brazilian Environmental Laws and Policies, 1934-2002: A Critical Overview[END_REF][START_REF] Jepson | A case of contested ecological modernisation: the governance of genetically modified crops in Brazil[END_REF]. Protected areas increased after the establishment of the Secretariat for the Environment (Portuguese acronym SEMA) (Decree 73.030, Oct. 30, 1973) and again with the creation of the National Conservation Unit system (Portuguese acronym SNUC) (Law 9.985, 2000). There are two statuses for legally protected areas in Amazonia: conservation units protected for environmental reasons (including areas under integral protection and areas for sustainable use) and areas protected for social reasons (indigenous lands, traditional populations, and quilombolas). It is noteworthy that both types of protected areas have proved to be efficient as far as the local preservation of the environment is concerned [START_REF] Bruner | Effectiveness of Parks in Protecting Tropical Biodiversity[END_REF]. In 2010, 3,241,178 hectares were protected for environmental purposes in Mato Grosso (Conservation Units, MMA 2015) whereas a further 22,768,647 hectares were defined as indigenous lands (FUNAI 2014), representing 28.7 per cent of the total area of the State (fig. 5).

From competing to complementary development and environmental policies

Whereas the historical process of frontier expansion was characterized by competing development and environmental policies, the last decade has been marked by the establishment of a more effective governance model [START_REF] Tritsch | Transition in environmental governance in the Brazilian Amazon: emergence of a new pattern of socio-economic development and deforestation[END_REF], which both (i) benefits from investments originated from a decade of economic prosperity in the agricultural sector, and (ii) turns compliance to environmental legislation a mandatory condition for future socio-economic development.

The forest code and its recent evolution

The environmental governance model in the Amazon has long been based on the Forest Code, which sets out a framework to control deforestation. This code, originally introduced in 1934 (Decree No. 23.793, 1934) and revised in 1965(Law No 4.771, Sept. 15, 1965), defines subareas in private rural properties such as (i) the Permanently Protected Areas (PPAs), along water bodies and in sloping ground, and (ii) the Legal Reserve Areas (LRAs), corresponding to areas to be preserved in native vegetation, i.e. 80% of the entire property area in the Legal Amazon, 35% in Cerrado areas located in the Legal Amazon and 20% elsewhere. Although the Forest Code has long been recognized as an important policy tool to prevent deforestation, the way it was implemented has been severely criticized, what led to its recent revision [START_REF] Stickler | Defending public interests in private lands: compliance, costs and potential environmental consequences of the Brazilian Forest Code in Mato Grosso[END_REF][START_REF] Tollefson | Brazil set to cut forest protection[END_REF]. After years of debate [START_REF] Roriz | A construção do Código Florestal Brasileiro e as diferentes perspectivas para a proteção das florestas[END_REF], a new Forest Code has been approved, which reduces the requirements for protecting natural vegetation on private farm land [START_REF] Roriz | A construção do Código Florestal Brasileiro e as diferentes perspectivas para a proteção das florestas[END_REF][START_REF] Soares-Filho | Cracking Brazil's Forest Code[END_REF]): (i) PPAs are now included in the computation of the LRAs and (ii) local governments can reduce the proportion of the LRAs from 80% to 50% in states or municipalities where Conservation Units or Indigenous Lands cover more than 65% of the total area (i.e. more than 80% of the municipalities in the Amazon).

On the one hand, the new Forest Code may appear to be disappointing as it grants amnesty for illegal deforestation in 90 per cent of Brazilian rural properties [START_REF] Soares-Filho | Cracking Brazil's Forest Code[END_REF]).

But it is actually the result of a "pragmatic" or "realistic" (Le Tourneau 2015) understanding of (i) the past situation marked by a long history of non-compliance by Brazilian producers;

(ii) the high cost of restoring natural vegetation, and (iii) the interests of the agribusiness sector, which considers environmental legislation as an obstacle to the development of the agricultural sector. In this regard, the Forest Code has been adapted so as not to curtail the socio-economic development.

On the other hand, the new Forest Code also gives possibility for farmers to compensate for their lack of LRAs by protecting natural vegetation outside their farms. While the Forest Code indicates that the compensation must occur in areas that belong to the same biome and thus potentially in another state, the Decree 420/2016 specifies that compensations from Mato Grosso land owners must occur primarily in the state until no land remain available for compensation. Such compensation mechanism also exists at collective scale through the ICMS-Ecológico (Imposto sobre Circulação de Mercadorias e Serviços), which is a tax collected by Brazilian states (Mato Grosso adopted it in 2000) and then redistributed to municipalities according to environmental criteria, such as the presence of protected areas (including indigenous lands in the case of Mato Grosso). In that sense, the new Forest Code and the ICMS-Ecológico can both be conceptualized as compensation systems to reinvest benefits from past socio-economic development towards the reinforcement of the environmental governance model.

New tools to ensure compliance with the Forest Code

The revised Forest Code has been designed to promote a win-win situation, e.g. support agricultural development in already cleared areas and better protect still standing forests. However, such situation can only be achieved if the new legislation is effectively enforced and respected to prevent that the expected economic development support new clearings (as it has been the case during many years). For this reason, new monitoring and licensing systems have been designed and reinforced to detect land use conversions and their corresponding land tenure. [START_REF] Almeida | High spatial resolution land use and land cover mapping of the Brazilian Legal Amazon in 2008 using Landsat-5/TM and MODIS data[END_REF]. This project has recently been extended to the Brazilian cerrado (TerraClass cerrado) which was hitherto understudied although it had long been known to suffer from intense land use conversions.

Secondly, the Rural Environmental Registry (CAR for Cadastro Ambiental Rural, in Portuguese) was implemented in 2012 to ensure compliance of rural private properties with the new Forest Code. The CAR implies the registration of PPAs and LRAs of all rural private properties on the SiCAR platform (Sistema Nacional de Cadastro Ambiental Rural) with the exception of few states which implemented their own system. In the state of Mato Grosso, 176.870 properties had been registered by September 2016, that is about 93% of all properties (SFB 2016). A major reason for the acceptance by land owners to contribute to the CAR system relies on the fact that registration is mandatory to get access to credit [START_REF] Salomon | O novo Código Florestal e a regularização do passivo ambiental dos imóveis rurais: o caso de Querência[END_REF]. As a result, [START_REF] Assunção | Does Credit Affect Deforestation? Evidence from a Rural Credit Policy in the Brazilian Amazon[END_REF] estimated that one third of the rural credit (i.e. around R$2.9 billion) have not been allocated between 2008 and 2011, what resulted in about 2.700 km² of avoided deforestation. Secondly, after realizing that 36 municipalities were responsible for 45% of the 2007 Amazon deforestation, the Ministry of Environment pointed at the collective responsibility of farmers through the public release of a list of Prioritary Municipalities [START_REF] Assunção | Municípios Prioritários: Reputação ou Fiscalização?[END_REF]. Frozen credit and targeted operations from IBAMA on these listed municipalities thus allowed to significantly curb the deforestation rates. In Mato Grosso, 24 municipalities were put on that list between 2008 and 2011, and thus came under the spotlight. In Alta Floresta, one of these municipalities which suffered economically from being on that list, the mayor thus expresses his thoughts as follows: "We thought we were pathfinders, and we suddenly became bandits!". But Alta Floresta finally received R$ 2.8 million from the Amazon Fund and then become one of the first municipality to leave the list in 2012.

Obviously, turning such punitive measures effective requires important efforts to penalize environmental offenders. While studies after the establishment of the Environmental Crimes Law (Lei de Crimes Ambientais, Law No. 9.605, 1998) estimated that less than 10 per cent of the fines for illegal clearings claimed by the Brazilian Institute of Environment (IBAMA) were actually paid by the culprits [START_REF] Barreto | A Impunidade de Infratores Ambientais em Áreas Protegidas da Amazônia. IMAZON[END_REF], Telles do Vale (2016) now emphasizes on the impressive recruitments that were necessary to join a staff of 10.000 environmental officers and over 1.000 prosecutors that enable IBAMA to organize many operations against deforestation (e.g. Curupira operation in 2004, Arco do Fogo operation in 2008). In 2013, 3.500 fines for illegal clearings in the Legal Amazon were attributed, corresponding to a collected value of R$ 1.5 billion (Telles do Vale 2016).

Towards a new integrated agricultural model

The efforts to integrate environmental considerations in the socio-economic development model are exacerbated in the case of the agricultural sector. As agricultural intensification has been severely criticized due to its impacts on ecosystem services [START_REF] Matson | Agricultural Intensification and Ecosystem Properties[END_REF][START_REF] Tilman | Colloquium Paper: Global environmental impacts of agricultural expansion: The need for sustainable and efficient practices[END_REF][START_REF] Tilman | Agricultural sustainability and intensive production practices[END_REF], new agricultural practices respecting the basics of Conservation agriculture (FAO 2015) are thus promoted to initiate an ecological intensification process [START_REF] Cassman | Ecological intensification of cereal production systems: Yield potential, soil quality, and precision agriculture[END_REF]. Such process lies on the adoption of a whole-landscape approach that emphasizes the role of tropical agricultural landscapes to achieve multiple objectives such as food production, biodiversity conservation, climate mitigation, etc (DeFries and Rosenzweig 2010). On the other hand, the 2005-2006 crisis (see the negative profits on figure 4) forced the agricultural sector to review its economic model by (i) signing voluntary zero-deforestation agreements to ensure access to global markets and (ii) initiating a "verticalization" process intended to transform raw materials on site.

The ABC program

At the Brazilian scale, the ecological intensification process is being supported through the implementation of the ABC plan ("Plano para uma Agricultura de Baixo Carbono", i.e. Low Carbon Agriculture program) in 2010 by the Ministry of Agriculture (MAPA -Ministério da Agricultura, Pecuária e Abastecimento), as part of the national policy on climate change. The objectives of the ABC plan concern the restoration of degraded pastures, the promotion of integrated crop-pasture-forest systems, the generalization of no-tillage practices, the improvement of biological nitrogen fixation, the increase in forest plantations, the animal waste recycling and the adaptation to climate change. The state of Mato Grosso, due to its strategic position in the national agricultural sector, assumes its role of leadership for the adoption of new environmental-friendly practices. For example, no-tillage practices, which mainly consists in planting a second crop after the soybean harvest in order to improve the quality of the soil by limiting erosion and by retaining water for a longer period [START_REF] Landers | How and why the Brazilian zero tillage explosion occurred[END_REF][START_REF] Scopel | Impacts des systèmes de culture en semis direct avec couverture végétale (SCV) sur la dynamique de l'eau, de l'azote minéral et du carbone du sol dans les Cerrados brésiliens[END_REF], have been widely adopted. The CONAB (Companhia Nacional de Abastecimento) estimates that 90 per cent of the area under soybean is sown under no-tillage conditions in Sorriso and Lucas do Rio Verde, two main agricultural municipalities). Also, integrated systems such as crop-livestock systems, livestock-forestry systems, crop-forestry systems and crop-livestock-forestry systems are now promoted by research institutes and already covers about 500,000 ha in Mato Grosso, of which 89 per cent are crop-livestock systems [START_REF] Gil | Adoption and development of integrated croplivestock-forestry systems in Mato Grosso, Brazil[END_REF]. Finally, collaborative initiatives to promote reforestation merit special emphasis, such as the Lucas do Rio Verde Legal project [START_REF] Tnc | Agronegócio e sustentabilidade: Lucas do Rio Verde Legal[END_REF] or the Y Ikatu Xingu campaign launched in 2004. As an example, the Sorriso Vivo project encouraged farmers to reforest 600 ha of riparian forests with native species in the municipality of Sorriso between 2006 and 2009 in order to comply with the Forest Code [START_REF] Arvor | Développement, crises et adaptation des territoires du soja au Mato Grosso: l'exemple de Sorriso[END_REF].

Although this area may seem quite small compared with the area under soybean in that municipality (around 600,000 ha), this process is evidence for the appearance of new environmental considerations (Le [START_REF] Tourneau | Assessing the impacts of sustainable development projects in the Amazon: the DURAMAZ experiment[END_REF] .

Market-oriented agreements to promote new agricultural practices

While the ABC program serves as a framework to orient the agricultural sector towards a new development model, the concrete promotion of new agricultural practices is mainly the result of market-oriented agreements involving the cooperation of various stakeholders, e.g. NGOs, farmers associations, private companies and public authorities. This type of cooperation started in 2006 with the launch of the Soy Moratorium, whose objective was to reduce the impacts of soybean expansion on deforestation: farmers who grew soy on land cleared after 26 July 2006 were no longer able to sell to participating buyers [START_REF] Nepstad | Slowing Amazon deforestation through public policy and interventions in beef and soy supply chains[END_REF]). The reference date has now been changed to 22 July 2008 under the frame of the new Forest Code (ABIOVE 2016). The Soy Moratorium was launched a few months after Greenpeace published a report stressing the link between soy production and deforestation [START_REF] Greenpeace | Eating up the Amazon[END_REF]) and signed by members of the Brazilian Association of Vegetable Oil Industries (ABIOVE) and the Brazilian Cereal Exporters Association (ANEC), which include the ADM, Amaggi, Bunge, Cargill, Dreyfus and Fiagril private companies. A working group, the Soybean Working Group (GTS in Portuguese), now supported by several NGOs (WWF Brazil, IPAM, CI Brazil, TNC and Greenpeace), was then created to monitor the implementation of the agreement [START_REF] Gibbs | Brazil's Soy Moratorium[END_REF]. In 2008, the Brazilian government (Ministry of Environment), the Brazilian Space Agency (INPE) and the Bank of Brazil entered the group. In Mato Grosso, remote-sensing based analysis emphasized the effectiveness of the Soy Moratorium [START_REF] Azevedo | Commodity production in Brazil: Combining zero deforestation and zero illegality[END_REF][START_REF] Rudorff | The Soy Moratorium in the Amazon Biome Monitored by Remote Sensing Images[END_REF].

Three years after the Soy Moratorium, the Beef Moratorium (2009) was established in the State of Pará to hamper deforestation due to pasture expansion, which partially resulted from soy expansion on pastures through indirect land use changes [START_REF] Arima | Statistical confirmation of indirect land use change in the Brazilian Amazon[END_REF]. The Federal Public Ministry (MPF) and NGOs pressured the beef sector by punishing farmers producing livestock on illegally cleared areas and by forcing industries not to buy products from these farms through the establishment of Conduct Adjustment Agreements (Termos de Ajustamento de Conduta, [START_REF] Gibbs | Did Ranchers and Slaughterhouses Respond to Zero-Deforestation Agreements in the Brazilian Amazon?: Brazil's zero-deforestation pacts[END_REF]. Such agreements were then exported to other states, including Mato Grosso, Acre, Rondônia, Amazonas, so that they are now signed by two thirds of beef industries in the Legal Amazon inspected by Federal Inspection Service (SIF) of the Ministry of Agriculture.

In continuation with these successful voluntary zero-deforestation agreements, the agricultural sector also established new partnerships to encourage the adoption of new environmentallyfriendly agricultural practices. In 2009, the Brazilian Roundtable on Sustainable Livestock (GTPS) was constituted as a multi-stakeholder initiative that convenes many stakeholders (including producers, industries, commerce and services, civil society organizations, research and academic institutions, and the government) to increase the sustainability of the cattle supply chain (GTPS 2012). In 2012, the Instituto Centro de Vida (ICV) developed the Novo Campo program in the municipality of Alta Floresta (in northern Mato Grosso) to encourage cattle ranchers to adopt new practices developed by Embrapa in an area with a high potential to increase productivity [START_REF] Marcuzzo | Programa Novo Campo: Estratégia de pecuária sustentável na Amazônia[END_REF]. In this regard, the recent announcement (August 2016) of the MacDonald group to exclusively buy Amazonian beef originating from « sustainable » livestock confirms the necessity for farmers to adapt to the continuously evolving market demand and environmental legislation, but overall to consider it as a new opportunity for development.

In the meanwhile, the soybean sector evolved quite similarly. In Mato Grosso, The Nature Conservancy, an international NGO, launched the Lucas do Rio Verde Legal project in 2006 with the objective to turn local rural properties compliant with the socio-environmental legislation, what implied to reduce the use of agrochemicals, reforest the PPAs and respect the social laws such as workers social rights. It has been quickly followed by the Soja Mais Verde project launched in 2007 in Bali (COP 13). These initiatives were then generalized to the entire state by the Mato Grosso Soybean and Corn Producers Association (Aprosoja) through the Soja Plus program (started in 2011(started in , APROSOJA 2016)). In this regard, the final announced objective is to promote the production of a "green" or "sustainable" soybean through an environmental certification supported by the Round [START_REF] Rtrs | Round Table For Sustainable Soy[END_REF]. In 2013, the Amigos da Terra Club (CAT) in partnership with the WWF Brazil, Solidariedad, IDH and Bel company started the project "People that produce and preserve" (in Portuguese "Gente que produz e que preserva") to encourage producers from the municipality of Sorriso to certificate their proprieties.

Industrialization

In addition to the efforts to adapt crop and beef production to emerging environmental considerations, another dimension of the new agricultural model lies in the "verticalization" process. This process aims at diversifying the sources of income by transforming raw agricultural materials on site, thus decoupling the socio-economic development from the frontier expansion and its associated environmental impacts. With the noticeable exception of Manaus where incentives to attract electronic enterprises were introduced in 1967, the economic model developed in the Amazon has always been based on the export of raw materials to other Brazilian regions or to other countries, making it vulnerable to economic fluctuation and resource depletion. To overcome this issue, fiscal incentives programs established in the 1980s enabled firms to invest what they would have paid as income tax in regional enterprises, the latter being granted tax exemption for a 10-year period [START_REF] Anderson | Smokestacks in the rainforest: Industrial development and deforestation in the Amazon basin[END_REF]). Mato Grosso benefited from similar incentives for industrial development after the creation of the Program for Industrial Development of the State of Mato Grosso (Portuguese acronym PRODEI) in 1988 that included special terms for companies concerning for the payment of taxes. This program produced subprograms (PROALMAT, PROARROZ, PROSOJA, PROALCOOL) aimed at the development of agro-industries for the processing of raw material including cotton, rice, soybean and sugar cane. In 2003, PRODEI was replaced by the Program for Industrial and Commercial Development of the State of Mato Grosso (Portuguese acronym PRODEIC) and included compliance with the Mato Grosso Environmental Code. These programs convinced several agro-industrial companies to relocate to Mato Grosso in the last decade in order to process soybeans and other agricultural products.

According to the Federation of Mato Grosso Industry (Portuguese acronym FIEMT), the production of soybean oil and meal increased by 236 per cent and 194 per cent, respectively, between 2001 and 2010 (table 1). Other soybean derived products are also currently produced such as textured protein, glycerin or lecithin, which was not the case in 2001. Finally, another way to profit from soybean consists in raising pigs, poultry or fishes, whose production has also increased dramatically in the last decade, illustrating the recent trend to develop industrial agriculture in Mato Grosso. and the signature of market-oriented agreements (e.g. Soy and Beef moratoriums), which were actually more efficient contain deforestation than public policies [START_REF] Gibbs | Brazil's Soy Moratorium[END_REF].

From an environmental conservation perspective, the dramatic decrease in deforestation observed since 2005 is certainly the first major achievement of this new strategy.

However, the past analysis of the agricultural frontier in the Brazilian Southern Amazon has emphasized a long history of ambivalent development and environmental policies. For this reason, the recent efforts to promote complementary policies at the integration stage should be considered carefully and critically: 1) the reduction in deforestation was enabled by the adoption of a very intensive agricultural model (Arvor et al. 2012) whose impacts on soil and water resources are still understudied, 2) farmers may be changing their way to clear forest in order not to be detected by the new elaborated monitoring systems developed by INPE [START_REF] Richards | Are Brazil's Deforesters Avoiding Detection?: Are deforesters avoiding detection[END_REF], 3) the recent revision of the Forest Code appears to contradict recent efforts towards forest preservation since it tends to cancel the environmental debts of farmers, 4) it is unclear how compensation systems will be effective to protect new areas of native vegetation, 5) markets and banks still do not always differentiate whether a property is in compliance with the Brazilian Forest Code or not before allocating credits (Azevedo et al. All these considerations may actually question the underlying reasons for changing the agricultural model, better evidencing the high potential of the agricultural sector to rapidly adapt to constraining market conditions than witnessing a real willingness to replace the past expansionist agricultural model. The Brazilian Amazon agricultural frontier thus appears to be at a tipping point where first positive results need to be confirmed and validated in spite of an unstable economic and political situation. As a guarantee of its intention to continue in that direction, the State of Mato Grosso, under the frame of its new strategy "Produce, Conserve, Include" (PCI), recently announced ambitious objectives at the COP21: to restore 2.9 million hectares of degraded land by 2030 and ensure the end of illegal deforestation by 2020. But, while the new governance model proved to be efficient to contain deforestation from largescale crop farmers and cattle ranchers, recent studies showed that continuing deforestation despite environmental legislation currently appears to be a sign of socio-economic precariousness [START_REF] Tritsch | Transition in environmental governance in the Brazilian Amazon: emergence of a new pattern of socio-economic development and deforestation[END_REF]. As a consequence, most deforestation is nowadays performed by small-scale farmers so that achieving these objectives require other policies than traditional command-and-control punitive measures and market-oriented agreements.

New incentive measures such as payment for ecosystem services (PES) will especially be required to really turn environmental preservation a source of economic development instead of an obstacle to development [START_REF] Tritsch | Transition in environmental governance in the Brazilian Amazon: emergence of a new pattern of socio-economic development and deforestation[END_REF]. For all these reasons, Mato Grosso may thus remain in the spotlight for a while, still being at the leading edge of the experimentation of innovative governance models in the tropics.

Figure

  Figure 1 about here

  targets. During the National Development Plan (Plano Nacional de Desenvolvimento, PND II) launched in 1975, the government decided to open the Legal Amazon to private capital through the Program for Agricultural, Livestock and Mineral poles in Amazonia (Portuguese name Polamazônia), which emphasized the development of large-scale export-oriented development poles dedicated to mining, livestock and agriculture

Figure

  Figure 3 about here

Figure 5

 5 Figure 5 about here

Figure

  Figure 6 about here

Firstly

  , the National Institute for Spatial Research (INPE) implemented important systems to monitor and quantify land use changes in the Amazon. Beyond the well-known PRODES program (Programa de Cálculo do Desflorestamento da Amazônia) created in 1988 and which produces digital annual deforestation map in the Amazon based on Landsat-TM data since 1997, INPE also developed the DETER program (Near Real Time Deforestation Detection System, based on MODIS data) in 2004 for the near-real time detection of largescale deforestation events within the Legal Amazon. This program was implemented to support land use policies in the Amazon and is now being completed by the DETER-B program based on the use of AWIFS data to detect small deforestation areas less than 25ha. After 2005 and the beginning of the decrease in deforestation rates, new programs emerged such as the DETEX/DEGRAD (2007) to map selective logging in the Amazon and the TerraClass program focused on land use mapping in deforested areas

  3.1.3. Punitive measures to ensure compliance to the Forest Code This last point (the access to credit) actually emphasizes the importance of punitive measures to restrict socio-economic development in environmentally non-compliant areas, at both individual and collective levels. Firstly, the 3.545 resolution of the Brazilian Central Bank (2008) obliges individual land owners to show evidence of their adherence to the Forest Code.

  2015), 6) the emergence of a new soybean frontier in the Brazilian Cerrado (Maranhão, Tocantins, Piaui and Bahia states) or even in Southern Africa[START_REF] Gasparri | The Emerging Soybean Production Frontier in Southern Africa: Conservation Challenges and the Role of South-South Telecouplings: The emerging of soybean frontier in Southern Africa[END_REF]) may counteract the decline of deforestation observed in the Amazon through indirect land use change (ILUC), 7) the on-going construction of numerous hydroelectric dams to support the urbanization and industrialization process[START_REF] Fearnside | Environmental and Social Impacts of Hydroelectric Dams in Brazilian Amazonia: Implications for the Aluminum Industry[END_REF], 8) the expected development of irrigation as a main strategy to adapt to climate change raise important social and environment issues, 9) small-scale agriculture has been set aside from the efforts to "greenwash" the agricultural sector, and 10) the devaluation of the Brazilian Real may support exports and encourage new conversions into croplands[START_REF] Richards | Exchange rates, soybean supply response, and deforestation in South America[END_REF]; see the similarities between the 2015 situation and the early 2000s on figure4).In light of these points, it is worth mentioning that the current Brazilian political and economic crisis may even exacerbate the historical ambivalence between environmental and development policies and jeopardize recent positive results. While political instability has been evidenced to weaken deforestation control in the Amazon[START_REF] Rodrigues-Filho | Election-driven weakening of deforestation control in the Brazilian Amazon[END_REF], the recent Proposta de Emenda a Constituição (PEC241/2016) to restrict government spending may dramatically affect the application of command-and-control measures, which need large investments to be effective. Finally, the nomination of Blairo Maggi, also known as 'The King of Soybean", as Ministry of Agriculture may even represent a new milestone towards the return of a development-oriented agricultural model, and also a return to previous stages of the frontier model.

Figures:Figure 1 .

 1 Figures:

Figure 2 .

 2 Figure 2. Stages of the evolution of the agricultural frontier and the corresponding land use

Figure 3 .

 3 Figure 3. Changes in the area under soybean in Mato Grosso, in soybean yields (Brazil an

Figure 5 .

 5 Figure 5. Increase in urban/rural population and protected areas (indigenous lands and

Figure 6 .

 6 Figure 6. Extended conceptual model of the agricultural frontier including the conservation

  Table on Responsible Soy (RTRS) created in November 2006. By June 2011, first producers were certified in Argentina, Brazil and Paraguay

Table 1 .

 1 Evolution of the industrialization process in Mato Grosso in the 2000s.

		2001		2010		Variation (%)
		US$		US$		US$
	Product	Thousands	Tons	Thousands	Tons	Thousands Tons
	Soybean meal 280.768	1.508.363 1.554.501	4.434.547 454	194
	Soybean oil	37.039	119.940	270.004	403.008	629	236
	Soy lecithin	-	-	6.235	2.028	-	-
	Textured Soy
	Protein	-	-	10.706	17.567	-	-
	Soy Glycerin
	(sub-product of
	biodiesel)	-	-	5.962	33.254	-	-
	Pig	25	17	72.803	30.121	-	-
	Poultry	10.058	11.633	297.682	170.779	2.860	1.368
	Beef	64.105	31.102	734.599	190.783	1.046	513
	(http://www.fiemt.com.br/site/arquivos/689_a_industria_de_mato_grosso_na_1a_decada_do_
	seculo_xxi.pdf)

the agricultural frontier at a tipping-point

  About eighty years after the agricultural frontier began to expand in Mato Grosso, successive federal and state policies have led to the emergence of a "soy-belt" as a new agro-ecosystem at the interface between the forest and cerrado biomes. Many efforts have then been made during the last decade to promote an integrated model of development, characterized by a better balance between environmental conservation, social considerations (supporting compliance with labour laws) and economic development. This was mainly done through an efficient articulation between institutions and sector-specific stakeholders (private companies, NGOs), often supported by international funding, and overall with different interests. These efforts consisted in the establishment of command-and-control punitive measures (e.g. implying effective monitoring and licensing systems to ensure compliance with Forest Code)

Acknowledgements

The authors wish to thank (i) the French National Agency for Research (ANR) which funded the DURAMAZ2 project (grant agreement ANR-11-BSH1-0003), (ii) the USP-COFECUB project "Public Policies and Impacts of Climate Change at Local & Regional Scale on Fragile Areas" (Uc-Sh-131/11) and (iii) the European Union which funded the H2020-MSCA-RISE-2015 ODYSSEA project (Project Reference: 691053).


Alexandre Bérard
email: alexandre.berard@ed.univ-lille1.fr

Olivier Pietquin
email: olivier.pietquin@univ-lille1.fr

Laurent Besacier

Christophe Servan

Listen and Translate: A Proof of Concept for End-to-End Speech-to-Text Translation

Introduction and background

Current speech translation systems integrate (loosely or closely) two main modules: source language speech recognition (ASR) and source-to-target text translation (MT). In these approaches, source language text transcript (as a sequence or as a graph) appears as mandatory to produce a text hypothesis in the target language. In the meantime, deep neural networks have yielded breakthroughs in different areas including machine translation and speech recognition. Current systems have an "encoder-decoder" architecture where a sequence of input symbols (or an input signal) is projected into a continuous low dimensional space and the output sequence is generated from this representation. This type of architecture has been proposed for machine translation [START_REF] Sutskever | Sequence to Sequence Learning with Neural Networks[END_REF][START_REF] Bahdanau | Neural Machine Translation by Jointly Learning to Align and Translate[END_REF] and for automatic speech recognition [START_REF] Chorowski | Attention-Based Models for Speech Recognition[END_REF][START_REF] Chan | Listen, Attend and Spell: A Neural Network for Large Vocabulary Conversational Speech Recognition[END_REF][START_REF] Zweig | Advances in All-Neural Speech Recognition[END_REF]. If we exclude some pioneering attempts to directly translate from a source phone sequence to a target word sequence [START_REF] Besacier | Towards speech Translation of Non Written Languages[END_REF] or to discover a bilingual lexicon from parallel phone-word sequences [START_REF] Godard | Preliminary Experiments on Unsupervised Word Discovery in Mboshi[END_REF], the only attempt to translate directly a source speech signal into target language text is that of [START_REF] Duong | An Attentional Model for Speech Translation Without Transcription[END_REF]. However, the authors focus on the alignment between source speech utterances and their text translation without proposing a complete end-to-end translation system. The same authors [START_REF] Anastasopoulos | An Unsupervised Probability Model for Speech-to-Translation Alignment of Low-Resource Languages[END_REF] also propose to jointly use IBM translation models (IBM Model 2), and dynamic time warping (DTW) to align source speech and target text, but again, only the alignment performance is measured in their work.

Consequently, this paper proposes a first attempt to build an end-to-end speech-to-text translation system, which does not use source language text during learning or decoding. Relaxing the need for source language transcription would drastically change the data collection methodology in speech translation, especially in under-resourced scenarios. For instance, in the former project DARPA TRANSTAC (speech translation from spoken Arabic dialects), a large effort was devoted to the collection of speech transcripts (and a prerequisite to obtain transcripts was often a detailed transcription guide for languages with little standardized spelling). Now, if end-to-end approaches for speech-to-text translation are successful, one might consider collecting data by asking bilingual speakers to directly utter speech in the source language from target language text utterances. Such an approach has the advantage to be applicable to any unwritten (source) language.

Description We compare two end-to-end models: one for standard machine translation, and one for speech translation. Both models are attention-based encoder-decoder neural networks [START_REF] Sutskever | Sequence to Sequence Learning with Neural Networks[END_REF][START_REF] Bahdanau | Neural Machine Translation by Jointly Learning to Align and Translate[END_REF].

Given an input sequence (x 1 , • • • , x A ), the encoder (a multi-layered bidirectional LSTM) produces a sequence of outputs h = (h 1 , • • • , h A ). We initialize the decoder state with s 0 = tanh(W init s A ) where s A is the last state of the encoder. The next states of the decoder are computed as follows:

s t , o t = LST M (s t-1 , Ez t-1 ) (1) s t is the new state of the LSTM, while o t is its output. During training, z t-1 is the previous symbol in the target (reference) sequence. During evaluation, z t-1 is the predicted symbol at the previous time-step. E is the target embedding matrix.

We compute an attention vector d t (over the encoder output h), which is concatenated to the LSTM's output o t :

y t = W proj (o t ⊕ d t ) + b proj d t = attention(h, s t ) (2)
This vector is then mapped to a vector of the same size as the target vocabulary, to compute a probability distribution over all target words. At each time-step t, the greedy decoder picks the word w t with the highest probability according to this distribution.

p(w t |y t-1 , s t-1 ) = sof tmax(W out y t + b out ) (3)
Attention mechanism For text input, we use the same attention model as [START_REF] Vinyals | Grammar as a Foreign Language[END_REF]:

attention(h, s t ) = A i=1 a t i h i (4)
a t i = sof tmax(u t i ) u t i = v T tanh(W 1 h i + W 2 s t + b 2 ) (5)
Convolutional attention For speech input, we use the same attention model as [START_REF] Chorowski | Attention-Based Models for Speech Recognition[END_REF], which uses a convolution filter F to take into account the attention weights at the previous time-step. This allows the attention model to "remember" and not translate the same part of the signal twice. This is especially useful for speech as the input sequence can be quite long.

u t i = v T tanh(W 1 h i + W 2 s t + b 2 + f t,i µ) f t = F * a t-1 (6) W init ∈ R 2m×2m , E ∈ R n× V , W proj ∈ R m×2m , W out ∈ R V ×m , W 1 ∈ R m×m , W 2 ∈ R m×2m , µ ∈ R m , F ∈ R k ,
where n is the embedding size, m the size of the LSTM layers (the state size is 2m), k the size of the convolution filter, and V the target vocabulary size.

Implementation Our implementation is based on the seq2seq model implemented by TensorFlow [START_REF] Abadi | TensorFlow: Large-Scale Machine Learning on Heterogeneous Systems[END_REF]. It reuses some of its components, while adding a number of features, like a bidirectional encoder [START_REF] Bahdanau | Neural Machine Translation by Jointly Learning to Align and Translate[END_REF], a beam-search decoder, a convolutional attention model and a hierarchical encoder [START_REF] Chorowski | Attention-Based Models for Speech Recognition[END_REF]. 4 Our implementation also allows pre-training, multiple encoders [START_REF] Zoph | Multi-Source Neural Translation[END_REF] and multi-task training [START_REF] Luong | Multi-task Sequence to Sequence Learning[END_REF]. Contrary to the reference implementation by TensorFlow, which uses a bucket-based method with static (unrolled) RNNs, we use symbolic loops. This makes model creation much faster, and removes the need to manually configure bucket sizes.

Model settings We describe two models: one for text translation, and one for speech translation.

Both models use a decoder with 2 layers of 256 LSTM units, with word embeddings of size 256. The speech model does not have source embeddings, as the input is already a sequence of vectors (of 40 MFCCs + frame energy). Both encoders are multi-layer bidirectional LSTMs, with 256 units. The text model's encoder has 2 layers. The speech model has a hierarchical encoder with 3 layers, i.e., like [START_REF] Chorowski | Attention-Based Models for Speech Recognition[END_REF], the 2 nd and 3 rd layers read every other output from the previous layer, resulting in a sequence of 1/4th the size of the input. For the text model, we use a standard attention model, while the speech model uses convolutional attention (with a single filter of size 25). The latter also has two fully connected layers of size 256 between the input and the first layer of the encoder.

For training, we use the Adam algorithm with an initial learning rate of 0.001 [START_REF] Kingma | Adam: A Method for Stochastic Optimization[END_REF], and a mini-batch size of 64. We apply dropout (with a rate of 0.5) during training on the connections between LSTM layers in the encoder and decoder [START_REF] Zaremba | Recurrent neural network regularization[END_REF].

Experimental Settings

As we do not have any good-sized speech translation corpus, we generated one with speech synthesis. We decided to use the French→English BTEC corpus, which is a small parallel corpus (see Table 1). BTEC (Basic Travel Expression Corpus) is very clean and contains short sentences (10 words/sentence on average), with a small vocabulary (9218 unique tokens on the French side, 7186 on the English side). This corpus also has multiple references (7 references per source sentence for test1 and test2), which we use for BLEU evaluation. We lowercase and tokenize all the data with the Moses tokenizer.

Synthetic speech was generated using Voxygen5 , a commercial speech synthesis system, for 4 different female voices (Agnes, Marion, Helene, Fabienne) and 3 different male voices (Michel, Loic, Philippe).

It is important to note that this is corpus-based concatenative speech synthesis [START_REF] Schwarz | Corpus-Based Concatenative Synthesis: Assembling sounds by content-based selection of units from large sound databases[END_REF] and not parametric synthesis. So, for each speaker's voice, speech utterances are generated by concatenation of units mined from a large speech corpus (generally around 3000 sentences/speaker). This means that despite having very little intra-speaker variability in our speech data, there is a realistic level of inter-speaker variability. To challenge the robustness of our system to inter-speaker variability, we concatenate the training data for 6 speakers, and leave the last speaker (Agnes) for evaluation only.

Like [START_REF] Chan | Listen, Attend and Spell: A Neural Network for Large Vocabulary Conversational Speech Recognition[END_REF], as input for our speech model, we segment the speech raw data into frames of 40 ms, with a step-size of 10 ms, and extract 40 MFCCs for each frame, along with the frame energy.

Experiments

Table 2 shows the results of our Machine Translation experiments. The main reason why we perform these experiments, is to assess whether it makes sense to train NMT models on such a small and specialized corpus. Our best system (an ensemble of 5 models with a language model) gives similar results in terms of BLEU score to a baseline SMT system. This is rather surprising, considering the small amount of data used. Also, even though the models seem to overfit quite a lot (see train.1000 scores), this does not seem to be a problem during evaluation. Table 3 shows the results of our Speech Translation experiments. Our best results are behind, but not very far from those of the baseline (which uses Google Speech API and a specialized SMT system).

The results on a new speaker (Agnes) are also encouraging, considering that we did not use any speaker adaptation technique.

Figure 1 shows an example of alignment performed by the attention mechanism during training, for text and for speech. We trained our models for 20k steps, which takes less than 2 hours for the text models, and roughly 8 hours for the speech models (on a single GTX 1070).

Conclusion

We proposed a model for end-to-end speech translation, which gives promising results on a small French-English synthetic corpus. These results, however, are to be mitigated due to the synthetic nature of the data: there is not much variability (except across speakers), which makes it easier for the network to learn. In any case, the experiments show that our architecture is able to generalize quite well to a new speaker.

Future work includes the evaluation of this model on non-synthetic data. Some datasets that could be used are: TED talks (there exists a parallel corpus and a speech corpus, but their alignment is not straightforward); or books from the Gutenberg project6 (public-domain books in many languages, along with some human-read audiobooks). We also wish to evaluate this model in a multi-source setting: does it help when translating text to have access to a human-read version of it, or other kinds of information such as part-of-speech or images?

Figure 1 :

 1 Figure 1: Alignments performed by the attention model during training

Table 1 :

 1 On the full corpus, there is on average 9.8 words/sent on the French side, and 9.3 on the English side. On the French audio side (with Agnes as a speaker), there is on average 281 frames/sent (2.8 sec/sent).

	Corpus	Lines	French Words Chars Frames Duration (h) Words Chars English
	BTEC train 19972 201k 1020k 5715k	15:51	189k	842k
	BTEC dev	1512	12.2k 61.9k	357k	0:59	11.5k 50.3k
	BTEC test1	469	3.9k	19.5k	111k	0:18	3.6k	15.6k
	BTEC test2	464	3.8k	19.2k	110k	0:18	3.6k	15.8k
	Corpus	BLEU score Greedy +BeamSearch +LM +Ensemble SMT
	dev		42.5	43.6	45.1	51.6	54.3
	test1		39.8	41.7	43.0	47.1	49.4
	test2		41.0	41.0	42.8	47.9	45.8
	test1 (7 refs)	50.7	53.4	54.7	60.3	60.0
	test2 (7 refs)	47.0	47.3	49.6	55.3	53.2
	train.1000	78.4	80.5	82.9	89.6	76.6

Table 2 :

 2 Results of the Text Translation task on BTEC, under different settings of the decoder.

"Greedy" uses a greedy decoder. "BeamSearch" adds a beam-search decoder with a beam size of 8. "LM" adds an external trigram language model estimated on the target side of BTEC train. "Ensemble" uses a log-linear model with 5 NMT models trained independently (+ language model). The train corpus used in evaluation is a subset of 1000 sentences from BTEC train. For all the non-ensemble configurations, the best model out of 5 is used (according to its score on dev). The SMT baseline is a phrase-based model (Moses) trained on BTEC train, and tuned on BTEC dev.

Table 3 :

 3 Results of the speech translation experiments on BTEC. The models are trained with 6 different speakers (including Michel). Agnes is not used for training. The Ensemble configuration uses 5 models trained independently. The baseline system uses a pipeline Google Speech ASR + SMT system trained on BTEC (we trained a new system on French without punctuation, as Google Speech API does not output any punctuation symbol, except when actually pronounced). The WER scores obtained by the baseline ASR system range between 23% and 26%. The last column from Table2provides a baseline assuming a perfect ASR.

	Corpus	Speaker	BLEU score Greedy +BeamSearch +LM +Ensemble Baseline
	dev		30.1	32.3	33.5	40.2	43.7
	test1	Agnes	29.2	31.9	32.7	38.6	42.1
	test2		29.0	30.6	31.0	37.1	39.6
	test1 (7 refs)	Agnes Michel	37.6 40.6	40.1 43.1	41.8 44.4	48.8 50.4	52.7 51.9
	test2 (7 refs)	Agnes Michel	33.6 37.3	35.6 39.6	36.7 41.0	43.1 46.7	46.7 46.4
	train.1000	Michel	53.8	60.8	61.8	82.6	60.5

Our source code is available online at github.com/eske/seq2seq

www.voxygen.fr

www.gutenberg.org


DynAstVO: the Europlanet orbital Near-Earth asteroid database

Introduction & Context

DynAstVO is a new orbital database dedicated to Near-Earth Asteroids. It presents an independent service for orbits and ephemerides of NEAs. The database also provides information about the orbital uncertainty (covariance matrix) enabling to validate the orbit and to deal with risk assessment in addition to other services (ASTORB, MPCORB, NEODyS and JPL HORIZONS). The database is updated daily in respect to MPECs, accessible through VO protocols and conforms to EPN-TAP environment.

Conclusion and prospectives

DynAstVO provides the orbits, ephemerides, close approaches of NEAs (14807 objects on 10 October 2016). In the short-term future, we plan to extend the database to all minor planets, to provide precision of ephemerides in our service, and to extend the database of close approaches to all planets and some selected asteroids.

Abstract

DynAstVO is a new orbital database dedicated to Near Earth Asteroid orbits, developed within the Europlanet 2020 RI framework. It provides parameters of asteroid orbits: orbital elements, observational information, minimum distance with Earth and planets, ephemeris and in particular, orbit uncertainty and associated covariance matrix. This database is updated daily on the basis of the Minor Planet Electronic Circulars. Orbit determination and improvement are computed as soon as new observations are available or an object is discovered. This database conforms to EPN-TAP environment (Erard et al. 2014) and is accessible through VO protocols or classical web access. Auxiliary data such as SPICE kernels for their ephemerides are provided. Finally, we present a comparison with other classical databases such as Astorb or MPCORB, NEODyS and JPL Horizons.

Processing of DynAstVO

The Minor Planet Center publishes daily MPECs that provide new discovered asteroids and new observations. On the basis of MPECs, DynAstVO proceeds to update or create orbit through the following functional scheme:

DynAstVO is finally built into the EPN-TAP environment (Erard et al., 2015) and accessible through VO protocols or a web access.

Parameters of DynAstVO

For each asteroid, DynAstVO provides: An additional table also provides the orbital elements and the state vector at a current epoch, identical for all asteroids.

Dynamical model and observations

The orbit determination process comes from Desmars (2015) and consists in an integration of equations of motion and variational equations. Orbital elements are determined by a Levenberg-Marquadt algorithm. The dynamical model takes into account the gravitational perturbations of the Sun, the eight planets, the Moon and Pluto (positions are from INPOP13c [START_REF] Fienga | INPOP new release: INPOP13c[END_REF])), the gravitational perturbations of the four main asteroids (Ceres, Pallas, Vesta and Hygiea), the corrections of relativistic effects of the Sun, the flatness of Sun J 2⊙ and the flatness of the Earth J 2⊕ . Corrections from bias in stellar catalogues are applied and the weighting scheme presented in Farnocchia et al. (2015) is used. Observations and radar measurements come from the Minor Planet Center database.

  Dates, minimum distances (and their uncertainties) of close approaches with Mercury, Venus, Earth, Moon and Mars are presented. name, number and designations orbital elements and the state vector at the epoch corresponding approximatively to the middle of the observational period number of observations and radar measurements, dates of first and last observations used for the orbit determination magnitude parameters (H and G slop) covariance matrix and Sky-Plane uncertainty (uncertainty in the position at epoch) Earth-MOID (minimum orbital intersection distance) ephemeris in Spice Kernel format (bsp file) We compare DynAstVO with MPCORB, ASTORB, and NEODyS by computing the apparent position from geocentre at reference epoch. Figures show the difference in position for 2238 numbered NEAs in right ascension and declination. Small differences can be explained by different processes of propagation (as epoch is 2016.11.08 for ASTORB and 2016.07.31 for MPCORB and NEODyS).

  We present comparisons between ephemerides provided by DynAstVO and two other ephemerides service providers (ASTDyS/ NEODyS and JPL HORIZONS) for two characteristic objects (99942 Apophis and newly discovered NEA 2016TU), during 2000-2020.

  Josselin Desmars -email : desmars@imcce.fr DynAstVO database : http://vespa.

  obspm.fr

				EPN-H2020
		Minor Planet
		Center (MPC)	DynAstVO
		database	Functional scheme
	Daily Orbit
	Update
	Detect changes ? Aux. database • Supp. Obs. • Planetary encounters	Extraction Processing Orb. Elemts+ observations	Processing: • Fitting model to obs. • Covar. Matrix • Orbital elements • MOID calculation • Mini. Earth Dist • Uncertainty criterion • Chebychev repres.
	Web access	IMCCE Aux. data	IMCCE DynAstVO Orbital database	VO access

Acknowledgements

This work is done in the framework of Europlanet 2020 RI which has received funding from the European Union's Horizon 2020 research and innovation programme under grant agreement No 654208.