Pierre Le Doussal

Satya N Majumdar

Alberto Rosso

Grégory Schehr

Exact short-time height distribution in 1D KPZ equation and edge fermions at high temperature

Keywords: numbers: 05.40.-a, 02.10.Yn, 02.50.-r

We consider the early time regime of the Kardar-Parisi-Zhang (KPZ) equation in 1 + 1 dimensions in curved (or droplet) geometry. We show that for short time t, the probability distribution P (H, t) of the height H at a given point x takes the scaling form P (H, t) ∼ exp -Φ drop (H)/ √ t where the rate function Φ drop (H) is computed exactly for all H. While it is Gaussian in the center, i.e., for small H, the PDF has highly asymmetric non-Gaussian tails which we characterize in detail. This function Φ drop (H) is surprisingly reminiscent of the large deviation function describing the stationary fluctuations of finite size models belonging to the KPZ universality class. Thanks to a recently discovered connection between KPZ and free fermions, our results have interesting implications for the fluctuations of the rightmost fermion in a harmonic trap at high temperature and the full couting statistics at the edge.

It is by now well known that many stochastic growth models in one dimension belong to the celebrated Kardar-Parisi-Zhang (KPZ) universality class [1][2][3]. These models are usually described by a field h(x, t) that denotes the height of a growing interface at point x at time t. At the center of this class resides the continuum KPZ equation [1] where the height evolves as

∂ t h = ν ∂ 2 x h + λ 0 2 (∂ x h) 2 + √ D ξ(x, t) , (1)
where ξ(x, t) is a Gaussian white noise with zero mean and ξ(x, t)ξ(x , t ) = δ(xx )δ(tt ). We use everywhere the natural units of space x * = (2ν) 3 /(Dλ 2 0 ), time t * = 2(2ν) 5 /(D 2 λ 4 0 ) and height h * = 2ν λ0 . At late times in all these growth models, including the KPZ equation itself, while the average height increases linearly with t, the typical fluctuations around the mean height grow as ∼ t 1/3 [2]. Moreover even the probability distribution function (PDF) of the centered and scaled height is universal and is described by the Tracy-Widom (TW) [4] and Baik-Rains [6,7] distributions, with a parameter that depends on the class of initial conditions (flat, droplet, stationary) [3,[START_REF] Johansson | [END_REF][6][7][8][9][10][11]. Some of these predictions have also been verified in experiments [12][13][START_REF] Halpin-Healy | For a review of recent advances in the KPZ problem[END_REF]. Recently, these late times studies have been extended to compute exactly the large deviations of the height distribution going beyond the TW regime [15], uncovering a third order phase transition [16,17] in growth models belonging to the KPZ universality class, including the KPZ equation itself.

While the distribution of the height fluctuations is thus well understood at late times, in this Letter we study exactly the full distribution of the height fluctuations at small times t 1 in the KPZ equation growing in the curved geometry. Remarkably, our short time results are directly relevant to an apriori different quantum problem of N non-interacting fermions in a one-dimensional harmonic trap. A recent mapping was indeed established between these two problems [18], where the time t in the KPZ equation corresponds to the temperature T in the fermion problem via the relation t ∼ N/T 3 for large N [18]. Thus at T = 0 (t → ∞ limit in the KPZ problem), the rightmost fermion position is described by the TW distribution. Our results for short times t in the KPZ equation thus provide exact predictions for the distribution of the rightmost fermion position at high temperature, providing a generalization of the T = 0 TW distribution.

Before presenting our exact results at short times, it is useful first to recall the late time results in the KPZ equation in the curved geometry. The distribution P (H, t) of the height H at a given space point (suitably centered) takes the form at large times [15]

P (H, t) ∼      e -t 2 Φ-(H/t) , Φ -(z) = |z| 3 12 , z < 0 (2) e -tΦ+(H/t) , Φ + (z) = 4 3 z 3/2 , z > 0 (3)
while the central region H ∼ t 1/3 is governed by the TW distribution associated with the Gaussian Unitary Ensemble (GUE). The result in the right tail in (3), also holds for the flat initial condition.

It is then natural to wonder: are these tails P (H, t) ∼ e -|H| 3 /(12t) (H large negative) and ∼ e -4 3 H 3/2 /t 1/2 (H large positive) visible only at late times, or do they appear even at early times? It is well known that the central typical regime at early times is described by a Gaussianobtained from the Edwards-Wilkinson's (EW) equation [19] setting λ 0 = 0 in the KPZ equation. What about the tails? Recently, Meerson et al. [20] studied this question for the flat initial condition using the weak noise theory (WNT) (see also earlier results [21]), valid for short drop (H) (20). The dashed black lines correspond respectively to the left and right tails given in ( 5), (7) and the solid (purple) line corresponds to the Edward-Wilkinson Gaussian regime (6). Inset: Log-log plot of the left tail compared with the asymptotics [START_REF] Johansson | [END_REF].

times. For the right tail they found ∼ e -4 3 H 3/2 /t 1/2 , i.e. the same leading order result as late times. This shows that the asymptotic right tail is established even at early times. In contrast, for the left tail they found P (H, t) ∼ e -8 15π |H| 5/2 /t 1/2 at early times (in our units). This |H| 5/2 tail behavior for large negative H for flat initial condition is manifestly different from the |H| 3 tail behavior at late times for the droplet initial condition. This raises the question whether this difference is due to the change in initial conditions, or whether early and late time left tails are different for any given initial condition -providing yet another motivation for studying the full PDF P (H, t) at short times in the curved geometry.

In this Letter, we show that the early time PDF P (H, t) for the droplet initial condition takes the form

P (H, t) ∼ exp - Φ drop (H) √ t , (4)
which holds for any value of H and small time t 1, and where Φ drop (H) is given explicitly by Eq. ( 20) below. The asymptotic behaviors of Φ drop (H) are obtained as

Φ drop (H)                4 15π |H| 5/2 , H → -∞ (5)
H 2 √ 2π , |H| 1 (6) 4 3 H 3/2 , H → +∞ . (7)
The first three cumulants of H obtained from Eqs. ( 4) and ( 20) are in agreement with the leading small time behavior obtained in [9], while here we obtain all cumulants. In the case of the flat initial condition one expects a similar form [20],

P (H, t) ∼ e - Φ flat (H) √ t
. However, the function Φ flat (H) has not been obtained explicitly apart from the tails [22, 23] and the first two cumulants [20,24]. Therefore the |H| 5/2 left tail seems to hold for a variety of initial conditions. Interestingly, as discussed below, our main results, Eqs. ( 4) and (20), turn out to be very reminiscent of the universal large deviation fluctuations obtained in the stationary regime of finite-size models in the KPZ universality class [25][26][27][28][29][30][START_REF] Prolhac | Exact methods for the asymmetric simple exclusion process[END_REF].

In addition, in the context of finite temperature free fermions in a harmonic potential, our results provide exact predictions for the fluctuations of the position of the rightmost fermion x max near the edge x edge of the Fermi gas, via the following relation [18] x maxx edge w N ≡ in law h(0, t)

+ t 12 + γ t 1/3 (8)
where ≡ in law means identical PDF's. Here, on the l.h.s. N is large, x edge = √ 2N and w N = N -1/6 / √ 2. On the r.h.s. γ is a Gumbel distributed random variable with PDF given by P (γ) = e -γ-e -γ , independent of the height h(0, t). This equivalence in law is valid in the limit N → +∞, T → +∞ but with the ratio t = N/T 3 fixed. This leads to an exact prediction (27) for the high temperature behavior of the rightmost fermion.

For definiteness we focus on the narrow wedge initial condition, h(x, 0) = -|x|/δln(2δ), with δ 1. This initial condition gives rise to a curved (or droplet) mean profile as time evolves [3,[8][9][10][11]. We focus on the shifted height at a given space point, and define [START_REF]The continuum solution is related to the physical solution up to a non-universal shift (i.e. renormalization). Let us call h phys (x, t) the solution to a physical KPZ problem with a regularized, i.e. smooth noise at small scale. Then, above a correspondingly small time and length scale, the continuum and physical solutions are related as follows h(x, t) =[END_REF]

H(t) = h(x, t) + x 2 4t + t 12 + 1 2 ln(4πt) . (9)
The starting point of our calculation is the exact formula, valid for all times t, for the following generating function, obtained in [8][9][10][11] exp -e H(t)-st

1/3 √ 4πt = Q t (s) (10)
Q t (s) := Det[I -P 0 K t,s P 0 ] (11)
where . . . denotes an average over the KPZ noise. Here Q t (s) is a Fredholm determinant associated to the kernel

K t,s (r, r ) := +∞ -∞ du Ai(r + u)Ai(r + u)σ t,s (u) (12)
defined in terms of the Airy function Ai(x) and the weight functions

σ t,s (u) := σ(t 1/3 (u -s)) , σ(v) := 1 1 + e -v . (13)
In (11), P 0 denotes the projector on the interval r ∈ [0, +∞[. Even though the formal relation in Eq. ( 10) is valid at all times t, extracting from it the height distribution P (H, t) explicitly is very hard. Previously, exact results have been extracted only for large t, both for typical [8][9][10][11] and atypical [15] height fluctuations. Below, we show that the full height distribution P (H, t) for all H can be extracted from (10) at short time t 1. It is convenient to introduce the kernel Kt,s (u, u ) = K Ai (u, u )σ t,s (u ) [START_REF] Halpin-Healy | For a review of recent advances in the KPZ problem[END_REF] defined in terms of the Airy kernel

K Ai (u, u ) = +∞ 0 drAi(r + u)Ai(r + u ) . (15)
From ( 14) and ( 15), one checks that Tr Kp t,s = Tr(P 0 K t,s P 0 ) p for any integer p ≥ 1, which allows us to rewrite [START_REF]We recall that, for a trace-class operator K(x, y) such that TrK = dxK(x, x) is well defined, det(I -K) = exp [-∞ n=1 Tr K n /n], where Tr K n = dx1 • • • dxnK([END_REF] ln Det[I -

P 0 K t,s P 0 ] = ln Det[I -Kt,s ] = +∞ p=1 -1 p Tr Kp t,s (16)
a convenient form to study the small t limit. Indeed, as detailed in [34], we show that, in the limit t → 0 and s → ∞, keeping s = s t 1/3 fixed, the traces Tr Kp t,s in ( 16) take a rather simple form, for any p ≥ 1, given by Tr Kp t,s

I p (s)/ √ t , (17)
where

I p (s) := 1 π 0 -∞ dv |v| (σ(v -s))
p . The series (16) can then be summed up, leading to (using s = s t 1/3 )

ln Q t (s) - 1 √ t Ψ(e -s t 1/3 ) , Ψ(z) = - 1 √ 4π Li 5 2 (-z) ( 18
- z √ 4πt e H(t) ∼ e -1 √ t Ψ(z) (19)
where we use z = e -s . Note that the l.h.s. is finite only for z > 0 (for z < 0 it is infinite). From this, assuming the form (4) and inserting it in (19) for any z > 0, we obtain Φ drop (H) by a saddle point analysis [34], as

Φ drop (H) =              -1 √ 4π min z∈[-1,+∞[ [ze H + Li 5 2 (-z)], H ≤ H c -1 √ 4π min z∈[-1,0[ [ze H + Li 5 2 (-z) -8 √ π 3 (-ln(-z)) 3 2 ], H ≥ H c (20)
where One can also compute the cumulants of the height as, H(t) q c = t q-1 2 φ (q) (0), where φ (q) is the q-th derivative of (6). The triangles, circles and squares correspond respectively to t = 128, t = 256 and t = 512. We see that when t increases the agreement with the short time continuum limit improves.

H c = ln ζ(3/2) =
φ(p) = max H (pH -Φ drop (H)) . (21
We display here the first four cumulants

H 2 c = π 2 t 1/2 , H 3 c = ( 8 3 √ 3 - 3 2
)πt ( 22)

H 4 c = (18 + 15 √ 2 -16 √ 6) π 3/2 3 t 3/2 . ( 23
)
Remarkably, these cumulants are very similar to the ones obtained for the stationary fluctuations of the total integrated particle current for the TASEP on a finite ring [25,26]. This similarity holds for all higher cumulants as well (see [34]). In fact, the generating function associated with these cumulants, called G in [25,26] also appears in the stationary regime of the ASEP and of the KPZ equation on a finite ring [27][28][29][30][START_REF] Prolhac | Exact methods for the asymmetric simple exclusion process[END_REF], and is different, but structurally somewhat similar to our function Ψ. It remains a puzzle why this universal function G describing the late time stationary regime in a finite system should be similar to our short time large deviation function in an infinite system. Our results also describe the high temperature limit of lattice directed polymer models (DP), which allows for a numerical test. We simulate a DP growing on a 2D square lattice with unit Gaussian site disorder. For inverse temperature β 1, the number of steps t corresponds to the time of the continuum model as t = 2 tβ 4 [9] (see [34] for details). The result for P (H, t) is shown in Fig. 2: the data shows (slow) convergence to our prediction.

Fermions in an harmonic trap. Consider now the quantum problem of N non-interacting spinless fermions of mass m in an harmonic trap at finite temperature T , described by the Hamiltonian H = N i=1

p 2 i 2m + 1 2 mω 2 x 2 i . We use x * =
/mω and T * = ω as units of length and energy. At T = 0, i.e., in the ground state, and for large N , the average fermion density is given by the Wigner semi-circle law, with a finite support [-x edge , x edge ] where x edge = √ 2N . At finite temperature, the behavior of physical quantities in the bulk changes on a temperature scale T ∼ N (bulk scaling), while near the edge it varies on a scale T = N 1/3 /b (edge scaling), where b is a dimensionless parameter of order unity [18]. Here we are interested in the position x max (T ) of the rightmost fermion (see [18] for a precise definition). Its cumulative distribution function (CDF) was shown [18] to be given by the same Fredholm determinant as in Eq. ( 11)

Prob

x max (T ) -

x edge w N < s = Q t=b 3 (s) (24)
where w N = N -1/6 / √ 2. Since we have already analysed the small time limit t 1 of the Fredholm determinant Q t (s) (as in Eq. ( 18)), this provides us with an explicit formula for the fermion problem, valid in the high temperature region b 1 of the edge scaling regime. To use the result in (18), we first set s = s/t 1/3 in (24) where t 1/3 = N 1/3 /T . The regime t 1 corresponds to T N 1/3 . This leads us to define a new random variable

ξ = x max (T ) -x edge N (T ) (25)
with

N (T ) := T N -1/3 w N = T / √ 2N (26)
where w N = N -1/6 / √ 2 is the scale of fluctuations of x max at T = 0. Thus N (T ) in (26) sets the scale of fluctuations of x max for T N 1/3 . Using (18) in the limit t = b 3 = N/T 3 1, we find that the CDF of ξ takes the asymptotic form (replacing s by s for convenience)

Prob(ξ < s) ∼ exp T 3 4πN Li 5/2 (-e -s ) . (27)
Using Li 5/2 (y) y for small y, it is easy to see that the PDF of ξ is peaked around the typical value ξ = ξ typ = 1 2 ln(T 3 /4πN ), with typical fluctuations ξ = ξξ typ described by a Gumbel law, i.e., P ( ξ) = e -ξ-e -ξ (see [36] for a similar observation in a related model).

Our formula (27), however, holds beyond the typical fluctuation regime and also describes the large deviations away from ξ typ . While the right tail is exponential, as given by the Gumbel distribution, using

Li 5 2 (-z) z→+∞ -8 15 √ π (ln z) 5
2 in ( 27), we find that the left tail exhibits a distinct, stretched exponential decay Prob(ξ < s) ∼ exp -4 15π

T 3 N |s| 5/2 . (28)
Note that in this edge regime quantum correlations are still important. At much higher temperatures T ∼ N , the positions of the fermions become completely independent variables, and the fluctuation of x max (T ) is also described by a Gumbel distribution, albeit different from the one obtained here [37]. The above method is easily extended to obtain the full counting statistics (FCS) of the fermions near the edge for temperatures T N 1/3 . This is a generalisation of the T = 0 result for the FCS in the edge regime [38]. Denoting by N (s) the number of fermions in the interval [x edge + s N (T ), +∞[ we obtain the characteristic function (see Eq. ( 18) in [34]) and, from it, the cumulants

N (s) p c - T 3 4πN Li 5 2 -p (-e -s ) (29)
for all positive integer p ≥ 1. In the typical region defined above, sξ typ = O(1) the statistics is Poisson with mean N (s) e ξtyp-s [34]. There are deviations from Poisson in the tails, in particular for sξ typ → -∞ where the distribution becomes peaked around N (s) and zero higher cumulants [34].

In conclusion we have studied the statistics of the height fluctuations for the continuum KPZ equation at short time with the droplet initial condition. We obtained the exact analytical rate function Φ drop (H) and compared with numerics. It confirms, and extends, through an exact solution, recent approaches using weak noise theory developed for the flat geometry and unveils puzzling similarities with other large deviation results for finite-size system. We demonstrate that, remarkably, the right tail coincides with the Tracy-Widom result already at short time. This result agrees with rigorous bounds [START_REF]More precisely, the result e nH(t) ∼n→+∞ e 1 12 n 3 t is proved in: X. Chen[END_REF] valid at any fixed time t, P (H > s) ≤ e -4 3 s 3/2 /t 1/2 . By contrast the convergence towards the left TW tail ∼ (-H) 3 appears to be much slower, with ∼ (-H) 5/2 behavior at short time. Our short-time results for the KPZ equation also provide exact asymptotic predictions for the PDF of the rightmost fermion in a harmonic trap at high temperature T N 1/3 . We hope that the present results will stimulate further investigations of extreme value questions in the KPZ class [42] and also in cold atom systems.

  ) in terms of the poly-logarithm function Li ν (x) = +∞ p=1 x p /p ν . Hence the exact formula for the generating function(10) takes the following form at small time exp

  FIG.2. Numerical determination of P (H, t = 1/8). In the main figure, the solid (purple) line corresponds to the Edward-Wilkinson Gaussian regime(6). The symbols correspond to the numerical data for the discrete model with = 256, β = 1/16 (with 2 .10 8 samples). Note that we have imposed H = 0. The solid (black) line corresponds to P (H, t) = c(t)e -Φ drop (H)/ = 1.23487 . . .. Inset: Plot of the ratio R = P (H, t)/PGauss(H, t) for t = 1/8, where PGauss(H, t) corresponds to the Gaussian regime

	P (H, t = 1/8)	R 0.8 1 1.2 1.4
		0.6
		-3	-2	-1	H	0	1	2
						H
	∞ 0 dHe -Φ drop (H)/ √	t , with c(1/8)		√ t (20) where c(t) =

We thank I. Corwin, D. S. Dean, K. Johansson, D. Khoshnevisan, B. Meerson, J. Quastel, T. Sadhu and K. Takeuchi for useful discussions. We acknowledge support from PSL grant ANR-10-IDEX-0001-02-PSL (PLD). We thank the hospitality of KITP, under Grant No. NSF PHY11-25915.


Jean-Christophe Lapouble

The Socio-Economic Context of Africa and its Impact on Doping and Anti-Doping

Keywords: Corruption, development, doping, public administration, public health

The fight against doping is organized at the global level under the aegis of the World Anti-Doping Agency (WADA) in application of the 2005 UNESCO convention which made the application of the World Anti-Doping Code mandatory for all countries wishing to participate and organize international sports competitions. In fact, it appears that for a variety of reasons, the application of the World Anti-Doping Code is largely theoretical in Africa. Indeed, if most African countries adhere to the system set up by WADA, it appears that very few are able to apply it effectively. The numerous difficulties that African countries may experience due to a degraded socio-economic context confine anti-doping policies to the rank of non-priority public policies. Thus, the difficulties experienced by different countries in terms of development, structuring of the sports movement through associations, public administration, public health and corruption must lead us to consider that the fight against doping in Africa cannot be free of the socio-economic context and must therefore be adapted accordingly. This adaptation must be based on the reality of the functioning of sports organizations in the countries and not on theoretical considerations that are far removed from reality.

Introduction

The fight against doping in Africa cannot be approached without placing this fight in the more global context of African countries, for which the issue of doping is only an epiphenomenon in the midst of all the challenges that these countries must face. Nor can the fight against doping be considered a priority within public policy, given a whole series of socio-economic factors. Even if the indices relating to economic development or human development can be criticized, it seems interesting to us to situate the African continent with some indicators in order to be able to describe the real situation of the fight against doping and not a situation based solely on the ratification by most African countries of the World Anti-Doping Code as required by the 2005 UNESCO Global Convention on Doping, which was adoptedat the global level by 191 countries, including almost all African countries with the exception of Guinea-Bissau and South Sudan.

It appears that the fight against doping in Africa cannot be considered in a theoretical manner, that is, taken out of its socio-economic context. The experience of the Covid-19 epidemic in Africa has clearly shown that the response modalities of African countries cannot be the same as those of other countries. Indeed, the organization of the public health system and the public administration in general contributed to the effectiveness of the response. Therefore, there is no reason to believe that the fight against doping, which is as much a matter of education as of public health, is not influenced by such elements. So,we will look at the level of development in general, freedom of association, the state of the administration in general, corruption and public health. All of these elements are not without consequences on the fight against doping in African countries.

Development

In order to better understand the framework in which anti-doping policies should be conducted in Africa, we thought it would be useful to look at a few indicators such as GDP per capita, the poverty rate, the peace index and the human development index. These different indicators, imperfect as they may be, nevertheless allow us to understand that the fight against doping in Africa cannot be a priority but a policy carried out in a residual manner in certain states that have a particular interest in doing so, such as winning medals at the Olympic Games, because the registration of athletes can only be carried out insofar as the latter undertake to respect the World Anti-Doping Code.

It is very clear that the GDP per capita in Africa is the lowest of the five continents over the period from 1970 to 2019 even if this data conceals significant differences between countries. Thus, the average in Africa is 1884 dollars for 2019 while for the most favoured continent in North America it is 42796 dollars. The GDP in Africa varies from 17052 dollars for the Seychelles against 275 dollars in South Sudan. The latter country has recorded a 78% drop compared to the previous year. It thus appears that in Africa significant drops in GDP are not uncommon, which is certainly a peculiarity of this continent.

In 2019, countries with the highest poverty rate at the US$2.15-a-day poverty line were mostly in Sub-Saharan Africa ((Word Bank, 2022, p. 37). Poverty remains highly concentrated in Sub-Saharan Africa, with a poverty rate that is about four times higher than that of the second-poorest region in the world, and the evidence on the pace of poverty reduction in the region is unaffected (World Bank, 2022, p.38). If we address the question of the human development index (United Nations Development Programme, 2021/2022, p. 311), among the 66 countries that are listed as having a very high level of human development, there are no African countries. The highest index is obtained by Switzerland (0.962). The first African country is Algeria which is in 91st place (index 0.745). South Sudan is in 191st and last place with an index of 0.385 for 2021.

According to the Global Peace Index analysis,"Sub-Saharan Africa recorded a slight fall in peacefulness in the 2022 GPI, with the average country score deteriorating by 0.022 points, or one per cent. Of the 44 countries in the region, 21 improved in score, while 22 deteriorated and one remained unchanged" (Institute for Economics and Peace 2022, p. 21).

When reading these different indicators, it is clear that the fight against doping cannot be a major issue in Africa as there are other urgent matters to be dealt with. It is appropriate to ask whether such a fight is not an unattainable luxury whose social utility is questionable.

Associations

In the sports world, most clubs and federations are set up as non-profit associations. This legal form, which may seem harmless, does not appear to be a legal structure whose creation is free in many countries where the risk of creating an opposition political party leads to controls and provisions that sometimes make the creation of associations very difficult. Article 20 of Universal Declaration of Human Rights provides that everyone has the right to freedom of peaceful assembly and association and that no one may be compelled to belong to an association. The Banjul Charter guarantees in its article 10 the freedom of association in the following form:

1. Every individual shall have the right to free association provided that he abides by law. 2. Subject to the obligation of solidarity provided for in 29 no one may be compelled to join an association. » Article 29 of this Charter provides for a number of duties to be respected, including the obligation not to jeopardize the security of the State.

Moreover, freedom of association also includes the freedom to form a trade union. This freedom is also guaranteed by international conventions adopted under the aegis of the International Labour Organization. Thus, freedom of association is a strong marker of democratic development in general, but also of the reality of collective bargaining: The exercise of freedom of association and the right to collective bargaining is based on the defence of fundamental civil liberties, including the right to liberty and security of person, freedom of opinion, expression and assembly, the right to a fair trial by an impartial and independent tribunal, and the right to protection of property of employers' organizations and trade unions" (Bureau International du Travail, 2008, p. 5). ILO Convention 87 concerns freedom of association and protection of the right to organize. Convention No. 98 concerns the application of the principles of the right to organize and collective bargaining. As for the Banjul Charter, a large majority of African countries have ratified these two conventions (over 90%) since 1950.

What can be observed in both common law and civil law countries is that, in general, sports associations do not seem to have any particular difficulty in being legally constituted, even in countries where the freedom of association is closely controlled. Indeed, the declared (if not proven) apolitical nature of the sports world in general and of the International Olympic Committee in particular, does not lead States to exercise close control over the creation and functioning of sports clubs. The list of National Olympic Committees recognized by the International Olympic Committee (IOC, 2023) shows that the creation of a structure of this type is not particularly difficult.

Public administration

The state of the administration in Africa can be understood with some international indicators. It should be noted, however, that the indicators never refer to the administrations in charge of sport.

It is true that, depending on the country, if this type of administration exists, it may be attached to the education or health sector. Even if the Doing Business index is no longer published until another index is, data on the quality of the administration in each country can be mentioned, at least to give an overall state of the administration. Given that sports administration is rarely on the government's agenda, the indications given at the aggregate level can help to assess the state of sports administration in the various African countries. Overall, it is clear that some regions of the world are more favourable for doing business and it is clear that many African countries are poorly ranked (Doing Business, 2020, p. 32).

As a first step, it may be interesting to look at the overall score for the different indicators included in the Doing Business ranking, which gives an idea of the modernization and efficiency of the administration of the countries in question. For example, it is possible to analyse the data for Sub-Saharan Africa (Doing Business,2020, , p. 5). Overall, few African countries are ranked in the top 100 (for the global indicator) although the first is Mauritius, ranked 13th with an index of 81.5, while most other Sub-Saharan African countries are ranked after the top 100. The last country ranked with an index of 20 is Somalia (ranked 190). In terms of sectoral indicators, on a maximum base of 100, the best score achieved is 80.1 for starting a business but other indicators can be much lower (Resolving Insolvency: 31.3).

If we take two indicators among others, such as the connection to electricity and the payment of taxes, this can give an idea of the state of the administration in general, which is certainly imperfect, but insofar as the administration in charge of sport is not a priority, it is difficult to imagine that the two indicators chosen do not constitute priorities for African countries, since they are markers in terms of development. In other words, if these indicators are not good, there is no reason to believe that the administration of sport in the country (with extraordinary exceptions) can be in a satisfactory state.

Thus, it appears that the time to obtain an electricity connection in the area concerned is longer than in the rest of the world. Moreover, this average reflects huge disparities between countries such as Liberia where the connection time was 482 days in 2020 compared to 37 days in Rwanda.

In terms of the number of payments to be made, the cumbersome nature of most African administrations is evident. Tanzania's index is 59, while South Africa's is 7for a regional average of 36.6. It is also possible to take a more basic indicator of the functioning of administrations essential to the population, such as the registration of births, which therefore also concerns the entire population and not primarily the urban population. There was an increase of 2% in the proportion of under-five children whose births were registered in Africa from 49% in 2008 to 51% 2020. Projection scenarios built on existing trend show that, unless progress is accelerated, the number of unregistered children in Africa will continue to rise and will exceed 100 million by 2030 (World Health Organisation, 2022, p. 114). These elements, which globally show a poor functioning of the administration in general, can lead one to think that the administrations in charge of the fight against doping are not very structured, nor very efficient. Information from the World Anti-Doping Agency corroborates this observation.

The provisions of the World Anti-Doping Code state that in each country an independent agency should be responsible for the fight against doping. Article 20.5 and following of the World Anti-Doping Code (WADA, 2021) govern the conditions for the implementation of such an agency. Thus, the agency must be independent and free of any conflict of interest with respect to both sports organizations and the government. In terms of education, this is the responsibility of national anti-doping agencies (WADA 2023). In terms of funding, even though Africa's contribution has been limited to 0.5% of the total budget, which represents 46 million dollars in 2023, each African country must contribute an amount that varies from 802 dollars for countries such as Malawi or Somalia to 5141 dollars for South Africa (WADA 2023). The total amount of these contributions is certainly modest ($117,924), but given the lack of resources, it is difficult to see how such a small amount can help WADA's operations, even though, due to an underresourced administration, anti-doping programs are almost non-existent. It is true that a distinction must be made between the contribution due and the contribution actually paid. Thus, for the year 2022 (WADA 2022), only 59541 dollars were actually collected by WADA for a total amount of 109189 dollars. It should be noted that South Africa is in a special situation in the fight against doping because not only does it have the only analytical laboratory on the African continent but also a local WADA office in the city of Cape Town.

However, it is important to qualify this observation, which suggests that anti-doping tests are not carried out. Indeed, the analysis of the controls carried out in Athletics in Africa allows to have a more nuanced vision. Obviously, athletics is the sport that brings the most medals to African countries.

The data provided by the World Anti-Doping Agency for the year 2021 (WADA 2021) shows that Kenya is ranked 8th in the world in terms of controls in this discipline (684 controls), just before Spain, which shows that at the level of controls, some African anti-doping organizations are doing real work. The other African countries that follow in the ranking are respectively Morocco, South Africa and Nigeria. However, at the global level, only 19 African countries have carried out controls in athletics. Some, like Burkina Faso, have done only one. The same applies to Ivory Coast. Given the political and economic situation of Burkina Faso, this figure is not surprising. On the other hand, it is much more surprising for Ivory Coast, whose indicators in terms of administrative efficiency are much better. This shows that if the global state of the administration of a state can be correlated with the state of the administration in charge of sport, there are always particularities. Thus, Egypt has carried out 162 controls, which is the 5th rank among African countries, while this country is ranked 114 in Doing Business. However, the number of audits carried out in Egypt is just higher than those carried out in Norway, ranked 7 in Doing Business. However, these differences can be well explained. The population of the two countries is not at all comparable (110 million in Egypt versus 5.5 million in Norway). In addition, athletics is not a sport that is widely practiced in Norway.

Another indicator of the weakness of controls is the number of analyses carried out by the South African laboratory, the only one accredited in Africa, which carried out a little less than 1.65% of the world total in 2021 (WADA 2021). It should be noted that not all samples taken in Africa are necessarily analysed there. At the level of the anti-doping administrations themselves, one can only note that the obligation of independence from the sports movement as requested by the World Anti-Doping Agency is not always respected. This is particularly the case when tests are conducted by a national Olympic Committee, as in Botswana, Rwanda, Tanzania, Namibia or Madagascar. It is true that the principle of independence is not respected either when the test is requested by the Ministry of Sports, as in Lesotho.

Faced with these shortcomings, the aid proposed by the Olympic movement to structure African sport does not seem sufficient. The Olympic Solidarity Program does not provide for specific aid for the establishment of national anti-doping agencies. Even though Africa is the leading continent in terms of Olympic Solidarity (Olympic Solidarity and NOC Services, 2021) with 54 National Olympic Committees, there is no budget line that directly concerns the fight against doping and the support of national anti-doping agencies. In fact, the aid mainly concerns aid for teams so that they can participate in the Olympic Games or individual grants for athletes. However, there is a specific program designed to help structure national Olympic committees or local sports federations, such as the one in Cape Verde (Olympic Solidarity and NOC Services, 2021, p. 7). In terms of initiatives carried out specifically in Africa, it appears that the fight against doping is addressed through workshops or in some cases, the payment of the contribution due by some countries to the World Anti-Doping Agency (Olympic Solidarity and NOC Services, 2021, p. 30). There is a specific program aimed at structuring National Olympic Committees but which is not specific to the fight against doping: "Management and Knowledge Sharing" (Olympic Solidarity and NOC Services, 2021, p. 29) to ensure the implementation of good governance practices. The amount of this program at the global level for the year 2021amounts to 18 875 000 dollars. Within this framework, 50 African Olympic Committees have been assisted (Olympic Solidarity and NOC Services, 2021, p. 53). At the level of the promotion of the values of Olympism, the Olympafrica Foundation for the support of community centres (Olympic Solidarity and NOC Services, 2021, p. 36).

Corruption

For Alina Mungiu-Pippidi "Corruption emerges when someone has monopoly power a good or service, has the discretion to decide who receives it and how much they receive, and is not accountable" (Mungiu-Pippidi, 2015, p. 116). However, it is clear that the sports world is essentially based on a series of monopolies entrusted to non-governmental organizations with little control.

Sport is not immune to corruption and it must be recognized that if the level of corruption in a country is high, there is no reason to think that the sports world will be spared. Thus, even in countries where corruption is the lowest, corruption cases can reach the sports movement (Sport, Transparency International, 2016). In the field of doping, there is no reason to think that corruption does not affect the sports world, especially since some cases have led to the exclusion of Russia from international competitions because of manipulations during the analysis of the Sochi Olympic Games. The Court of Arbitration for Sports recognized the non-conformity of the actions of the Russian Anti-Doping Agency in a decision of December 17, 2020. These actions are not isolated and had given rise in the past to other errors, particularly in terms of access to data from the ADAMS system. Cases relating to corruption in the fight against doping have thus affected African countries such as Kenya in 2015 or Senegal with the former president of the International Federation of Athletics in 2016 who was convicted by the French justice for corruption.

Overall, Africa's corruption ranking is clearly not satisfactory (Transparency International, 2021). Sub-Saharan Africa has the worst score, with an average score of 33, the lowest of all regions in the world. This score reflects a wide range of situations, none of which is satisfactory. The worst score is for South Sudan (11/100), while the Seychelles has the best score (70/100) (Transparency International, 2021, p. 14). We can notice that the two other countries that stand out are Cape Verde (58/100) and Botswana(55/100). If we look at the Middle East and North Africa zone, the global score is hardly better as it is 39, just after Eastern Europe and Asia.

The findings on the level of sports organizations are not very encouraging. ccording to Chris Tsuma, Africa remains stunted by a combination of talent drain (mainly to Europe), a lack of government investment and policy guidelines, corruption and gross mismanagement (Tsuma, 2016). He adds that major events are a main avenue of abuse and corruption in sport in Africa.

Faced with such an observation, it is not surprising that efforts are being made to improve the functioning of African sports organizations, even if it seems illusory to want to make sports organizations function in a transparent manner in an environment that is not transparent.

Within the framework of the Olympic Solidarity Program, some actions are carried out in the field of integrity education as well as to promote the good governance of sports organizations (Olympic Solidarity and NOC Services, p.43). It is certainly no coincidence that the assistance given to the structuring of the Olympic Committee has been successful, given the low level of corruption in this country (Olympic Solidarity and NOC Services, p. 30). These elements are corroborated by the analysis of the number of controls carried out by Cape Verde in Athletics (18 controls) for a population of 562 000 inhabitants (WADA, 2021, p. 47). It is thus clear that the fight against corruption in Africa in the field of anti-doping must take on a transnational dimension (Hatchard J., 2014, p. 333).

Public Heath

Insofar as the fight against doping is often presented as a public health problem, it must be noted that in the face of the health challenges facing the African continent, the issue of the fight against doping appears to be a marginal phenomenon. In fact, since the Covid-19 epidemic has severely tested all the health systems in the world, it is clear that African countries have only been able to face such a challenge with limited means. Therefore, the African continent has a population that represents 14.4% of the world's people, but it accounts for only 1% of the global health spending (World Health Organisation, 2022). As the maps show, access to basic health services is still not guaranteed for a large part of the African population.

As the fight against doping is also a fairly sophisticated medical field, it is easy to understand that most African countries are not in a position to implement prevention and/or repression policies. The level of health emergency on the continent shows that doping prevention can only be a very specific policy, especially when Olympic medals are at stake. Moreover, the effective implementation of Athlete Biological Passport is a challenge for African athletes.

Currently only one anti-doping laboratory is accredited for the entire African continent. It is, namely the South African Doping Control Laboratory in Bloemfontein namely (WADA, 2023). Faced with a lack of equipment and limited road infrastructure, Africa may be an interesting fall back for some non-African athletes to carry out doping product cures such as anabolic agents whose effects persist over time, even though detection must be carried out within a limited period of time after taking them. Having made this assumption at the time of the generalization of out-of-competition testing with the implementation of the ADAMS system, it appears that some athletes have tried to take advantage of the difficulties of access to Africa to avoid testing. For example, a French athlete went to train in Marrakech where she failed to be tested, resulting in a four-year ban from competitions by Conseil d'Etat, the French higher administrative court.

Conclusion

At the end of this analysis, it is very clear that the ratification by almost all African countries of the UNESCO Convention on doping and therefore the adoption of the World Anti-Doping Code is, for many countries, a mere display measure, as much more important priorities remain to be addressed. Rather than questioning the countries, which are de jure forced to ratify a convention that they know they cannot apply in order for their athletes to participate in international competitions, we should question the blatant shortcomings of the World Anti-Doping Agency, which imposes legislation that it knows will not be applied. It is a pity that we prefer the display to the recognition of the enormous difficulties encountered in the field. As far as the fight against doping in Africa is concerned, one can only regret this inflation of normative texts, which are inapplicable considering the problems that this continent is facing. In other words, in view of the African socio-economic context, the application of the World Anti-Doping Code constitutes a legislative doping without real effect in most of the states.


Media adaptations of archives in scientific communication: A study of the 'transfrontier mountain tourism' semiotic scenario

Marie-Hélène HERMAND -Université Bordeaux Montaigne

Translated by Hayley Wood

The object of study: 'transfrontier mountains'

In geography, mountains in their configuration as a frontier are seen as a boundary and a discontinuity to which various meanings are attached [START_REF] Debarbieux | La (M)montagne comme figure de la frontière: réflexions à partir de quelques cas[END_REF]. As a topographical obstacle, they have represented a strategic argument and a framework for the military mapping of borders since states first emerged in Europe. As a symbolic obstacle, they can represent the triumph of the collective and popular will, as was the case with crossings of the Rocky Mountains in the United States in the nineteenth century. Associated with an ideal of modernity, expressions of the mountain-as-boundary encompass both aesthetic representations (paintings, maps and literature) and stereotypes that supply a vast frontier mountain imaginary. The mountain-as-boundary is a highly visual landmark that separates countries but also potentially linguistic, economic and religious areas [START_REF] Debarbieux | Le mont Royal. Forme naturelle, paysages et territorialités urbaines[END_REF], outlining the imaginary potential of the association 'mountain + frontier' and validating the territorial constructions associated with transfrontier mountain borders.

In the context of transnationalisation, the mountain configuration provides a new way of looking at space and scale. From a social and cultural point of view, transfrontier mountain spaces connect populations that are separated by a natural obstacle but often share similarities [START_REF] Fourny | Cette montagne que l'on partage. Frontière et montagne dans les coopérations transfrontalières de régions alpines[END_REF]. From a political, legal and organisational point of view, they reveal a desire to cooperate and pursue projects structured by funding programmes in order to address common issues [START_REF] Jacob | La montagne transfrontalière: entre innovation, compétitivité, valeur ajoutée et nécessité de préservation de l'environnement[END_REF]. [START_REF] Oiry-Varacca | Montagnards dans la mondialisation -Réseaux diasporiques et mobilisations sociales dans l'Atlas (Maroc), les Highlands (Écosse) et les Alpes françaises[END_REF] shows that transnationalisation does not in any case preclude territorialisation: individuals and groups continue to identify with spaces, but the scales are modified and reference points other than that of the state are created.

Depending on the context, transfrontier mountains are seen in a variety of positive and negative ways. In some cases they have been dismissively seen as geographically marginalised or economically weak areas, giving rise to images of mountain dwellers forced into exile for their economic survival. In others, enhanced by investment from industry or tourism, they have produced social distinction, supported by policies to support the delivery of highperformance technology and transport infrastructure and by an influx of wealthy residents. Today, transfrontier mountains are coming under heavy anthropogenic pressure and in many places have become a hub for international tourism and the site of predatory property practices.

These various motifs are evidence of the contribution made by transfrontier mountain spaces to the construction of a vast transfrontier semantic universe that can already be observed in many other areas (including health, education and economics).

Study question and hypothesis

While the purpose of tourism communication is to attract visitors to the mountains, the purpose of scientific communication is to disseminate constructed knowledge regarding this particular ecosystem. In order to understand how this process of communication is adapted to different local realities, I will identify the components, aims and forms taken by the 'transfrontier mountain tourism' scenario in scientific communication.

My primary hypothesis consists of confirming, using situated examples, that the use of archives -as legitimate or legitimised reservoirs of discourse -frames our perceptions, representations, attitudes and behaviours in relation to mountains. First, these archives (re)connect mountains to their cultural and social dimensions, a necessary condition for management of ecology in the broadest sense; and second, they make the transition from a diverse range of tourism motifs historically associated with transfrontier mountains to the contemporary argument of ecotourism. To test this hypothesis, I will situate the 'transfrontier mountain tourism' communication scenario within the transfrontier semantic universe under construction, then identify a 'structure of transformations' (Greimas and Courtés, 1982: 349) of a semiotic nature that might affect this scenario. This approach, inspired by Foucault's archaeology of knowledge, is in line with contemporary work to develop 'libraries of semantic models describing an area or object of knowledge using conceptual graphs' (Stockinger, 2018: 8). It consists of establishing a hierarchy of concepts to address an area, defining the relationships between these concepts, and then analysing the system of topoi that supplies the area by assigning characteristics and values to it. It also contributes to examining the key issue of the active reuse of data and archives -made possible by forms of conversion or qualitative adaptations -in response to specific needs, audiences and uses. This adaptation process gives the archive the status of a resource that can be exploited by means of various intellectual operations (such as recontextualising, redrawing, rewriting and re-editorialising) based on a determined need.

Theoretical and methodological framework

Natural heritage, mountain tourism and the green transition

Rather than considering the preservation and exploitation of nature in oppositional terms, [START_REF] Boidin | Biens communs, biens publics mondiaux et propriété. Introduction au dossier[END_REF] connect them by emphasising the management of relations between humans and nature. This is a valuable approach as it not only defines mountains as 'a natural resource understood as an existing raw material, one that can be exploited or protected' but as 'a social, cultural and symbolic resource that makes biodiversity a socially, economically and culturally constructed reality' [START_REF] Tardy | Patrimoines culturel et naturel: Analyse des patrimonialisations[END_REF]. It is from this perspective of a natural heritage that is living and embedded in histories, territories and social processes that I will look at various scientific communication devices.

The development of mountain tourism has been inextricably linked to high mountain areas since the second half of the eighteenth century, and can be roughly divided into two models: day trips with a 'light' impact on the ecosystem, and winter sports tourism, which has a major impact [START_REF] Dérioz | Preface. Mountain tourism and sustainability[END_REF]. The discrepancy between collective representations of a 'mythical space of evasion' (ibid.) and the harsh environmental reality calls for a change of model in various parts of the world. The factors that might influence a shift in the model include shaping the environmental awareness of the public -a key lever that scientific communication seeks to influence.

Making use of natural heritage archives

Archival disciplines describe communication processes that enable the exchange, appropriation and transformation of knowledge and values in society [START_REF] Jeanneret | Faire trace: un dispositif de représentation du social[END_REF]. Associated with the concepts of source, trace, data and document, archives invite us to observe the rewriting processes that facilitate the appropriation of a specialised discourse by others. As polysemous resources that can be interpreted based on the context, archives have an ability to draw on or postulate a past that is useful for understanding the present. Emphasising the distorting and creative nature of archives -or their 'triviality,' as this is understood by Yves [START_REF] Jeanneret | Penser la trivialité. Volume 1: la vie triviale des êtres culturels[END_REF] -enables us to observe how scientific communication becomes fundamentally political (as it is designed to frame our perceptions) and social (as it promotes human communication).

The archive-based approach is particularly suited to studying natural heritage communication since, as Anna Pajard and Bruno Ollivier emphasise (2017: 386), 'the UNESCO Convention features documentation prominently in its definition of safeguarding.'1 The 'documentological' approach [START_REF] Couzinet | Métamorphoses du document: enjeux d'un objet médiateur fondamental[END_REF], which combines a description of documents with a contextualised analysis of their content, enables us to examine multifaceted, complex contemporary documents by identifying in them influences of memory, inherited motifs and historical roots.

According to Davallon (2015: 210), 'the heritagisation of intangible objects is without doubt the most archive-generating activity, as if the object were scattered across documents.' In addition to administrative documents, collective memories and recorded traces of the intangible heritage object provide opportunities for developing scientific and cultural archives in the form of written, visual and audiovisual documents. These documents can then be gathered into databases, exploited, and even commercialised, in the form of cultural and scientific products. The production of archives lies at the heart of questions about the socioeducational role of the scientific education of citizens [START_REF] Albe | Finalités socio-éducatives de la culture scientifique[END_REF], and also poses the question of how the documents developed are organised, not only by researchers but also by the authorities and the public.

Semantic modelling of discourse

With respect to the genealogy of transfrontier discourses, in a separate article (Hermand, forthcoming) I have proposed a theoretical and methodological framework centred on the identification of 'self-constituting discourses' [START_REF] Maingueneau | L'analyse des discours constituants[END_REF] and 'edifying narratives': two categories that are useful for thinking about the referential discourses and inaugural narratives that condition the existence of discourses about the transfrontier space. Since the discursive genealogy of transfrontier mountains provides enough material for a study in its own right, here I have chosen to focus directly on discursive adaptations of scientific communication content. My aim is to pursue the construction of a semio-pragmatic analytical model of the transfrontier universe of discourse, with the aim of this ultimately being able to connect situated discursive structures with their historical construction.

My approach is guided by three key concepts: topos, scenario and argument.

A topos (or commonplace of argument) is a central concept in argumentation theory [START_REF] Amossy | L'argumentation dans le discours[END_REF] by which an analytical representation of discourses about a referent can be proposed by taking into consideration various discursive genres [START_REF] Martí | Analyse de réseaux discursifs à partir de la théorie de l'argumentation dans la langue[END_REF]. Shared by society and relatively stable in nature, a topos -which can be general or specific (Perelman and Olbrechts-Tyteca, 2000: 112) -gives meaning to a discourse, and represents a fundamental cognitive mechanism through which we interpret reality.

The concept of the scenario has been developed in semiotics by Peter Stockinger (2005: 10) to analyse digital scenes, and is a constituent element of the topos. It refers to 'the content of a web service, the ways in which it is appropriated, and the expression and staging of the service via editing regions and zones in the form of a communication interface.' A scenario can be subjected to various semiotic operations, such as the expansion of content (Hermand, forthcoming) or, as we shall see here, the adaptation of content to specific contexts, media types, resources, audiences or uses.

Finally, the concept of argument refers to the development of a scenario in the form of a narrative or an example, with a view to establishing the pertinence of the topos. Arguments in support of the topos are opposed to counter-arguments that in turn sketch out a 'counterdiscourse' (Auboussier, 2015). Arguments are identified by the use of various verbal means (such as the appeal to reason or to emotions, sympathetic figures, rhetorical figures and the implicit) that are designed to 'secure agreement with a thesis, to modify or strengthen representations and opinions' (Amossy, 2010: 36) in relation to a specific issue.

Study corpus

The study corpus has been compiled to explore how scientific communication constructs transfrontier mountain environmental study regions by using, enriching and adapting archives. The chosen medium is shared by the constituent elements of the corpus: the web, as a distribution channel, makes it possible to consider a range of media types (websites, an exhibition, documentary, online conference and game). The content is taken from two different sets of situated examples: one from the Dolomites (with immediate transfrontier interactions between Austria and Italy) and one from the High Atlas (with delayed and longrange transfrontier interactions between the Maghreb region and Europe/the Maghreb region and Asia). Using a variety of examples is useful for understanding how mountains as an object of meaning form part of different communication contexts.

The examples from the Dolomites are designed to raise awareness about the impact of humans on transformation of the landscape and the introduction of forms of transport that are sensitive to the mountain environment. They consist of a multifaceted bilingual (Italian-German) website entitled Connessioni montane: Viaggio dalla guerra al turismo/Bergverbindungen: Reise vom Krieg zum Tourismus, which forms part of a subdomain (2021.euregio.info) of the institutional website of the Tyrol-South Tyrol-Trentino Euroregion (euregio.info). Within the media framework of the Year of Museums 2021, it brings together a set of archives provided by various contributors (museums, universities, foundations, nonprofit organisations and tourist information centres) from both sides of the Italian-Austrian border. Finally, the series includes digital exhibitions copyrighted to the Euroregion, and university webinars. The various enunciators pursue the same objective of transfrontier cooperation in response to the environmental issues faced by a shared mountain area.

The examples from the Maghreb region are designed to raise awareness about the nutritional value of mountain landscapes, here in particular the dimorphic ash tree and the need to preserve this species. Silvopastoral practices are examined in a documentary entitled Bergers sculpteurs d'arbres du Haut Atlas (2016), an online conference of the same name (2020) and the downloadable game ChèvreFeuille (2021). These three scientific communication devices have been developed by public scientific research bodies (a research institute, universities and laboratories) and inform the public about the historical process of preserving trees in response to nutritional needs. Here the intention of the enunciators stems from one of the missions of research institutions, namely, to provide scientific communication media to enable citizens to better understand research concerns, consisting here of global environmental change and relations with countries in the Mediterranean and intertropical zone.

Table 1 presents a summary of the study corpus:

Series of examples

Mountain context

Editorial responsibility

Distribution channel

Types of media

Results

Step 1: the situation of the 'transfrontier mountain' topos

In Figure 2 below, a partial, provisional representation of the transfrontier universe of discourse enables us to situate the topos that recounts the 'drama' (in the sense of theatrical staging) of transfrontier mountains and to identify the archives that supply it.

6 https://www.ird.fr/ 7 https://www.canal-u.tv/chaines/labexmed/bergers-sculpteurs-d-arbres-du-haut-atlas; https://youtu.be/JnKocP5E9ac 8 https://www.ird.fr/e-conference-bergers-sculpteurs-darbres-du-haut-atlas-de-mohamed-alifriqui 9 https://www.ird.fr/chevrefeuille-un-jeu-autour-du-developpement-durable The left-hand and central parts of the diagram show various (general and specific) topoi that proliferate in the transfrontier universe of discourse. The general topos of 'transfrontier landscape', for example, develops concomitantly with other highly general topoi (such as health, education and economics). It gives rise to a specific 'transfrontier mountain' topos and other specific concomitant topoi (rivers, forests and parks) that are found in numerous discursive manifestations (in political, institutional, economic, non-profit and media contexts). Specialised scenarios -understood as compositions of specialised scenes and documents -develop and are responsible for supplying the specific topoi. The 'transfrontier mountain tourism' scenario, together with other scenarios (including agriculture and sylviculture), thus supplies the 'transfrontier mountain' specific topos. Broadly speaking, the specific topoi diversify while the scenarios that supply them are developed and transformed in order to enrich the transfrontier universe of discourse.

The right-hand part of Figure 2 shows the diverse range of archives -in the sense of historical sources (textual, visual and audio) -and contributors identified in the scenarios.

Step

2: adaptations of the 'transfrontier mountain tourism' scenario

Several aspects of the process of semiotic adaptation of the 'transfrontier mountain tourism' scenario were identified in the study corpus: diversification, substitution, expansion and displacement.

The diversification of archives is particularly apparent in the Dolomite series, in which photographs, videos, posters, patents, maps and objects supply the narrative of how mountain populations are 'connected' to one another and highlight the challenge of sustainable transport in a landscape that has changed a great deal since the last century (Image 1).

1. Photograph (connected by cable car).

2. Video (connected by cable car).

3. Objects on display (connected by the telephone).

4. Objects on display (connected by travel).

5. Posters (connected by the railway)

Interactive map (connected by the route)

Image 1. Taken from series no. 1 (Dolomites) of the study corpus: ©2021.euregio.info.

These archives document the historical evolution of the region and herald the transition between the past and the future of transfrontier mountain transport. The emphasis is on the evolution of infrastructure dating from the early twentieth century and the First World War (cable car stations and railway lines), the conditions of population mobility (immigration and travel), travel paraphernalia (trolleys and suitcases) and modes of transport related to winegrowing (back-carrying and wagons). The archives also illustrate life stories centring on endurance and striving for economic survival: two values that can be transposed to the present goal of environmental survival.

The diversification of archives can also be observed in the examples from Morocco's High Atlas, in which the depiction of various ancestral acts gives the message a historical dimension (Image 2).

1. Act (plough making).

2. Act (protecting ash seedlings).

Image 2. Screenshots from the documentary Bergers sculpteurs d'arbres (IRD et al., 2016).

Muscle memory supplies the memory dimension of the High Atlas and illustrates a cyclical narrative (life cycle of the ash tree, cycle of pastoralism, nutrient cycle). It also introduces the concept of 'culturally modified landscapes', meaning a historical, cultural, functional and evolving landscape heritage to be passed on to future generations.

Substitution, expansion and displacement are other forms of semiotic adaptation that can be observed in the two geographical contexts of the study.

In the High Atlas example, they are particularly apparent when comparing the documentary Bergers sculpteurs d'arbres (2016) with the game ChèvreFeuille (2021), which is presented as a derivative of the documentary. This board game is aimed at an audience aged 8 years and up, and simulates the management of trees as a food resource. The changes made between the documentary and the game include:

-substitution of the geographical area of the Global South for that of the Global North: the documentary depicts the memories and history of a Moroccan shepherd on his ancestral lands, while the game shows a French family appropriating this history.

-expansion of the initial intention of transmission to the younger generation: the documentary calls for the transmission of endogenous knowledge to young people living in the High Atlas, while the game poses the French family with the problem of landscape conservation. The documentary also expands its message to the countries immediately adjacent to the Maghreb region and to the more remote mountains of Western Asia, which face the same problem of managing dimorphic ash trees.

-displacement of the context of use of media archives: from informational (in the documentary) to edutainment purposes (in the game).

In the Dolomites example, they consist of:

-substitution of the geographical area of the Dolomites for that of the Balkans and the Caucasus: the content of the Connessioni montane/Bergverbindungen section is reused and re-promoted on the website of the Osservatorio Balcani e Caucaso Transeuropa.

-expansion of the initial intention of transmission to the younger generation: the Connessioni montane/Bergverbindungen section is aimed at a tourist audience, while the university webinars are aimed at a student audience.

-displacement of the context of use of media archives, from the act of informing the general public (via digital exhibitions) to the act of educating the academic public (via webinars).

The adaptations of the scenario vary according to the geographical area (Italy-Austria, Maghreb-France), the intention of the communicators (to inform, exhibit, explain or entertain), the target audience (museum visitors, tourists or students), the use (cultural, educational or entertainment), the output device (exhibition, webinar, documentary, conference or game), which aspects of memory are highlighted (life story, object or act) and scientific communication practices. By scientific communication practices, I mean the various rewriting operations conducted on archives that enable the circulation and evolution of the scientific communication discourses specific to mountain regions. More specifically, I identified the typical practices of demonstration, rewording, illustrated explanation, commentary and translation. To provide two examples:

-explanations illustrated by diagrams or maps show the shift from the linguistic to the visual, which is designed 'to fix, condense and interpret' (Jacobi, 1999: 183-184) the communication discourse (Image 3); -translation from one language to another, which enables a wider audience to access the information, here in the form of subtitling or multilingual text. Subtitling, a linguistic practice that consists of providing written text so that viewers can understand what individuals are saying, marks the shift from the oral code to the written [START_REF] Perego | La traduzione audiovisiva[END_REF] Step 3: arguments for and against the 'transfrontier mountain tourism' scenario

In the Dolomites example, the form of tourism being promoted is described in terms of 'sustainable transport' (mobilità sostenibile/nachhaltige Mobilität). In the North African example, the term 'tourism' only occurs once, when the expression 'tourism and local development' is used in the voice-over. The recurring procedures by which arguments are provided for a form of tourism that is centred on sustainable transport and respects local development include:

-the appeal to reason, which requires the mountain's nourishing function to be preserved in order to ensure human survival in the High Atlas and economic survival in the Dolomites.

-the appeal to emotion, supported by sympathetic figures such as the shepherd attached to his home in the High Atlas, or the groups of people previously displaced by war and poverty in the Dolomites. -identifying the threat to life, namely to subsistence in the High Atlas and biodiversity in the Dolomites.

Counter-arguments can also be identified in the lexicon. In the Dolomites, 'sustainable transport' clashes with the 'ecological damage' (Umweltbelastung) and 'environmental pollution' (ambientale inquinamento) that are rife in the region. In the High Atlas, the scientific communication discourse very explicitly identifies four counter-arguments -the 'limited interest of the younger generation', 'market development', the 'availability of other construction materials' and 'opposition from the educational system' -that hinder the transmission of endogenous knowledge with a strong cultural dimension and its role in global environmental change. Here we see the opposition, more or less direct depending on the context of communication, between a discursive formation in favour of a shared mountain seen as a living heritage and a counter-discourse in favour of its speculative exploitation or even for it to simply abandoned. This opposition confirms that the main challenge for the scientific communication discourse consists of (re)framing the representations circulating in the public space.

Conclusion

After explaining the motivation behind associating the ideas 'mountain + frontier' within a transfrontier semantic universe under construction, I have demonstrated the existence of the 'transfrontier mountain tourism' semiotic scenario in a scientific communication corpus. Drawing on the concepts of topos, scenario and argument has proven useful in beginning to structure the transfrontier universe of discourse (whose domain of reference here is the mountain area as an object of tourism with varying degrees of intensity) and to describe its transformations in two different contexts: the Dolomites and the High Atlas. The transfrontier component is understood here at the level of immediately neighbouring populations (between Austria and Italy, and between Morocco and countries neighbouring the Maghreb region) or as a long-range connection (between Morocco and France, and between the Maghreb and Asia).

The study corpus, focusing on the question of the consideration of a shared mountain area, has been examined through the prism of media transformation of archives. In the Dolomites context, the tourism scenario is made very explicit and is served by archives organised around the theme of connecting transfrontier mountain populations: the idea of ensuring mobility while respecting the natural obstacle is to the forefront of the communicators' intentions. In the Maghreb context, the tourism scenario is a by-product: it is not a central concern but arises from discussing the fundamental question of preserving a nourishing landscape in the context of a subsistence economy.

The common feature of these scenarios is that they attribute a pedagogical value to 'transfrontier mountain tourism' that is systematically backed by history (war infrastructure, traditional agricultural practices, the cultural practices of mountain peoples and ancestral acts). The archives on which they draw provide evidence of practices, knowledge and policies applied to a shared mountain area, whether it is under significant pressure or is being neglected. They play a crucial role in explaining, illustrating and projecting the natural and cultural heritage of the mountain in relation to decision-makers, contributors and citizens.

The complex process of their use in scenario building, which as I have shown provides fertile ground for adaptation, remains a semiotic question to be explored in greater depth.

More broadly, the approach has made it possible to supply my semio-pragmatic model for describing and interpreting the emerging transfrontier semantic universe and to situate the mountain topos within it (Figure 4).

Figure 1

 1 Figure 1 below shows how these main concepts are connected in my provisional model of semiotic description of the transfrontier universe of discourse.

Figure 1 .

 1 Figure 1. Initial model of semiotic description of the transfrontier universe of discourse.

Figure 2 .

 2 Figure 2. Partial representation of the transfrontier universe of discourse based on the 'transfrontier mountain' specific topos.

1.

  Drawn diagram (Maghreb context, taken from the Bergers sculpteurs d'arbres documentary). 2. Hand-drawn map (Dolomites context, taken from the Connessioni montane/Bergverbindungen section).Image 3. Examples of illustrated explanations, here using a diagram and a map.

  , as in the case of the Moroccan shepherd, whose words are subtitled into French (Image 4, left). The practice of multilingual text can be seen in posters, with the order of the languages varying according to the communication context -Austrian or Italian (Image 4, right). 1. Subtitled translation at the bottom of the screen (North African example, Bergers sculpteurs d'arbres documentary).2. Multilingual text (Dolomites example, Connessioni montane/Bergverbindungen section).

Image 4 .

 4 Examples of translation practices using subtitling or simultaneous language versions.

Figure 3

 3 Figure 3 below provides a summary of the variations thus observed in the semiotic scenario.

Figure 3 .

 3 Figure 3. Variations of the 'transfrontier mountain tourism' scenario.

Figure 4 .

 4 Figure 4. Results of the modelling approach applied to the transfrontier mountain topos.

Table 1 .

 1 Summary of the study corpus.

	Series no. 1 Dolomites	Tyrol-South Tyrol-	Euroregion	-Year of Museums
		Trentino	institutional	2021 subsite,
		Euroregion +	web portal 2	bilingual section,
		partners		'Connessioni
		(museums,		montane/
		universities,		Bergverbindungen' 3
		foundations, non-		-digital exhibition 4
		profit		-webinars 5
		organisations and

UNESCO,

2003, Article 2.

www.euregio.info

https://2021.euregio.info/it/connessioni-montane-viaggio-dalla-guerra-al-turismo/; https://2021.euregio.info/bergverbindungen-reise-vom-krieg-zum-tourismus/

https://www.mountain-connections.eu/

https://webconference.uibk.ac.at/b/tob-edm-wdn-3xx