Nadia Bertin

Ilink Pećinar

Dragana Rančić

Sofija Pekić Quarrie

Slaviša Dordević

Radenko Radošević

Catherine Cheniclet

Benefit of bilateral project between Serbia and France to improve the expertise in histological analysis of tomato pericarp exposed to different irrigation techniques

ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

BENEFIT OF BILATERAL PROJECT BETWEEN SERBIA AND FRANCE TO IMPROVE THE EXPERTISE IN HISTOLOGICAL ANALYSIS OF TOMATO PERICARP EXPOSED TO DIFFERENT IRRIGATION TECHIQUES

Bertin, Nadia1, Pećinar, Ilinka 2 , Rančić, Dragana 2 , Pekić Quarrie, Sofija 2 , Đorđević, Slaviša 2 , Radošević, Radenko2, , Cheniclet, Catherine 3 and Stikić, Radmila al., 2009). Approach which combines different methods to assess both quantitative and qualitative histological and cytological traits has been rarely performed on fleshy fruit. The bilateral project between Serbia and France (2012-2013, Pavle Savic) aimed to bring together several teams with complementary expertise and technical means for evaluating the effects of contrasted irrigation practices on tomato fruit, with the emphasis on its anatomical and cytological background. French partners from INRA (National Institute of Agronomic Research) in Bordeaux and Avignon, world recognized experts in the cytological and histological aspects of tomato fruit growth regulation, provided a technical platform of cytology and image analysis as well as the expertise and skills for the histological and cytological study. The French partners mainly focus on the interactions between genetic and environmental factors, the study of early development and the build-up of quality traits for tomato fruits. At the Faculty of Agriculture, research focuses on the effects of different irrigation treatments on cultivated plants, especially tomato. This collaboration allowed an original investigation of the effects of water deficit on the histological and cytological properties during tomato fruit development. During the project, Serbian young researchers spent more than 10 weeks in INRA France and had the chance to improve their skills and knowledge thanks to the expertise and experience of dr.

Bertin in cytological analysis of tomato fruit pericarp, while detailed cytological analysis of cell size and shape was supervised by dr. Cheniclet. This project was useful for scientific teams of both sides. This collaboration resulted in a better understanding of the effects of different irrigation treatments on the processes of division and differentiation in fruit pericarp during ageing. It also permitted to compare different quantitative and qualitative cytological techniques. The project resulted in joint publications and it will be followed by further scientific collaboration among partners. This bilateral project was beneficial especially to the Serbian PhD students, who expanded their international experience and broaden their expertises especially in the field of cytological and image analysis. The scientific benefits of the project are reflected in the fact that obtained results will represent a significant part of a PhD thesis in progress and they will also be implementated in a national project. On a longer term, the joint research will benefit to tomato growers and breeders and help them to adjust their practices and improve tomato yield under sustainable irrigation conditions.

Keywords: histology, cytology, image analysis, water deficit, tomato growth, bilateral project


Antoine Beretti

Charles Figuieres
email: charles.figuieres@supagro.inra.fr

Gilles Grolleau

Charles Figuières

«An Instrument that Could Turn Crowding-out into Crowding-in »

Keywords: crowding-out, heterogeneity, moral motivation, environmental regulation. JEL Classification: D03, D64, H23, Q58

Using a simple decision-theoretic approach, we formalize how agents with different kinds of intrinsic motivations react to the introduction of monetary incentives. We contend that empirical results supporting the existence of a crowding-out effect in various contexts hide a more complex reality. We also propose a new policy instrument which taps into agents' heterogeneity regarding intrinsic motivations in order to turn a situation subject to crowding-out into a crowding-in outcome. This instrument uses a self-selection mechanism to match adequate monetary incentives with individuals' types regarding intrinsic motivations.

Introduction

Monetary incentives matter and are a powerful instrument to change behaviour. They are a part of the story but not all the story. Indeed, the crowding-out effect, which has recently received considerable attention in economic literature, stresses that the preferred leverage of economists, monetary incentives and disincentives can backfire and lead to inferior outcomes. Such a counter-productive effect could be due to an interaction -still poorly understood -between intrinsic motivation and extrinsic (dis)incentives introduced by the monetary instrument. The issue has been investigated, theoretically (Bénabou and Tirole, 2003) and empirically (see [START_REF] Bowles | Policies Designed for Self-Interested Citizens May Undermine "The Moral Sentiments[END_REF] for a recent review). It has been proven to be relevant in a wide variety of contexts such as blood donation [START_REF] Titmuss | The gift relationship: From human blood to social policy[END_REF]Mellstrom andJohannesson, 2008, Goette, Stutzer &[START_REF] Goette | Prosocial Motivation and Blood Donations: A Survey of the Empirical Literature[END_REF], acceptance of a polluting infrastructure [START_REF] Frey | The Cost of Price Incentives: An Empirical Analysis of Motivation Crowding-Out[END_REF] or to address late coming parents in day-care centers (Gneezy and Rustichini, 2000) or bed-blocking in hospitals [START_REF] Tor | Does monetary punishment crowd out pro-social motivation? A natural experiment on hospital length of stay[END_REF].

Most papers consider that all agents behave similarly when facing monetary incentives. Nevertheless, it is more realistic to assume that people are heterogeneous and have various intrinsic motivations according to the considered domain [START_REF] Bénabou | Incentives and Prosocial Behavior[END_REF][START_REF] Beretti | Using Money to Motivate Both Saints and Sinners: a Field Experiment on Motivational Crowding-Out[END_REF]. This heterogeneity is probably the source of many difficulties encountered in defining the concept of intrinsic motivation, and controversies about its usefulness (Reiss, 2006;Bruno, 2012). Psychologists frequently consider that intrinsic motivations are those that arise from within -doing something because you want to -while extrinsic motivations mean people are seeking a reward, such as money or a trophy at a sporting event. Intrinsic motivation is that which is pleasurable per se, while extrinsic motivation is not. Put differently, one could resort to a means-end logic in order to determine whether a motivation is intrinsic or extrinsic: intrinsic motivation is doing what we want, whereas extrinsic motivation is doing something to get something else. Recently, [START_REF] Bolle | A Price Is a Signal: on Intrinsic Motivation, Crowding-out, and Crowding-in[END_REF] proposed to define extrinsic motivations as added motivations that interfere and disturb a well-defined situation. This well-defined situation constitutes the reference where intrinsic motivations play their role. Their definition along with others are collected in Table 1 below. To measure intrinsic motivation, various approaches have been used such as self-reported measures of engagement and interest in the activity, observation of free-choice engagement in the activity when no rewards or other extrinsic motivators are present. Moreover, there are some studies investigating the possible neural basis of intrinsic motivation (e.g., Lee et al, 2012). They report differences in neural activation between intrinsic and extrinsic motivations. We argue that any agent shelters a unique combination of various intrinsic motivations, and that this individual heterogeneity across agents is not without consequences on the effectiveness of public interventions. In particular, its overall impact in a whole population supporting or not the existence of a crowding-out effect can overlook the fact that various subgroups of this whole population react differently when facing the introduction of monetary incentives. Indeed, moderate monetary incentives can both motivate people who were originally not intrinsically motivated and harm the intrinsic motivations of people who were originally intrinsically motivated. Several studies reveal that incentive-based programs do not produce identical reactions across individuals [START_REF] Gneezy | When and Why Incentives (Don't) Work to Modify Behavior[END_REF] and psychologists recognize that different people are motivated in different ways (Reiss, 2006;Lindenberg, 2001). Natural candidates for this heterogeneity can be related to contextual parameters (Vohs, 2007) or other parameters such as intentions attributed to others or education. This heterogeneity is also stressed by Ryan and Deci (2000) who states that individuals 'vary not only in level of motivation (i.e., how much motivation) but also in orientation of that motivation (i.e., what type of motivation). Orientation of motivation concerns the underlying attitudes and goals that give rise to action -that is, it concerns the why of actions'. Even if they adopt a different viewpoint on intrinsic motivation, Bateman and Crant (2003) acknowledge individual differences in motivational orientation.

Plainly, taking into account the heterogeneity regarding intrinsic motivations is very important for policymaking, insofar as it provides a better description of human behaviour. Unfortunately most papers to date neglect this aspect and, in addition, do not propose alternatives to address the crowding out effect; they merely propose to eliminate monetary incentives. Our paper addresses these two issues in a theoretical model that (i) allows to take into account the heterogeneity of individuals when faced with the introduction of monetary incentives (ii) suggests a mechanism to reduce the likelihood of getting a crowding-out result by tapping into the heterogeneity of individuals. We assume that monetary incentives matter and change behaviours in predictable directions according to the matching between to whom they are directed (i.e. paying the individual versus paying the cause) and the preexisting level of intrinsic motivation of the individual (i.e., low versus high level). Our model can explain a large variety of outcomes stressed in recent empirical studies and has policy relevance by suggesting a new instrument which eventually turns crowding-out into crowding-in (e.g., [START_REF] Beretti | Using Money to Motivate Both Saints and Sinners: a Field Experiment on Motivational Crowding-Out[END_REF].

2 Crowding-out with heterogenous agents: a simple model This section constructs a simple behavioral model in which it is possible to explore the logical implications of various external monetary incentives on contributions when agents have heterogeneous intrinsic motivations. The model is framed in the environmental realm to fix ideas, but it is nevertheless clear that it could could be applied to many domains where there is a mix of intrinsically motivated individuals and extrinsically motivated ones, such as volunteering or giving 1 .

In the kind of situation we analyze in this paper, people know that they affect each other by their decisions, but their interactions are largely anonymous. They clearly don't know the set of strategies of the other individuals, nor do they know their utility functions. Actually they even ignore how many "others" there are. Therefore we prefer to analyze the issue using a "decisiontheoretic approach", in connection with the work of [START_REF] Bolle | A Price Is a Signal: on Intrinsic Motivation, Crowding-out, and Crowding-in[END_REF], rather than with a "gametheoretic approach" as in [START_REF] Bénabou | Incentives and Prosocial Behavior[END_REF].

There is a continuum of agents of unit mass. Each agent i is endowed with an exogenous income y i . The decision x i of agent i is to contribute (x i = 1) or not (x i = 0) to some environmental cause and the opportunity cost of contributing, in monetary terms, is c(x i ). The standard assumption is that this cost is an increasing function: c (0) < c(1). Units are chosen in such a way that c (0) = 0, c(1) = c > 0. The remainder of the agent's income is affected to some alternative use

c i = y i -c(x i ).
The conceptual challenge of the present article is most entirely contained in the formulation of the objective function that the agents presumably maximize. Recall that we wish to capture heterogenous intrinsic motivations. And we want to give a role not only to the level of the motivation but also to its orientation. This last aspect in particular means that procedural or frame consideration is an argument in the agents' objective functions, i.e. the same decision x i performed under two different frames can result in different perceived consequences by the agents. For evidence that people value not only outcomes, but also the procedures or frames that lead to the outcomes see for instance Frey, Benz & Stutzer (2004). Recognition of procedural concerns in agents' choice has recently led to reconsider both the field of decision theory (see [START_REF] Salant | A, f): Choice with Frames[END_REF], for an axiomatic analysis of individual choices with frames) and that of social choice and social welfare (see [START_REF] Suzumura | Consequences, opportunities, and procedures[END_REF][START_REF] Suzumura | Characterizations of consequentialism and non consequentialism[END_REF][START_REF] Suzumura | Consequences, opportunities, and generalized consequentialism and non-consequentialism[END_REF][START_REF] Bernheim | Toward Choice-Theoretic Foundations for Behavioral Welfare Economics[END_REF][START_REF] Bernheim | Beyond revealed preference: choice theoretic foundations for behavioral welfare economics[END_REF][START_REF] Fleurbaey | Behavioral welfare economics and redistribution[END_REF]. And, inevitably, one must also reconsider the design of policy instruments, because instruments not only have an effect on x i , but also because they are part of frames, and frames affect choices directly by themselves. This paper can be seen as a step in that direction.

Let f refers to the frame that agent i faces in a particular choice situation. And assume that agent i is endowed with decision-relevant preferences, defined over bundles (x i , f ), numerically represented a decision utility function U i (x i , f ) .We use here the popular distinction between decision utility which prompts actions, and experienced utility, or hedonic satisfaction2 , which results from actions (see for instance [START_REF] Kahneman | Back to Bentham? Explorations of Experienced Utility[END_REF]. It is fairly possible that the same decision x i made under two different frames f and f , produces different decision utilities:

U i (x i , f ) = U i (x i , f ) . Put differently, to each frame f corresponds a particular decision utility function U i f (x i ) ≡ U i (x i , f
). We propose to study the effects of different frames, with a focus on their interactions with intrinsic motivations. Based on previous studies, Bowles and Polania-Reyes (2012 and references therein) have identified four ways by which those interactions could take place. First, extrinsic incentives may provide information about the person or principal who has chosen the incentives. Second, extrinsic incentives reframe an interaction from one in which effort is required based on moral reasoning to one in which effort becomes a choice because the incentives highlight a possible tradeoff that was not considered previously. Third, extrinsic incentives compromise a control averse individual's sense of autonomy. Fourth, providing extrinsic incentives affect the process by which people learn new preferences.

We consider four distinct frames where all those ways are at play to different degrees: (N) a neutral treatment without external monetary incentives, (A) a treatment where individuals are paid for their contribution x i , (B) a treatment where agents' decision to contribute is accompanied by a payment directed to a cause supporting the environment (say an relevant association or NGO), (C) a treatment where the agent is offered the choice regarding the orientation of the payment (for himself or for an association). The corresponding decision utility functions are denoted respectively

U i N (x i ) , U i A (x i ) , U i B (x i ), and U i C (x i ) .
Below we make use of behavioral models, using specific funtional forms for each

U i f (x i ) , f = N, A, B, C.
Beyond those functional forms, the interested reader is invited to check that generalisations of the results of the present paper are possible. The advantage of the simple forms we use is to offer a quick and clear way to highlight the logic we are studying.

Neutral Treatment (N): pristine altruism alone

In the neutral treatment there is no incentive scheme and altruism is the only intrinsic motivation at work. Assume the decision utility function reads as:

U i N (x i ) = y i -c(x i ) + a i t N x i . (1)
In expression (1):

• t N is the marginal "monetarized" benefits produced by the agent's contribution x i on the other agents. This information parameter is frame-dependent and it is associated here to the situation without external incentives;

• and a i ∈ [0, 1] is a parameter that captures an attitude towards the other individuals via the environment, a sort of ecologically-mediated, or 'green', altruistic concern 3 . Those parameters are uniformly distributed on [0, 1] and each agent can be identified with a particular point in this interval. At one extreme, Agent 0 with a 0 = 0 does not feature any environmental concern; at the other polar case, Agent 1 with a 1 = 1 has a strong ecological conscience.

Assume that, for the most altruistic agent, with a 1 = 1, the marginal benefit of contributing covers its marginal cost, that is c (1) -c (0) = c < t N . Individuals choose to contribute or not with a view to maximize (1). Hence, agents who settle for zero contributions are those such that:

y i -c(0) > y i + a i t N -c(1) ,
and the others contribute. Put differently, those in the interval 0, a N where

a N = [c (1) -c (0)] /t N = c/t N , (2)
are non-contributors, with a mass a N , and those in the interval

C N ≡ a N , 1
are contributors. The total number of contributors is

1 -a N . (3)

Direct Treatment (A): distorted altruism and moral repugnance

When individuals are paid for their contribution to the environment their decision utility function becomes:

U i A (x i ) = y i -c(x i ) + wx i + a i t A x i -m (a i , w, x i ) , ( 4
)
where w is the monetary payment for participation. The introduction of the payment has two effects as far as intrinsic motivations are concerned. First, the altruistic motivation is distorted. The idea is that the presence of a monetary transfer acts as a signal of the value of participation (Bolle and Otto, 2010), upon which the agents' marginal benefits of the agents' altruism becomes a i t A instead of a i t N , with t A < t N . Moreover we assume that this price signal for altruism is at least equal to the payment offered (t A ≥ w).

Second, agents who have a concern for the environment now suffer from a moral repugnance associated with the fact of being paid for contributing. This aspect is captured by function m (., ., .) in expression [START_REF] Bernheim | Toward Choice-Theoretic Foundations for Behavioral Welfare Economics[END_REF]. Putting a price onto a territory previously immune to the market forces is one of the list of events that generally spark the yuck factor argument (see for instance [START_REF] Sandel | What money can't buy: the moral limits of markets[END_REF], and also the discussion about obnoxious markets in [START_REF] Kanbur | On Obnoxious Markets[END_REF]. The monetarized value of this psychological "cost" is m (a i , w, x i ) ≥ 0 . It is natural to assume that the larger the green altruism a i , or the larger the payment w, and the larger the moral repugnance. To put it formally, m (a i , w, x i ) is non decreasing in the two first arguments:

∂ ∂a i m (a i , w, x i ) ≡ m a (a i , w, x i ) ≥ 0, ∂ ∂w m (a i , w, x i ) ≡ m w (a i , w, x i ) ≥ 0.
We also assume that the marginal moral repugnance increases when altruism gets larger:

∂ 2 (∂a i ) 2 m (a i , w, x i ) ≡ m aa (a i , w, x i ) ≥ 0 .
On the other hand, the mere fact to contribute could mitigate moral repugnance, so m (a i , w, x i ) is non increasing in the last argument: m (a i , w, 0) ≥ m (a i , w, 1) .

Finally, without altruism, or without payment (when w = 0 or/and x i = 0), there is no moral repugnance, therefore

m (0, w, x i ) = m (a i , 0, x i ) = m (a i , w, 0) = 0 .
Agents decide to contribute or not by comparing the levels of utility attached to each possibility. Define the utility change of contributing:

U i A (a i , w) ≡ U i A (1) -U i A (0) , = w + a i t A + c(0) -c(1) + m (a i , w, 0) -m (a i , w, 1) , = w + a i t A -c -m (a i , w) , (5)
where m (a i , w) ≡ m (a i , w, 1) -m (a i , w, 0) = m (a i , w, 1) . Function U i A (a i , w) is supposed to be of class C 1 . (meaning that m (., ., 1) as a function of a i and w is itself C 1 .) Notice that increasing the degree of green altruism can have two opposite effects on the utility change. The first effect is positive; it goes through the marginal benefit on others that is more valued by a more altruistic agent. The second effect is negative, because more altruism goes along with a more stringent moral repugnance under direct treatment A.

Contributors are those agents with U i A (a i , w) ≥ 0 and non contributors are agents i with U i A (a i ) < 0.

Assumption 1. Assume that:

lim a i →0 U i A (a i , w) = w -c < 0 , (6)
lim a i →1 U i A (a i , w) = w + t A -c -m (1, w) < 0 , (7)
lim a i →0 d da i U i A (a i , w) = t A -m a (0, w, 1) > 0 , (8)
lim a i →1 d da i U i A (a i , w) = t A -m a (1, w, 1) < 0. (9)
Item ( 6) of Assumption 1 focuses the analysis to payments w that are not high enough to encourage participation of the less altruistic agents (the payment alone is not enough to compensate the opportunity cost of contributing). This is the most interesting case, because if extrinsic incentives are too strong, no crowding-out effect can occur. Item [START_REF] Bowles | Policies Designed for Self-Interested Citizens May Undermine "The Moral Sentiments[END_REF] of Assumption 1 means that for the most altruistic agents, contributing is not optimal because their feeling of altruism towards others, though important, is overwhelmed by their moral repugnance of being paid. From items ( 8) and ( 9) of Assumption 1, given that:

d 2 (da i ) 2 U i A (a i , w) = -m aa (a i , w, 1) ≤ 0,
and by the intermediate value theorem, ∃a * i such that t A -∂ ∂a i m (a * i , w, 1) = 0. Therefore function U i A (a i ) has an inverted U shape: it is first increasing, until a * i , then decreasing. Assume that U i A (a * i ) > 0. Then there exists a neighborhood

C A (a * i ) ≡ [a * i -ε, a * i + ε] [0, 1]
of contributing agents around a * i , i.e. U i A (a i , w) ≥ 0,

∀a i ∈ C A (a * i ) . Note that C A (a * i ) is a 180 proper subset of [0, 1]
, for all the elements of [0, 1] do not belong to C A (a * i ); in particular, because of parts ( 6) and ( 7) of Assumption 1, agents a 0 and a 1 are not contributors. It is interesting to emphasize the peculiarity of this treatment. The choice to contribute can be explained by two intrinsic motivations of different natures: a degree of altruism sufficiently high or a moral repugnance not too strong (precisely in the most altruistic agents).

185

For future reference, let us denote:

a D = a * i -ε , a D = a * i + ε .
the agents who, among those who contribute, have the lowest and largest altruism respectively. By definition, those two values solve the equation:

U i A (a i , w) = w + a i t A -c -m (a i , w) = 0. (10)
Does crowding-out necessarily occur? To answer this question, one has to compare the mass of 1 -a N of contributors under the neutral treatment with the mass a D -a D of contributors under treatment A. Unless more structure is given to the moral repugnance function m (a i , w), equation ( 10) cannot be solved explicitly for a D and a D . Still, important qualitative pieces of information can be obtained. The possibility of crowding-out depends on the relative position of a N with respect to a D and a D . The answer is ambiguous when a N ∈ a D , a D and when a N > a D , but there is crowding-out for sure when a N ≤ a D . All those situations can be associated with particular conditions on parameters. Since U i A (a i ) has an inverted U shape and takes on positive values around a * i , by construction a N ∈ a D , a D if and only if:

U i A a N , w ≥ 0.
Using [START_REF] Bernheim | Beyond revealed preference: choice theoretic foundations for behavioral welfare economics[END_REF] and the fact that a N = c/t N (see ( 2)):

U i A a N , w ≥ 0 ⇔ w + c t N * t A -c -m c t N , w, 1 ≥ 0 . ( 11
)
By the same logic, if a N < a D or if a N > a D , then necessarily:

U i A a N , w < 0 ⇔ w + c t N * t A -c -m c t N , w, 1 < 0 . ( 12
)
The last inequality means that, for agent a N , the payment alone does not provide sufficient incentives to compensate the cost of moral repugnance and the decrease in altruistic motivation following the change of benefits on others from t N to t A . This is consistent both with a too low value for w and with a too high value (recall that moral repugnance increases with w). This assessment of the weakness of monetary incentives is not absolute, but relative to parameters t N and t A . So, rewriting equality (12):

Definition ((N/A)-weak extrinsic incentive). Extrinsic incentives are (N/A)-weak when:

w < c t N -t A t N + m c t N , w, 1 .
The above reasoning has therefore established:

Proposition 1. If a N < a D , incentives are (N/A)-weak and there is crowding out.

A last question is about the interactions between internal and external incentives. It is generally considered that the phenomenon of crowding-out gets weaker as external (monetary) incentives gets stronger. Let us analyze the effect of increasing the external incentive w on the upper and lower bounds of C A (a * i ), i.e. on a D and a D . By equation [START_REF] Frey | Introducing procedural utility: not only what, but also how matters[END_REF] and the implicit function theorem, using the properties that t A -m a > 0 until a * i and t A -m a < 0 after a * i , and under the assumption that moral repugnance increases less than proportionally with the external incentive, m w < 1, we can conclude:

da dw a=a D = - 1 -m w a D , w, 1 t A -m a (a D , w, 1) < 0 , da dw a=a D = - 1 -m w a D , w, 1 t A -m a a D , w, 1 > 0 .
Therefore, as w increases the mass of contributors C A (a * i ) = a D , a D gets wider. But it is important to notice that a crowding-out is not a necessary consequence of the direct treatment. A necessary condition for crowding in is a D < a N . This may well happen if the monetary payment w is high enough. But this condition is not sufficient, because there is a mass of highly altruistic agents, 1-a D , who do not participate. By continuity, when w increases so that a D decreases and falls below a N , and if:

da dw a=a D < da dw a=a D ,
that is if at the margin the increase of lower-end contributors is less than the decrease of upper-end non contributors, there is a continuum of values for w consistent with crowding-in, even though the less altruistic agent who participates under the direct treatment is less altruistic than the less altruistic agent who participates in the neutral treatment.

To summarize, Proposition 2. Under Assumptions ( 8), ( 9), and when moral repugnance increases less than proportionally with the external incentive, m w < 1, the stronger the external incentive w, the weaker the crowding-out effect, if any, under the direct treatment.

Indirect Treatment (B): distorted altruism alone

Under this design the payment is no longer given to contributors; rather it is directed to a cause supporting the environment, for example a related association or NGO. Hence individual i no longer bears the cost of moral repugnance, but of course his altruistic motivation is activated, for participation still generates a benefit to the environment. The decision utility functions are now:

U i B (x i ) = y i + a i t B x i -c(x i ) ,
where t B is the corrected marginal percieved benefits on the environment.

Regarding the fact that a payment is directed to the cause supported by the individual, we can reasonably consider that the perceived benefit on the environment of his participation is higher than when the same amount of money is directed to the individual's pocket, because the chosen destination, by its very nature, reinforces the belief of the agent on the presence of high environmental values, or because the association is more efficient than individuals in transforming a given amount of contributions in environmental gains. An assumption on parameters consistent with that view is

t A ≤ t B .
Hence, agents who settle for zero contributions are those such that:

y i -c(0) > y i + a i t B -c(1),
and the others contribute. Put differently, there is an interval 0, a I , where

a I = c t B , (13)
of non-contributors, and an interval C B ≡ a I , 1 of contributors. The total number of contributors is

1 -a I . (14)
Compared to the neutral treatment there is crowding-out when t B ≤ t N , because the mass of contributors has shrunk (compare expression [START_REF] Kelly | Yuck! The Nature and Moral Significance of Disgust[END_REF] with expression (3)). This non ambiguous result is rather intuitive: there is no direct own benefit and the estimation of the benefits on others has been cut down (t B ≤ t N ), so the incentives to participate are weaker compared to the neutral treatment. However, the comparison with the direct treatment is more subtle. It is worth noting that there is a mass of agents near a 1 who contribute under the indirect treatment and who do not contribute under the direct treatment. In two cases, when a I ∈ a D , a D and when a I > a D , we cannot state which policy better encourages participation. But the indirect treatment out-performs the direct treatment for sure when a I < a D . Again all those situations can be associated with particular conditions on parameters. For a D ≤ a I ≤ a D , a necessary and sufficient condition on the fundamentals of the model derives from the observation that U i B a I , w = U i B c/t B , w ≥ 0 in such a situation. Or equivalently, using (5):

w ≥ c * t B -t A t B + m c t B , w, 1 . (15)
When this condition is not met, a necessary condition is obtained for a I < a D :

Definition ((B/A)-weak extrinsic incentives). Extrinsic incentives are (B/A)-weak when:

w < c * t B -t A t B + m c t B , w, 1 .
When a I < a D , incentives are (B/A)-weak and crowding-out is unambiguously less important under the indirect treatment. Intuitively, even if there are no monetary rewards for the agents under policy B, altruistic motives are less corroded than under the direct treatment and, in addition, the extrinsic motivation is not strong enough under policy A to compensate the weaker altruistic motivation and moral repugnance.

In a nutshell: Proposition 3. When the estimations of the benefits on others are such that t A ≤ t B ≤ t N , if a I < a D the extrinsic incentives are (B/A)-weak and the indirect treatment unambiguously mitigates the crowding-out effect compared to the direct treatment. When extrinsic incentives are not (B/A)weak, or when a I > a D , the ability of the indirect treatment to improve participation compared to the direct treatment is ambiguous. However, in any case, participation under the indirect treatment is never larger than under the neutral treatment, a N ≤ a I .

Choice Treatment (C): auto-selection of motivations

Under this treatment, individuals can choose whether the payment is directed to themselves or to an environmental association. Giving the choice to individuals (keeping the reward for themselves or giving it to the 'environmental cause') could motivate a wider set of individuals, possibly leading to a higher overall contribution 4 . In a sense, by choosing the target of the payment individual i chooses which decision utility function to activate. Then, agent i's decision utility function U i C exists in two expressions:

• it is: U i C (x i ) = U i A (x i ) = y i -c(x i ) + wx i + a i t A x i -m (a i , w, x i )
, when the payment is direct.

• and it is:

U i C (x i ) = U i B (x i ) = y i + a i t B x i -c(x i ) , when the payment is indirect.
Does the choice treatment minimize the countervailing effect of external incentives? Notice first that the utility attached to non participation is the same, whatever the chosen target:

U i C (x i ) = U i N (0) = U i A (0) = U i B (0) = y i .
But the utility derived from participation differs according to the target of the payment. Agents who increase their utility by contributing are those who belong to at least one of the sets of contributors previously identified. Clearly, the set C C of contributors under the choice treatment is the union of the two sets of contributors of each separate treatment, i.e. C C = C B ∪ C A . The set C C encompasses agents a i such that U i B (a i ) ≥ 0, and/or U i B (a i ) ≥ 0 and, therefore, the choice treatment promotes participation as least as much as the two policies A & B separately do. But more precision can be added.

We will keep on assuming that estimations of the benefits of altruism are such that t A ≤ t B ≤ t N . Even under this assumption, several configurations for the different sets of contributors are possible:

Case 1 A first case is when a N ≤ a I < a D , so the extrinsic motive is both (N/A)-weak and (B/A)-weak (definitions 2.2 and 2.3). Then the different sets of contributors are such that:

C A C B = C C C N .
Contributors under the choice treatment are exactly those who contribute under the indirect treatment and they are not more numerous than those who contribute under the neutral treatment.

Case 2 A more interesting case is when the monetary payment is sufficiently important to produce the following ranking a N ≤ a D < a I ≤ a D , that is the extrinsic motive is (N/A)-weak but it is not (B/A)-weak. The sets of contributors are then in the following configuration:

C A , C B C C C N .
Contributors under the choice treatment are more numerous than those who contribute under any of the two separate treatments. But the choice treatment does not perform any better than the neutral treatment.

Case 3

The most interesting case is when the monetary incentives are pushed slightly further so that a D < a N < a I ≤ a D . The sets of contributors are such that:

C A , C B C N C C .
This is a case featuring crowding-out under each separate treatment, but there is crowdingin under the choice treatment. This possibility occurs because several intrinsic motivations exists and because agents are heterogenous. As a results those who contribute are not necessarily identical across treatments and, even more, C A is neither a proper subset of C B nor a proper subset of C N . The corresponding necessary and sufficient conditions on parameters have been identified in [START_REF] Frey | Beyond Outcomes: Measuring Procedural Utility[END_REF] and [START_REF] Gneezy | When and Why Incentives (Don't) Work to Modify Behavior[END_REF]. They must be imposed simultaneously, as a new assumption:

Assumption 2 (Conditions for crowding-in).

w Case 4 Finally when a D < a N < a D ≤ a I . It is not possible to conclude -without further information on the moral repugnance function -about the extent of the crowding-out phenomenon, if any, because there is a mass of agents characterized by intermediate degrees of altruism in the interval a D , a I who are not contributors. However, this situation is discarded when the extrinsic motivation is not t B -weak.

To summarize, the choice treatment combines the incentive effects of both the direct and indirect treatments: Proposition 4. Let Assumption 1 holds and assume also t A < t B ≤ t N . Participation under policy C (choice treatment) is at least as large as under policies A & B. The choice treatment even results in crowding-in, although there is crowding-out under policies A & B, if and only if Assumption 2 is satisfied.

Conclusion

We made a strong case for how different intrinsic motivations among agents can play an instrumental role in explaining the effectiveness of introducing monetary incentives. We have formalized how the heterogeneity of intrinsic motivations among agents impacts their reactions to the introduction of monetary incentives. We showed that overall results supporting (or not) an undesired crowdingout effect can occult a more complex reality where some individuals contribute thanks to these additional monetary incentives while others reduce their contributions. Moreover, we proposed a new instrument which taps into agents' heterogeneity in order to suppress, or at least to reduce, the risk of crowding-out effect. This instrument avoids a 'one-size-fits-all' policy and allows agents to self-select the most relevant arrangement. A considerable advantage of our mechanism is that it does not require that policy makers have an extensive knowledge about the various levels of intrinsic motivations of agents.

Theoretically, the proposed instrument respects the freedom of choice of individuals. Indeed, they decide about the final use of the received monetary incentives. Nevertheless, we are conscious that the possibility of choice might also strongly vary with the framing of the task and could change the social behaviour leading to different normative expectations. In line with the traditional maxim stressing that the evil is in the details, we encourage a careful framing of real-world instruments by pre-testing their various versions in pilot experiments.

Table 1 .

 1 Intrinsic motivation: definitions

	Definitions

For instance, let us consider that intrinsically motivated donators are those who enjoy donating for its own sake. If we study experimental results of dictator games, we get a whole range of individuals from those giving nothing to those giving their own endowments.

Experienced utility functions would rather incorporate altruism, and capture the public good collectively created by inserting the others' aggregated contribution as an argument in utility functions of the kind U i (x i , x -i , f ).

The parameter a i could also represent the degree of altruism or reciprocity.

Moreover, in addition to obvious intuitive reasons based on empirical evidence, we argue that people enjoy the possibility of choosing by themselves, even at a cost[START_REF] Benz | Introducing Procedural Utility: Not Only What, but Also How Matters[END_REF][START_REF] Frey | Beyond Outcomes: Measuring Procedural Utility[END_REF].

Documents de Recherche parus en 2015

DR n°2015 -01:

Antoine BERETTI, Charles FIGUIERES et Gilles GROLLEAU «An Instrument that Could Turn Crowding-out into Crowding-in » Contact :

Stéphane MUSSARD : mussard@lameta.univ-montp1.fr


Gilles Paintaud
email: paintaud@med.univ-tours.fr

Christophe Passot

David Ternant

Bertolotto Antonio

Theodora Bejan-Angoulvant

Dora Pascual-Salcedo

Denis Mulleman

Prof Gilles Paintaud

Rationale for therapeutic drug monitoring of biopharmaceuticals in inflammatory diseases

Biopharmaceuticals bring together a number of specific characteristics as compared with other drugs. However, as done for most drugs, an individual adjustment of their dose may be necessary. Similar to "chemical" drugs, biopharmaceuticals used in immuno-inflammatory diseases have a rather narrow therapeutic range, lack good early clinical or biological marker of response, have variable pharmacokinetics, and their serum concentration are most often related with response. Monoclonal antibodies (mAbs) have additional specific sources of pharmacokinetic variability. Low concentrations may increase the risks of immunization, plasmapheresis may increase their elimination, and subcutaneous formulations may be associated with decreased adherence. For all these reasons, pharmacokinetic therapeutic drug monitoring may be useful. However, few randomized controlled TDM studies have been published. For mAbs, a precise definition of the therapeutic concentrations is challenging because of the interindividual variability in their concentration-effect relationship.

Rationale for TDM of drugs

Drug monitoring is the process of observing, recording, or detecting the effects of a drug administered to an individual. 1 Therapeutic drug monitoring (TDM) based on pharmacokinetics uses the concentration of the drug, usually measured in blood, to adjust its dose individually. Its aim is to personalize the dose of the drug according to the pharmacokinetic characteristics of the patient. The interest of TDM for a given drug is studied if this drug fulfills specific criteria. The four main criteria are (1) a narrow therapeutic range with dose-dependent adverse side effects; (2) the lack of good early clinical or biological marker of response allowing to adjust the dose individually; (3) a variability in pharmacokinetics, both between patients and for a given patient, over time; and (4) the observation of relationships between the concentration of drug (or active moieties) and both therapeutic and toxic effects. In addition, TDM may theoretically be useful in specific cases, i.e. (5) when the risk of poor compliance is high; (6) when low concentrations increase the risk of resistance development; or (7) when artificial serum clearance is necessary.

Because TDM allows to reach an effective concentration more rapidly while minimizing drug toxicity, it increases the control of the disease and decreases the need for other treatments. It also limits the use of unnecessary high doses. For these reasons, TDM may lead to lower treatment costs. Since TDM has its own costs, this needs to be confirmed by cost-benefit studies.

Potential interest of TDM for biopharmaceuticals

Similarities with "chemical" drugs

Narrow therapeutic range

Biopharmaceuticals may be considered as drugs with a good benefit/risk ratio. However, like "chemical" drugs, they are not devoid of adverse side effects. Besides immunization, the most common adverse effect associated with monoclonal antibodies (mAbs) directed against TNF (e.g., infliximab), CD20 (e.g., rituximab), or IL-6R (e.g., tocilizumab) is the increased risk of infections. [START_REF] Ternant | Clinical pharmacokinetics and pharmacodynamics of monoclonal antibodies approved to treat rheumatoid arthritis[END_REF] The risk of infections was found to be related to the dose of anti-TNF mAbs in some meta-analyses [START_REF] Singh | Risk of serious infection in biological treatment of patients with rheumatoid arthritis: a systematic review and metaanalysis[END_REF] but not in others. [START_REF] Michaud | The comparative safety of tumor necrosis factor inhibitors in rheumatoid arthritis: a meta-analysis update of 44 trials[END_REF] With rituximab, B-cell depletion may be prolonged, leading to a persistent immunodeficiency. [START_REF] Makatsori | Hypogammaglobulinaemia after rituximab treatment-incidence and outcomes[END_REF][START_REF] Roberts | Rituximab-associated hypogammaglobulinemia: incidence, predictors and outcomes in patients with multisystem autoimmune disease[END_REF]

Lack of good clinical or biological marker

The dose of most drugs needs to be adjusted individually. At the treatment initiation, the recommended dose for intravenous drugs, including biopharmaceuticals, is usually defined according to weight or body surface area. On the other hand, the dose of subcutaneous biopharmaceuticals is often fixed. Afterward, the dose should be adjusted according to patient's therapeutic response or dose-dependent side effects. Although the target-antigen of mAbs is very well known, the blood concentration of the target-antigen is not used as biomarker to monitor the effects of mAbs during the treatment. This may be explained (1) by a lack of proportionality between blood concentration of target-antigen and its total amount in the body, (2) by difficulties in measuring the concentration of the target-antigen either because assays do not differentiate its free form and the immune complex or because of its poor stability in blood samples. Therefore, indirect assessments of the target-antigen, using biomarkers such as C-reactive protein for anti-TNF mAbs or B-cell numeration for anti-CD20 mAbs, may be useful. In multiple sclerosis, pharmacodynamic monitoring of interferon is available. [START_REF] Caldano | Therapeutic drug monitoring of biological agents used in the treatment of Multiple Sclerosis[END_REF] However, these biomarkers are not always related to the clinical response. Disease activity scores such as DAS28 in rheumatoid arthritis and CDAI in Crohn's disease are commonly used to monitor patients' response to treatment. However, they are not assessed before several weeks of treatment, and most of these indices suffer from subjectivity, either from the patient´s own evaluation or from the clinician. In multiple sclerosis, the evaluation occurs even later because it is based on the occurrence of the relapse and/or MRI disease activity. Also, clinical monitoring is complicated by the fact that several end points are used for a given disease, e.g., for Crohn's disease. [START_REF] Papay | Optimising monitoring in the management of Crohn's disease: a physician's perspective[END_REF] Therefore, measurement of blood concentration of the mAb, which reflects the exposure to the drug, appears as a convenient tool of monitoring, available from the first weeks of treatment.

Variability in pharmacokinetics

The interindividual (between patients) and intraindividual (over time in a given patient) variability in pharmacokinetics of mAbs is well known and was reported for all. [START_REF] Ternant | Pharmacokinetics and concentration-effect relationships of therapeutic monoclonal antibodies and fusion proteins[END_REF][START_REF] Munnink | Therapeutic drug monitoring of monoclonal antibodies in inflammatory and malignant disease: translating TNF-α experience to oncology[END_REF] This variability is also observed for other biopharmaceuticals such as the fusion protein etanercept [START_REF] Jamnitski | Patients non-responding to etanercept obtain lower etanercept concentrations compared with responding patients[END_REF] or interferon beta. [START_REF] Hu | Pharmacokinetics and pharmacodynamics of peginterferon beta-1a in patients with relapsing-remitting multiple sclerosis in the randomized ADVANCE study[END_REF] Similar to chemical drugs, pharmacokinetics of mAbs used in immuno-inflammatory diseases is significantly influenced by body weight and/or body surface area. [START_REF] Bai | A guide to rational dosing of monoclonal antibodies[END_REF] Other sources of variability, more specific to mAbs, are discussed infra.

Concentration-effect relationship

A relationship between serum concentration and biological and/or clinical responses was reported for most mAbs. This is particularly the case for anti-TNF such as for infliximab in rheumatoid arthritis, [START_REF] St Clair | The relationship of serum infliximab concentrations to clinical improvement in rheumatoid arthritis: results from ATTRACT, a multicenter, randomized, doubleblind, placebo-controlled trial[END_REF][START_REF] Mulleman | Trough infliximab concentrations predict efficacy and sustained control of disease activity in rheumatoid arthritis[END_REF][START_REF] Wolbink | Relationship between serum trough infliximab levels, pretreatment C reactive protein levels, and clinical response to infliximab treatment in patients with rheumatoid arthritis[END_REF][START_REF] Bendtzen | Individualized monitoring of drug bioavailability and immunogenicity in rheumatoid arthritis patients treated with the tumor necrosis factor alpha inhibitor infliximab[END_REF][START_REF] Van Den Bemt | The combined use of disease activity and infliximab serum trough concentrations for early prediction of (non-)response to infliximab in rheumatoid arthritis[END_REF] spondyloarthritis, [START_REF] Plasencia | Influence of immunogenicity on the efficacy of long term treatment of spondyloarthritis with infliximab[END_REF] psoriasis, [START_REF] Reich | EXPRESS study investigators. Infliximab induction and maintenance therapy for moderate-to-severe psoriasis: a phase III, multicentre, double-blind trial[END_REF][START_REF] Dannepond | Serum infliximab concentrations and disease activity: a descriptive study of patients with psoriasis[END_REF] Crohn's disease [START_REF] Maini | Therapeutic efficacy of multiple intravenous infusions of anti-tumor necrosis factor alpha monoclonal antibody combined with low-dose weekly methotrexate in rheumatoid arthritis[END_REF][START_REF] Maser | Association of trough serum infliximab to clinical outcome after scheduled maintenance treatment for Crohn's disease[END_REF][START_REF] Cornillie | Postinduction serum infliximab trough level and decrease of C-reactive protein level are associated with durable sustained response to infliximab: a retrospective analysis of the ACCENT I trial[END_REF] and ulcerative colitis. [START_REF] Adedokun | Association between serum concentration of infliximab and efficacy in adult patients with ulcerative colitis[END_REF] Regarding adalimumab, a concentrationresponse relationship was reported in rheumatoid arthritis, [START_REF] Bartelds | Clinical response to adalimumab: relationship to anti-adalimumab antibodies and serum adalimumab concentrations in rheumatoid arthritis[END_REF][START_REF] Pouw | Key findings towards optimising adalimumab treatment: the concentration-effect curve[END_REF] Crohn's disease, [START_REF] Karmiris | Influence of trough serum levels and immunogenicity on long-term outcome of adalimumab therapy in Crohn's disease[END_REF][START_REF] Mazor | Adalimumab drug and antibody levels as predictors of clinical and laboratory response in patients with Crohn's disease[END_REF] ulcerative colitis, [START_REF] Baert | Prior response to infliximab and early serum drug concentrations predict effects of adalimumab in ulcerative colitis[END_REF] and psoriasis. [START_REF] Menting | Developing a therapeutic range of adalimumab serum concentrations in management of psoriasis: a step toward personalized treatment[END_REF] Moreover, such a relationship was reported for other anti-TNF biopharmaceuticals, such as etanercept [START_REF] Jamnitski | Patients non-responding to etanercept obtain lower etanercept concentrations compared with responding patients[END_REF] and certolizumab pegol 32 in rheumatoid arthritis. A concentration-response relationship was reported for mAbs binding to other target-antigens, such as tocilizumab in rheumatoid arthritis, [START_REF] Levi | Exposure-response relationship of tocilizumab, an anti-IL-6 receptor monoclonal antibody, in a large population of patients with rheumatoid arthritis[END_REF][START_REF] Ohta | Mechanism-based approach using a biomarker response to evaluate tocilizumab subcutaneous injection in patients with rheumatoid arthritis with an inadequate response to synthetic DMARDs (MATSURI study)[END_REF] vedolizumab (an anti-α4β7) in Crohn's disease and ulcerative colitis, [START_REF] Rosario | Population pharmacokineticspharmacodynamics of vedolizumab in patients with ulcerative colitis and Crohn's disease[END_REF] and ustekinumab (an anti-IL-12/IL-23) in psoriasis. [START_REF] Papp | Efficacy and safety of ustekinumab, a human interleukin-12/23 monoclonal antibody, in patients with psoriasis: 52-week results from a randomised, double-blind, placebo-controlled trial (PHOENIX 2)[END_REF] In inflammatory arthritis, high infliximab concentrations were recently reported to be correlated with a higher risk of a first serious infectious episode. [START_REF] Bejan-Angoulvant | Brief report: relationship between serum infliximab concentrations and risk of infections in patients treated for spondyloarthritis[END_REF] Conversely, no concentration-effect relationship was observed for rituximab in rheumatoid arthritis. [START_REF] Thurlings | Clinical response, pharmacokinetics, development of human anti-chimaeric antibodies, and synovial tissue response to rituximab treatment in patients with rheumatoid arthritis[END_REF]

Risk of poor compliance

An increasing number of biopharmaceuticals is administered subcutaneously. This mode of administration may be associated, theoretically, with a risk of decreased compliance. [START_REF] Deleu | Will new injection devices for interferon β-1a s.c. affect treatment adherence in patients with multiple sclerosis? An expert opinion in the Middle East[END_REF] Some publications have already shown that self-administration was a risk factor for discontinuation of mAbs from the own accord of the patient as was a low level of pain [START_REF] Betegnie | Why do patients with chronic inflammatory rheumatic diseases discontinue their biologics? An assessment of patients' adherence using a self-report questionnaire[END_REF] while others found a very good adherence, in psoriasis for instance. [START_REF] Hsu | Patient adherence to biologic agents in psoriasis[END_REF]

Low concentrations increase the risk of resistance development

A parallel may be drawn between the risk of resistance development associated with subtherapeutic doses of anti-infectious drugs and the risk of immunization against biopharmaceuticals. Low serum concentrations of infliximab at the treatment initiation were indeed associated with an increased risk of immunization both in rheumatoid arthritis [START_REF] Bendtzen | Individualized monitoring of drug bioavailability and immunogenicity in rheumatoid arthritis patients treated with the tumor necrosis factor alpha inhibitor infliximab[END_REF][START_REF] Ducourau | Antibodies toward infliximab are associated with low infliximab concentration at treatment initiation and poor infliximab maintenance in rheumatic diseases[END_REF] and in ankylosing spondylitis. [START_REF] Ducourau | Antibodies toward infliximab are associated with low infliximab concentration at treatment initiation and poor infliximab maintenance in rheumatic diseases[END_REF] Nevertheless, these associations have been only reported for mAbs and at the initiation of the treatment. More studies are therefore needed.

Artificial clearance

Because of their molecular weight, mAbs are not eliminated during hemodialysis. However, their clearance is increased during plasmapheresis, a therapeutic procedure used to get rid of pathogenic immunoglobulins, with a resulting 40% decrease in rituximab concentrations in certain patients. [START_REF] Azzopardi | Influence of plasma exchange on rituximab pharmacokinetics[END_REF] When progressive multifocal leukoencephalopathy, a severe complication of natalizumab, develops, plasmapheresis and immunoadsorption are used for accelerating its clearance. [START_REF] Vennegoor | Application of serum natalizumab levels during plasma exchange in MS patients with progressive multifocal leukoencephalopathy[END_REF]

Criteria specific to mAbs

Except for weight and body surface area, the sources of interindividual variability in pharmacokinetics of mAbs are mostly different from those of "chemical drugs."

Recycling by FcRn

As other circulating proteins, mAbs are passively internalized in cells, notably vascular endothelial cells. However, they are protected from degradation in lysosomes by a specific receptor for IgG, the neonatal Fc receptor or FcRn, which recycle them. FcRn protection and recycling explain their long half-life, varying from two to four weeks. Studies reported an influence of a variable number tandem repeat polymorphism of the gene encoding FcRn, FCGRT, on the pharmacokinetics of monoclonal antibodies. [START_REF] Passot | Influence of FCGRT gene polymorphisms on pharmacokinetics of therapeutic antibodies[END_REF][START_REF] Caulet | Bevacizumab pharmacokinetics influence overall and progression-free survival in metastatic colorectal cancer patients[END_REF]

Immunization

Monoclonal antibodies are recombinant proteins, and the risk of immunization is important with mAbs used in immuno-inflammatory diseases. The development of antibodies towards the mAb, usually called anti-drug antibodies (ADA), alters dramatically the pharmacokinetics and leads to a drop in mAb blood concentrations, as shown, e.g., for infliximab, [START_REF] Baert | Influence of immunogenicity on the longterm efficacy of infliximab in Crohn's disease[END_REF][START_REF] Hu | Population approach for exposure-response modeling of golimumab in patients with rheumatoid arthritis[END_REF][START_REF] Pascual-Salcedo | Influence of immunogenicity on the efficacy of long-term treatment with infliximab in rheumatoid arthritis[END_REF][START_REF] Ternant | Relationship between inflammation and infliximab pharmacokinetics in rheumatoid arthritis[END_REF][START_REF] Ternant | Pharmacokinetics of adalimumab in Crohn's disease[END_REF] hence loss of response. [START_REF] Baert | Influence of immunogenicity on the longterm efficacy of infliximab in Crohn's disease[END_REF][START_REF] Wolbink | Development of antiinfliximab antibodies and relationship to clinical response in patients with rheumatoid arthritis[END_REF] Many immunogenicity assays, with different characteristics, are available for testing ADA. Monitoring of immunogenicity and the different types of assays are discussed in a short review. [START_REF] Bloem | Immunogenicity of therapeutic antibodies: monitoring anti-drug antibodies in a clinical context[END_REF]

Target-mediated drug disposition

A part of the clearance of mAbs is related to their binding to the target-antigen, which may lead to internalization when the target is a membrane receptor or to the formation of immune complexes for circulating targets. The size of these immune complexes is another parameter that influences this clearance. This target-mediated drug disposition (TMDD) is an important source of interindividual and intraindividual pharmacokinetic variability. [START_REF] Gibiansky | Target-mediated drug disposition model: relationships with indirect response models and application to population PK-PD analysis[END_REF] The clearance of anti-TNF mAbs was observed to increase with the level of inflammation in rheumatoid arthritis [START_REF] Ternant | Relationship between inflammation and infliximab pharmacokinetics in rheumatoid arthritis[END_REF] and in Crohn's disease. [START_REF] Ternant | Assessment of the influence of inflammation and FCGR3A genotype on infliximab pharmacokinetics and time to relapse in patients with Crohn's disease[END_REF] A study performed in a cohort of patients monitored with the same assay observed that the underlying disease influences infliximab pharmacokinetics. [START_REF] Passot | The underlying inflammatory chronic disease influences infliximab pharmacokinetics[END_REF] Another consequence of TMDD is non-linear pharmacokinetics because it is related to the amount of target-antigen. In immuno-inflammatory diseases, this non-linearity is particularly marked for tocilizumab. [START_REF] Frey | Population pharmacokinetic analysis of tocilizumab in patients with rheumatoid arthritis[END_REF]

Digestive loss in inflammatory bowel disease

Infliximab is lost into stools of patients with ulcerative colitis and high fecal concentrations of infliximab are associated with the lack of a primary response. [START_REF] Brandse | Loss of infliximab into feces is associated with lack of response to therapy in patients with severe ulcerative colitis[END_REF]

Theoretical justification of TDM of biopharmaceuticals

The characteristics that constitute the basis of TDM of "chemical" drugs are relevant for biopharmaceuticals. In addition, mAbs have specific mechanisms of disposition (notably their recycling by FcRn and TMDD) that may reinforce the interest of TDM. Also, individual dose-adjustment is difficult without TDM because of their long half-life and their non-linear pharmacokinetics. If pharmacoeconomic considerations are taken into account because of the high cost of biopharmaceuticals, TDM could be used to develop drug-sparing strategies.

Levels of evidence for TDM of mAbs

Although relationships between serum concentrations of biopharmaceuticals and response were reported, few prospective studies analyzed the impact of individual dose adjustment based on drug concentrations on clinical response and outcomes. In a prospective non-comparative study, a significant clinical improvement was observed in rheumatoid arthritis patients in whom an infliximab dose increase was justified by high disease activity and low infliximab concentrations. [START_REF] Mulleman | Infliximab concentration monitoring improves the control of disease activity in rheumatoid arthritis[END_REF] The results of controlled studies performed in inflammatory bowel disease are described in a review. [START_REF] Detrez | Current practice for therapeutic drug monitoring of biopharmaceuticals in inflammatory bowel disease[END_REF] Other short reviews have addressed the level of evidence in rheumatoid arthritis, [START_REF] Medina | Therapeutic drug monitoring of biopharmaceuticals in rheumatoid arthritis[END_REF] spondyloarthritis, [START_REF] Medina | Therapeutic drug monitoring of biopharmaceuticals in spondyloarthritis[END_REF] multiple sclerosis, 7 psoriasis, [START_REF] Hermans | Current practice of therapeutic drug monitoring of biopharmaceuticals in psoriasis patients[END_REF] and pediatrics. [START_REF] Murias | TDM of biopharmaceuticals in Paediatrics[END_REF] The need for TDM of belatacept, a fusion protein of the extracellular domain of CTLA4 and the Fc domain of human IgG1, in kidney transplantation was reviewed. [START_REF] De Graav | Therapeutic drug monitoring of belatacept in kidney transplantation[END_REF] More randomized studies assessing the potential clinical benefits of TDM of biopharmaceuticals are clearly needed.

Study design

Similar to all clinical trials, TDM studies should include patients who are representative of the treated population. One of the challenges in the design of controlled trials studying the benefit of TDM is the choice of the target concentrations of the biopharmaceutical. First, therapeutic concentrations for a given drug may be different in different diseases (e.g., infliximab concentrations predictive of clinical response in rheumatoid arthritis and Crohn's disease are different). Second, therapeutic concentrations for a given drug in a specific disease may be influenced by disease activity. A pharmacokinetic-pharmacodynamic (PK-PD) modeling of adalimumab in rheumatoid arthritis has indeed observed an influence of baseline disease activity, assessed by DAS28, on sensitivity to the mAb, assessed by IC50. [START_REF] Ducourau | Towards an individualised target concentration of adalimumab in rheumatoid arthritis[END_REF] The target concentration of the mAb should therefore be based on PK-PD modeling [START_REF] Passot | Therapeutic drug monitoring of biologicals will benefit of pharmacokinetic and pharmacokinetic-pharmacodynamic modelling[END_REF] and could be adjusted to individual disease activity. Pharmaceutical companies should support such studies and assist academic and clinical laboratories setting up external quality assessment schemes for the biopharmaceuticals they commercialize.

Conclusion

Therapeutic mAbs and biopharmaceuticals, in general, are drugs with a complex dose-concentration-effect relationship. The sources of interindividual variability in clinical response are mostly different from those of "chemical" drugs. There are many arguments in favor of a TDM of biopharmaceuticals used in immuno-inflammatory disease, both similar to those relevant to "chemical" drugs and specific for biopharmaceuticals. Randomized controlled studies must be conducted to confirm the theoretical interest of TDM and these need to individually address targetantigens, the different mAbs, and their different indications.

Acknowledgments

The authors of the present manuscript participate in the Consortium "Monitoring of monoclonal Antibodies Group in Europe" (MAGE) for inflammatory diseases. The MAGE Consortium is supported by LE STUDIUM Loire Valley Institute for Advanced Studies (http://www.lestudium-ias.com/).

GP reports grants received by his research team from Novartis, Roche Pharma, Genzyme, MSD, Chugai, and Pfizer, outside of the submitted work. CP has nothing to disclose. DT has given lectures for Amgen and Sanofi. AB received honoraria for serving in the scientific advisory boards of Almirall, Biogen, Merck and received speaker honoraria from Biogen, Merck, Teva, Bayer, Sanofi-Genzyme, and Novartis; his institution has received research support from Almirall, Biogen, Bayer, Merck, Sanofi-Genzyme, Novartis, Teva, from the Italian Multiple Sclerosis Society, Fondazione Associazione Ricerca Biomedica and San Luigi Onlus.

Funding

This project was not supported by any specific grants from commercial companies, and there were no conflicts of that kind in either the preparation or support for this manuscript.

Authors' contributions GP drafted the manuscript, CP, DT, TBA, DT, DPS, and DM reviewed and improved the manuscript. All authors read and approved the final manuscript.


François Villeneuve'

François Latour'

Théophile Théry

Patricia Erard

Christine Fournier

Marie-Christine Daunay'

Screening of solanaceous wild relatives for graft affinity with eggplant (Solanum melongena L.)

Eggplant (Solanum melongena L.), an important solanaceous crop in tbe world, is susceptible to soilbome bio-agressors, the main of which, in temperate areas, being Verticillium wilt (Verticillium sp.) and root knot nematodes (Meloidogyne spp.). Grafting on resistant rootstock is an alternative rnethod to soil disinfection. In France, the generalization of grafting spread over the 2000's. After several years of utilization of resistant tornato rootstocks for eggplant production, and to a lesser extent, of Solanum torvum rootstocks, damaging wilt-like-symptoms are often observed by growers. Renee it is necessary to identify alternative rootstocks, able to sustain the soil pathogenic cornplex by a combination of vigor and genetic resistance. However, graft affinity between potential rootstocks and eggplant (scion) is the fust step to investigate. Solanaceae family offers a wide choice of candidate rootstock species. The objective ofthis research was to identify solanaceous species baving a good graft affinity with eggplant, Screening of a wide set of genetic resources was carried out at the Centre Technique Interprofessionnel des Fruits et Légumes -Ctifl-(Lanxade and Balandran center) in collaboration with INRA. Experirnents were carried out during a five years period (2011)(2012)(2013)(2014)(2015). Several So/anum species displayed a good graft affinity with eggplant and are candidates for further agronomie evaluation.

Introduction

Eggplant (Solanum melongena L.) is an important solanaceous crop in the world and represents an important source of income for growers. The species is susceptible to several soilborne bio-agressors. Verticillium wiIt (Verticillium sp.) and root knot nematodes (Meloidogyne spp.) are the major limiting factors for eggplant production in temperate conditions, worldwide. Up ta a recent past, both diseases were controlled by soil fumigation with methyl bromide prior to planting. However, since this chemical is no more authorized for this use in European countries since 2005, no alternative chemicals have provided sufficient control of soilborne diseases. Grafting on resistant rootstock is an alternative method to soil disinfection. ln France, the research on grafting for vegetables production started in the 1950's, and grafting onto Verticillium resistant tomato rootstocks started in the 1960's for commercial production [START_REF] Messiaen | Trois années d'essai de greffage d'aubergines sur tomates résistantes à diverses maladies[END_REF][START_REF] J} Beyries | Le greffage des solanacées maraîchères[END_REF]. The generalization of grafting spread over the 2000's and nowadays 63% of French eggplant surfaces are grafted [START_REF] Torres | Le greffage des cultures légumières en France et dans le monde: État des lieux et programmes de recherche[END_REF]. After several years of utilization of resistant tomato rootstocks for eggplant production, and to a lesser extent, of Solanum torvum rootstocks, damaging wilt-like-symptoms are often observed by growers. A survey by [START_REF] Villeneuve | Greenhouse eggplant crop in France: success and failures of grofting for •controlling Verticillium sp[END_REF] in two main French production areas indicated that Verticillium, as weIl as at least two additional fungi, were responsible of the wiIt symptoms observed on grafted plants, thus revealing the development ofnew pathogenic complexes in intensively cultivated soils. Hence it is necessary to identify alternative rootstocks, able to sustain the new soil pathogenic complexes by a combination of vigor and genetic resistance. Graft affinity between potential rootstocks and eggplant (scion) is the fust step to investigate. Solanum genus, and more largely, Solanaceae family, offer a wide cboice of candidate rootstock species. The objectives ofthis research were to identify solanaceous species baving a good graft affinity with eggplant and yîelding good agronomie results. Screening of a wide set of genetic resources was carried out at the Centre Technique Interprofessionnel des Fruits et Légumes -Ctifl-(Lanxade and Balandran center) in collaboration with INRA.

Materiels and method

Graft affinity between eggplant and candidate rootstocks was investigated in a two steps process, (i) screening of rootstocks on young plants in semi-controlled conditions, and (ii) for the best rootstock-scion combinations, evaluation of agronomie results in greenhouse conditions.

Plant materials

Seventy five accessions of several genera and species belonging to the Solanaceae family, as well as five interspecific hybrids between eggplant and related Solanum species, were included in this study (table 1). Seeds were obtained frOIDINRA 01egetables Genetic Resources Centre, CRB-Leg, GAFL, Montfavet, and Ploudaniel) and also from the French institute of Tabaco (Bergerac, France), the Universitat Politècnica de València (Spain) and the Radboud University (Nijmegen, The Netberlands). The interspecific hybrids (Fl) were created at INRA GAFL. Germination was secured with a 500 ppm gibberellic acid (GA3) treatment applied to the seeds 24 hours before sowing in a substrate containing 67% of compost and 33% of quartz. Two leaf stage plantlets were transplanted in pots containing the same substrate (1.51).

Early sereening for graft affrnity

The experiments were carried out from 2011 to 2014 in greenhouse at Lanxade center of Ctifllocated in southwestern France (lat.: 44.86, long.: 0.40). Controls were (i) the non-grafted 'Monarca Fi' eggplant variety (Rijk Zwaan, Aramon, France), (ii) the self-grafted 'Monarca Fi', and (iii) the commercial tomato rootstock 'Maxifort' (Monsanto, France) which is an interspecific hybrid S. lycopersicum X S. habrochaites.

Plants of the 'Monarca FI' scion at tbe 2-4 true leaves stages (20-50 days old) were grafted onto rootstock plants having 3-4 true leaves (40-50 days old) using the cleft grafting method. To be sure that scions and rootstocks were to have sirnilar stem diameter at grafting time, sowing was made three times for the variety, at one week interval. After grafting, plantlets were kept for 5 days within a closed plastic shelter in a greenhouse with a day/night thermoperiode maintained between 25°and 18°C. Later on, grafted plantlets were progressively acclimatized by perforating the plastic. After acclimatization, grafted plants were placed in greenhouse under natural lighting for 150 days. Grafting combinations were randomized in a complete block design, with three replications of 5 plants per treatment. Success of graft union was recorded as weil as, 100 days after grafting, plant height and fresh weight of aerial part. Each graft union was longitudinally eut in order to observe the presence of browning (data 110tshown).

Agronomie trials

Tbe experiments were carried out in 2012 to 2015 in a greenhouse at Balandran center of Ctifl in southeastern region of France (lat.: 43°75', long.: 4°.45'N). Seeds were sown at INRA and grafting (tongue approach).was realized by a professional nursery. Experimental design and controls were the same as for the early screening assays.

Mortality throughout the cultivation period, plant height at the end of trial (150 days after transplanting) -data not shown-were recorded. Early and total yield (kg/rn-) were measured for each individual plant. Early yield was calculated over the fust three weeks of harvest. 80, ' " e g 60-•~----------------~M~o-n-a-rc-a-g-ra~ft~e~d-on~M~o-na-r-ca------------------------~n-:;; c: ~40+---------------------------1~--------------------------~~1~1 Ẽ ~20r_--------------------------L------- Different Solanum species are spiny, but as the spines are soft at an early plant development stage, they are not problematic.

Agronomie trials

We recorded some mortality shortly after plantation for Cyphomandra betacea and Nicandra physaloides and later (after the third harvest) for S. atropurpureum (75% of plants) and S. coccineum (53%). Mortality was less for S. mauritianum, S. trachycarpum and S. viarum. Some Solanum species produce suckers, very strongly for S. acanthoideum, S. trachycarpum and S. linnaeanum and at a lower level for S. aculeastrum, S. atropurpureum, S. pyracanthos and the interspecific hybrid S. linnaeanum x S. melongena. When the suckers have dense and sharp spines, like S. pyracanthos, this may be a problem in cultivation.

Early production is an important aspect for growers. Nicandra physaloides and S. rostratum are part of the earliest rootstocks, with also good total commercial yield, unlike S. trachycarpum and S. atropurpureum which present also a good early production but a low total yield By contrast, some botanical species used as rootstock induce a delayed production like S. hastifolium, S. erianthum and s. coccineum (figure 2). For the total commercial yield, the interspecific hybrid (S melongena X S incanum group C) gives much better results tban tbe commercial rootstock con trois 'Maxifort' and S torvum STT3 (figure 3). Yield of the two interspecific bybrids FI (S. aethiopicum Gilo X S. melongena) and FI (S linnaeanum x S melongena), as well as S aethiopicum gr Gilo, S anguivi, S incanum group A and D, S. macrocarpon, S pyracanthos, S rostratum, and S violaceum is similar to the yield of tbe two controls (figure 3). On the contrary, several rootstocks provide low to very low yields like S. trachycarpum, S mauritianum and S hastifolium. Globally the interspecific hybrids have comparable or better results than tbeir botanical parent. The data obtained during this prospective research on diverse parameters measuring graft affinity between eggplant (scion) and numerous Solanaceous species, from graft success to commercial yield, reveals the potentialities as rootstocks of several Solanum species, in particular S. aethiopicum gr. aculeatum, S. aethiopicum group Gilo, S. anguivi, S. incanum (group A, B, C, D) and S. macrocarpon, as weIl as interspecific hybrids (F 1 S. aethiopicum group Gilo x S. melongena, FIS. melongena x S. incanum group C and D and FIS. linnaeanum x S. melongena) present also interest. Similar promising results, although obtained with less rootstocks germplasm, were obtained by [START_REF] Gisbert | Eggplant relatices as sources of variation for developing new rootstocks: Effects of grafting on eggplant yield and fruit apparent quality and composition[END_REF].

40+-----------------------------------------------------------------M onarca grafted on Maxifort 20+---~------------------------------------------------------------~1 ~O+-------~~---------------------------------------------------------I ~O+-------~----------------------------------------------------------I
Further research is still needed before developping commercial new rootstocks. Indeed the agronomie performances of the best rootstocks identified has to be retested in different production conditions. Furtber, it is necessary to estimate their root vigor as weIl as their level of resistance to tbe major elements of the soil pathogenic complex, in particular Vertici/lium dahliae, Colletotrichum coccodes and Meloidogyne species. Furtbermore, the alkaloid content of the eggplant fruits produced on these rootstocks bas also to be looked at carefuIly.

  Figure 1.-Scion growth for the rootstocks displaying up ta 80% grafl success, expressed on the basis of the control Monarca auto-grafted, taken as a growth reference of zero, Ë3rootstocks with 100% rate of grafting success; D rootstocks with 80-99% rate of grafling success; DMonarca F1, not grafted (control); .rootstock Maxifort (commercial control).

Figure 2 :

 2 Figure 2: Effect ofrootstock on early production (in kg/m 2 ) jar the three first weeks ofproduction

Figure 3 :

 3 Figure 3: Relative total commercial yields 60 days after plantingfor the different botanical species tested as rootstock grafted onto the variety Monarca. The yield of the control Monarca grafted on Maxifort is taken as the reference of zero.

Table 1 :

 1 Plant material used as experimental rootstocks

	Species	Accession number	Seed source	Accessions used in confirmation trials
	Capsicum annuum	RV6	InraGAFL
	C. baccatum	PM 1034	Inra GAFL
	Cestrum parqui	874750007	Nijmegen
	Cyphomandra betacea Hyoscyamus niger Iochroma australe Lycianthes rantonetii Lycium barbarum Nicandra physaloides	894750221 88475005 904750118 814750064 MM 1378	Nijmegen Nijmegen Nijmegen Nijmegen InraGAFL Nijmegen	2012-13 2013

884750065 Institut du tabac Nicotiana tabacum nOl MS270 Institut du tabac N. tabacum n02 Inra GAFL Physalis edulis MS 33518 Inra GAFL P. peruviana MM 1321 InraGAFL 2013 Solanum acanthoideum MM 1358 Inra GAFL 2012-13 S. aculeastrum MM 12296 Inra GAFL S. aculeatissimum MM 1425 InraGAFL 2013-15 S. aethiopicum group Gilo MM 369 Inra GAFL 2013-14-15 S. aethiopicum group Aculeatum MM 232 bis InraGAFL 2013-14-15 S. anguivi agg. MM 134 Inra GAFL 2015 S. arundo Inra GAFL 2012-13 S. atropurpureum MM 1689 InraGAFL S. burchellii MM 1369 COMAV S. canense COMAV s. caripense MM 1526 InraGAFL 2015 S. catombelense MM 987 InraGAFL S. cerasiferurn UPV 23386 Inra Ploudaniel S. chacoense UPV 23372 InraGAFL S. citrullifolium MM 1218 InraGAFL 2015 S. coccineum InraGAFL 2014 S. cyaneo-purpureurn MM 866 InraGAFL S. dasyphyllum Inra GAFL S. dennekense MM 1174 InraGAFL S. dinteri MM 992 Inra GAFL S. elaeagnifolium MM 994 InraGAFL 2015 InraGAFL S. erianthurn (verbascifolium) MM 1137 InraGAFL 2015 S. glaucophyllurn MM 1312 Inra Ploudaniel S. hastifolium MM 1221 InraGAFL 2012-13-15 S. hougasii MM 1534 InraGAFL 2013-15 S. incanum group A MM l326 InraGAFL 2013-15 S. incanum group B MM 1793 InraGAFL S. incanum group C MM 1349 bis InraGAFL 2013-15 S. incanurn group C Inra GAFL S. incanum group D InraGAFL S.jatrophifolium MM716 InraGAFL 2013 S. kurzii (sanitwongsei) MM 1428 InraGAFL S. laciniatum MM 664 InraGAFL 2013 S. lidii MM 684 InraGAFL 2013-15 S. linnaeanum MM 1248 InraGAFL S. macrocarpon MM 1529 InraGAFL S. rnammosurn MM 1003 InraGAFL 2012-2013 S. rnarginatum Inra GAFL S. mauritianurn MM 370 InraGAFL S. rnelanospermurn MM 1005 Inra GAFL S. rnuricaturn MM 195 Inra GAFL 2012-13-14 S. palinacanthum MM 1136 InraGAFL S. pyracanthos MM 1715 InraGAFL 2013 S. renschii MM 824 InraGAFL S. richardii Inra GAFL S. rigescens MM 573 InraGAFL 2014 S. rigescentoides MM 1350 Inra GAFL 2015 S. rostratum MM 1821 InraGAFL S. rubetorum (rigescens auct. non Jacq) MM 1762 InraGAFL MM 1014 Inra GAFL S. scabrum Inra Ploudaniel S. schimperianum MM 1015 Inra GAFL S. sisymbriifolium MM 1753 Inra GAFL S. stoloniferum MM 1224 InraGAFL S. stramonifoliurn MM 1226 Vilmorin 2012-13-15 S. supinum MM 1190 COMAV 2012-13 S. tomentosum MM 1018 InraGAFL S. torvum MM 831 InraGAFL 2012-13-14 S. trachycarpum MMî2192 InraGAFL 2012-13-14 S. trilobatum MM 284 InraGAFL S. viarum (without spines) InraGAFL S. violaceurn S. virginianum MM416 Withania somnifera MM 1022

Acknowledgements

Many thanks to aIl the students who worked on this project. This research was supported by the Frencb Ministry of Agriculture through a CASDAR project evASCULEG) and was labeled GIS PicLég.

159


Sylvie Bureau

Stephane Georgé

Annie Perrin

Catherine M G C Renard

Use of mid-infrared spectroscopy to monitor shelf

come

Use of mid-infrared spectroscopy to monitor shelf-life of ready-made meals The objective of this work is to evaluate the possibility of using mid-infrared spectroscopy as a rapid analytical method to monitor the change in stored ready-made meals over time, for example oxidation phenomena occurring particularly in ready-made meals in plastic packaging. Six ready-made meals models (lentils, mashed potatoes, mashed potatoes with cheese, béchamel sauce, vegetable soup, Bolognese sauce) were prepared and packaged in plastic bags. They were stored at 23°C and at a partial oxygen pressure of 96 KPa to accelerate the oxidation phenomena. Two plastic packaging, Alu and Alox, were used presenting in these conditions an oxygen permeability of respectively 0.028 and 0.040 cm3/(packaging.day). Three bags of each ready-meal x plastic packaging combinations were sampled at 6 different times: T0 the start of the experiment, 20 days (equivalent to 3 months), 40 days (equivalent to 6 months), 59 days (equivalent to 9 months), 79 days (equivalent to 12 months) and 119 days (equivalent to 18 months). Samples were then frozen at -20°C until measurements. After thawing, samples were directly, without grinding, measured in attenuated total reflectance mid-infrared spectroscopy between 4000 and 650 cm -1 performing five replications to evaluate the sample heterogeneity. Multivariate analyses applied on spectral data allowed to highlight some changes in the global profile. For example, in the case of Bolognese sauce, samples were clearly discriminated (i) from 12 months, (ii) according to the packaging at 18 months with a greater oxidation in the Alox packaging. The eigenvectors allowed to identify several clear absorption bands which increased over storage, such as 2918 cm -1 , 2850 cm -1 , 1741 cm -1 and 1164 cm -1 . These absorption bands could be attributed to fats, which thus appeared to have a major effect in sample discrimination. The Mid-infrared spectroscopy was shown in this study to be a simple, rapid and relevant tool for discriminating the oxidation state of canned ready-made meals and might be used to determine their shelf-life.

Keywords: FTIR-ATR, multivariate analyses, oxidation over time, two plastic packaging.

  Sylvie Bureau* 1 , Stéphane Georgé 2 , Annie Perrin 2 , Catherine M.G.C. Renard 1 1 INRA, UMR408 Sécurité et Qualité des Produits d'Origine Végétale, F-84000 Avignon, France 1 Université d'Avignon et des Pays de Vaucluse, UMR Sécurité et Qualité des Produits d'Origine Végétale, F-84000 Avignon, France. 2 CTCPA, Avignon et Bourg en Bresse, France * Email of the corresponding author: sylvie.bureau@avignon.inra.fr


domain: math info

text:
Variables and domains

Definition

Set X = {x 1 , • • • , x n } of variables, each with a domain D i Set Φ of functions ϕ S involving variables of S ⊂ X (scope).

A joint function on X, x ∈ D X :

F(x) = ϕ S ∈Φ ϕ S (x S )
Why Graphical ? a vertex per variable an edge when 2 variables interact in a ϕ S ∈ Φ Allows to describe knowledge on a lot of variables concisely Usually hard to manipulate (NP-hard queries). Can we color all vertices in such a way that no edge connects two vertices of the same color ?

x 1

x 2

x 3

Variables and domains as usual

Cost functions ϕ S : D S → {0, . . . , k} (k finite or not)

Combined by bounded addition 8

F(x) = ϕ S ∈Φ ϕ S (x[S]) ϕ ∅ : lower bound A solution has cost < k. Optimal if minimum cost.

Benefits Defines feasibility and cost homogeneously

A constraint is a cost function with range {0, k} only

Stochastic Graphical Models

Markov Random Fields, Bayesian Networks Random variables X with discrete domains joint probability distribution p(X) defined through the product of positive real-valued functions:

p(X = x) ∝ ϕ S ∈Φ ϕ S (x S )

Stochastic Graphical Models

Markov Random Fields, Bayesian Networks Random variables X with discrete domains joint probability distribution p(X) defined through the product of positive real-valued functions:

p(X = x) ∝ ϕ S ∈Φ ϕ S (x S )
Massively used in Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

2

We can extend this to D i for x 1 . . .

x i 3 Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 ) 4
Store f i as a message Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

We can extend this to D i for x 1 . . .

x i Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 )
Store f i as a message MP -Dynamic Programming [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems, Networks of Plausible Inference[END_REF][START_REF] Frank R Kschischang | Factor graphs and the sum-product algorithm[END_REF] Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

We can extend this to D i for x 1 . . .

x i Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 )
Store f i as a message MP -Dynamic Programming [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems, Networks of Plausible Inference[END_REF][START_REF] Frank R Kschischang | Factor graphs and the sum-product algorithm[END_REF] Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

We can extend this to D i for x 1 . . .

x i Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 )
Store f i as a message MP -Dynamic Programming [START_REF] Pearl | Probabilistic Reasoning in Intelligent Systems, Networks of Plausible Inference[END_REF][START_REF] Frank R Kschischang | Factor graphs and the sum-product algorithm[END_REF] Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

We can extend this to D i for x 1 . . .

x i Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 )

Store f i as a message

Assume that the optimum cost on x 1 . . . x i-1 is known for every value of D i-1

We can extend this to D i for x 1 . . .

x i Let f i = min x i-1 (ϕ i-1 + ϕ i,i-1 )

Store f i as a message

Solves Berge acyclic MRF/BN (acyclic Factor Graphs) Does not converge on graphs (Loopy Belief Propagation) Massively used to produce "good" solutions (turbo-decoding [START_REF] Thomas | The capacity of low-density parity-check codes under message-passing decoding[END_REF] ) Not an equivalence preserving transformation! Tightening by cost shifting Assume that initially ϕ ∅ = 0, k = 4

Shift 1 to left b ← 1 3 1 x 1 x 2 1 3 x 1 x 2 a b a b ⇓ Shift 1 from ϕ 1 to ϕ ∅ Shift 1 to left b ← x 1 x 2 3 1 3 x 1 x 2 a b a b ⇓ Shift 1 from ϕ 1 to ϕ ∅ ϕ ∅ = 1
Tightening by cost shifting Assume that initially ϕ ∅ = 0, k = 4

Shift 1 to left b ← x 1 x 2 1 3 x 1 x 2 a b a b ⇓ Shift 1 from ϕ 1 to ϕ ∅ ϕ ∅ = 1
Preserves the joint function F(•) below k

Properties

Solves tree structured problems, optimum in ϕ ∅

Reformulation: incremental

May loop indefinitely (graphs)

No unique fixpoint (when it exists)

Already used by Ukrainian school [START_REF] Schlesinger | Sintaksicheskiy analiz dvumernykh zritelnikh signalov v usloviyakh pomekh (Syntactic analysis of two-dimensional visual signals in noisy conditions)[END_REF][START_REF] Va Kovalevsky | A diffusion algorithm for decreasing energy of max-sum labeling problem[END_REF][START_REF] Vk Koval | Two-dimensional programming in image analysis problems[END_REF][START_REF] Werner | A Linear Programming Approach to Max-sum Problem: A Review[END_REF] and for a subclass of ILP. [START_REF] Wedelin | An algorithm for large scale 0-1 integer programming with application to airline crew scheduling[END_REF] Independently introduced in 2003 in ML as "reparametrizations" 51 q ija : amount of cost shifted from ϕ ij to a ∈ D i OSAC [START_REF] Schlesinger | Sintaksicheskiy analiz dvumernykh zritelnikh signalov v usloviyakh pomekh (Syntactic analysis of two-dimensional visual signals in noisy conditions)[END_REF][START_REF] Koster | Frequency assignment: Models and Algorithms[END_REF][START_REF] Cooper | Optimal soft arc consistency[END_REF][START_REF] Werner | A Linear Programming Approach to Max-sum Problem: A Review[END_REF][START_REF] Cooper | Soft arc consistency revisited[END_REF] Maximize n i=1 u i subject to

ϕ i (a) -u i + (ϕ ij ∈Φ) q ija ≥ 0 ∀i ∈ {1, . . . , n}, ∀a ∈ D i ϕ ij (a, b) -q ija -q jib ≥ 0 ∀ϕ ij ∈ Φ, ∀(a, b) ∈ D ij M C.
c i (a) • x ia + c ij ∈C a∈D i ,b∈D j c ij (a, b) • y iajb s.t a∈D i x ia = 1 ∀i ∈ {1, . . . , n} (1)
b∈D j y iajb -

x ia = 0 ∀c ij /c ji ∈ C, ∀a ∈ D i (2)
1 v ia : value a used for variable x i .

2 p iajb : pair (a, b) used for x i and x j

The MRF local polytope [START_REF] Werner | A Linear Programming Approach to Max-sum Problem: A Review[END_REF]

Minimize

i,a c i (a) • x ia + c ij ∈C a∈D i ,b∈D j c ij (a, b) • y iajb s.t a∈D i x ia = 1 ∀i ∈ {1, . . . , n} (1) b∈D
j y iajb -x ia = 0 ∀c ij /c ji ∈ C, ∀a ∈ D i (2)
OSAC is its dual: u i multiplier for (1) and q ija for (2).

1

Soft convergent ACs find feasible (but non necessarily optimal) solutions of the dual.

1

Soft convergent ACs find feasible (but non necessarily optimal) solutions of the dual.

Optimal does not mean more efficient for tree search.

2015: universality of the local polytope

Prusa and Werner [START_REF] Prusa | Universality of the local marginal polytope[END_REF] showed that any "normal" LP can be reduced to such a polytope in linear time (constructive proof).

1

Soft convergent ACs find feasible (but non necessarily optimal) solutions of the dual.

Optimal does not mean more efficient for tree search.

2015: universality of the local polytope

Prusa and Werner [START_REF] Prusa | Universality of the local marginal polytope[END_REF] showed that any "normal" LP can be reduced to such a polytope in linear time (constructive proof).

Could soft arc consistency (eg. VAC) speed-up LP?

Genetic mapping with CarthaGene GM learning + TSP optimization. CFN: decision variables + cost functions/utilities/feasibility distribution.

Mixed graphical models with decision and stochastic variables

Influence diagrams [START_REF] Ronald | Influence diagrams[END_REF] Stochastic constraint programming [START_REF] Walsh | Stochastic constraint programming[END_REF] Plausability-feasibility-utility networks 37

1 Variables and domains 2 ϕ

 2 S are Boolean functions (constraints, t ≡ 0 < 1 ≡ f)3 Minimize joint function (⊕ = ∧ = max) F(x) = max ϕ S ∈Φ ϕ S (x S )Graph coloring/RLFAP-feas 1 A graph G = (V, E) and m colors.

2

 2

4 Shift 1

 41 1 use ϕ ∅ and ϕ i (•) to store optimum cost over (x 1 , . . . , x i ) 2 Preserves equivalence by "cost shifting" 45,53,42 T. Schiex. "Arc consistency for soft constraints". In: Principles and Practice of Constraint Programming -CP 2000. Vol. 1894. LNCS. Singapore, Sept. 2000, pp. 411-424Assume that initially ϕ ∅ = 0, k =

S

  . de Givry, M. Bouchez, P. Chabrier, D. Milan, et al. "CarthaGene: multipopulation integrated genetic and radiation hybrid mapping. " In: Bioinformatics 21.8 (2005), pp. 1703-4 V. Laurent, E. Wajnberg, B. Mangin, T. Schiex, et al. "A composite genetic map of the parasitoid wasp Trichogramma brassicae based on RAPD markers. " In: Genetics 150.1 (1998), pp. 275-82 Gene finding with EuGene Semi-CRF + optimization. RNA Gene finding: MilPat, Darn! CSP/CFN + string algorithms P. Thebault, S. de Givry, T. Schiex, and C. Gaspin. "Searching RNA motifs and their intermolecular contacts with constraint networks. " In: Bioinformatics 22.17 (2006), pp. 2074-80 M Zytnicki, C Gaspin, and T Schiex. "DARN! A soft constraint solver for RNA motif localization". In: Constraints 13.1 (2008), pp. 91-109 MendelSoft: pedigree debugging CFN for MPE on Bayesian nets M Sanchez, S de Givry, and T Schiex. "Mendelian error detection in complex pedigrees using weighted constraint satisfaction techniques". In: Constraints 13.1 (2008), pp. 130-154 T. Faraut, S. de Givry, P. Chabrier, T. Derrien, et al. "A comparative genome approach to marker ordering. " In: Bioinformatics 23.2 (2007), e50-6 MRF/BN: stochastic variables + probability distribution. Can be learnt (RBM for deep learning).

  H. Fargier, J. Lang, R. Martin-Clouaire, and Thomas Schiex. "A constraint satisfaction framework for decision under uncertainty". In: Proc. of the 11 th Int. Conf. on Uncertainty in Artificial Intelligence. Montréal, Canada, Aug. 1995

H. Fargier, J. Lang, and T. Schiex. "Mixed Constraint Satisfaction: a framework for decision problems under incomplete knowledge". In: Proc. of AAAI'96. Portland, OR: AAAI Press, Aug. 1996 C Pralet, G Verfaillie, and T Schiex. "An algebraic graphical model for decision with uncertainties, feasibilities, and utilities". In: Journal of Artificial Intelligence Research 29 (2007), pp. 421-489

use ϕ ∅ and ϕ i (•) to store optimum cost over (x 1 , . . . , x i )

Preserves equivalence by "cost shifting"[START_REF] Schlesinger | Sintaksicheskiy analiz dvumernykh zritelnikh signalov v usloviyakh pomekh (Syntactic analysis of two-dimensional visual signals in noisy conditions)[END_REF][START_REF] Wedelin | An algorithm for large scale 0-1 integer programming with application to airline crew scheduling[END_REF][START_REF] Schiex | Arc consistency for soft constraints[END_REF]

Breaking the loops, strengthening ϕ ∅ 2000: Arc consistency[START_REF] Schiex | Arc consistency for soft constraints[END_REF][START_REF] Larrosa | On Arc and Node Consistency in weighted CSP[END_REF] 2003: Full Directional AC[START_REF] Cooper | Reduction operations in fuzzy or valued constraint satisfaction[END_REF][START_REF] Larrosa | In the quest of the best form of local consistency for Weighted CSP[END_REF][START_REF] Larrosa | Solving weighted CSP by maintaining arc consistency[END_REF] 2005: Existential DAC[START_REF] Larrosa | Existential arc consistency: getting closer to full arc consistency in weighted CSPs[END_REF] 2008: Virtual AC[START_REF] Martin C Cooper | Virtual Arc Consistency for Weighted CSP[END_REF][START_REF] Cooper | Soft arc consistency revisited[END_REF] 2007: Optimal Soft AC[START_REF] Cooper | Optimal soft arc consistency[END_REF] (LP)

q ija : amount of cost shifted from ϕ ij to a ∈ D i

Optimal does not mean more efficient for tree search.

Exact solvers: DEE/A * (DEE [START_REF] Desmet | The dead-end elimination theorem and its use in protein side-chain positioning[END_REF] ), ILP [START_REF] Carleton L Kingsford | Solving and analyzing side-chain positioning problems using linear and integer programming[END_REF] By far the most used: simulated annealing (Rosetta 21 ).

Seydou Traoré, David Allouche, Isabelle André, Simon de Givry, et al. "A new framework for computational protein design through cost function network optimization". In: Bioinformatics 29.17 (2013), pp. 2129-2136