Patrice Loisel

Patrice Loisel Faustmann

Faustmann Rotation and Aquaculture in the presence of an epidemic risk

Faustmann Rotation and Aquaculture in the presence of an epidemic risk Patrice Loisel * †

Introduction

For the management of natural resources, the first question that arises is : what is the optimal duration of cycle production. This is the case both in forestry, aquaculture, production of renewable resources. In the case where a calculation method to predict earnings for various terms of the cycle is available, Faustmann [START_REF] Faustmann | Berechnung des Wertes welchen Waldboden sowie noch nicht haubare Holzbestände für die Weldwirtschaft besitzen[END_REF] proposed a formalism based on the expected discounted yield. Many authors have successively improved or reformulated the method, Ohlin [START_REF] Ohlin | Concerning the question of the rotation period in forestry[END_REF], Pearse [START_REF] Pearse | The optimal forest rotation[END_REF]. Clark [START_REF] Clark | Mathematical Bioeconomics[END_REF] has applied this method to natural resources. Bjorndal [START_REF] Bjorndal | Optimal Harvesting of Farmed Fish[END_REF] analyzes the optimal duration of farmed fish. Arneson [START_REF] Arneson | Optimal Feeding Schedules and Harvesting Time in Aquaculture[END_REF] studied optimal feeding and harvest time with respect to fish-growth function. Heaps [START_REF] Heaps | The optimal feeding of farmed fish[END_REF] analysed optimal feeding schedules and harvesting policies for farmed fish. The preceeding works are characterized by the absence of risk of destructive events. The risk of destruction has been introduced to forest stands by Martell [START_REF] Martell | The optimal rotation of a flammable forest stand[END_REF] and Routledge [START_REF] Routledge | Effect of potential catastrophic mortality and other unpredictable events on optimal forest rotation policy[END_REF] in discrete time. Thereafter, Reed [START_REF] Reed | The Effects of the Risk of Fire on the Optimal rotation of a Forest[END_REF] has studied the optimal forest rotation in continuous time with the risk of fire. Thorsen and Helles [START_REF] Thorsen | Optimal stand management with endogenous risk of sudden destruction[END_REF] maximized a not discounted criterion taking into account the risk and using a population model. Most of the work on Faustmann rotation and in particular the study of Reed [START_REF] Reed | The Effects of the Risk of Fire on the Optimal rotation of a Forest[END_REF] are developed in the context of forestry but are not specific to forestry and can be applied to the production of renewable resources. In the context of random prices in aquaculture Guttormsen [START_REF] Guttormsen | Faustmann in the Sea -Optimal Rotation Time in Aquaculture[END_REF] studies a method based on dynamic programming.

For the absence of risk of epidemic events all the production cycles are carried out to the same term. When the risk of destructive event exists and is taken into account, the authors cited above assume that the operator systematically decides to interrupt the current cycle and begin a new cycle. This is fully justified in the case of severe epidemic. In the case of an epidemic of limited impact on mortality, to the first question about the optimal term a second question is added : should we interrupt the current cycle and begin a new cycle or is it better to continue the current cycle ? If there are alternatives, what is the criterion to choose ? To fulfill this goal, we define a criterion for choice. We consider an averaged fish model, inspired by the models of Hannesson [START_REF] Hannesson | Optimal thinning of a year-class with density-dependent growth[END_REF] and Heaps [START_REF] Heaps | Density dependent growth and the culling of farmed fish[END_REF]. For specific decisions and thus specific criteria, we study two particular cases. In the first case, the operator systematically interrupts the cycle in case of a epidemic event, we generalize the results obtained by Reed [START_REF] Reed | The Effects of the Risk of Fire on the Optimal rotation of a Forest[END_REF] under less restrictive assumptions. We show that the results obtained in [START_REF] Reed | The Effects of the Risk of Fire on the Optimal rotation of a Forest[END_REF] are valid under the assumption that the operator does not harvest during the production cycle. The proposed method takes into account intermediate harvesting. In the second case, the operator continues the cycle even in case of epidemic events (which makes sense if the epidemic is minor) and we deduce the corresponding expected discounted yield. In a first part, we determine the Faustmann value without or with the presence of risk. In a second part, for a fixed rotation period. we compare the results of the optimization with respect the intermediate culling in the absence and presence of risk. Then we deduce the impact of the presence of a risk for aquacultural system. In a third part, we optimize the rotation period and the culling.

The Faustmann value

In the first part we study the Faustmann value without the risk of epidemic event through a model of population dynamics. Then we study the same Faustmann value with the risk of epidemic event.

Without the risk of epidemic event

We first consider an aquacultural system without the presence of risk of epidemic event. The study of this case will allow us to define a benchmark management of the system.

For a rotation period T , a culling h(.) and a feeding f (.) the Faustmann value W 0 (up to a constant c 1 ) is the discounted value of cutting incomes net cost of start-up :

W 0 = +∞ i=1 (V(h(.), f (.), T ) -c 1 )e -iδT = (V(h(.), f (.), T ) -c 1 )e -δT 1 -e -δT = V(h(.), f (.), T ) -c 1 e δT -1
where V(h(.), f (.), T ) is the income generated by the cutting at time T and c 1 is the cost of start-up. V(h(.), f (.), T ) is by definition the sum of the culling income on period [0, T ] and the income at final rotation period T .

The Faustmann value can also be interpreted as, W 0 is the instantaneous value of income in time T discounted at the initial time and is solution of :

W 0 = (W 0 + V(h(.), f (.), T ) -c 1 )e -δT
The population dynamic model To take into account the culling in the calculation of the Faustmann value, i.e. to express V(h(.), f (.), T ), we introduce a model of population dynamics. The considered model is an average fish model : the state variables are the number n of fishes and the weight w. The evolution of these two variables is governed by the system of ordinary differential equations :

dn(t) dt = -(m(t) + h(t))n(t) dw(t) dt = G(f (t), n(t), w(t))
where m(.) is the natural mortality, G(., ., .) is the possibly density dependent growth function : individual fish-growth may depends on the fish density n(t). f (t) is the amount of feed per fish per week.

The net income

Once chosen the model of population dynamics we can express the total income. Total income V(h(.), f (.), T ) for fixed culling h(.) and fixed feeding f (.) is the sum of the culling income net the feeding and fixed costs H(h(.), f (.), T ) on the period [0, T ] and the final income V 0 (T ) :

V(h(.), f (.), T ) = H(h(.), f (.), T ) + V 0 (T )
The culling income net the feeding and the fixed costs H(h(.), f (.), t) on [0, t] actualized to time t are :

H(h(.), f (.), t) = t 0 [p(w(u))h(u)n(u) -sf (u)n(u) -k]e δ(t-u) du
where n(.) and w(.) are solutions of the dynamic model, s is the feeding costs and k fixed costs.

Calculation of the Faustmann value

Finally the Faustmann value is given by :

W 0 = V(h(.), f (.), T ) -c 1 e δT -1 with : V(h(.), f (.), T ) = T 0 [(p(w(u))h(u) -sf (u))n(u) -k]e δ(T -u) du + V 0 (T )
The maximal value of the Faustmann value for a fixed f (.) is obtained by solving the problem :

(P F 0 ) : max h(.),T V(h(.), f (.), T ) -c 1 e δT -1
The maximization of the Faustmann value W 0 with respect to the culling h(.), the feeding f (.) and the rotation period T can be decomposed in two steps : first we maximize V(h(.), f (.), T ) with respect to h(.) : and f (.

) : U 0 (T ) = max h(.),f (.) V(h(.), f (.), T ) then we maxi- mize U 0 (T ) -c 1 e δT -1
with respect to T with U 0 (T ) resulting from the first step.

In the presence of risk of epidemic event

We suppose that epidemic events occur in a Poisson process i.e. that epidemic events occur independently of one another, and ramdomly in time.

The distribution of the epidemic event time is an exponential with mean 1 λ : F (x) = 1-e -λx where λ is the expected number of epidemic events per unit time. No assumption is made on the type of epidemic events. We assume that θ t is the proportion of survival fishes following a epidemic event. We define the expectations

α(t) = E(θ t ) ≤ 1.
When the risk of epidemic event exists and is taken into account, in the literature, the authors classically assume that the operator systematically decides to interrupt the current cycle and begin a new cycle. This is fully justified in the case of severe epidemic. In the case of an epidemic of limited impact on mortality, to the first question about the optimal term a second question is added : should we interrupt the current cycle and begin a new cycle or is it better to continue the current cycle ? If there are alternatives, what is the criterion to choose ? To fulfill this goal, we define a possible criterion for choice based on a function z of θ t ? We assume z increasing with 0 ≤ z(θ) ≤ 1 . We choose a level z 0 such that, in the case of epidemic event :

-if z(θ) < z 0 (severe epidemic), we decide to interrupt the current cycle and begin a new cycle.

-if z(θ) > z 0 (minor epidemic), we decide to continue the cycle.

It is also possible to suppose that z depends on the survival fish at the date of the epidemic event.

Here, we study two particular cases. In the first case, the operator systematically interrupts the cycle in case of a epidemic event (z 0 > 1). In the second case, the operator continues the cycle even in case of epidemic events (which makes sense if the epidemic is minor) (z 0 < 0).

In case of epidemic event, the cycle is interrupt

For a rotation period T , a fixed culling h(.) and a fixed feeding f (.), the Faustmann value W 0 is the actualized value at initial time of the sum of two terms. The first one is the sum of the Faustmann value and the expectation V 1 (h(.), f (.), t) of the total income V(h(.), f (.), θ, t) for the period [0, t] in case of a epidemic event at time t. The second one is the sum of the Faustmann value and the total income V(h(.), f (.), T ) for the period [0, T ] in case of no epidemic event.

V(h(.), f (.), θ, t) is the sum of the culling income net the feeding and fixed costs H(h(.), f (.), t) during [0, t] actualized at time t and the final income V F (θ, t) at time t. The final income V F (θ, t) is assumed proportional to the final income without risk of epidemic event V 0 (T ) and is given by : V F (θ, t) = θV 0 (t). Then the total income is : V(h(.), f (.), θ, t) = H(h(.), f (.), t) + θV 0 (t). From definition of α we deduce the final income expectation :

V 1 (h(.), f (.), t) = E(V(h(.), f (.), θ, t)) = H(h(.), f (.), t) + α(t)V 0 (t)

Calculation of the Faustmann value

From (1) and expression of V 1 (h(.), f (.), t) we deduce that, in the presence of the risk of epidemic event the Faustmann value is given by :

W 0 = δ + λ δ V λ (h(.), f (.), T ) -c 1 e (δ+λ)T -1 - λ δ (c 1 + c 2 )
As in the case without risk, we find that the Faustmann value can be deduced from the income V λ (h(.), f (.), T ). The parameter δ is replaced by δ + λ. The major difference is the following : V 1 (T ) is not as in the case without risk the total income but a modified expression of the income V λ (h(.), f (.), T ). This difference is reflected by the substitution in the cases without risk of term H(h(.), f (.), T ) by a term H λ (h(.), f (.), T ), or even more precise replacing p(w(t))h(t)n(t) -sf (t)n(t) -k by [p(w(t))h(t)n(t) -sf (t)n(t) -k + λα(t)V 0 (t)]e λ(T -t) .

The maximal value of the Faustmann value is obtained by solving :

(P F 1 ) : max h(.),T W 0 = δ + λ δ V λ (h(.), f (.), T ) -c 1 e (δ+λ)T -1 - λ δ (c 1 + c 2 )
As in the case without risk, the maximal value of the Faustmann value with respect to the culling h(.), the feeding f (.) and the rotation period T can be decomposed in two steps : first we maximize V λ (h(.), f (.), T ) with respect to h(.) and f (.) : U λ (T ) = max h(.),f (.)

V λ (h(.), f (.), T )

then we maximize δ + λ δ U λ (T ) -c 1 e (δ+λ)T -1 - λ δ (c 1 + c 2 )
with respect to T with U λ (T ) resulting from the first step.

In case of epidemic event, the cycle is not interrupt

The Faustmann value is obtained by considering the value without risk but calculated with the expected number of survival fish.

3 Optimisation for a fixed rotation period T and a fixed feeding f

We first consider the limiting case of no density dependent growth which will be used as a reference in the case study of density dependent growth.

Without risk of epidemic event

Let us consider the case with fixed feeding f . In this case the evolution of the fish-weight w does not depend of a control.

We study the maximization of the Faustmann value with respect to culling h(.) for a fixed rotation period T :

(S 0 ) max h(.) V(h(.), f (.), T ) = T 0 [(p(w(t))h(t) -sf (t))n(t) -k]e δ(T -t) dt + V 0 (T ) with the constraint 0 ≤ h(t) ≤ h.
Assume that the final income is given by : V 0 (n, w) = p(w)n. From the no density dependence of the individual growth, p(w(t)) is independent of the cullings and only depends on t. Then we define R(t) = p(w(t)). We denote the function π 0 :

π 0 (t) = R (t) -(δ + m(t))R(t) - sf (t).
Applying the maximum Pontryagin Principle to the problem P m,0 we can deduce the optimal culling :

-if π 0 (T ) ≥ 0 then h * ≡ 0 in the vicinity of T -if π 0 (T ) < 0 then h(t) = h in the vicinity of T .

In the presence of risk of epidemic event

In case of epidemic event, the cycle is interrupt

We study the maximization of the Faustmann value with respect to culling h(.) for a fixed rotation period T and a fixed feeding f (.) :

(S 1 ) V λ (h(.), f (.), T ) = max h(.) H λ (h(.), f (.), T ) + V 0 (T ) with the constraint 0 ≤ h ≤ h.
Using the expression of V 0 (T ) we deduce that, compared to the case without risk, p(w(t))h(t)sf (t) is replaced by [p(w(t))h(t)-sf (t)+λα(t)p(w(t))]e λ(T -t) in presence of risk of epidemic event. Thus we deduce that, for the fixed rotation period T , the optimization differs and depends explicitly on λ and α. So we will pay attention to the consequence for the aquacultural practice.

We consider, as in the case without risk, a non density dependent growth for the fishes to facilitate the comparaison.

Let denote the function π 1 : π 1 (t) = R (t)-(λ(1-α(t))+δ +m(t))R(t)-sf (t). Applying the maximum Pontryagin Principle to the problem P m,λ , we deduce the optimal culling :

-if π 1 (T ) ≥ 0 then h * ≡ 0 in the vicinity of T -if π 1 (T ) < 0 then h(t) = h in the vicinity of T 3.2.

In case of epidemic event, the cycle is not interrupt

We study the maximization of the Faustmann value with respect to culling h(.) for a fixed rotation period T .

From the expression of the expected of survival fish N (t) :

N (t) = n(0)e - R t 0 (m(u)+h(u)+λ(1-α(u)))du ,
applying the maximum Pontryagin Principle to the problem P m+λ(1-α),0 we can deduce the optimal culling :

-if π 1 (T ) ≥ 0 then h * ≡ 0 in the vicinity of T -if π 1 (T ) < 0 then h(t) = h in the vicinity of T .

Comparaison : without and with presence of risk

By comparing the three propositions, for the optimal solution in the vicinity of rotation period, the natural mortality m(t) in the case without risk is replaced by the mortality due to events m(t) + λ(1 -α(t)) in the presence of risk. It is equivalent also, from a mathematical point of view, to replace the fixed discount rate δ by the variable discount rate δ + λ(1 -α(t)) in the previous problem.

By comparing the results of the two propositions we deduce that, for a fixed rotation period T , it is usually best to do culling at least at the end of the period in the presence of risk. From π 1 (t) = π 0 (t)-λ(1-α(t))R(t), we deduce that even if h ≡ 0 in the unrisky case, for sufficently large value of λ(1 -α(T )), h = h in the vicinity of T .

Comparing the results of the two proposals is permitted if the rotation periods are identical. If we consider the maximization problem, with respect to the rotation period, the rotation periods have no reason to be the same. In that case the comparison is not permitted and only simulations can allow us to compare the respective culling. We will therefore perform simulations.

4 Optimization with respect to the rotation period T

We now consider the case where individual growth is density dependent. If the growth is weakly density dependent, by continuity with the case of no density dependent growth, the obtained results are still valid at fixed rotation period T . If this is not the case, we cannot obtain analytical results for the solutions, then simulations are required.

The function of individual growth is given by : G(f, n, w) = w(0.04 -0.01w -10 -9 w 2 n f ) [START_REF] Heaps | Density dependent growth and the culling of farmed fish[END_REF]. The structure of the growth function is generic and can be used for other species. The price is assumed to depend on the weight : p(w) = p 0 w -c 0 .

Instead of estimating the feeding function f (.) as in [START_REF] Heaps | Density dependent growth and the culling of farmed fish[END_REF], to simplify the optimization problem, we decide to search the function f (.) in a parametrized family : f (t) = aw(t) b with a and b unknown coefficients. The determination of the rotation period T is important because of its impact on optimization. To better describe the optimization in the presence of random risk, it is wiser to look at the effective cutting age T and the effective final fish-weight S. Thus we calculate the respective expectations and variances :

E(T ) = T 0 tdF (t) + T (1 -F (T )) = F (T ) λ V ar(T ) = T 0 (t - F (T ) λ ) 2 dF (t) + (T - F (T ) λ ) 2 (1 -F (T )) = 2 λ 2 (1 -F (T ))(F (T ) - λT ) + F 2 (T ) λ 2 E(W) = T 0 w(t)dF (t) + w(T )(1 -F (T )) and V ar(W) = T 0 w 2 (t)dF (t) + w 2 (T )(1 - F (T )
) can be derived from the simulations.

Results and Discussion

The unit of time for the rotation period is the week. We suppose : m = 0.0042 week -1 , λ = 0.005 week -1 , δ = 0.001 week -1 , h = 0.06 week -1 . The results are included in Table 1, to complete, the parameter of optimal feeding function are a = .5748, b = 1.1907 for the unrisky case and a = .5739, b = 1.1698 in presence of risk. The standard deviation of the effective rotation period was calculated.

Risk

We asumme that the expected proportion of safe fish after an epidemic event is equal to .5. Without risk and with the presence of risk, there is culling for the optimal solution (Table 1).

The presence of risk involves earlier culling. The earlier culling provides a kind of selfinsurance against risk.

By observing the curves of the Faustmann value W 0 depending on the rotation problem T with optimal culling, we find that the Faustmann value least varies in the vicinity of the optimal rotation period with risk than without risk. This is another consequence of the fact that, with risk the optimal rotation period T is achieved with a relatively low probability.

Conclusion

We have studied the management of an aquacultural system in the presence of risk of epidemic event. In order to determine the optimal culling relative to the Faustmann criterion, we have considered a model of population dynamics, the choosen model is of average fish type. This model has allowed us to make the comparison without and with risk and highlighted the influence of the presence of risk of epidemic event on optimal culling. Specifically, the obtained Faustmann values, without or with the risk of epidemic event, highlighted differences in the criteria to be maximized. In the case of no density dependent individual growth, we have highlighted the impact of the presence of risk on the strategies, generically regardless of the considered species.

In the case of density dependent growth, the calculations for an aquacultural system have shown that the presence of risk of destruction event involves earlier culling for the optimal strategy.

The obtained results are conditioned by the choice of an individual fish growth model and by the specification of a weight model and a price model of fishes. Other studies using models adapted for other species would make the obtained results more generic.

Table 1 :

 1 Optimal culling for α = 0.5, n(0) = 1500000 fish.

		h(.)	T	W 0
	No	h(t) = h, 91.9 ≤ t ≥ 104.5 117.6	16.4n 0
	Yes h(t) = h, 88.6 ≤ t ≥ 101.4 115.2 (87.6) 12.1n 0


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In Europe, the rapid increase of intensification of farming practices which occurs since 1970's, is partly responsible of decline of farmland biodiversity. The Rio de Janeiro Declaration on Environment and Development in 1992 confirmed this fact and urged governments to encourage sustainable development, and especially sustainable agriculture. Organic farming is seen as a farming production system to satisfy this sustainability, by for example extensification of farming practices. This potential of organic farming had largely confirmed for animal taxa and weed species, but less for permanent grassland vegetation. We want to describe and explain dynamics of permanent grassland vegetation after the conversion to organic farming, in the case of a dairy farm in conversion since October of 2004. The aims of the present study is to highlight the influence of changes in farming practices on permanent grassland vegetation, and to know if organic farming practices favor certain grassland plant species according to their dissemination traits. We clustered 63 permanent grassland fields in 4 groups according to farming practices applied (amounts of inorganic and organic nitrogen sprayed, number of mowing by year and grazing intensity). The herbaceous vegetation of centre and margin was sampling in 23 fields during the spring of 2006. This work shows that farming practices which decrease plant diversity in the centre of the fields, have the same influence on vegetation of field margins. Plant species richness and diversity are greater in field margins than in centre of the fields, broadly and for quasi each distinguished class. Thus, permanent grassland margins acts as refugia for plant species which are absent in the centre and which will be able to establish them in field centre after extensification of farming practices.

The main interest of our work is to explain the differences observed in our study between centres and margins with the awareness of plant strategies particularly the plant functional traits implied in the plant spreading. This analysis is in progress and it is completed by the use of spatial statistical methodologies in order to highlight the spatial patterns of plant spreading at field scale.

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  Grassland field margins are able to maximise plant diversity at field scale Etienne Gaujour, Bernard Amiaud, Catherine C. Mignolet, Sylvain Plantureux To cite this version: Etienne Gaujour, Bernard Amiaud, Catherine C. Mignolet, Sylvain Plantureux. Grassland field margins are able to maximise plant diversity at field scale. EcoSummit 2007 -Ecological Complexity and Sustainability: Challenges and Opportunities for 21st-Century's Ecology, May 2007, Beijing, China. hal-02751011

MARGINS ARE ABLE TO MAXIMISE PLANT DIVERSITY AT FIELD SCALE. Authors & affiliations:

	Gaujour E., Amiaud B., Mignolet C., Plantureux S.
	UMR 1121 INPL(ENSAIA)-INRA, Laboratoire Agronomie-Environnement,
	2 avenue de la forêt de Haye, F-54505 Vandoeuvre-les-Nancy
	etienne.gaujour@ensaia.inpl-nancy.fr
	Abstract:

Title: (upper case)

GRASSLAND FIELD (Your abstract must use Normal style and must fit in this box. Your abstract should be no longer than 400 words. The box will 'expand' over 2 pages as you add text/diagrams into it.)


2

The necessity of agricultural prices management

• A market is "optimal" if price equates long run marginal cost

• Agricultural markets never equate marginal cost with price….

-Who can admit that long run marginal cost of production change from 50 to 200 in a few months ? -Prevents credit… » No banker will lend in such risky endeavors -And capital accumulation » The only way of increasing labor productivity and removing poverty Specific to agriculture :

Remark : average tomatoes prices are increasing, car prices decreasing…. The necessity of agricultural prices management Where do shocks come from ?

• Two alternative theories -1 -Exogenous shocks

• drought, frost, etc..; Out of operators control.

-2 -Endogenous motion The exogenous fluctuations theory

• Shocks from nature (drought, epidemy, etc… )

• Individually small and numerous -Every year are good or bad somewhere in the world

• Independently distributed

-to what extent ? : geographical y ? Throughout time ? ) ;

• Risk not depending upon remedies -(irrigation does not change rainfalls )

• Therefore, the law of large numbers holds

• Therefore insurance works • Within limits : a drought involves large surfaces • The larger the surface, the easier mutualizing risks :

-Throughout space : transportation, removing duties …. etc… -Throughout time : stockpiling , financial reserves… » "catbonds", "revenue insurance" etc.. -Throughout activities : futures markets etc… In fact :

• Both theories hold ! -The existence of climatic or epidemic shocks cannot be denied

• (and taken in consideration when elaborating policies)

-Yet, most of the international agricultural price volatility derives from endogenous phenomena

• It means that apparently contradictory policies must be pursued :

Insurance based methods to cope with exogenous yield risk :

-Provides large room for private insurance -Should yield insurance be subsidized ?

• In principle, no ! • Yet, poor even poorer than they feel… (a redistribution issue, not an efficiency issue)

Regulation to cope with endogenous market risk

• Cutting links between agriculture and market -Prices must be administered -And quantities too, for it is impossible to manage prices without considerations of quantities -Easy, because demand is fairly easy to know ! -Allows for "multifunctionnality"

• Not contradictory with the existence of residual markets, for marginal adjustments -Will be stabilized by intervention (the tip of iceberg)

• Not contradictory with trade ! -But incompatible with "ad valorem tariffs" which assume the problem is solved

  model missed both the surge and the down fall The chaotic ID3 model predicted both in 2005 (from 2001 data)

• Where does agricultural price volatility come from ? • One unanimous agreement, and two antagonistic theories ! Unanimous agreement on : Where does price volatility come from ?

	Every economists congregate : from a rigid demand which
	magnifies shocks..
	Elastic demand : large shock,	Inelastic demand : small shock,
	small price change	Large price change
	• But where do shocks come from ?

Here is the rational for liberalizing agriculture ! Liberal recipes OK for exogenous shocks. Do they works with endogenous shocks ?

	The efficiency of liberal prescription with exogenous shocks A more realistic cobweb scheme….. In a chaotic context, …..can result in chaotic series : « nature is wicky »
	12	Price
	Widening markets • Endogenous shocks : what is it ? Return force 8 10 • Because operators will react to new stabilizes prices • The cobweb model : 4 6 circumstances, any step creates opposite
	Suppressing production quotas and prices guaranties is also efficient Example of false expectations driven 2 alpha=-0.5;a=0.35; b=2; beta= 10; A=.005; ptilde=6.0; X0=5; reactions 0 fluctuations Not satisfactory (nothing prevents Repelling 1 21 41 61 81 101 121 141 161 181 201 Time • Exemple : stabilizing prices for any equilibrium point supplied quantity likely to generate prices and quantities being negative) Yet, shows how the equilibrium point Return force Return force overproduction, because producers are • This simulated price series looks like the tomatoes price series. sensitive to risk as well as to price.
	can be « repellent » (or the • Important notice : Nothing random ! • Implies that most « liberal » recipe will not equilibrium unstable) • Completely different properties ! work any more	9 10 11

• These are always liberal prescriptions • Let's see a few examples ….

The world wheat price has been less volatile during the years of high price policies in developped countries

		US Wheat Price (Constant yr 2000 $ / bushel ), 1866-
	16
	14
	12
	10
	8
	6
	4
	2
	0
	1866	1886	1906	1926	1946	1966	1986	2006
	Prices were higher and more volatile before 1935…
	Internal stabilisation policies do not increase volatility…
			….and help decreasing average price !	17

Concluding remarks :

• These views not shared by WTO and International institutions advisers.

-They lack economic analysis, satisfied with the « physiocrats » of 18th century -A pity they did not derive lessons from the 1930's ! • They mix up three different aspects of market :

-Comparative advantage and trade : undisputable ! -Efficiency effect of competition : present with elastic demand, not the case for agricultural (and other !) commodities. -The objectivity of income distribution : Very disputable ! But this is another story !


Dirk Seifert
email: dirk.seifert@loria.fr

An Executable Formal Semantics for a UML State Machine Kernel Considering Complex Structured Data

We present a comprehensive formal semantics for a UML state machine kernel which also considers the use and manipulation of complex structured data. We refer to the UML standard Version 2.1.1 which was published in year 2007. There has been no work that completely integrates complex structured data into a UML state machine semantics. We follow a "semantics-first" approach (in opposite to a "complete-notation-first" approach) in which we consider a sound basic kernel of the UML state machine notation, and extend this kernel only ater a thorough investigation of the impacts. We define an operational semantics which is intended to be implemented in a standard programming language. Currently we use such an implementation to automatically generate test cases out of a state machine specification. This document is intended to be adapted if necessary. We will indicate that by the version number given above, whereat the major version number indicates changes of the considered subset and the minor version number indicates adoptions and corrections.

The considered UML state machine subset includes:

1. Hierarchically and orthogonally structured states.

2. Multi-level transitions.

3. Use and manipulation of an associated data space.

4. Events comprising complex structured data. 5. Complex guards to control the firing of transitions.

6. Complex actions to update the data space and to generate new events.

Introduction

The Unified Modeling Language (UML) comprises thirteen diagram types to specify structure and behavior of a system or a system component [START_REF]Unified Modeling Language: Infrastructure and Superstructure. Object Management Group[END_REF]. The included state machines are used to either describe the discrete reactive behavior of a system (behavioral state machines) or to describe the usage protocol of a system (protocol state machines). We focus on behavioral state machines and use them to specify the states a system can take and actions it can execute during its lifetime in response to internal and external events. The discrete reactive character of state machines and the possibility to completely specify the behavior of a system make state machines appropriate to model reactive systems.

State machines are an object-oriented extension of the classical Harel Statecharts [START_REF] Harel | Statecharts: A Visual Formulation for Complex Systems[END_REF]. They are mathematical models with a graphical representation: the nodes depict simple or composed states of the system and the labeled edges depict transitions between these states. Composite states are used to hierarchically and orthogonally structure the model, thus reducing its graphical complexity. Simple composite states contain exactly one region and orthogonal states contain at least two regions. In every region only one state must be active at a time. The state which is entered by default if the enclosing region is entered, is marked by a transition emanating from a filled circle (called the default transition). Labels express conditions under which transitions can be taken and the actions that will be executed when the transitions are taken. Events are used as triggers to activate transitions and can be parameterized to exchange data. Optional, every state machine has a data space that can be read and manipulated by the state machine during its execution. More precisely, it is possible to read data values to describe fine-grained conditions when a transition can be taken, or to manipulate data values and exchange information within the actions. A transition comprises a source state, a trigger event, an optional guard, an optional effect (which consists of a sequence of actions), and a target state. A guard describes with a possible reference to the state machines data space a fine-grained condition that must evaluate to true to enable the transition. Hence, the activation of the source state, the available trigger event and the fulfilled guard condition constitute the precondition of the transition. An action can either be a statement manipulating the data space or the generation of new events. Hence, the action sequence and the subsequently reached target state constitute the postcondition of the transition. In opposite to the classical Statecharts, the event processing takes place in a so-called run-to-completion step. This asynchronous event processing demands the processing of the previous step to be completely finished before the next step can be executed. In the following we introduce the state machine notation by means of an simple example, namely a Car Audio System. The principle user interface of this system is shown in Figure 1. The textual requirements for the Car Audio System could be as follows:

It should be possible to turn the Car Audio System on and off. When turned on, it should play one of three different audio sources, namely radio, tape or compact disc, respecting the presence of a tape or a compact disc. It should be possible to change between available sources. Furthermore, it should be possible to switch between four radio stations, to spool a tape backward or forward, and to select the previous or the next track of a compact disc. Based on the textual requirements we introduce the following events to model the required behavior: power, src (to switch between the different sources), next, back and play. We also introduce events signaling the insertion and the ejection of a tape or a compact disc as well as events to signal system reactions (cd insert, cd eject, tape insert and tape eject). Furthermore, we use data variables to store detailed information about the current state. We use an integer variable trackCount to store the number of titles of an inserted compact disc, and the two boolean variables inCDFull and inTapeFull to store if a compact disc and a tape are inserted into the Car Audio System. We will use this variables to control the switching between the different sources. In most applications a state machine is assigned to a class diagram describing the behavior of the class instances. In this setting, the class attributes constitute the data space of the state machine. The events of a state machine will also be represented as classes having their own attributes. We differentiate between events which are referenced by the state machine (i.e., to send events to other system components) and events which will be processed by the state machine. Figure 2 shows the class diagram for the Car Audio System and the related state machine model. Figure 3 shows a state machine model of the Car Audio System and the related data space. At the highest level of abstraction the state machine CarAudioSystem consists of an orthogonal state which comprises three regions. The two regions CD Player and Tape Player model if a tape or a compact disc are present in the system. The more complex region Audio Player models the control unit of the Car Audio System. It is refined by two states, namely Off and On. By default the system is assumed to be switched off. If an event occurrence power is processed the system is switched on and starts to play the radio (due to the default transition). The composite state On is refined into states modeling the three signal sources. The transitions between these states describe the changes between the sources as reaction to an event occurrence src. For example, if the system is in Tuner Mode and a tape and a compact disc are inserted into the system (i.e., the boolean variables inCDFull and inTapeFull are true) and an event occurrence src is processed, the system can either switch to the tape mode or switch to the compact disc mode since both transitions are enabled. All three substates of Audio Player are further refined to describe the particular behavior in reaction to the events next, back and play in each state. If a transition is taken (the transition is said to fire) the associated action sequence is executed. That includes the generation of new event occurrences and the manipulation of the data space. For example, if the transition from state CD Empty to state CD Full in region CD Player fires, the attribute assignments changes such that inCDFull is set to true and that trackCount is set to the value of the first parameter of the triggering event occurrence cd insert.

Src

Semantic Variation Point 1 (Expression Language)

The UML standard indicate that the expression language which can be used to specify guards and actions depends on the chosen action language for the state machine (usually the target programming language). This allows a wide application domain for state machines. But it considerably complicates formal reasoning about state machine models. Currently, we use a subset of the JAVA programming language [10] to specify guard and action expressions. For the future we propose to define an independent expression language which can be mapped to an action language but which allows formal reasoning.

The hierarchical alignment of state machine states forms a tree structure with a region as the root node, simple states at the leaves and alternating composite states and regions in between. Figure 3 shows this structure for the state machine Car Audio System. Regions are depicted as dotted nodes and have an optional name. State are depicted as simple framed nodes, whereat default states are depicted as double framed nodes. The transitions are depicted as dashed arrows. In the tree structure it is easily identifiable which state will be left and which state will be entered if a transition is taken. Affected by the transition is the subtree which contains both the source state and the target state. Most transitions are within one hierarchy level. But it is also possible that a transition crosses multiple hierarchy levels. Such transitions are called multi level transitions. For example, the transition leaving state Tape Mode and entering state Off is a multi level transition. The transition could model, for example, that if the tape reaches its end the Car Audio System is turned off. The affected subtree can be also easily identified.

We use for all definitions as the basic notation the Z Formal Specification Notation. An introduction to Z and its formal semantics can be found in [START_REF] Spivey | The Z Notation: A Reference Manual[END_REF][START_REF] Woodcock | Using Z. Specification, Refinement, and Proof[END_REF][START_REF]International Organisation for Standardization. Information Technology -Z Formal Specification Notation -Syntax, Type System and Semantics[END_REF][START_REF] Potter | An Introduction to Formal Specification and Z[END_REF]. With respect to a tuple p == (c 1 , . . . , c n ), we denote with p.1 = c 1 , . . . , p.n = c n the corresponding component of p.

2 Abstract Syntax

States and Regions

A state machine is composed of hierarchically and orthogonal structured states. The nodes set comprises the states as well as the regions of a state machine. Regions are used to group refining states. States, which are not further refined, are called simple states. States, which are further refined, are called composite states. Composite states which are refined by exactly one regions are called simple composite states. Composite states which are refined by at least two regions are called orthogonal states.

Definition 1 (Node Set)

Let N denote the given non-empty, finite set of states and regions.

We distinguish among the states in N four types, namely region, simple, simple composite and orthogonal.

Definition 2 (Type Function)

Let N be the set of nodes. The function type takes a node as input and yields the type of the node. type : N → {region, simple, simple composite, orthogonal} Remark: Regions and states of a state machine are represented in the UML standard as separate classes. Hence, they are distinguished by their type. The different state types are distinguished based on three class attributes. The boolean attribute issimple indicates if the state is a simple state. The boolean attribute isComposite indicates if the state is further refined. Finally, the boolean attribute isOrthogonal indicates if the state is an orthogonal state. Using a type function avoids unnecessary redundancy since invalid attribute combinations are avoided. The relation between these class attributes and the function type is as follows.

Definition 3 (Attribute Mapping)

The following relation exists between the used node types and the UML class attributes.

simple ⇔ isSimple simple composite ⇔ ¬ isSimple ∧ isComposite ∧ ¬ isOrthogonal orthogonal ⇔ ¬ isSimple ∧ isComposite ∧ isOrthogonal
Remark: Simple composite states are also called xor-states and orthogonal states are also called andstates. This is motivated by the number of simultaneously active direct substates. Refined states contain regions. Within a region exactly one state must be active at a time. Simple composite states contain exactly one region in which exactly one state is active (i.e., there is a exclusive choice among the states: xor).

Orthogonal states contain at least two regions. Consequently there are at least two states simultaneously active at a time (i.e., exactly one state in every region: and).

The node hierarchy of a state machine is given by a tree (N, H), where N denotes the node set and H : P(N × N) denotes the non-empty subnode relation. A tuple n → n : H indicates, that node n is refined by node n (i.e., n is a subnode of n). Based on the subnode relation we define relative to a node three different nodes sets.

Definition 4 (Subnodes Sets) Let (N, H) be the node hierarchy, and let H + denote the transitive closure of H. The functions subnodes : N → P N takes a node n : N as input and yields a set of direct subnodes of n. The functions subnodes + and subnodes * yield the transitive and transitive-reflexive closures, respectively.

subnodes(n) == {n : N | n → n ∈ H} subnodes + (n) == {n : N | n → n ∈ H + } subnodes * (n) == {n} ∪ subnodes + (n)
Is n 2 ∈ subnodes * (n 1 ) we say that n 1 is a supernode of n 2 , and that n 2 is a subnode of n 1 . Due to the reflexivity of subnodes * n is supernode as well as subnode of oneself. Is n 2 ∈ subnodes + (n 1 ) we say that n 1 is a strict supernode of n 2 , and that n 2 is a strict subnode of n 1 .

It is required that a region is refined by at least one state, a simple composite state is refined by exactly one region, and an orthogonal state is refined by at least two regions. This implies that regions and state alternate in the tree structure and that the leaves are simple states.

Definition 5 (Well-formed Node Hierarchy)

A well-formed node hierarchy (N, H) must preserve the following constraints.

∃ 1 n : N • n / ∈ ran H ∧ n ∈ dom H ∧ ∀ n : N \ {n} • ∃ 1 n : N • n → n ∈ H (1) ∀ n : N | type (n) = region • (∀ n : subnodes(n) • type (n ) = region) (2) ∀ n : N | type (n) = simple • subnodes(n) = ∅ (3) ∀ n : N | type (n) = simple composite • (∀ n : subnodes(n) • type (n ) = region) ∧ (#subnodes(n) = 1) (4) ∀ n : N | type (n) = orthogonal • (∀ n : subnodes(n) • type (n ) = region) ∧ (#subnodes(n) > 1) (5)
Constraint ( 1) requires in a well-formed node hierarchy a tree structure. That means, that there exists a distinguishable root node, all remaining nodes have exactly one supernode, and that there exists no loops in the structure. From the UML standard it follows that the root node must be a region (cf. Definition 6). Constraint (2) to ( 5) characterize the different refinement variants for states and regions. They include, that the leaves of the tree structure are simple states (∀ n :

N | n : N • n → n : H • type (n) = simple).
Definition 6 (Root Region) Let (N, H) be the node hierarchy. root denotes the root region of the inherent tree structure in H.

root == µ n : N | n / ∈ ran H type (root) = region
The substate relation H is injective and, except for the root region, surjective. The inverse relation H -1 is a partial function which yields the container of a node.

Definition 7 (Container Function)

Let (N, H) be the node hierarchy. The partial function container : N → N takes a node n : N \ {root} as input and yields the direct supernode n : N of n. We call n container of n.

container (n) == µ n : N | n → n ∈ H
We call the state which will be activated if one of its supernodes is activated default state. This is in opposite to the common literature. There, such states are called initial states. We use a different term since not all default states are initially active (e.g., if an enclosing orthogonal state is not initially active).

Definition 8 (Default States)

Let (N, H) be the node hierarchy. The set N ⊆ N comprises all default states.

∀ n : N | type (n) = region • ∃ 1 d : N | d ∈ subnodes(n) • d ∈ N 2.

Events

Events are used to trigger transitions. They can be parameterized to exchange detailed information. An event comprises of a name and a finite number of data partitions. In practice, the event name corresponds to the class name and the particular data partitions correspond to the attributes of this class.

Definition 9 (Event Names)

Let E denote the given set of event names.

Definition 10 (Event Instances) Let K be an index set with n elements, and let (P i ) i:K a family of sets P i . The set E ν denotes the set of all event instances to an event name ν : E .

E ν == ν P 1 × . . . × P n
Definition 11 (Event Set) Let E be the set of event names. The set E denotes the set of all event instances with respect to E .

E == | ν:E E ν
The set E is the disjunctive union of all particular set of event instances. We call a member of the event set event instance and denote it ν(. . . ). To demonstrate the construction of an event set we give a small example.

Example 1 (Set of Event Instances)

Let E 1 = {a, b} be a set of event names, and let a have two parameters of type N and bool, and let b have one parameter of type B. The set E 1 denotes the set of all event instances with respect to E .

Parameter sets: The transitions of a state machin SM can only be triggered by a subset of the event instances in E. In anticipation of the following definitions we distinguish four subsets of E. First, a subset which comprises all event instances which can trigger transitions of the state machine: E SM ⊆ E. Second, a subset which comprises all event instances which are sent by the state machine to other system components: E ENV ⊆ E.

P a 1 = N ∧ P a 2 = B P b 1 = B Sets of event instances: E a = a N, B = {a(0,
We further distinguish two subsets in E SM . Third, a subset which comprises all event instances which can only by used by the state machine itself: E prv SM ⊆ E SM . Forth, a subset which comprises all event instances which can also be used by the environment E pub SM ⊆ E SM . This set represents the public interface of the state machine SM. With respect to these subsets the following constraints apply:

E prv SM E pub SM = E SM and E SM E ENV = E.

Data Space

A data space is associated to every state machine comprising a finite number of data partitions. These partitions can be read and manipulated during the execution of a state machines. In practice, the class attributes correspond to the data partitions of an associated state machine.

Definition 12 (Data Space)

Let K be an index set with n elements, and let (P i ) i:K a family of sets P i . The set D denotes the set of all data space assignments.

D == P 1 × . . . × P n

Guards

A guard is a condition that provides a fine-grained control over the enabling of a transition. It is a function which with takes an event instance and a data space assignment as inputs and yields a boolean value indicating, if the specified condition is fulfilled. The expression language for guards is defined by the used action language (cf. Semantic Variation Point 1). From the UML standard it is only required that guards should be pure expressions without any side effects. Guards with side effects are ill formed. Please note that the event instance is not part of Definition 13 and 14. It will be added in Definition 15.

Definition 13 (Guards)

Let D be the data space. The set G denotes the set of all guard functions.

G == D → B

Actions

The effect of a transition is a sequence of actions which will be executed if the transition fires. An action can either be a statement updating the data space or the generation of a new event instance. Updating the data space means that a new data space assignment will be selected. Generating a new event instance means that an event instance will be selected. In practice, the effect correspond to the execution of the action code and the generation of new event class instances.

Definition 14 (Actions)

Let D be the data space, and let E be the set of all event instances. The set A denotes the set of all action functions.

A

== event D → E | update D → D (6)

Transitions

Transitions describe the state changes in state machines. Graphically, they are directed labeled edges between the source state and the target state. A label comprises a trigger, an optional guard and an optional sequence of actions. We denote with n 1 e [g] / A

----→ n 2 a transition graphically, where n 1 denotes the source state, e denotes the triggering event instance, g denotes the guard, A denotes a sequence of actions, and n 2 denotes the target state of the transition.

Definition 15 (Transitions)

Let (N, H) be the node hierarchy, let E be the set of event names, let E be the set of all event instances, let G be the set of all guards, and let A be the set of all actions. The set T :

P(N × (E → G × seq A) × N)
denotes the set of all transitions. A well-formed transition set must preserves the following constraints.

∀ t : T • ∃ 1 ν : E • E ν ⊆ E SM ∧ dom t.2 = E ν (7)
(∀ f : D → E | a = event(f ) • d ∈ dom f ) ∧ (∀ f : D → D | a = update(f ) • d ∈ dom f )) (8)
Constraint 7 requires that a label function must be defined for all event instances to an event name, whereat the set of possible event instances is restricted to that of the state machine. Constraint 8 requires that if the label function is applied to an event instance and the guard function applied to a data space assignment evaluates to true, all action functions must be defined as well.

State Machine

Definition 16 (State Machine) Let (N, H) be the node hierarchy, let N be the set of default states, let E be the set of event instances, let D be the data space, let G be the set of guards, let A be a set of actions, and let T be a set of transitions. The tuple SM denotes a state machine.

SM == ((N, H), N, E, D, G, A, T) (9)
A state machine is well-formed if Definition 5 and Definition 15 apply.

Semantics

The semantics of state machines is defined by means of executing a hypothetical machine (i.e., to processes events and to executes transitions). This comprises the execution of semantic steps which describe the transition from one semantic state to the subsequent semantic state.

Active State Configuration

A state machine can be in more than one state at a time due to its hierarchical and orthogonal structure. We call a set of simultaneously active states an active state configuration or just configuration.

Definition 17 (Active State Configuration)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine, and let root be the root region of SM. The set C : P P N denotes the set of all active state configurations of SM.

C == {c :

P N | ( ∀ s : c • type (s) = region ∧ ∃ 1 s : subnodes(root) • s ∈ c) ∧ (∀ s : c | type (s) = simple • ∀ r : subnodes(s) • ∃ 1 s : subnodes(r) • s ∈ c )}
An active state configuration comprises no regions. It is required that exactly one direct substate of the root region is contained in an active state configuration. For all states in an active state configuration which are composite states it is required that for every region refining this state, exactly one direct substate is also contained in the active state configuration. An active state configuration can be visualized as a complete subtree of the state machine's tree structure. We call an active state configuration c start configuration if it comprises only default states c ⊆ N.

Event Store

Information exchange is realized by sending and receiving of events to and from the environment of a state machine. Events for internal communication and events which will be received from the environment will be buffered until they are processed.

Semantic Variation Point 2 (Event Store)

Events will be buffered in a state machine until they are processed. The nature of this event store is not specified by the UML standard.

It is left open to the user of state machines to specify the behavior of the event store. To respect this variation point we define the inductive data type event store. An event store is either empty or it is composed of an event instance and an event store.

Definition 18 (Event Store) Let E be the set of event instances. Q denotes the data type of an event store.

Q == | add Q × E (10)
We use the function ⊕ : Q × seq E → Q to add a sequence of event instances to an event store and we use the partial function : Q → Q × E to remove an event instance from a non-empty event store. With it we abstract from a special order of event instances in an event store. In most practical applications, the type Q is instantiated by a FIFO-queue.

Semantic State -Status

A semantic state of a state machine, called a status, comprises an active state configuration, an event store and a data space assignment.

Definition 19 (Status)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine, let C be the set of configurations, and let Q be the set of event stores. The set Z denotes the set of all status of SM.

Z == C × Q × D (11)
We denote with [[c, q, d ]] a member of Z. An initial status comprises the start configuration.

Transition Selection

During a semantic step the state machine moves from one status to the subsequent status. If an event instance is selected for processing one or more transitions can be activated for firing. If no transition is activated, the event instance will be discarded. Please note, currently we do not use the notion of deferring events.

Semantic Variation Point 3 (Discarding Events)

Although the UML standard defines that an event instance which does not enable a transition and which is not in the deferred event list will be discarded, we note that in practice this behavior could be unwanted.

For this reason we mark the discarding of event instances as a semantic variation point.

A transition is called enabled, if the source state of the transition is included in the current configuration, the event name is equal to the trigger name and the guard evaluates to true.

Definition 20 (Enabled Transition)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine, let [[c, q, d ]] : Z be a status, and let (q , e) == q be the result from removing an event instance e from the event store q. The function enabled : Transition are allowed to cross multiple level in the node hierarchy. We call such transitions multi-level transitions. To correctly deal with multi-level transitions we need to know the scope of a transition. The scope allows to identify the set of states which will exited and entered if a transition is fired. This information is needed to identify conflicting transitions among the set of enabled transitions. The scope of a transition is identified by the least common ancestor of the source and target state. It is of type region or orthogonal.

T × C × E × D → B

Definition 21 (Transition Scope)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine. The function lca : T → N takes a transition t : T as input and yields the least common ancestor of the source and target state.

lca (t) == µ n : N | (t.1 ∈ subnodes + (n)) ∧ (t.3 ∈ subnodes + (n)) ∧ ( n : N | n ∈ subnodes + (n) • t.1 ∈ subnodes + (n ) ∧ t.3 ∈ subnodes + (n )) (13)
Based on the scope we can identify the main source and the main target of a transition. These two states represent the root nodes of the subtrees which are affected by a transition.

Definition 22 (Main Source and Main Target)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine. The function mainSource : T → N and the function mainTarget : T → N take a transition t : T as input and yield the main source and the main target of t, respectively.

mainSource (t) == µ s : subnodes(lca (t)) | t.1 ∈ subnodes * (s) if type (lca (t)) = region lca (t) if type (lca (t)) = orthogonal (14) mainTarget (t) == µ s : subnodes(lca (t)) | t.3 ∈ subnodes * (s) if type (lca (t)) = region lca (t) if type (lca (t)) = orthogonal (15)
The set of states which will be exited if a transition fires contains all substates of the main source that are included in a configuration.

Definition 23 (Exit Set)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine, and let Z be the set of status. The function exits : T → P N takes a transition t : T and a status [[c, q, d ]] : Z as input and yields the set of states which will be exited by transition t.

exits (t, [[c, q, d ]]) == subnodes * (mainSource (t)) ∩ c ( 16
)
The set of states which will be entered if a transition fires contains all substates of the main target which contain the target state or which are implicitly entered by the transition (default states).

Definition 24 (Enter Set) Let SM = ((N, H), N, E, D, G, A, T) be a state machine. The recursive function enters : N × N → P N takes two nodes n 1 , n 2 : N as input and yields with respect to n 1 the set of states which will be entered if n 2 is entered.

enters (n 1 , n 2 ) ==                  {n 1 } if type (n 1 ) = simple {n 1 } ∪ n ∈subnodes(n 1 ) enters (n , n 2 ) if type (n 1 ) = simple composite ∨ orthogonal enters (n , n 2 ) if type (n 1 ) = region (17)
Where

n = µ n : subnodes(n 1 ) | (n 2 ∈ subnodes * (n )) ∨ (n ∈ N ∧ n 2 / ∈ subnodes + (n 1 )).
If parameter n 1 is of type simple, just this state will be entered. Is parameter n 1 is of type simple composite or orthogonal, this state and its contained regions will be entered (subnodes(n 1 )). If parameter n 1 is of type region, we differentiate two alternatives. Either, the direct substate n will be entered which contains the target state -target ∈ subnodes * (n ) or the direct substate n will be entered which is the default state.

The former is the case, if we are moving down the node hierarchy to the target state. The latter is the case, if we already passed the target state and are moving down to the leaves of the state hierarchy (i.e., the target state is not a substate of n 1 ) -n ∈ N ∧ target / ∈ subnodes + (n 1 ). This situation arises, if the target state is a refined state or we have to enter an orthogonal regions which is not directly entered by the transition.

The function enters initially applied to the main target (initial parameter n 1 ) and target of a transition (parameter n 2 ) yields all states which will be entered by the transition. We use the abbreviation enters (t) instead of enters (mainTarget (t), t.3).

It is possible that more than one transition is enabled by an event instance. If more than one transition is enabled it may be the case that one or more transitions are in conflict with each other. Such a conflict appears, if two transitions exit same states. Firing both transitions would lead to an ill-formed status. A set of non-conflicting transitions must be selected for firing.

Definition 25 (Conflict Relation)

Let SM = ((N, H), N, E, D, G, A, T) be a state machine. The relation ∦ : T × T relates two transitions t 1 , t 2 : T if they are in conflict with each other.

∦ == {(t 1 , t 2 ) : T × T | exits (t 1 ) ∩ exits (t 2 ) = ∅} (18)
We call two transitions t 1 , t 2 : T conflict-free, denoted t 1 t 2 , if they are not in conflict ( == ¬ ∦).

Conflict resolution is carried out in two steps. In the first step, transitions with the highest priority are selected. The used priority scheme is defined on the relative positions of the source states in the node hierarchy. A transition, whose source state is a strict substate of the source state of another transition has priory over this transition.

Definition 26 (Priority Relation) Let SM = ((N, H), N, E, D, G, A, T) be a state machine. The relations ≺ : T × T relates two transitions t 1 , t 2 : T if t 1 has priority over t 2 , denoted t 1 ≺ t 2 .

≺ == {(t 1 , t 2 ) : T × T | t 1 .1 ∈ subnodes + (t 2 .1)} (19)
If there are still conflicts among selected transitions, we identify sets of transitions in a second step, which are maximal with respect to their cardinality and in which all transitions are pairwise conflict-free. Altogether, a so-called transition selection algorithm selects conflict-free subsets of enabled transitions using the given priority scheme.

Definition 27 (Firing Transition Set) Let SM = ((N, H), N, E, D, G, A, T) be a state machine, let Z be the set of status, let Q be the set event stores, let q : Q be an events store and e : E be an events instance such that (q , e) = (q), and let [[c, q, d ]] : Z be a status of SM. A firing transition set T ⊆ T must fulfill the following constraints.

∀ t : T • enabled (t, c, e, d) (20)
∀ t 1 , t 2 : T | t 1 = t 2 • t 1 t 2 (21) t : T \ T | enabled (t , c, e, d) • ∀ t : T • t t ∨ t ≺ t (22)
Constraint 20 requires all transitions in a firing transition set to be enabled. Constraint 21 requires all transitions in a firing transition set to be pairwise conflict-free. Constraint 22 requires that there exists no transition outside the set which is enabled and conflict free with respect to all transitions in the set, or which is enabled and has priority over a transition in the set.

Semantic Variation Point 4 (Firing Transition Set Selection)

It is possible that there exists more than one valid firing transition set at a time. The UML standard does not specify which set to choose for the next semantic step.

the execution or firing of a transition is defined in three steps. First, the source state and all effected states will be exited. Second, the actions of the transition will be executed. Third, the target state and all effected states will be entered. If the chosen firing transition set contains more than one transition the order in which the transition are executed is not fixed.

Semantic Variation Point 5 (Firing Transition Set Execution Order)

The UML standard does not specify an order in which transitions in a firing transition set will be executed.

Semantic Step

A semantic step describes the transition from one status to the subsequent status. We distinguish two cases.

The first case covers the situation in which the event store does not contain an event instance. And the second case covers the situation in which an event instance can be removed from the event store. In the first case, the configuration and the data space assignment remain unchanged. Only event instances received from the environment are added to the event store. In the second case, a firing transition set is identified and the contained transitions are executed. This may comprise updating the data space and generating new event instances. Generated event instances which belong to the state machine are added to the event store. Finally, event instances received from the environment are added to the event store.

A semantic step is atomic and the next semantic step can only be executed, if the current semantic step is completely finished -a so-called run-to-completion semantics. We denote with [[c, q, d ]]

E in ,E out ----→ [[c , q , d ]] a semantic step ([[c, q, d ]], E in , E out , [[c , q , d ]]) : Z × seq E pub SM × seq E ENV × Z.
Definition 28 (Semantical Step) Let SM = ((N, H), N, E, D, G, A, T) be a state machine, let Z be the set of status, let [[c, q, d ]] : Z be a status, let T ⊆ T be a valid firing transitions set, and let E in : seq E pub SM a sequence of received event instances. A semantic step [[c, q, d ]]

E in ,E out ----→ [[c , q , d ]] : Z × seq E pub SM × seq E ENV × Z is defined as follows. q =<> q = ⊕(q, E in ) [[c, q, d ]] E in , --→ [[c, q , d ]] (23)
q ∈ ran add (q , e) = (q) c = (c \ ∀ t:T exits (t)) ∪ ∀ t:T enters (t)

A seq ∈ perm({t : T • t.2(e).2}) (d , E gen ) = performAll( / A seq )(d) (E int = E gen E SM ) ∧ (E out = E gen E ENV ) q = (q ⊕ E int ) ⊕ E in [[c, q, d ]] E in ,E out ----→ [[c , q , d ]] (24)
Where E out : seq E ENV denotes the sequence of generated outgoing event instances and E int : seq E SM denotes the sequence of generated internal event instances.

The event instances in E out are sent by the state machine to the environment (i.e., to the particular system components). The function perm : P seq X → P seq(seq X) takes a set as input and yields the set of possible permutations. The function / : seq(seq X) → seq X flattens a sequence of sequences (i.e., the particular sequences will be concatenated to a single sequence). The function performAll : seq A → D → (D, seq E) takes a sequence of actions and a data space assignment as input and yields an ordered pair comprising the new data space assignment and the sequence of generated events. performAll calculates the intrinsic effect which results from the execution of all transitions in the firing transition set. To illustrate Definition 28 we list a sample ML implementation in Section 5.

Remark: From the literature related to the semantics of Statecharts (e.g., [START_REF] Harel | The STATEMATE Semantics of Statecharts[END_REF][START_REF] Helke | Verification of Statecharts Including Data Spaces[END_REF]) it is well known that write conflicts to data variables can happen due to the parallel execution of transitions. This happens if two transition try to write to the same data variable. A lot of conflict resolution strategies have been proposed, for example, the so-called interleaving semantics, where conflicts are resolved in non-determinism. Such conflicts cannot happen during the execution of transitions in UML state machines. These conflicts are avoided by the sequential execution of transitions.

Summary

The UML state machines semantics is adapted from the STATEMATE semantics [START_REF] Harel | The STATEMATE Semantics of Statecharts[END_REF] to fit into the objectoriented paradigm [START_REF] Harel | Executable Object Modeling with Statecharts[END_REF]. The Statemate semantics itself is related to the classical Harel Statecharts [START_REF] Harel | Statecharts: A Visual Formulation for Complex Systems[END_REF][START_REF] Pnueli | What is in a Step: On the Semantics of Statecharts[END_REF][START_REF] Harel | Some Thoughts on Statecharts, 13 Years Later[END_REF].

We presented an operational semantics which is complete for the considered subset and which includes all necessary definitions to implement it. Moreover, it is the first formalization which includes all definitions related to the use of complex structured data in state machines. The presented semantics partly benefits from previous works (e.g., [START_REF] Balser | Interactive Verification of UML State Machines[END_REF]18,[START_REF] Porres | Modeling and Analyzing Software Behavior in UML[END_REF][START_REF] Eshuis | Requirements Level Semantics for UML Statecharts[END_REF][START_REF] Lilius | Formalising UML State Machines for Model Checking[END_REF][START_REF] Lilius | The Semantics of UML State Machines[END_REF][START_REF] Latella | Automatic Verification of a Behavioural Subset of UML Statechart Diagrams Using the SPIN Model-checker[END_REF][START_REF] Latella | Towards a Formal Operational Semantics of UML Statechart Diagrams[END_REF]21,[START_REF] Fecher | 29 New Unclarities in the Semantics of UML 2.0 State Machines[END_REF]). A review of several semantics can be found in [START_REF]STL: UML Semantics Project[END_REF]. Most approaches focus on specialized applications and use specialized notations, or the used subset differs from ours. Moreover, there have been major changes in UML 2 that require a deep revision of previous works.

Sample ML Implementation

) ( * f o l d ( o , [ f , g , h ] ) ( n ) = h o ( g o ( f o n ) ) * ) f u n f o l d ( f , n ) ( [ ] ) = n | f o l d ( f , n ) ( x : : x s ) = f o l d ( f , f ( x , n ) ) ( x

Figure 1 :

 1 Figure 1: User interface of the Car Audio Sysem.

Figure 2 :

 2 Figure 2: Class diagram for the Car Audio System.

Figure 3 :

 3 Figure 3: State machine model of the Car Audio System and the associated tree structure.

  true), a(0, false), a(1, true), a(1, false), . . . } E b = b B = {b(true), b(false)} Set of all event instances: E 1 = E a | E b = E a E b = {a(0, true), a(0, false), . . . , b(true), b(false)}

  Figure 4 illustrates the partition into the different subsets.

Figure 4 :

 4 Figure 4: Partitioning of the set of event instances E.

  s i g n a t u r e SM STRUCTURE = s i g t y p e D; ( * t y p e o f d a t a s p a c e * ) t y p e E ; ( * t y p e o f e v e n t s * ) end ; s i g n a t u r e STATEMACHINE = s i g t y p e D; ( * t y p e o f d a t a s p a c e * ) t y p e E ; ( * t y p e o f e v e n t s * ) ( * t y p e o f g u a r d s : p r e d i c a t e o v e r an e v e n t ( from t r a n s i t i o n ) and * ) ( * a d a t a s p a c e a s s i g n m e n t * ) d a t a t y p e G = g u a r d o f D -> b o o l ; ( * t y p e o f a c t i o n s : f u n c t i o n t h a t c r e a t e s an e v e n t o r u p d a t e s a * ) ( * d a t a s p a c e w r t an e v e n t ( from t r a n s i t i o n ) and a d a t a s p a c e * ) ( * a s s i g n m e n t * ) d a t a t y p e A = e v e n t o f D -> E | u p d a t e o f D -> D; ( * t y p e o f t r a n s i t i o n s ( i n c o m p l e t e ) * ) d a t a t y p e T = t r a n s i t i o n o f E -> G * A l i s t ; ( * e x a m p l e s t e p i m p l e m e n t a t i o n * ) ( * n o t c o n s i d e r i n g t h e c o n f i g u r a t i o n and t h e e v e n t p o o l * ) v a l p a r t i a l S t e p : T -> E * D -> D * E l i s t ; end ; f u n c t o r SM( s t r u c t u r e s m s t r u c : SM STRUCTURE) : STATEMACHINE = s t r u c t t y p e D = s m s t r u c . D; t y p e E = s m s t r u c . E ; d a t a t y p e G = g u a r d o f D -> b o o l ; d a t a t y p e A = e v e n t o f D -> E | u p d a t e o f D -> D; d a t a t y p e T = t r a n s i t i o n o f E -> G * A l i s t ; ( * p e r f o r m one s i n g l e a c t i o n * ) ( * i n p u t : d a t a s p a c e a s s i g n m e n t and l i s t o f ( g e n e r a t e d ) e v e n t s * ) ( * y i e l d s : new d a t a s p a c e a s s i g n m e n t and new e v e n t l i s t * ) ( * p e r f o r m s i n g l e a c t i o n : a p p e n d a new g e n e r a t e d e v e n t t o t h e * ) ( * e v e n t l i s t o r u p d a t e t h e d a t a s p a c e ; f u n c t i o n f h o l d s t h e * ) ( * a c t i o n * ) f u n p e r f o r m A c t i o n ( e v e n t ( f ) ) ( d , e s ) = ( d , e s @ [ f ( d ) ] ) | p e r f o r m A c t i o n ( u p d a t e ( f ) ) ( d , e s ) = ( f ( d ) , e s ) ( * f o l d l e f t : f u n c t i o n f w i l l be t h e c o m p o s i t i o n f u n c t i o n o and * ) ( * t h e n e u t r a l e l e m e n t w i l l be t h e i d f u n c t i o n *

1 :

 1 s ) ; ( * s e q u e n t i a l c o m p o s i t i o n o f a l l a c t i o n s * ) ( * p e r f o r m a l l a c t i o n s : a p p l y p e r f o m A c t i o n t o e v e r y a c t i o n and * ) ( * t h e n ( s e q u e n t i a l l y ) compose a l l a c t i o n s * ) f u n p e r f o r m A l l A c t i o n s ( a c t i o n s ) ( d ) = f o l d ( o , f n x => x ) ( map ( p e r f o r m A c t i o n ) ( a c t i o n s ) ) ( d ) ; ( * c o m b i n a t i o n o f g u a r d c h e c k i n g and p e r f o r m i n g a l l a c t i o n s * ) ( * y i e l d s a new d a t a s p a c e a s s i g n m e n t and a l i s t o f a l l * ) ( * g e n e r a t e d e v e n t s i f t h e g u a r d i s s a t i s f i e d o r t h e o l d d a t a * ) ( * s p a c e a s s i g n m e n t and an empty l i s t o t h e r w i s e * ) f u n p a r t i a l S t e p ( t r a n s i t i o n ( t ) ) ( e , d ) = l e t v a l ( g u a r d ( g ) , a c t i o n s ) = t ( e ) ; i n i f g ( d ) t h e n p e r f o r m A l l A c t i o n s ( a c t i o n s ) ( d , Sample Implementation of a Semantical Step partialStep(t1) a(3, true), (3, true) ⇒ (5, true), [a(4, true), a(8, true), b(false)]

  u s e " s t a t e m a c h i n e . ml " ;( * e x a m p l e s t r u c t u r e o f a s t a t e m a c h i n e * ) s t r u c t u r e s m 1 s t r u c = s t r u c t ( * t h e d a t a s p a c e i s c o n s t i t u t e d o f an i n t v a l u e and a b o o l e a n * ) boolean p2 = true; int p1 = 3; A B Example State Machine a(x,y)[x == p1] / p1++ ; a(p1,p2) ; p1++ ; a(p1 + x, p2) ; b(not y)

Figure 5 : 2 (Listing 2 :

 522 Figure 5: State Machin for the Listing 2


domain: sdv sde

text:
Y Capowiez
email: capowiez@avignon.inra.fr

S Cadoux

P Bouchant

H Boizard

J Roger-Estrade

G Richard

"Sustainability -its Impact on Soil Management and Environment" HOW TO EVALUATE THE ROLE OF EARTHWORMS IN THE ELIMINATION OF HIGLY COMPACTED ZONES IN FIELD CONDITIONS

Earthworms as ecosystem engineers influenced a great number of physical, chemical and biological processes in soil. It is often claimed that earthworms can have a great influence on the elimination of compacted zones in the soil. We wanted to put this assumption to the test. A field experiment was initiated in 1989 in northern France to evaluate the effects of cropping systems on the structure of the tilled layer in a loamy soil. Three levels of compaction were considered depending on the rotation and on the time of field operations because of high axle loads. Tillage (and no-tillage) was considered as a second factor. Earthworm populations were sampled in the different systems. If densities were high (between 100 and 400 ind./m2), only four earthworms species were found (L. terrestris, N. giardi, A. rosea and A. caliginosa). Tillage had a small negative effect on earthworm density (especially on N. giardi which seemed to be very sensitive). The cropping system (and level of compaction) had almost no effect on earthworm density but we observed that A. caliginosa was almost absent from cropping system II and III in reduced tillage. To determine if the remaining worms could decrease the importance of compacted zones, observations of macroporosity were made on horizontal planes at different depths. We observed that macroporosity was significantly higher in reduced tillage plots. To go further, a controlled compaction experiment was carried out in the field. Then, number of earthworms and macropores were counted regularly (every season) and compared between wheel and inter-wheel zones. We observed that if recolonization by earthworms is a rapid process, the related increase in macroporosity is much slower.

Introduction

The structure of the tilled layer of cultivated fields changes with time because of human actions (tillage, compaction due to field traffic) and weathering, root growth and fauna activity (especially earthworms). Mechanised cultivation produces stresses within the soil which cause fragmentation, compaction and displacement of the soil. A long term field experiment was conducted in Northern France since 1989 to evaluate the cumulative effects of cropping systems on the structure of the ploughed layer in a plough tillage system and showed that the change in soil structure in a plough tillage system depend to a large extent on the scheduling of cultivation operations. Plots with late harvesting in autumn had the highest proportion of highly compacted zones which varied in the experiment from 20 and 70%. But the highly compacted zones could quickly disappear from the ploughed layer. The question arises whether earthworms are responsible for quick disappearance. Because (i) Northern France is an area of intensive agriculture with an oceanic climate and loess soils where compaction frequently occurs and (ii) increasing proportion of farmers abandons mouldboard plough tillage system, there is a need to better understanding change in soil structure with no-till or reduced tillage systems. The Estrées-Mons long term experiment was altered in 1999: ploughing was suppressed on half of the experimental plots, while it was continued on the other part. Tillage was reduced to 0-5 cm superficial cultivation in RT treatment when the same cultural operations were maintained in CT treatments.

If we want to clearly understand (and model) changes in soil structure, it is necessary to evaluate the role of earthworm in these processes. First of all, we studied which species or ecological types (anecic and endogeic) are present in function of different agricultural practices (tillage and cropping systems) and then we focused on the evolution of earthworm communities in a very compacted zones to gain insight into the dynamics of re-colonisation and their effects in term of macroporosity.

Materials and Methods

Site and soil

The field experiment began in 1989 in northern France at the INRA experimental centre of Estrees-Mons (Péronne, 50°N latitude, 3°E longitude, 85 m elevation). Three cropping systems were compared from 1990 to 2005 (Boizard et al., 2002).

-cropping system I. The rotation was pea (Pisum sativum L.)/winter wheat (Triticum aestivum)/rape (Brassica Napus L.)/winter wheat. Rape was replaced by linen (Linum usitatissimum) in 1999. Sowing and harvesting were always carried out in summer or early autumn, i.e. during a dry period of the year. Pea and linen sowing were managed so as to avoid sowing and harvesting in wet conditions.

-cropping systems II and III. The rotation was sugar beet (Beta vulgaris L.)/winter wheat/maize (Zea mays L.)/winter wheat. Cropping system II was managed so as to avoid sowing and harvesting in wet conditions. Cropping system III was managed so as to maximise light interception by sugar beet and maize: sugar beet and maize were sown in early spring and harvested in late autumn, during wet periods of the year. Each crop was grown every year, giving 12 treatments. The experimental design consisted of two blocks (total of 24 0.40 ha. plots) with a plough tillage system up to 1999. From 1999 the plough tillage system was continued in the first block and reduced tillage system was introduced in the second block. The plot size made it possible to reproduce the traffic patterns of machinery found in commercial farms.

The soil was classified as a silt loam (Luvisol Orthic, FAO classification). It contained an average of 190 g clay kg -1 , 738 g silt kg -1 , 50 g sand kg -1 , 17 g organic matter kg -1 , 5 g CaCO 3 kg -1 and had a pH of 7.6. Soil water contents at -10, -50, -100 and -1500 kPa were 0.252, 0.213, 0.164 and 0.083 g g -1 respectively. The long-term average annual air temperature at the site is 9.6°C and the annual rainfall is 667 mm. The climate was much contrasted during the 2000-2005 years period with especially three dry years in 2003, 2004 and 2005. The annual rainfall from 2000 to 2005 was 733, 802, 720, 414, 498 and 483 mm respectively and the autumn rainfall (September, October and December) was 262, 242, 201, 82, 101 and 99 mm. For this experiment, only 6 plots were analysed. Observations (earthworms sampling and macroporosity estimations) were carried out at 4 dates (autumn 2003, spring and autun 2004 and spring 2005). In one of the plot, we performed a controlled compaction experiment. Compacted was caused by a vehicle (weight = 8 t) in humid conditions. Four compacted zones (under the wheels) of 20 m length were obtained and were compared with uncompacted (between the wheels) zones.

Earthwormsand macroporositymeasurements

Earthworms were sampled using diluted mustard (15 g/l) as a repellent. After 30 mn, the soil was dug and carefully sorted to find earthworms that did not go to the surface (depth = 30 cm). In each plot at each date, 4 sampling zones (40 cm x 40 cm) were analysed near to the zone where observations of soil structure were carried out [START_REF] Boizard | Effect of different soil mangement and cropping systems on changes in soil structure with time[END_REF]. Only 4 earthworms species were find in the plots, 2 anecic species (Lumbricus terrestris and Nicrodrilus giardi) and 2 endogeic one (Aporrectodea caliginosa and Aporrectodea rosea). It was difficult to discriminate very small juveniles (< 0.1 g) coming from the two endogeic species and therefore we classed into a "juvenile endogeic" category. To estimate macroporosity related to earthworm activity, four horizontal planes (20 cm x 20 cm) were gently scratched with a knife and "cleaned" by an air-vacuum at four depths (-10, -20, -30 and -40 cm) in each plot. Photographs were then taken (at a distance of 40 cm). Images were analysed with the freeware NIH-Image and macropores were manually underlined (according to their shape) to estimate macropore number and area. Cracks were discarded. Comment citer ce document : Capowiez, Y., Cadoux, S., Bouchant, P., Boizard, H., Roger-Estrade, J., Richard, G., International Soil Tillage Research Organisation (2006). How to evaluate the role of earthworms in the elimination of highly compacted zones in field conditions. In: Internationl Soil Tillage Research Organisation 17th Triennial Conference (p. 6 p.). Presented at 17 Triennial.

Results

Effects of tillage and cropping system on earthworm communities and macroporosity

Cropping systems has consequences on soil compaction (see [START_REF] Boizard | Effect of different soil mangement and cropping systems on changes in soil structure with time[END_REF]: cropping system II and III has statistically more compacted (delta) zones. As far as total earthworm abundance is concerned, tillage and cropping systems have very limited effects (Figure 1). However some earthworm species were more or less sensitive to tillage and cropping systems. Anecic species were less present in conventional tillage plots (as described by Chan 2001) even if L. terrestris seems to be less sensitive than N. giardi. Cropping system has not clear effect in conventional tillage but we observed in reduced tillage that A. caliginosa populations were greatly decreased in cropping system II and III contrarily to the two anecic species and especially N. giardi whose populations increased in these cropping systems. Regarding macroporosity, macropores between 2 mm (limit for visual detection in the images) and 4 mm are far more numerous that bigger pores (Figure 2). No significant difference was observed for cropping system (results not shown). Tillage has a significant effect for both size classes: the number of macropores was decreased in CT. This effect is not only due to difference in earthworm abundances but was related to the fact that tillage has as well a direct effect by destroying macropores.

Effects of tillage and cropping system on earthworm communities and macroporosity

Comment citer ce document : Capowiez, Y., Cadoux, S., Bouchant, P., Boizard, H., Roger-Estrade, J., Richard, G., International Soil Tillage Research Organisation (2006). How to evaluate the role of earthworms in the elimination of highly compacted zones in field conditions. In: Internationl Soil Tillage Research Organisation 17th Triennial Conference (p. 6 p.). Presented at 17 Triennial. Soil density in the compacted zone (1.61) was significantly higher than in uncompacted zones (1.49). A few days after compaction, we observed a significant decrease in earthworm numbers in compacted zones (-60%). This difference completely disappeared 8 months after compaction (Figure 3). The compacted zones (width = 30 cm) were rapidly re-colonized by earthworms.

Months after compaction

Figure 4. Mean number of macropore (m -2 ) at -10 cm (plain) and -20 cm depth (dashed lines) in uncompacted (squares) and compacted (circles) zones.

It was surprising to observe a seasonality in number of earthworm macropores in uncompacted zones (Figure 4). There was a decrease in macropore number between spring and autumn.

Comparing macropores number in compacted and uncompacted zones revealed that the number of macropores remained higher in uncompacted zones during 20 months for the horizontal planes at - 10 cm depth. For the deeper horizontal plane, we observed that the numbers of macropores became very similar only 20 months after compaction.

Conclusions

Tillage and cropping systems had limited effect on earthworm abundances but different effects can be observed for different earthworm species. However it should be noted that the system effect reported here is not only linked to soil compaction. There are other differences between cropping system I on one hand and cropping systems II and III on the other hand: crops and therefore pesticides could also have an effect on earthworm communities and activities.

Regarding the controlled compaction experiment in the field, we concluded that even if recolonisation by earthworms can be rapid in field conditions, the retrieval of macroporosity is a much slower process. This means that estimating earthworm communities only is not sufficient to fully understand the processes that earthworm can influence and their dynamics.

Figure1.

  Figure1. Mean earthworm densities (m -2 ) in conventional (CT) or reduced timlmage (RT) and the 3 different cropping systems (I,II and III) (right dashed = L. terrestris ; white = N. giardi ; dotted = juvenile endogeic ; black = A. rosea and left dashed = A. caliginosa).

Figure 2 .

 2 Figure 2. Mean number of macropore (m-2) in reduced (RT) or convetional tillage (CT). Two classes of equivalent pore diameter are considered.

Figure 3 .

 3 Figure 3. Mean earthworm densities (m -2 ) in compacted (black) and uncompacted (white) zones with time.


Sebastien Elis

Hayden-William Courtland

Yingjie Wu

Hui Sun

Karl J Jepsen

Shoshana Yakar

Elevated levels of serum IGF-1 restore peak bone properties and mechanical functionality in the absence of autocrine/paracrine IGF-1 1 ENDO 09, Washington, 6.12.09

IGF-1 is an endocrine, and autocrine/paracrine modulator of growth and metabolism

Summary

Tissue IGF-1 is critical for neonatal and early postnatal growth (before 4w).

 increase in body weight.

 increase bone morphological traits  increase in mechanical properties.

Postnatally, elevated serum IGF-1 levels :

Elevated serum IGF-1 levels fully compensate for a postnatal absence of tissue IGF-1 :

Morphologically & Mechanically THANK YOU


domain: math info sdv

text:
A hit (for a read) is a position in the genome

We separate reads mapped once and mapped several times. Reads mapped too often provide little information to the end user and are actually rarely considered. A unique read is a read mapped at only one location. Reads originate from a random position (drawn uniformly) in the genome. We look whether this original position is retrieved by the software.

The maximum number of hits asked to the software is limited to 200. Some softwares were not able to align 10 millions reads on the reference genomes (mostly because the memory requirements were too demanding). These softwares do not appear in the tables.

Softwares were run on a single CPU core (even though most softwares allow multithreading).

We used a 2.3 GHz CPU (64 bits) with 16 GB of memory.

We separate reads mapped once and mapped several times. Reads mapped too often provide little information to the end user and are actually rarely considered. A unique read is a read mapped at only one location. Reads originate from a random position (drawn uniformly) in the genome. We look whether this original position is retrieved by the software.

The maximum number of hits asked to the software is limited to 200. Some softwares were not able to align 10 millions reads on the reference genomes (mostly because the memory requirements were too demanding). These softwares do not appear in the tables.

Softwares were run on a single CPU core (even though most softwares allow multithreading).

We used a 2.3 GHz CPU (64 bits) with 16 GB of memory.

Results Results

• [bwa] Li

  H and Durbin R (2009). Fast and accurate short read alignment with Burrows-Wheeler Transform. Bioinformatics, 25:1754-60.• [ProbeMatch] Kim YJ,Teletia N, et alii (2009). ProbeMatch: rapid alignment of oligonucleotides to genome allowing both gaps and mismatches. Bioinformatics. Jun 1;25(11):1424-5. • [SHRiMP] Rumble SM, Lacroute P, et alii (2009). SHRiMP: Accurate Mapping of Short Color-space Reads. PLoS Comput Biol 5(5). • [Novoalign] Novocraft.com • [Bowtie] Langmead B, Trapnell C, Pop M, Salzberg SL (2009). Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biol 10:R25. • [SOAP2] Li R et alii (2009). SOAP2: an improved ultrafast tool for short read alignment. Bioinformatics, doi:10.1093/bioinformatics/btp336 • [BFAST] Homer N, Merriman B, Nelson SF (2009). BFAST: An alignment tool for large scale genome resequencing. PLoS ONE 4(11): e7767 doi:10.1371/journal.pone.0007767 • [maq] Li H, Ruan J, Durbin R (2008). Mapping short DNA sequencing reads and calling variants using mapping quality scores. Genome Res. 18(11):1851-8. • [MOM] Eaves H and Gao Y (2009). MOM: maximum oligonucleotide mapping. Bioinformatics 25(7):969-970; doi:10.1093/bioinformatics/btp092 • [bwa] Li H and Durbin R (2009). Fast and accurate short read alignment with Burrows-Wheeler Transform. Bioinformatics, 25:1754-60. • [ProbeMatch] Kim YJ, Teletia N, et alii (2009). ProbeMatch: rapid alignment of oligonucleotides to genome allowing both gaps and mismatches. Bioinformatics. Jun 1;25(11):1424-5. • [SHRiMP] Rumble SM, Lacroute P, et alii (2009). SHRiMP: Accurate Mapping of Short Color-space Reads. PLoS Comput Biol 5(5). • [Novoalign] Novocraft.com • [Bowtie] Langmead B, Trapnell C, Pop M, Salzberg SL (2009). Ultrafast and memory-efficient alignment of short DNA sequences to the human genome. Genome Biol 10:R25. • [SOAP2] Li R et alii (2009). SOAP2: an improved ultrafast tool for short read alignment. Bioinformatics, doi:10.1093/bioinformatics/btp336 • [BFAST] Homer N, Merriman B, Nelson SF (2009). BFAST: An alignment tool for large scale genome resequencing. PLoS ONE 4(11): e7767 doi:10.1371/journal.pone.0007767 • [maq] Li H, Ruan J, Durbin R (2008). Mapping short DNA sequencing reads and calling variants using mapping quality scores. Genome Res. 18(11):1851-8. • [MOM] Eaves H and Gao Y (2009). MOM: maximum oligonucleotide mapping. Bioinformatics 25(7):969-970; doi:10.1093/bioinformatics/btp092 Introduction Introduction Tools Tools

MIG -Mathématique, informatique et génome MIG -Mathématique, informatique et génome Domaine de Vilvert, Domaine de Vilvert, 78352 Jouy-en-Josas 78352 Jouy-en-Josas This work is funded as part of the ANR project CBME This work is funded as part of the ANR project CBME MIG -Mathématique, informatique et génome MIG -Mathématique, informatique et génome Domaine de Vilvert, Domaine de Vilvert, 78352 Jouy-en-Josas 78352 Jouy-en-Josas This work is funded as part of the ANR project CBME

This work is funded as part of the ANR project CBME where the read is mapped.

• On reads produced by sequencers (instead of simulated ones)

• Incorporate model on the errors produced by sequencers • Other types of variations for the reads (gaps, mutations)

• Automate the evaluation process

• On SOLiD reads (colorspace)

• On paired-ends and mate-paired reads • On larger datasets (100M, 1G reads)

• On reads produced by sequencers (instead of simulated ones)

• Incorporate model on the errors produced by sequencers • Other types of variations for the reads (gaps, mutations)

• Automate the evaluation process

Future developments Future developments

We simulate two sets of reads of length 40 bp, that are drawn uniformly in a dataset. To reflect the diversity of genomic data, we use 2 kinds of datasets: the human genome (2.7G bp) and a concatenation of 900 bacterial genomes (1.7G bp). The sets contain 10M reads, close to the actual amount produced by NGS tools.

In the first set reads are simulated without errors, in the second, three mismatches are added at random positions. We monitor several indicators of the performance of each software: CPU time used, whether the read matches at its "original" position, number of match positions found for a given read, number of uniquely mapped reads.

We simulate two sets of reads of length 40 bp, that are drawn uniformly in a dataset. To reflect the diversity of genomic data, we use 2 kinds of datasets: the human genome (2.7G bp) and a concatenation of 900 bacterial genomes (1.7G bp). The sets contain 10M reads, close to the actual amount produced by NGS tools.

In the first set reads are simulated without errors, in the second, three mismatches are added at random positions. We monitor several indicators of the performance of each software: CPU time used, whether the read matches at its "original" position, number of match positions found for a given read, number of uniquely mapped reads.

Methodology Methodology


domain: sdv sde sdv.bv

text:
Bernadette Julier

Jean-Baptiste Pierre

Philippe P Barre

Christian C Huyghe

Effect

Effect of photoperiod on aerial morphogenesis of eight Medicago truncatula lines

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Effect of photoperiod on aerial morphogenesis of eight Medicago truncatula lines

Bernadette Julier, Jean-Baptiste Pierre, Philippe Barre and Christian Huyghe INRA, UR4, Unité de Recherche Pluridisciplinaire Prairies et Plantes Fourragères, 86600 Lusignan, France. Email: bjulier@lusignan.inra.fr

The influence of environmental factors on aerial morphogenesis is only partly described on the model legume Medicago truncatula. Such factors can affect phenotypic evaluation of genetic material such as recombinant inbred lines (RILs), mutants or natural accessions. The objective of this study was to describe the effects of photoperiod, genotype and the genotype x photoperiod interaction on morphogenesis.

In growth chambers, six parental lines of RILs populations and two Israeli accessions were grown under two photoperiods, 12 and 18h applied without significant change in total energy supply. Primary branch elongation was measured twice a week, flowering time was scored, and when stem elongation had ceased, the number of primary branches was counted and the length of the main stem was measured. For all traits, photoperiod and genotype effects were highly significant in analysis of variance but the effect of photoperiod was the highest. On average, plants flowered earlier and had longer main stem, shorter branch length and higher branch elongation rate at a long than at a short photoperiod. Duration of branch elongation and number of branches were lower at a long than at a short photoperiod. The interaction between genotype and photoperiod was always significant. Flowering of Jemalong6 and F83005.5 was more hastened by long photoperiod than that of the other genotypes. Branch length was shorter at a long than at a short photoperiod for five genotypes, longer for one genotype and little affected for two genotypes.

These results show that plant morphology is greatly affected by environmental conditions. A large genetic variation is available. Moreover, the interaction between conditions and genotypes is large, modifying the ranking of the genotypes. It indicates that the protocols for evaluation of RILs, mutants or natural accessions must be carefully chosen.

  Photoperiod

Acknowledgements

We thank Dr A. Samach from University of Jerusalem (Israel), Dr T. Huguet from INRA-CNRS at Toulouse (France) and J.M. Prosperi from INRA at Montpellier (France) for providing the seeds.