Studying vital ranges of European rabbits using GPS collars

Mélanie Larue 1 , Gilles Holé 1 , Jérôme Letty 1 & Stéphane Marchandeau 1 1 Direction de la Recherche et de l' Appui Scientifique (DRAS), Office Français de la Biodiversité (OFB), Juvignac, Nantes, France

Context

The European rabbit, Oryctolagus cuniculus, once abundant in France, is now in sharp decline. The species has become a problem for farmers because of the damage caused to crops. Currently, the main question is how to conserve the species while controlling the damage it is likely to cause. This study can help to better understand their spatial behaviour and provide management options to limit the risk of agricultural damage.

Material and method

Study area

We have conducted a three-year study in a rural area of southern France. This Mediterranean area area is mainly composed of winter cereal fields and vineyards.

GPS tracking/records scheduling

We monitored 18 adult wild rabbits (Table 1) between 2019 an 2021. Rabbits were captured and equipped with VHF/GPS collars (LiteTrack RF-30, LOTEK; weight: 35g). The GPS function allows for location at night (12 locations every 2 nights) ; the VHF radio function allows the animal to be located during the day and to download data. 0 1 2 3 4 5 ≥ 6 Total Females 0 2 2 0 1 1 1 7 Males 2 1 1 2 2 1 2 11 Total 2 3 3 2 3 2 3 18 Table 1. Number of rabbits per sex and monitoring duration (months).

Number of months of tracking

Accuracy and data selection

We first tested the dispersion of the GPS locations. As an indicator of accuracy we used the DOP (Dilution Of Precision), and took a DOP threshold value of 3.5 (with 93% of the GPS locations included within 10 meters).

Home range analysis

We used the method of the Minimum Convex Polygon (MCP, smallest polygon around the locations) to calculate the size of the home range. We only used complete monitoring months, and discarded the 1st month because of the stress due to capture.

Some examples of individual home ranges

The most important home range was observed in a male (5.41 ha; Map 1). Conversely, le smallest home range was observed in a female (0,69 ha ; Map 2). An interesting observation concerns two males captured a year apart, in two warrens 20 meters apart (Map 3). Behaviors seems to indicate an enduring pattern of territorial exclusion.

Go further

This first data exploration provided important insights into the size of the home range of a wild rabbit, sex differences and changes over the season. Further analyzes will allow to know the habitat selection of the species and provide recommendations to farmers to mitigate crop damages.

Results/Discussion

Total home range

The total home range of males was on average larger and more variable (2.29 ± 1.43 ha; mean ± SD) than that of females (1.06 ± 0.51 ha) (Figure 1). This could be explained by territorial competition or the dispersal behaviour of the breeders. The average range around the warren varied from 50 to 131 m, depending on the individual behaviour (reckless vs shy).

Monthly changes in home range

The same difference between the sexes was observed for the monthly home ranges (Figure 2). In females, the average monthly home range remained around 0,5 ha from March to July. The largest home range size was observed in August (due to the end of the breeding season or a decrease in food resources).

MCP method as an exploratory estimator

Use MCP method may be questionable to estimate home range size because it overestimate the surface (some areas which are not actually used by the individual). However, this first exploration of data was intended to be descriptive in order to get a first idea of the nocturnal use of the wild rabbit home range.

Thanks : we would like to thank the Villeneuve-lès-Maguelone municipal hunting society, in particular Francis Pérez, its president, as well as all the volunteers from the hunting team who made it possible to capture the rabbits. Field monitoring was also carried out by Julia Agziou and Valentin Gewinner as part of their university training.

Figure 1 .

 1 Figure 1. Rabbit total home range (MCP) estimates.

Figure 2 .

 2 Figure 2. Rabbit monthly home range (MCP) estimates from March to August.


Plan Symbolic Dynamics Categories for symbolic dynamics Applications Conclusion

Keywords:

Edge shift

An edge shift is the set of all biinfinite walks (on edges) in a finite graph 0 1 2 E. Jeandel, Strong Shift Equivalence and Bialgebras in traced monoidal categories,

An edge shift is the set of all biinfinite walks (on edges) in a finite graph Decidable for one-sided edge-shifts (Williams, 1973) The rewriting system on graphs is confluent.

M =   0 2 0 0 0 1 1 0 1   N =     0 0 1 0 0 0 1 0 0 0 0 1 1 1 0 1     R =   1 1 0 0 0 0 1 0 0 0 0 1   S =     0 1 0 0 1 0 0 0 1 1 0 1     E.

Folklore

The bialgebra PROP is exactly the PROP of nonnegative integer matrices.

A commutative monoid (η :

0 → 1, µ : 2 → 1) A cocommutative comonoid (ϵ : 1 → 0, ∆ : 1 → 2) E.

Folklore

The bialgebra PROP is exactly the PROP of nonnegative integer matrices.

A commutative monoid (η :

0 → 1, µ : 2 → 1) A cocommutative comonoid (ϵ : 1 → 0, ∆ : 1 → 2) Bialgebra rules = = = = E.

Trace

In this prop, we can associate a scalar t(M) to each matrix M. Is it true that t(M) = t(N) iff M and N are SSE ? Let D be a category with finite limits and colimits. Suppose one has a monoid X in a D wih a morphism h. It extends to a bialgebra using the diagonal map as a comonoid.

M =   0 2 0 0 0 1 1 0 1   E.

Theorem

Let M be a n × n matrix.

The object that is the coequalizer of X Let D be a category with finite limits and colimits. Suppose one has a monoid X in a D wih a morphism h. It extends to a bialgebra using the diagonal map as a comonoid.

Theorem

Let M be a n × n matrix.

The object that is the coequalizer of X n X n id n

h n •M is an invariant for SSE.

Starting with the monoid (Z, +) in the category of abelian groups, we obtain the Bowen-Franks group (1977)

  and Bialgebras in traced monoidal categories, arXiv:2107.10734 3/24 An edge shift is the set of all biinfinite walks (on edges) in a actactactact.actactactact . . . . . . teamteam.teamteam . . . .

  Starting with the monoid (Z[t], +) in the category of Z[t]-modules, we obtain the dimension group ofKrieger (1977)

	Plan
	Symbolic Dynamics
	Categories for symbolic dynamics
	Applications
	Conclusion
	10734	22/24

E. Jeandel, Strong Shift Equivalence and Bialgebras in traced monoidal categories, arXiv:2107.E. Jeandel, Strong Shift Equivalence and Bialgebras in traced monoidal categories, arXiv:2107.10734 23/24 Where to go from here ? We have a systematic way to find invariants Investigate new bialgebras to find new invariants! E. Jeandel, Strong Shift Equivalence and Bialgebras in traced monoidal categories, arXiv:2107.10734 24/24

K[X ] has a structure of a bialgebra

Product is the product of polynomials Coproduct is defined by ∆

Strong Shift Equivalence and Bialgebras in traced monoidal categories, arXiv:2107.10734 21/24

Product is the product of polynomials Coproduct is defined by ∆(X ) = 1 ⊗ X + X ⊗ 1 Solution: Replace K[X ] by formal series in a complete semiring (like R + ∪ {+∞}).

If we take the morphism h(X ) = tX we get:

Theorem

The quantity f M (t) = 1 det(I-tM) is an invariant for SSE


L'ordre des bassins

Benoît Hachet, sociologue, animateur du séminaire « Nager : une socio histoire » à l'Ehess (2021)(2022) J'ai appris à nager à la piscine Plein Ciel de Pau au mitan des années 1970, avec « maître Denis », comme on disait à l'époque. C'était en pleine vague des 1 000 piscines, un moment où la France a creusé des bassins partout, jusqu'en Navarre. Mes parents, eux, avaient appris à nager dans les rivières ou dans les retenues d'eau au bord de l'Océan, en été. Nous, on allait à la piscine presque tous les dimanches, quelle que soit la saison. Une de nos premières victoires d'apprentis nageurs était de traverser la piscine en largeur. Les adultes qui nous accompagnaient nageaient dans l'autre sens. Comme ils faisaient des longueurs, et nous des largeurs, on serpentait pour s'éviter. Personne n'allait droit. Il n'y avait pas de ligne de nage.

Au début des années 1990, un journaliste du New York Times, en réponse à une question d'un lecteur américain pour savoir où nager à Paris, écrivait en substance que la seule piscine dans laquelle on trouvait des lignes de nage dans la capitale était la piscine Suzanne Berlioux, piscine olympique construite quelques années auparavant au coeur du forum des Halles. Jusqu'à cette période, les bassins n'étaient pas divisés en couloirs ; ils le devinrent alors. Parmi les explications du changement de paradigme, les experts relèvent : la plus grande certification des Maîtres Nageurs Sauveteurs (MNS) qui ne veulent plus installer et désinstaller le matériel, mais qui ont besoin de lignes fixes pour organiser les activités scolaires en plein essor ; la volonté de sécuriser et de tranquilliser le bassin en décourageant « les bombes » ; et la progression de la mise en délégation de service public des nouvelles piscines, qui a encouragé les structures privées à rationaliser et rentabiliser l'espace, en pouvant proposer différentes activités en simultané, tout en louant éventuellement une ligne. Cette transformation de l'économie générale des bassins a sans doute aussi emporté avec elle les plongeoirs de 3 mètres ou de 5 mètres dans les piscines ordinaires. Autre souvenir d'enfance.

Finies donc les largeurs ! Aujourd'hui les piscines sont divisées en lignes. On nage dans des couloirs, en longueur. Deux couloirs à la Bourboule : « Lignes réservées aux nageurs » ; un à Mimizan : « Ligne réservée aux personnes désirant nager en longueur ». Dans les piscines parisiennes, l'essentiel du bassin est linéarisé, avec ou sans panonceaux indicateurs. A chaque piscine sa culture et son inspiration pour diviser l'espace. « Le pire, m'a dit un surveillant de la piscine Mathis, c'est les écriteaux "nageurs confirmés", ça ne dit rien de la vitesse, et ça crée des tensions ». Ailleurs on différencie les « nageurs rapides », des « nageurs moyens », ou des « nageurs lents », mais cela reste relatif et subjectif. Observée en 2020, la piscine Pailleron objectivait alors les vitesses en indiquant dans chaque couloir les temps minimum à réaliser pour faire un aller-retour « mais, m'a dit le chef du bassin, c'était aussi efficace avant quand il n'y avait aucune inscription ». D'autres distinguent les lignes avec et sans matériel, ou différencient les couloirs par types de nage : « Pas de brasse, merci » comme il est écrit, à la main, sur un panneau pliable à la piscine Rouvet. Les MNS de Georges Hermant expliquent qu'ils discutent souvent le matin pour savoir ce qui est le plus pertinent pour spécialiser les lignes, puis qu'ils adoptent un autre système le jour d'après.

Une fois les lignes posées, arrivent les nageurs. Il y a d'abord les matutinaux, qui sont là à 7h00 tous les jours, dans un entre soi de connus inconnus, qui se saluent sans connaître leur prénom, et échangent de menus propos, quand ils n'apportent pas une nouvelle plante pour décorer l'accueil. À 8h30, ils laissent la place aux scolaires, qui se répartissent par lignes et par niveaux. À 11h30, viennent les méridiens, qui préfèrent le chlore à la cantine d'entreprise. Ceux du soir viennent après leur journée de travail, dans les créneaux les plus chargés, et les nocturnes, plus jeunes, se retrouvent dans les rares piscines ouvertes tardivement. À chaque début de session, on trouve un petit groupe qui attend l'ouverture. Parmi eux, certains ont déjà leur maillot sur eux, ne passent pas par les cabines, et courent presque, tout en retenue, pour jouir du plaisir d'être les premiers dans l'eau, la piscine pour eux seuls…quelques secondes. Après s'être changés dans « leur cabine » et avoir déposé leurs affaires dans « leur casier », les habitués les plus assidus vont directement dans « leur ligne », celle où on nage le crawl, celle où les planches sont autorisées, celle qui a la meilleure exposition aux rayons du soleil, celle dans laquelle ils vont toujours… Les premiers installés donnent son caractère à une ligne. L'un commence à nager un crawl lent dans la ligne 3, l'autre une brasse coulée rapide dans la 4, une troisième le dos dans la 5. Ceux qui arrivent ensuite se posent un instant au bord du bassin pour jauger l'occupation et choisir la ligne qui leur conviendra le mieux, qui leur ressemblera le plus. Auto-répartition par affinité natatoire. Ensuite, au fur et à mesure des arrivées, le choix du couloir se fera en fonction du nombre de nageurs dans chaque ligne, et si ça déborde, certains, ou plus souvent certaines, changeront de ligne, quand d'autres partiront.

Quelle que soit la taille d'une piscine et la configuration des lignes en usage, l'espace aquatique est socialement ségrégé en trois zones. Sur les bords, près des plages, se regroupent les nageurs les moins aguerris, les plus lents, qui souvent ne portent pas de lunettes de natation, ne mettent pas la tête sous l'eau, et font de longues pauses. Ils sont plus âgés que la moyenne et ce sont plus souvent des femmes. Au centre, sur une ou deux lignes, on trouve des nageurs de crawl, tous avec des lunettes, qui font très peu de pause, et qui ont plus que les autres une tendance à se chronométrer. Ce ne sont pas forcément les lignes les plus jeunes mais elles sont à coup sûr plus masculines. Dans les zones intermédiaires, entre le centre et la périphérie, se réunissent des nageuses et des nageurs de crawl, de brasse ou de dos, qui utilisent plus que les autres des planches. C'est une zone mixte en termes de genre, comme de nages. Et de papillon, il est très peu question…Quand, grâce à un questionnaire, on demande d'une part aux nageurs, dans quelle ligne ils ont nagé, et d'autre part quel est leur niveau de diplôme, on obtient un magnifique gradient qui fait que plus on s'éloigne du centre et moins le niveau d'étude est élevé1 . La pratique de la natation demeure très discriminée culturellement.

On nage donc en silo, à quelques-uns dans un couloir de deux mètres cinquante d'envergure. Cinq ou six par ligne dans un bassin de 25 mètres, huit à neuf dans un bassin de 33 mètres, et jusqu'à douze dans un bassin de 50 -au-delà de ces nombres, ça se complique… On se repère vite les uns les autres : la fille qui nage très vite avec son maillot vert, et qu'on laisse passer lors des virements de bord, le type au bonnet blanc qui nage le dos avec des mouvements de bras trop larges qu'il faut éviter à chaque croisement, le jeune au bonnet rouge qui va presque au même rythme que nous mais pas tout à fait et qu'on hésite à doubler avant de faire une pause pour lui laisser du champ, et puis qu'on rattrape immanquablement. Ah, enfin, le dossiste est parti… Les normes de comportement dans une ligne, on les apprend par imprégnation. On nage dans le sens inverse des aiguilles d'une montre, en se serrant à droite ; on se sert plus encore si on est doublé ; on double par la gauche en veillant à ne heurter ni la personne dépassée, ni celle qui arrive en face ; on ne s'arrête pas en milieu de ligne ; lors des pauses on se met plutôt à droite sur le muret pour ne pas entraver le sens habituel de circulation ; enfin on adapte sa vitesse et son comportement pour faciliter la fluidité de l'ensemble. On peut rajouter avec la sociologue britannique Susie Scott trois règles tacites : on évite des contacts physiques ; on respecte les programmes de natation de chacun, en laissant en particulier la priorité aux nageurs les plus rapides ; on désexualise les corps, bien qu'ils soient presque nus, parce qu'ils sont presque nus. Les néophytes ou les irrespectueux se font rappeler à l'ordre par les autres nageurs qui, pour les plus expressifs, arrêtent ostensiblement leur mouvement, lèvent les bras, lancent des regards désapprobateurs ou, moins fréquemment, interpellent verbalement les contrevenants ou les dénoncent aux surveillants de bassin. Les MNS quant à eux disent le plus souvent qu'ils ne sont pas là pour faire la police, mais pour assurer la sécurité des baigneurs. La plupart du temps, ils laissent les nageurs se débrouiller.

Le confinement a été un moment compliqué, quand les bassins ont été fermés, puis ouverts, et à nouveau fermés. J'ai interrogé deux coiffeuses, nageuses régulières, qui me disaient que les douleurs ressenties dans les bras et les épaules à force de coupes de cheveux n'étaient plus compensées par les mouvements dans l'eau. Pour la réouverture, elles ont été les premières dans la queue, longue, puisqu'on était nombreux à attendre ce moment-là. Il fallait s'inscrire en amont et montrer patte blanche à l'accueil. En observateur participant consciencieux, je suis arrivé une demi-heure avant l'ouverture, j'étais deuxième dans la file, qui s'est finalement étendue sur 30 ou 40 mètres, chacun sagement derrière le précédent. Les gens souriaient. Et plus encore quand ils « entraient enfin de nouveau dans la matière aqueuse », comme je l'ai entendu. Première coulée. Frissons. Et retour dans l'ordre des bassins.

Les chloraddicts, dont je suis, gèrent leurs emplois du temps en fonction des horaires d'ouverture des piscines, possèdent plusieurs cartes d'abonnement, ont toujours un maillot et une serviette dans leur sac, veillent à ce que l'hôtel qu'ils réservent pour un déplacement professionnel soit proche d'un bassin, et quand ils vont à l'étranger, ils visitent d'abord les piscines. Ils savent se décaler pour trouver des lieux peu fréquentés et des créneaux dans lesquels il est possible de n'être que deux par ligne. À Paris, le meilleur moment pour nager c'est les vacances de Noël, parce qu'il n'y a personne dans les piscines, surtout si on a la chance qu'il fasse froid. Je mets aussi une option sur les mercredis et les samedis en début d'après-midi, juste de l'autre côté du périph. Ne le répétez pas !

HACHET B., FELY S., BONJOUR T.,

2023, Nager à Paris : une enquête sur l'ordre des bassins dans cinq piscines publiques du nord-est de la capitale, Sciences Sociales et Sport (annoncé pour janvier).


Cécile Tessier

Christiane Faure

Liliane Guerlou-Demourgues

Cathy Denage

Georges Nabias

Claude Delmas

Electrochemical study of zinc-substituted nickel hydroxide

come

Electrochemical Study of Zinc-Substituted Nickel Hydroxide Cécile Tessier 1,3 , Christiane Faure 1 , Liliane Guerlou-Demourgues 1 , Catherine Denage 1 , Georges Nabias 2 and Claude Delmas

Abstract :

The electrochemical behavior of α-and β(II)-type zinc-substituted nickel hydroxides is studied during a galvanostatic cycling in a KOH electrolyte. It is shown that these materials exhibit very stable capacities during long-term cycling. When using an 8 M KOH electrolyte, the β(III)/β(II) system is stabilized, after the initial formation of γ-type phases during the first charges. The higher the amount of zinc in the starting material, the faster this stabilization occurs. The substitution of zinc for nickel is also shown to delay the formation of the γ-phase upon charge, when various KOH electrolytes, with increasing concentrations, are successively used. A model is proposed to explain these results; it is based on several processes, occurring simultaneously either via the solution or through solid-state reactions, with a partial loss of zinc.


Leila Amgoud
email: amgoud@irit.fr

Yannis Dimopoulos
email: yannis@cs.ucy.ac.cy

Pavlos Moraitis

A Unified and General Framework for Argumentation-based Negotiation

Keywords: I.2.3 [Deduction and Theorem Proving]: Nonmonotonic reasoning and belief revision ; I.2.11 [Distributed Artificial Intelligence]: Intelligent agents Human Factors, Theory Argumentation, Negotiation

This paper proposes a unified and general framework for argumentation-based negotiation, in which the role of argumentation is formally analyzed. The framework makes it possible to study the outcomes of an argumentation-based negotiation. It shows what an agreement is, how it is related to the theories of the agents, when it is possible, and how this can be attained by the negotiating agents in this case. It defines also the notion of concession, and shows in which situation an agent will make one, as well as how it influences the evolution of the dialogue.

INTRODUCTION

Roughly speaking, negotiation is a process aiming at finding some compromise or consensus between two or several agents about some matters of collective agreement, such as pricing products, allocating resources, or choosing candidates. Negotiation models have been proposed for the design of systems able to bargain in an optimal way with other agents for example, buying or selling products in ecommerce.

Different approaches to automated negotiation have been investigated, including game-theoretic approaches (which usu-ally assume complete information and unlimited computation capabilities) [START_REF] Rosenschein | Rules of Encounter: Designing Conventions for Automated Negotiation Among Computers[END_REF], heuristic-based approaches which try to cope with these limitations [START_REF] Jennings | Automated negotiation: Prospects, methods and challenges[END_REF], and argumentation-based approaches [START_REF] Amgoud | Arguments, dialogue, and negotiation[END_REF][START_REF] Amgoud | Reaching agreement through argumentation: A possibilistic approach[END_REF][START_REF] Kakas | Adaptive agent negotiation via argumentation[END_REF][START_REF] Kraus | Reaching agreements through argumentation: a logical model and implementation[END_REF][START_REF] Parsons | Negotiation through argumentation-a preliminary report[END_REF][START_REF] Sycara | Persuasive argumentation in negotiation[END_REF][START_REF] Tohmé | Negotiation and defeasible reasons for choice[END_REF] which emphasize the importance of exchanging information and explanations between negotiating agents in order to mutually influence their behaviors (e.g. an agent may concede a goal having a small priority), and consequently the outcome of the dialogue. Indeed, the two first types of settings do not allow for the addition of information or for exchanging opinions about offers. Integrating argumentation theory in negotiation provides a good means for supplying additional information and also helps agents to convince each other by adequate arguments during a negotiation dialogue. Indeed, an offer supported by a good argument has a better chance to be accepted by an agent, and can also make him reveal his goals or give up some of them. The basic idea behind an argumentationbased approach is that by exchanging arguments, the theories of the agents (i.e. their mental states) may evolve, and consequently, the status of offers may change. For instance, an agent may reject an offer because it is not acceptable for it. However, the agent may change its mind if it receives a strong argument in favor of this offer.

Several proposals have been made in the literature for modeling such an approach. However, the work is still preliminary. Some researchers have mainly focused on relating argumentation with protocols. They have shown how and when arguments in favor of offers can be computed and exchanged. Others have emphasized on the decision making problem. In [START_REF] Amgoud | Reaching agreement through argumentation: A possibilistic approach[END_REF][START_REF] Kakas | Adaptive agent negotiation via argumentation[END_REF], the authors argued that selecting an offer to propose at a given step of the dialogue is a decision making problem. They have thus proposed an argumentationbased decision model, and have shown how such a model can be related to the dialogue protocol.

In most existing works, there is no deep formal analysis of the role of argumentation in negotiation dialogues. It is not clear how argumentation can influence the outcome of the dialogue. Moreover, basic concepts in negotiation such as agreement (i.e. optimal solutions, or compromise) and concession are neither defined nor studied. This paper aims to propose a unified and general framework for argumentation-based negotiation, in which the role of argumentation is formally analyzed, and where the existing systems can be restated. In this framework, a negotiation dialogue takes place between two agents on a set O of offers, whose structure is not known. The goal of a negotiation is to find among elements of O, an offer that satisfies more or less the preferences of both agents. Each agent is supposed to have a theory represented in an abstract way. A theory consists of a set A of arguments whose structure and origin are not known, a function specifying for each possible offer in O, the arguments of A that support it, a non specified conflict relation among the arguments, and finally a preference relation between the arguments. The status of each argument is defined using Dung's acceptability semantics. Consequently, the set of offers is partitioned into four subsets: acceptable, rejected, negotiable and non-supported offers. We show how an agent's theory may evolve during a negotiation dialogue. We define formally the notions of concession, compromise, and optimal solution. Then, we propose a protocol that allows agents i) to exchange offers and arguments, and ii) to make concessions when necessary. We show that dialogues generated under such a protocol terminate, and even reach optimal solutions when they exist. This paper is organized as follows: Section 2 introduces the logical language that is used in the rest of the paper. Section 3 defines the agents as well as their theories. In section 4, we study the properties of these agents' theories. Section 5 defines formally an argumentation-based negotiation, shows how the theories of agents may evolve during a dialogue, and how this evolution may influence the outcome of the dialogue. Two kinds of outcomes: optimal solution and compromise are defined, and we show when such outcomes are reached. Section 6 illustrates our general framework through some examples. Section 7 compares our formalism with existing ones. Section 8 concludes and presents some perspectives. Due to lack of space, the proofs are not included. These last are in a technical report that we will make available online at some later time.

THE LOGICAL LANGUAGE

In what follows, L will denote a logical language, and ≡ is an equivalence relation associated with it. From L, a set O = {o1, . . . , on} of n offers is identified, such that oi, oj ∈ O such that oi ≡ oj. This means that the offers are different. Offers correspond to the different alternatives that can be exchanged during a negotiation dialogue. For instance, if the agents try to decide the place of their next meeting, then the set O will contain different towns. Different arguments can be built from L. The set Args(L) will contain all those arguments. By argument, we mean a reason in believing or of doing something. In [START_REF] Amgoud | Reaching agreement through argumentation: A possibilistic approach[END_REF], it has been argued that the selection of the best offer to propose at a given step of the dialogue is a decision problem. In [START_REF] Amgoud | Explaining qualitative decision under uncertainty by argumentation[END_REF], it has been shown that in an argumentation-based approach for decision making, two kinds of arguments are distinguished: arguments supporting choices (or decisions), and arguments supporting beliefs. Moreover, it has been acknowledged that the two categories of arguments are formally defined in different ways, and they play different roles. Indeed, an argument in favor of a decision, built both on an agent's beliefs and goals, tries to justify the choice; whereas an argument in favor of a belief, built only from beliefs, tries to destroy the decision arguments, in particular the beliefs part of those decision arguments. Consequently, in a negotiation dialogue, those two kinds of arguments are generally exchanged between agents. In what follows, the set Args(L) is then divided into two subsets: a subset Args o (L) of arguments supporting offers, and a subset Args b (L) of arguments supporting beliefs. Thus, Args(L) = Args o (L) ∪ Args b (L).

As in [START_REF] Dung | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games[END_REF], in what follows, we consider that the structure of the arguments is not known. Since the knowledge bases from which arguments are built may be inconsistent, the arguments may be conflicting too. In what follows, those conflicts will be captured by the relation RL, thus RL ⊆ Args(L) × Args(L). Three assumptions are made on this relation: First the arguments supporting different offers are conflicting. The idea behind this assumption is that since offers are exclusive, an agent has to choose only one at a given step of the dialogue. Note that, the relation RL is not necessarily symmetric between the arguments of Args b (L). The second hypothesis says that arguments supporting the same offer are also conflicting. The idea here is to return the strongest argument among these arguments. The third condition does not allow an argument in favor of an offer to attack an argument supporting a belief. This avoids wishful thinking. Formally:

Definition 1. RL ⊆ Args(L) × Args(L) is a conflict relation among arguments such that: • ∀a, a ∈ Args o (L), s.t. a = a , a RL a • a ∈ Args o (L) and a ∈ Args b (L) such that a RL a
Note that the relation RL is not symmetric. This is due to the fact that arguments of Args b (L) may be conflicting but not necessarily in a symmetric way. In what follows, we assume that the set Args(L) of arguments is finite, and each argument is attacked by a finite number of arguments.

NEGOTIATING AGENTS THEORIES AND REASONING MODELS

In this section we define formally the negotiating agents, i.e. their theories, as well as the reasoning model used by those agents in a negotiation dialogue.

Negotiating agents theories

Agents involved in a negotiation dialogue, called negotiating agents, are supposed to have theories. In this paper, the theory of an agent will not refer, as usual, to its mental states (i.e. its beliefs, desires and intentions). However, it will be encoded in a more abstract way in terms of the arguments owned by the agent, a conflict relation among those arguments, a preference relation between the arguments, and a function that specifies which arguments support offers of the set O. We assume that an agent is aware of all the arguments of the set Args(L). The agent is even able to express a preference between any pair of arguments. This does not mean that the agent will use all the arguments of Args(L), but it encodes the fact that when an agent receives an argument from another agent, it can interpret it correctly, and it can also compare it with its own arguments. Similarly, each agent is supposed to be aware of the conflicts between arguments. This also allows us to encode the fact that an agent can recognize whether the received argument is in conflict or not with its arguments. However, in its theory, only the conflicts between its own arguments are considered.

Definition 2 (Negotiating agent theory). Let O be a set of n offers. A negotiating agent theory is a tuple A, F , , R, Def such that:

• A ⊆ Args(L). • F: O → 2 A s.t ∀i, j with i = j, F (oi) ∩ F (oj) = ∅.
Let AO = ∪F (oi) with i = 1, . . . , n.

• ⊆ Args(L) × Args(L) is a partial preorder denoting a preference relation between arguments.

• R ⊆ RL such that R ⊆ A × A • Def ⊆ A × A such that ∀ a, b ∈ A, a defeats b, denoted a Def b iff:
a R b, and

-not (b a)
The function F returns the arguments supporting offers in O. In [START_REF] Amgoud | Explaining qualitative decision under uncertainty by argumentation[END_REF], it has been argued that any decision may have arguments supporting it, called arguments PRO, and arguments against it, called arguments CONS. Moreover, these two types of arguments are not necessarily conflicting. For simplicity reasons, in this paper we consider only arguments PRO. Moreover, we assume that an argument cannot support two distinct offers. However, it may be the case that an offer is not supported at all by arguments, thus F (oi) may be empty.

Example 1. Let O = {o1, o2, o3} be a set of offers. The following theory is the theory of agent i:

• A = {a1, a2, a3, a4} • F(o1) = {a1}, F (o2) = {a2}, F (o3) = ∅. Thus, Ao = {a1, a2} • = {(a1, a2), (a2, a1), (a3, a2), (a4, a3)}
• R = {a1, a2), (a2, a1), (a3, a2), (a4, a3)}

• Def = {(a4, a3), (a3, a2)}
From the above definition of agent theory, the following hold:

Property 1. • Def ⊆ R • ∀a, a ∈ F(oi), a R a

The reasoning model

From the theory of an agent, one can define the argumentation system used by that agent for reasoning about the offers and the arguments, i.e. for computing the status of the different offers and arguments. Definition 3 (Argumentation system). Let A, F , , R, Def be the theory of an agent. The argumentation system of that agent is the pair A, Def .

In [START_REF] Dung | On the acceptability of arguments and its fundamental role in nonmonotonic reasoning, logic programming and n-person games[END_REF], different acceptability semantics have been introduced for computing the status of arguments. These are based on two basic concepts, defence and conflict-free, defined as follows:

Definition 4 (Defence/conflict-free). Let S ⊆ A.

• S defends an argument a iff each argument that defeats a is defeated by some argument in S.

• S is conflict-free iff there exist no a, a in S such that a Def a .

Definition 5 (Acceptability semantics). Let S be a conflict-free set of arguments, and let T : 2 A → 2 A be a function such that T (S) = {a | a is defended by S}.

• S is a complete extension iff S = T (S).

• S is a preferred extension iff S is a maximal (w.r.t set ⊆) complete extension.

• S is a grounded extension iff it is the smallest (w.r.t set ⊆) complete extension.

Let E1, . . . , Ex denote the different extensions under a given semantics.

Note that there is only one grounded extension. It contains all the arguments that are not defeated, and those arguments that are defended directly or indirectly by nondefeated arguments.

Theorem 1. Let A, Def the argumentation system defined as shown above.

1. It may have x ≥ 1 preferred extensions.

The grounded extensions is

S = i≥1 T (∅).
Note that when the grounded extension (or the preferred extension) is empty, this means that there is no acceptable offer for the negotiating agent. Example 2. In example 1, there is one preferred extension, E = {a1, a2, a4}. Now that the acceptability semantics is defined, we are ready to define the status of any argument. Definition 6 (Argument status). Let A, Def be an argumentation system, and E1, . . . , Ex its extensions under a given semantics. Let a ∈ A.

1. a is accepted iff a ∈ Ei, ∀Ei with i = 1, . . . , x.

2. a is rejected iff Ei such that a ∈ Ei.

3. a is undecided iff a is neither accepted nor rejected.
This means that a is in some extensions and not in others.

Note that

A = {a|a is accepted} ∪ {a|a is rejected} ∪ {a|a is undecided}. Example 3.
In example 1, the arguments a1, a2 and a4 are accepted, whereas the argument a3 is rejected.

As said before, agents use argumentation systems for reasoning about offers. In a negotiation dialogue, agents propose and accept offers that are acceptable for them, and reject bad ones. In what follows, we will define the status of an offer. According to the status of arguments, one can define four statuses of the offers as follows:

Definition 7 (Offers status). Let o ∈ O.
• The offer o is acceptable for the negotiating agent iff ∃ a ∈ F (o) such that a is accepted. Oa = {oi ∈ O, such that oi is acceptable}.

• The offer o is rejected for the negotiating agent iff ∀ a ∈ F (o), a is rejected. Or = {oi ∈ O, such that oi is rejected}.

• The offer o is negotiable iff ∀ a ∈ F(o), a is undecided. On = {oi ∈ O, such that oi is negotiable}.

• The offer o is non-supported iff it is neither acceptable, nor rejected or negotiable. Ons = {oi ∈ O, such that oi is non-supported offers}. Example 4. In example 1, the two offers o1 and o2 are acceptable since they are supported by accepted arguments, whereas the offer o3 is non-supported since it has no argument in its favor.

From the above definitions, the following results hold:

Property 2. Let o ∈ O. • O = Oa ∪ Or ∪ On ∪ Ons.
• The set Oa may contain more than one offer.

From the above partition of the set O of offers, a preference relation between offers is defined. Let Ox and Oy be two subsets of O. Ox Oy means that any offer in Ox is preferred to any offer in the set Oy. We can write also for two offers oi, oj, oi oj iff oi ∈ Ox, oj ∈ Oy and Ox Oy.

Definition 8 (Preference between offers). Let O be a set of offers, and Oa, Or, On, Ons its partition. Oa On Ons Or. Example 5. In example 1, we have o1 o3, and o2 o3. However, o1 and o2 are indifferent.

THE STRUCTURE OF NEGOTIATION THE-ORIES

In this section, we study the properties of the system developed above. We first show that in the particular case A = AO (ie. all of the agent's arguments refer to offers), the corresponding argumentation system will return at least one non-empty preferred extension.

Theorem 2. Let A, Def an argumentation system such that A = AO. Then the system returns at least one extension E, such that |E| ≥ 1.

We now present some results that demonstrate the importance of indifference in negotiating agents, and more specifically its relation to acceptable outcomes. We first show that the set Oa may contain several offers when their corresponding accepted arguments are indifferent w.r.t the preference relation . We now study acyclic preference relations that are defined formally as follows.

Theorem 3. Let o1, o2 ∈ O. o1, o2 ∈ Oa iff ∃ a1 ∈ F (o1), ∃ a2 ∈ F (o2),

Definition 9 (Acyclic relation).

A relation R on a set A is acyclic if there is no sequence a1, a2, . . . , an ∈ A, with n > 1, such that (ai, ai+1) ∈ R and (an, a1) ∈ R, with 1 ≤ i < n. The previous result is used in the proof of the following theorem that states that acyclic preference relations sanction extensions that support exactly one offer. Using the above results we can prove the main theorem of this section that states that negotiating agents with acyclic preference relations do not have acceptable offers.

Note that acyclicity prohibits pairs of arguments

Theorem 7. Let A, F , R, , Def be a negotiating agent such that A = AO and is an acyclic relation. Then the set of accepted arguments w.r.t A, Def is emtpy. Consequently, the set of acceptable offers, Oa is empty as well.

ARGUMENTATION-BASED NEGOTIATION

In this section, we define formally a protocol that generates argumentation-based negotiation dialogues between two negotiating agents P and C. The two agents negotiate about an object whose possible values belong to a set O. This set O is supposed to be known and the same for both agents. For simplicity reasons, we assume that this set does not change during the dialogue. The agents are equipped with theories denoted respectively A P , F P , P , R P , Def P , and A C , F C , C , R C , Def C . Note that the two theories may be different in the sense that the agents may have different sets of arguments, and different preference relations. Worst yet, they may have different arguments in favor of the same offers. Moreover, these theories may evolve during the dialogue.

Evolution of the theories

Before defining formally the evolution of an agent's theory, let us first introduce the notion of dialogue moves, or moves for short.

Definition 10 (Move).

A move is a tuple mi = pi, ai, oi, ti such that:

• pi ∈ {P, C} • ai ∈ Args(L) ∪ θ 1 • oi ∈ O ∪ θ • ti ∈ N * is the target of the move, such that ti < i
The function Player (resp. Argument, Offer, Target) returns the player of the move (i.e. pi) (resp. the argument of a move, i.e ai, the offer oi, and the target of the move, ti). Let M denote the set of all the moves that can be built from {P, C}, Arg(L), O .

Note that the set M is finite since Arg(L) and O are assumed to be finite. Let us now see how an agent's theory evolves and why. The idea is that if an agent receives an argument from another agent, it will add the new argument to its theory. Moreover, since an argument may bring new information for the agent, thus new arguments can emerge. Let us take the following example: Example 6. Suppose that an agent P has the following propositional knowledge base: ΣP = {x, y → z}. From this base one cannot deduce z. Let's assume that this agent receives the following argument {a, a → y} that justifies y. It is clear that now P can build an argument, say {a, a → y, y → z} in favor of z.

In a similar way, if a received argument is in conflict with the arguments of the agent i, then those conflicts are also added to its relation R i . Note that new conflicts may arise between the original arguments of the agent and the ones that emerge after adding the received arguments to its theory. Those new conflicts should also be considered. As a direct consequence of the evolution of the sets A i and R i , the defeat relation Def i is also updated. The initial theory of an agent i, (i.e. its theory before the dialogue starts), is denoted by A i 0 , F i 0 , i 0 , R i 0 , Def i 0 , with i ∈ {P, C}. Besides, in this paper, we suppose that the preference relation i of an agent does not change during the dialogue.

Definition 11 (Theory evolution). Let m1, . . ., mt, . . ., mj be a sequence of moves. The theory of an agent i at a step t > 0 is: A i t , F i t , i t , R i t , Def i t such that:

• A i t = A i 0 ∪ {ai, i = 1, . . . , t, ai = Argument(mi)} ∪ A with A ⊆ Args(L) • F i t = O → 2 A i t • i t = i 0 • R i t = R i 0 ∪ {(ai, aj) | ai = Argument(mi), aj = Argument(mj), i, j ≤ t, and ai RL aj} ∪ R with R ⊆ RL • Def i t ⊆ A i t × A i t
The above definition captures the monotonic aspect of an argument. Indeed, an argument cannot be removed. However, its status may change. An argument that is accepted at step t of the dialogue by an agent may become rejected at step t + i. Consequently, the status of offers also change. Thus, the sets Oa, Or, On, and Ons may change from one step of the dialogue to another. That means for example that some offers could move from the set Oa to the set Or and vice-versa. Note that in the definition of Rt, the relation RL is used to denote a conflict between exchanged arguments. The reason is that, such a conflict may not be in the set R i of the agent i. Thus, in order to recognize such conflicts, we have supposed that the set RL is known to the agents. This allows us to capture the situation where an agent is able to prove an argument that it was unable to prove before, by incorporating in its beliefs some information conveyed through the exchange of arguments with another agent. This, unknown at the beginning of the dialogue argument, could give to this agent the possibility to defeat an argument that it could not by using its initial arguments. This could even lead to a change of the status of these initial arguments and this change would lead to the one of the associated offers' status. In what follows, O i t,x denotes the set of offers of type x, where x ∈ {a, n, r, ns}, of the agent i at step t of the dialogue. In some places, we can use for short the notation O i t to denote the partition of the set O at step t for agent i. Note that we have: not(O i t,x ⊆ O i t+1,x ).

The notion of agreement

As said in the introduction, negotiation is a process aiming at finding an agreement about some matters. By agreement, one means a solution that satisfies to the largest possible extent the preferences of both agents. In case there is no such solution, we say that the negotiation fails. In what follows, we will discuss the different kinds of solutions that may be reached in a negotiation. The first one is the optimal solution. An optimal solution is the best offer for both agents. During a negotiation dialogue, agents exchange first their most preferred offers, and if these last are rejected, they make concessions. In this case, we say that their best offers are no longer defendable. In an argumentation setting, this means that the agent has already presented all its arguments supporting its best offers, and it has no counter argument against the ones presented by the other agent. Formally:

Definition 14 (Defendable offer). Let A i t , F i t , i t , R i
t , Def i t be the theory of agent i at a step t > 0 of the dialogue. Let o ∈ O such that ∃j ≤ t with Player(mj) = i and offer(mj) = o. The offer o is defendable by the agent i iff:

• ∃a ∈ F i t (o), and k ≤ t s.t. Argument(m k ) = a, or • ∃a ∈ A t \F i t (o) s.t. a Def i t b with -Argument(m k ) = b, k ≤ t, and
Player(m k ) = i -l ≤ t, Argument(m l ) = a
The offer o is said non-defendable otherwise and N D i t is the set of non-defendable offers of agent i at a step t.

Negotiation dialogue

Now that we have shown how the theories of the agents evolve during a dialogue, we are ready to define formally an argumentation-based negotiation dialogue. For that purpose, we need to define first the notion of a legal continuation.

Definition 15 (Legal move).

A move m is a legal continuation of a sequence of moves m1, . . . , m l iff j, k < l, such that:

• Offer(mj) = Offer(m k ), and

• Player(mj) = Player(m k )
The idea here is that if the two agents present the same offer, then the dialogue should terminate, and there is no longer possible continuation of the dialogue.

Definition 16 (Argumentation-based negotiation).

An argumentation-based negotiation dialogue d between two agents P and C is a non-empty sequence of moves m1, . . . , m l such that:

• pi = P iff i is even, and pi = C iff i is odd • Player(m1) = P , Argument(m1) = θ, Offer(m1) = θ,
and

Target(m1) = 0 2 • ∀ mi, if Offer(mi) = θ, then Offer(mi) oj, ∀ oj ∈ O\(O Player(m i ) i,r ∪ N D Player(m i ) i
)

• ∀i = 1, . . . , l, mi is a legal continuation of m1, . . . , mi-1

• Target(mi) = mj such that j < i and Player(mi) = Player(mj)

• If Argument(mi) = θ, then:

if Offer(mi) = θ then Argument(mi) ∈ F(Offer(mi))

-if Offer(mi) = θ then Argument(mi) Def Player(m i ) i
Argument(Target(mi))

• i, j ≤ l such that mi = mj

• m ∈ M such that m is a legal continuation of m1, . . . , m l Let D be the set of all possible dialogues.

The first condition says that the two agents take turn. The second condition says that agent P starts the negotiation dialogue by presenting an offer. Note that, in the first turn, we suppose that the agent does not present an argument. This assumption is made for strategical purposes. Indeed, arguments are exchanged as soon as a conflict appears. The third condition ensures that agents exchange their best offers, but never the rejected ones. This condition takes also into account the concessions that an agent will have to make if it was established that a concession is the only option for it at the current state of the dialogue. Of course, as we have shown in a previous section, an agent may have several good or acceptable offers. In this case, the agent chooses one of them randomly. The fourth condition ensures that the moves are legal. This condition allows to terminate the dialogue as soon as an offer is presented by both agents.

The fifth condition allows agents to backtrack. The sixth 2 The first move has no target.

condition says that an agent may send arguments in favor of offers, and in this case the offer should be stated in the same move. An agent can also send arguments in order to defeat arguments of the other agent. The next condition prevents repeating the same move. This is useful for avoiding loops. The last condition ensures that all the possible legal moves have been presented. The outcome of a negotiation dialogue is computed as follows:

Definition 17 (Dialogue outcome). Let d = m1, . . ., m l be a argumentation-based negotiation dialogue. The outcome of this dialogue, denoted Outcome, is Outcome(d) = Offer(m l ) iff ∃j < l s.t. Offer(m l ) = Offer(mj), and Player(m l ) = Player(mj). Otherwise, Outcome(d) = θ.

Note that when Outcome(d) = θ, the negotiation fails, and no agreement is reached by the two agents. However, if Outcome(d) = θ, the negotiation succeeds, and a solution that is either optimal or a compromise is found.

Theorem 8. ∀di ∈ D, the argumentation-based negotiation di terminates.

The above result is of great importance, since it shows that the proposed protocol avoids loops, and dialogues terminate. Another important result shows that the proposed protocol ensures to reach an optimal solution if it exists. Formally:

Theorem 9 (Completeness). Let d = m1, . . . , m l be a argumentation-based negotiation dialogue. If ∃t ≤ l such that O P t,a ∩ O C t,a = ∅, then Outcome(d) ∈ O P t,a ∩ O C t,a .
We show also that the proposed dialogue protocol is sound in the sense that, if a dialogue returns a solution, then that solution is for sure a compromise. In other words, that solution is a "common agreement" at a given step of the dialogue. We show also that if the negotiation fails, then there is no possible solution.

Theorem 10 (Soundness). Let d = m1, . . . , m l be a argumentation-based negotiation dialogue.

ILLUSTRATIVE EXAMPLES

In this section we will present some examples in order to illustrate our general framework.

Example 7 (No argumentation).

Let O = {o1, o2} be the set of all possible offers. Let P and C be two agents, equipped with the same theory: A, F , , R, Def such that

A = ∅, F (o1) = F (o2) = ∅, = ∅, R = ∅, Def = ∅.
In this case, it is clear that the two offers o1 and o2 are nonsupported. The proposed protocol (see Definition 16) will generate one of the following dialogues:

P: m1 = P, θ, o1, 0 C: m2 = C, θ, o1, 1
This dialogue ends with o1 as a compromise. Note that this solution is not considered as optimal since it is not an acceptable offer for the agents.

P: m1 = P, θ, o1, 0 C: m2 = C, θ, o2, 1

P: m3 = P, θ, o2, 2
This dialogue ends with o2 as a compromise.

P: m1 = P, θ, o2, 0

C: m2 = C, θ, o2, 1
This dialogue also ends with o2 as a compromise. The last possible dialgue is the following that ends with o1 as a compromise.

P: m1 = P, θ, o2, 0 C: m2 = C, θ, o1, 1

P: m3 = P, θ, o1, 2
Note that in the above example, since there is no exchange of arguments, the theories of both agents do not change. Let us now consider the following example.

Example 8 (Static theories). Let O = {o1, o2} be the set of all possible offers. The theory of agent P is A P , F P , P , R P , Def P such that: A P = {a1, a2}, F P (o1) = {a1}, F P (o2) = {a2}, P = {(a1, a2)}, R P = {(a1, a2), (a2, a1)}, Def P = {a1, a2}. The argumentation system A P , Def P of this agent will return a1 as an accepted argument, and a2 as a rejected one. Consequently, the offer o1 is acceptable and o2 is rejected.

The theory of agent

C is A C , F C , C , R C , Def C such that: A C = {a1, a2}, F C (o1) = {a1}, F C (o2) = {a2}, C = {(a2, a1)}, R C = {(a1, a2
), (a2, a1)}, Def C = {a2, a1}. The argumentation system A C , Def C of this agent will return a2 as an accepted argument, and a1 as a rejected one. Consequently, the offer o2 is acceptable and o1 is rejected.

The only possible dialogues that may take place between the two agents are the following:

P: m1 = P, θ, o1, 0 C: m2 = C, θ, o2, 1 P: m3 = P, a1, o1, 2 C: m4 = C, a2, o2, 3
The second possible dialogue is the following: P: m1 = P, θ, o1, 0 C: m2 = C, a2, o2, 1 P: m3 = P, a1, o1, 2

C: m4 = C, θ, o2, 3
Both dialogues end with failure. Note that in both dialogues, the theories of both agents do not change. The reason is that the exchanged arguments are already known to both agents. The negotiation fails because the agents have conflicting preferences.

Let us now consider an example in which argumentation will allow agents to reach an agreement.

Example 9 (Dynamic theories). Let O = {o1, o2} be the set of all possible offers. The theory of agent P is A P , F P , P , R P , Def P such that: A P = {a1, a2}, F P (o1) = {a1}, F P (o2) = {a2}, P = {(a1, a2), (a3, a1)}, R P = {(a1, a2), (a2, a1)}, Def P = {(a1, a2)}. The argumentation system A P , Def P of this agent will return a1 as an accepted argument, and a2 as a rejected one. Consequently, the offer o1 is acceptable and o2 is rejected.

The theory of agent

C is A C , F C , C , R C , Def C such that: A C = {a1, a2, a3}, F C (o1) = {a1}, F C (o2) = {a2}, C = {(a1, a2), (a3, a1)}, R C = {(a1, a2
), (a2, a1), (a3, a1)}, Def C = {(a1, a2), (a3, a1)}. The argumentation system A C , Def C of this agent will return a3 and a2 as accepted arguments, and a1 as a rejected one. Consequently, the offer o2 is acceptable and o1 is rejected.

The following dialogue may take place between the two agents:

P: m1 = P, θ, o1, 0 C: m2 = C, θ, o2, 1 P: m3 = P, a1, o1, 2 C: m4 = C, a3, θ, 3 C: m5 = P, θ, o2, 4
At step 4 of the dialogue, the agent P receives the argument a3 from P . Thus, its theory evolves as follows: A P = {a1, a2, a3}, R P = {(a1, a2), (a2, a1), (a3, a1)}, Def P = {(a1, a2), (a3, a1)}. At this step, the argument a1 which was accepted will become rejected, and the argument a2 which was at the beginning of the dialogue rejected will become accepted. Thus, the offer o2 will be acceptable for the agent, whereas o1 will become rejected. At this step 4, the offer o2 is acceptable for both agents, thus it is an optimal solution. The dialogue ends by returning this offer as an outcome.

RELATED WORK

Argumentation has been integrated in negotiation dialogues at the early nineties by Sycara [START_REF] Sycara | Persuasive argumentation in negotiation[END_REF]. In that work, the author has emphasized the advantages of using argumentation in negotiation dialogues, and a specific framework has been introduced. In [START_REF] Kraus | Reaching agreements through argumentation: a logical model and implementation[END_REF], the different types of arguments that are used in a negotiation dialogue, such as threats and rewards, have been discussed. Moreover, a particular framework for negotiation have been proposed. In [START_REF] Parsons | Negotiation through argumentation-a preliminary report[END_REF][START_REF] Tohmé | Negotiation and defeasible reasons for choice[END_REF], different other frameworks have been proposed. Even if all these frameworks are based on different logics, and use different definitions of arguments, they all have at their heart an exchange of offers and arguments. However, none of those proposals explain when arguments can be used within a negotiation, and how they should be dealt with by the agent that receives them. Thus the protocol for handling arguments was missing. Another limitation of the above frameworks is the fact that the argumentation frameworks they use are quite poor, since they use a very simple acceptability semantics. In [START_REF] Amgoud | Arguments, dialogue, and negotiation[END_REF] a negotiation framework that fills the gap has been suggested. A protocol that handles the arguments was proposed. However, the notion of concession is not modeled in that framework, and it is not clear what is the status of the outcome of the dialogue. Moreover, it is not clear how an agent chooses the offer to propose at a given step of the dialogue. In [START_REF] Amgoud | Towards a formal framework for the search of a consensus between autonomous agents[END_REF][START_REF] Kakas | Adaptive agent negotiation via argumentation[END_REF], the authors have focused mainly on this decision problem. They have proposed an argumentation-based decision framework that is used by agents in order to choose the offer to propose or to accept during the dialogue. In that work, agents are supposed to have a beliefs base and a goals base.

Our framework is more general since it does not impose any specific structure for the arguments, the offers, or the beliefs. The negotiation protocol is general as well. Thus this framework can be instantiated in different ways by creating, in such manner, different specific argumentation-based negotiation frameworks, all of them respecting the same properties. Our framework is also a unified one because frameworks like the ones presented above can be represented within this framework. For example the decision making mechanism proposed in [START_REF] Kakas | Adaptive agent negotiation via argumentation[END_REF] for the evaluation of arguments and therefore of offers, which is based on a priority relation between mutually attacked arguments, can be captured by the relation defeat proposed in our framework. This relation takes simultaneously into account the attacking and preference relations that may exist between two arguments.

CONCLUSIONS AND FUTURE WORK

In this paper we have presented a unified and general framework for argumentation-based negotiation. Like any other argumentation-based negotiation framework, as it is evoked in (e.g. [START_REF] Rahwan | Argumentation-based negotiation[END_REF]), our framework has all the advantages that argumentation-based negotiation approaches present when related to the negotiation approaches based either on game theoretic models (see e.g. [START_REF] Rosenschein | Rules of Encounter: Designing Conventions for Automated Negotiation Among Computers[END_REF]) or heuristics ([6]). This work is a first attempt to formally define the role of argumentation in the negotiation process. More precisely, for the first time, it formally establishes the link that exists between the status of the arguments and the offers they support, it defines the notion of concession and shows how it influences the evolution of the negotiation, it determines how the theories of agents evolve during the dialogue and performs an analysis of the negotiation outcomes. It is also the first time where a study of the formal properties of the negotiation theories of the agents as well as of an argumentative negotiation dialogue is presented.

Our future work concerns several points. A first point is to relax the assumption that the set of possible offers is the same to both agents. Indeed, it is more natural to assume that agents may have different sets of offers. During a negotiation dialogue, these sets will evolve. Arguments in favor of the new offers may be built from the agent theory. Thus, the set of offers will be part of the agent theory. Another possible extension of this work would be to allow agents to handle both arguments PRO and CONS offers. This is more akin to the way human take decisions. Considering both types of arguments will refine the evaluation of the offers status. In the proposed model, a preference relation between offers is defined on the basis of the partition of the set of offers. This preference relation can be refined. For instance, among the acceptable offers, one may prefer the offer that is supported by the strongest argument. In [START_REF] Amgoud | Explaining qualitative decision under uncertainty by argumentation[END_REF], different criteria have been proposed for comparing decisions. Our framework can thus be extended by integrating those criteria. Another interesting point to investigate is that of considering negotiation dialogues between two agents with different profiles. By profile, we mean the criterion used by an agent to compare its offers.

  such that a1 and a2 are accepted and are indifferent w.r.t (i.e. a b and b a).

  a, b such that a b and b a, ie., an acyclic preference relation disallows indifference.

Theorem 4 .

 4 Let A be a set of arguments, R the attacking relation of A defined as R ⊆ A × A, and an acyclic relation on A. Then for any pair of arguments a, b ∈ A, such that (a, b) ∈ R, either (a, b) ∈ Def or (b, a) ∈ Def (or both).

Theorem 5 .

 5 Let A be a set of arguments, and an acyclic relation on A. If E is an extension of <A, Def>, then |E ∩ AO| = 1. An immediate consequence of the above is the following. Property 3. Let A be a set of arguments such that A = AO. If the relation on A is acyclic, then each extension Ei of <A, Def>, |Ei| = 1.Another direct consequence of the above theorem is that in acyclic preference relations, arguments that support offers can participate in only one preferred extension. Theorem 6. Let A be a set of arguments, and an acyclic relation on A. Then the preferred extensions of A, Def are pairwise disjoint w.r.t arguments of AO.

Formally: Definition 12 (

 12 Optimal solution). Let O be a set of offers, and o ∈ O. The offer o is an optimal solution at a step t ≥ 0 iff o ∈ O P t,a ∩ O C t,a Such a solution does not always exist since agents may have conflicting preferences. Thus, agents make concessions by proposing/accepting less preferred offers. Definition 13 (Concession). Let o ∈ O be an offer. The offer o is a concession for an agent i iff o ∈ O i x such that ∃O i y = ∅, and O i y O i x .

  Property 4. Let d = m1, . . . , m l be a argumentationbased negotiation dialogue. If Outcome(d) = θ, then ∀t ≤ l,

	1. If Outcome(d) = o, (o = θ), then ∃t ≤ l such that o ∈
	O P t,x ∩ O C t,y , with x, y ∈ {a, n, ns}.
	2. If Outcome(d) = θ, then ∀t ≤ l, O P t,x ∩ O C t,y = ∅, ∀
	x, y ∈ {a, n, ns}.
	A direct consequence of the above theorem is the following:
	• O P t,r = O C t,a ∪ O C t,n ∪ O C t,ns , and
	• O C t,r = O P t,a ∪ O P t,n ∪ O P t,ns .

In what follows θ denotes the fact that no argument, or no offer is given


Laurence Dahéron

Rémi Dedryvère

Hervé Martinez

Michel Ménétrier

Cathy Denage

Claude Delmas

Danielle Gonbeau

Electron transfer mechanisms upon lithium deintercalation from LiCoO2 to CoO2 investigated by XPS

à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d'enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.


Rémi Sitta
email: <remi.sitta@inserm.fr

France Lert

Alice Gueguen

Bruno Spire

Rosemary Dray-Spira

R Mi Sitta

A D Bouhnik

No variability across centers in adherence and response to HAART in French hospitals: results from the ANRS

Keywords: Adult, Anti-HIV Agents, therapeutic use, Antiretroviral Therapy, Highly Active, Cross-Sectional Studies, Delivery of Health Care, Female, France, HIV Infections, drug therapy, Hospitals, Humans, Male, Medication Adherence, Middle Aged, Treatment Failure HIV infection, HAART, Treatment failure, Service provision, Centre effect, France

Introduction

Since the advent of AIDS, equality and non-discrimination in access to prevention and treatment have been major issues, because so high a percentage of patients belongs to stigmatised or disadvantaged groups, such as drug users, ethnic minorities, immigrants or women.

Disadvantaged groups have been shown to have less access to zidovudine treatment and pneumocystis carinii pneumonia (PCP) [START_REF] Stein | Differences in access to zidovudine (AZT) among symptomatic HIV-infected persons[END_REF] prophylaxis ; they also start HAART later . Aside from the barriers to health care due to patients financial situation and educational [START_REF] Easterbrook | Racial and ethnic differences in outcome in zidovudine-treated patients with advanced HIV disease. Zidovudine Epidemiology Study Group[END_REF] [3 ] ' level, physicians anticipation that patient compliance will be poor , has been shown to explain delayed initiation of HAART.

regarding treatment so that all patients can benefit from the most recent scientific advances. Such rapid changes might vary according to physician characteristics, type of setting and size of HIV caseload.

The purpose of this paper is to describe the heterogeneity of the hospital HIV treatment provided in France and its effect on treatment outcome.

Material and methods

Study design

This analysis used data from the 2003 ANRS-EN12-VESPA study, a large nationally representative two-stage cross-sectional survey, aimed at studying the social situation of HIV-infected persons in France. The study design has been detailed elsewhere . 85 hospitals [START_REF] Dray-Spira | Heterogeneous response to HAART across a diverse population of people living with HIV: results from the ANRS-EN12-VESPA Study[END_REF] providing HIV care were randomly selected among the 143 French hospitals with a HIV caseload greater than 60 patients, stratifying on geographic location and size of HIV caseload. As some large hospitals had several departments serving patients with HIV, the 85 hospitals were composed of 102 departments providing HIV care. Doctors in each of these departments randomly recruited a sample of outpatients (representing about 5 of their caseload) among those with the following eligibility criteria: having been diagnosed with HIV- Information was collected on the following characteristics for all eligible patients: sex, age, employment status, mode of transmission and last known CD4 cell count and viral load. This data allowed for the assessment of participation bias.

Participating patients answered a questionnaire administered in a face-to-face interview. Detailed information was collected on socio-demographic characteristics and on a wide range of social conditions (health care access and use, health behaviour, occupational status, income, housing, social support, HIV disclosure, discriminations encountered, sexual activity and reproductive life). Physicians recorded for each patient the mode of HIV acquisition, disease characteristics, and treatment information (date of diagnosis, date of HAART initiation, clinical stage, CD4 count and viral load at diagnosis, at HAART initiation and last known values).

Variables of interest

The heterogeneity of the departments delivering HIV care was studied for adherence and various measures of treatment outcome.

Adherence to HAART was assessed with a dichotomous outcome (high versus moderate or poor adherence) validated in previous cohort studies , . First, participants were asked about their compliance with HAART in the prior 7 days. They had to choose among [14 15 ] the following items, each corresponding to a level of adherence: I have followed scrupulously my treatment ( high adherence), I have

' ' = '
followed my treatment despite some small lapses ( moderate adherence), I have frequently modified doses or time schedule , I have

' = ' ' '
almost never complied with prescription instructions , I have stopped treatment ( poor adherence). Then, participants were asked whether

' ' ' =
or not they had missed at least one dose during the previous week-end, whether they had taken the whole daily dose in only one take in the previous 7 days, or whether they had failed to respect the time schedule for at least one dose during the same period. Participants previously ranked as highly adherents but who had answered yes to one of these three questions were reallocated to the moderate ' ' '

adherence category.

'

Treatment outcome was assessed using four different indicators, three defining failure and one denoting success:

Immunological response was defined as the absence of an increase of 100 CD4 cells/mm between HAART initiation and data ≥ 3 collection. This threshold was chosen on the basis of the review by May and colleagues , showing a median 100 cells increase in CD4 [START_REF] May | HIV treatment response and prognosis in Europe and North America in the first decade of highly active antiretroviral therapy: a collaborative analysis[END_REF] cell count in the first 6 month on HAART, which was here the minimum duration.

Virological failure was defined as having detectable HIV-RNA (<400 copies/ml) at data collection;

Immunovirological failure was defined as the combination of a CD4 cell count 200/mm and detectable HIV-RNA at data collection;

≤ = ' =
Our sensitivity analysis consisted in rerunning these models with restricting the analysis population first to the 601 patients of the 60 departments that had at least five participating patients, and secondly to the 378 patients of the 26 departments that had at least ten participating patients.

For adherence, as for the three first indicators of treatment failure, the absence of a centre effect was confirmed. Concerning immunovirological success, the random variable was still significant in the first restriction (p 0.030) and almost still significant in the = second restriction to departments with at least 10 patients (p 0.053). Adjusting on covariates measured on the individual level returned as = previously a non-significant random term.

Discussion

This study used data from a large random sample of hospitals providing HIV care, both representative at the national level and very diverse in terms of size, region, localisation in either metropolitan areas or medium-sized cities, activity, and specialisation. We observed a significant variation in the size of the HIV caseload, the provision of consultant services offered onsite, patient education to increase adherence, and support from PLWHA organisations. Nonetheless no centre effect was identified, either for adherence to treatment or in HAART outcomes: in France, regardless of where HIV patients are treated for their infection, treatment success or failure depends upon individual determinants. In a previous study of this population, we found that aside from the well-established determinants (such as age, time on HAART, history of interruption in HIV care, suboptimal adherence, HCV co-infection, CD4 cell count and HIV-RNA level and AIDS at HAART initiation), immigrant status and continuing IV drug use were associated with a greater risk of treatment failure .

[13 ]

Because of the cross-sectional design of the VESPA study, treatment failure might have been underestimated: deaths that occurred between diagnosis and data collection were not taken into account in the calculation of failure rate. In the HAART era, mortality remains much higher among patients diagnosed with advanced infection than among patients diagnosed before reaching the criteria for treatment initiation . In the former group, the physician s experience may play a critical role , , , , .

[ Our study considered only hospitals caring for a substantial number (60 or more) of persons with HIV. Patients followed in smaller HIV-oriented services are not included although they might have different HIV outcomes. However, the hospitals included provided care for an estimated 90 of the HIV patient population followed in hospitals.

%

Random sampling ensured the representativeness of each hospital department caseload, but differential participation was related to individual patient characteristics, including lower CD4 cell counts. Participation bias might thus explain the absence of centre effects, especially if patients with poor treatment outcomes had tended to participate less in the hospitals with the poorest outcome rates. As last known CD4 cell count and viral load were available for every eligible patient, we were able to verify that this was not the case, using a mixed binary model which explained the participation of eligible patients by their health status and the treatment outcome rate of their hospital department.

Despite a low number of participants in some departments, we believe that the absence of an observed centre effect is unlikely to be due to lack of power. The assumptions of the random coefficient model we use seem appropriate here, and neither the estimates nor p values changed substantially when the analysis was restricted to the two subsamples with the hospital departments reaching either five or

  21 . Braitstein P , Brinkhof MW , Dabis F . Mortality of HIV-1-infected patients in the first year of antiretroviral therapy: comparison between low-income and high-income countries .Lancet . 2006 ; 367 : 817 -24

Table 2

 2 Distribution of adherence and treatment outcomes among the departments and tests of centre effects

All departments Departments with at least 5 patients Departments with at least 10 patients Nd 97

  Hospital department entered as a random variable 1 Less than 100 CD4 increase since HAART initiation 2 HIV-RNA > 400 copies 3 CD4 < 200 and HIV-RNA > 400 copies 4 CD4 500 and HIV-RNA<400 copies

										=
		Mean	Median	IQR		p-value *	Median	IQR	p-value *	Median	IQR	p-value *
	Adherence	63.3%	61.5%	50 80 %-%	0.275	60.0%	51 79 %-%	0.225	58.6%	50 69 %-%	0.885
	Immunological failure 1	22.6%	20%	0 40 %-%	0.215	20.0%	14 32 %-%	0.285	19.4%	15 30 %-%	0.312
	Virological failure 2	12.5%	7.7%	0 20 %-%	0.098	14.3%	0 20 %-%	0.176	10.6%	5 19 %-%	0.081
	Immuno-virological failure 3	6.1%	0%	0 12.5 %-	%	0.181	6.3%	0 14 %-%	0.177	7.7%	0 13 %-%	0.136
	Immuno-virological success 4	40.2%	36.4%	13.3 50 %-%	0.026	36.6%	29 47 %-%	0.030	36.6%	30 47 %-%	0.053
	Adjusted for CD4 cell count at HAART initiation:				0.094			0.092			0.170
	Adjusted for immigration status:					0.200			0.192			0.280
	Nd: Number of hospital departments
	Np: Number of patients
	≥

= Nd 60 = Nd 26 = Np 699 = Np 601 = Np 378 *

 3 8Lastly, immunovirological success was defined as the combination of a CD4 cell count 500/mm and undetectable HIV-RNA at data ≥ 3 collection. [START_REF] Lewden | HIV-infected adults with a CD4 cell count greater than 500 cells/mm3 on long-term combination antiretroviral therapy reach same mortality rates as the general population[END_REF]

Population of interest

The VESPA study included 2932 participants from 102 different departments. For the present analysis, we included only the 699 participants (of 97 different departments) who had been diagnosed in 1996 or later and had received HAART for at least 6 months at the time of the study. The medical history of patients diagnosed before and after the HAART era is indeed too different to be pooled in an analysis on this topic. Furthermore, the much higher mortality before 1996 indicates much greater selection bias among the patients diagnosed before that year. A minimum of 6 months is assumed necessary before the treatment can be judged effective and thus classified as a success or failure.

Statistical methods

For each of the five outcomes, the existence of a centre effect was assessed by testing the department as a random variable in a binary mixed model, without any other covariate. If this random variable appeared to be significant, the next step of the analysis was to include in the models covariates measured at the individual level (age, sex, sexual orientation, immigration status, education, HCV coinfection, time since HAART initiation, CD4 cell count at HAART initiation, addictive behaviour, current trial participation, side effects, and adherence, when relevant). If the random variable was no longer significant, then the previously found effect was due only to differences in population structure and a given patient had the same chance of treatment outcome regardless of facility.

Because including centres with very few subjects could result in a lack of robustness, we performed a sensitivity analysis by restricting the analysis to departments with at least five participating patients and then with at least 10 participants. All statistical analyses were performed using SAS 9.1.

Results

Characteristics of departments regarding service provision

Among the 102 departments, the median size of the HIV caseload at data collection was 400 (IQR: 230 750 ). The median number of physicians providing HIV care per department was 3 (IQR:

), and the median number of outpatient appointments per week was 7 (IQR:

). Half of these departments specialised in infectious diseases, a quarter in internal medicine, and the others in haematology, [5 -10 ] dermatology, pneumonology or hepatology. Internal medicine departments tended to provide a wider range of consultant services than the others. These most often included nutrition (85 ), followed by dermatology (55 ) and psychiatry (53 ). More rarely offered were

Characteristics of participants

The median age of these patients was 42 years (IQR: 35 51 ); men accounted for 75 of the sample; 39 self-identified as homo-or As shown in , these different categories of participants were not uniformly distributed among the hospital departments: the Table 1 structure of the patient population appeared quite heterogeneous across centres. The median proportion of immigrants was 20 , with an % IQR from 0 to 40 . While men constituted a majority of patients, with a median proportion of 75 , this rate varied substantially (IQR:

). The median proportion of patients under 40 was 43 (IQR: 20 50 ), and the median proportion of patients with late

diagnosis was 40 (IQR: 29 57 ). Few departments treated patients with an IDU history: the median proportion of these patients was

0 and the upper quartile 12.5 .

%

For the analysis population, the mean number of participants per department was 7.2 and the median 6 (IQR:

).

Adherence and treatment outcomes

shows the distribution of adherence and treatment outcomes measured for each hospital department and the related tests for Table 2 centre effects. The mean percentage of highly adherent participants was 63.3 . The heterogeneity between departments was rather large: the IQR varied from 50 to 80 , with a median adherence rate of 62 . However, the existence of a centre effect was rejected when we

tested the department as a random variable (p 0.275).

=

The overall rate of immunological failure was 22.6 , with a departments median of 20 and an IQR of 0 to 40 . No centre effect % ' % % % existed here either (p 0.215). The overall rate of virological failure was 12.5 , with a median rate of 7.7 . Only a quarter of the = % % departments had rates above 20 , and 44.3 had no virological failures. Again, no centre effect was detected (p 0.098).

% % =

The mean immunovirological failure was 6.1 . Three quarters of the departments had a failure rate under 12.5 , and 61 had no

participants in immunovirological failure. The existence of a centre effect was rejected with a p-value of 0.181.

The criteria defining immunovirological treatment success, i.e. a CD4 count over 500/ml and undetectable HIV-RNA, were met by 40.2 of patients. The median department success rate was 36.3 : a quarter had rates only below 13.3 , and another quarter had rates % % % above 50 . The random variable appeared to be significant (p 0.026) for this indicator. A centre effect thus existed, at least when tested

for the entire population analysed. Nevertheless, the random term was not significant when a covariate measured on the individual level was introduced, such as the patient CD4 cell count 200/mm at HAART initiation (p 0.094) or the patients immigration status (p 0.200).

≤ 5 8

The data were collected in 2003, and could perhaps not reflect the current situation. The treatment practices and the structure of the patient population have evolved. However, since the context of high innovation and frequent improvements in treatment practices is the same today as it was from 1996 to 2003, it is plausible that the observed homogeneity still applies today.

With these limitations, adherence and response to HAART appeared not different across treatment sites despite the diversity in medical care provision. These findings contrast with studies in the US during the 1980s and early 1990s , , , . The very high [1 2 3 4 ] effectiveness of the current combinations of antiretroviral drugs, when accessible to all who need them, may well be acknowledged as the principal factor for the observed results. The frequent updating of treatment guidelines (at least every two year) may also contribute to the improvement of treatment practices. Moreover, in France, HIV care has been coordinated at the local level since 1988, to facilitate scientific communication, availability of the range of treatment services and care coordination. Dissemination of recent scientific findings among HIV specialists may be facilitated by their participation in clinical research: 83 of the departments included participate in clinical % trials and 79 in cohort studies. Such participation provides the opportunity of frequent contacts between HIV experts at national and % international levels.

Two decades after the advent of AIDS, at country level, HIV care has become a lay medical specialty. The HIV medical community has remained relatively small, while becoming closely networked. The pioneers have not yet started to retire . These factors, combined [START_REF] Lert | Psychological stress among hospital doctors caring for HIV patients in the late nineties[END_REF] with the experience acquired, may account for the relatively homogeneity of good care that could explain the results we observed in the VESPA study. International goals for 2010 include universal antiretroviral treatment for all who need it , including in countries with a [START_REF] Who | Towards universal access: Scaling up Priority HIV/AIDS Interventions in the Health Sector: Progress Report[END_REF] scarcity of skilled human resources. Studies show that when treatment is provided at no charge, its efficacy reach the same levels in southern countries as it does in northern countries . Accessibility will require that antiretroviral treatment be provided through medical [21 ] facilities in the community. Long-term networking and training of HIV care providers to improve and maintain high standard skills should be planned to ensure the equal outcomes that should accompany truly equal access to effective treatment.

Ackowledgements:

The authors would like to thank all the patients, physicians and nurses who have participated in the ANRS-EN12-VESPA Study.

The


Keywords: Thin films, BaTi1-xZrxO3 sputtering, Dielectric properties, Structural properties

come

  Structural and electrical properties of BaTi1-xZrxO3 sputtered thin films: effect of the sputtering conditions Vincent Reymond, Sandrine Payan, Dominique Michau, Jean-Pierre Manaud, Mario Maglione To cite this version: Vincent Reymond, Sandrine Payan, Dominique Michau, Jean-Pierre Manaud, Mario Maglione. Structural and electrical properties of BaTi1-xZrxO3 sputtered thin films: effect of the sputtering conditions. Thin Solid Films, 2004, 467 (1-2), pp.54-58. 10.1016/j.tsf.2004.03.005. hal-00159589

Structural and electrical properties of BaTi