AMPLIA LEARNING ENVIRONMENT

A Proposal for Pedagogical Negotiation

Cecilia Dias Flores, João Carlos Gluz, Rosa Maria Vicari, Louise Seixas

Instituto de Informática – Universidade Federal do Rio Grande do Sul (UFRGS)

Po. B 15.064 – 91.501-970 – Porto Alegre – RS – Brazil

Keywords: Artificial intelligence, Pedagogical n

egotiation, Learning environment

Abstract: AMPLIA supports training of diagnostic reasoning and modelling of domains with complex and uncertain

knowledge. It focuses on the medical area, and it helps a learner to create a Bayesian network for a certain

problem. A pedagogic negotiation process (managed by an intelligent Mediator Agent) aids handle the

differences of topology and probability distribution between the model the learner built and the one built-in

in the system. The negotiation process occurs between the agents that represent the expert knowledge

domain and the agent that represents the learner knowledge. As a consequence, the learner visualises the

organisation of his/her ideas, creates and tests hypothesis, and discuss them with the system .

1 INTRODUCTION

AMPLIA (Vicari et al 2003), primarily designed as

an extra resource for the education of Medical

students, aims to support the diagnostic reasoning

development and modelling of diagnostic

hypotheses in the medical field. It employs Bayesian

networks for knowledge representation and

reasoning about some case study or illness.

We are developing this Learning Environment

r the research on negotiation and argumentation in

agents’ societies.

Negotiation is a complex interaction process

etween two (or more) agents that want to reach a

common agreement over a certain situation. There is

a wide range of possibilities, depending on the

situation and the agents involved. Negotiations may

happen, from the solution of conflicts between

competitive agents up to task division among co-

operative agents. In the present work, we considered

negotiation basically as a process of decision that

serves to solve conflicts that may arise from the

interaction among agents. Thus, the process of

pedagogic negotiation is defined as the solution of

conflicts that may happen among agents involved in

a teaching-learning environment, exclusively using

strategies with a pedagogical profile for the solution

of these conflicts.

For a real application, this definition is still

complete because it doesn’t specify the kind of

agents that take part in a teaching-learning process,

what is the result expected, which conflicts may

arise and, finally, which pedagogical strategies

should be adopted to solve these conflicts.

There is not an exchange of economic goods in

any

pedagogical negotiation process. We may

suppose that negotiation mechanisms derived from

Games Theory and Market Theory (Sandholm,

1999) (Jennings, 2001), would not be useful for this

kind of negotiation. However, these mechanisms

were generalised to operate with more abstract

versions than economic values, such as utilities and

preferences. We examine their applicability,

checking whether the notions of preference or utility

are appropriated in a process of pedagogical

negotiation.

2 MULTI-AGENT

ARCHITECTURE

AMPLIA provides the possibility of integrating

the resources that an ITS offer and the learning

resources related to the domain being studied. This

could lead to courseware or to a human partner

(either teacher or student) who may help the student

to solve a problem.

279

Dias Flores C., Carlos Gluz J., Maria Vicari R. and Seixas L. (2004).

AMPLIA LEARNING ENVIRONMENT - A Proposal for Pedagogical Negotiation.

In Proceedings of the Sixth International Conference on Enterprise Information Systems, pages 279-286

DOI: 10.5220/0002633602790286

 SciTePress

Communication

between the

agents

ediatorA

ent

omainA

ent

earchA

ent

earnerA

ent

Teacher

earnerA

ent

Figure 1: Multi-agent Architecture of the AMPLIA Environment.

A diagnostic component is compulsory to be

there, for the development of an individualised

teaching. The human agent may take part of this

process, helping to identify the problem the student

is facing when the software agent fails. This way, an

architecture based on agents provides a natural

synergy between human beings and software agents

(diagnostic components, pedagogical agents, on-line

help systems, intelligent web searching based on the

semantic selection of support material)

This is the scenario we intend to reach with

AMPLIA. The Figure 1 presents an outline of the

AMPLIA Environment's Multi-agent Architecture.

The starting point of our efforts is to set a co-

ordination mechanism among the agents that inhabit

this society. The interactions that occur between the

personal agent, which represents the student in this

society, and the diagnostic agent are seen as a

pedagogic negotiation process, in which conflicts are

solved with the aid of a pedagogical agent whose

function is to set the discussion topic as the student’s

modelling task advances. The autonomous agents

represent users (students, teachers and applications),

and take part in a social interaction based on

objectives in which they communicate, co-operate

and negotiate between themselves.

Each agent has two different user's models that

represent: (1) the objectives' model to be reached,

either from the human user or from the application

(in the case of human users, the user’s objectives

and preferences), and (2) a model of available

resources of each user and/or application, which in

the case of a user includes his/her cognitive

resources (knowledge domain models, registers of

experiments and skills). These models make possible

that the agents argue about their objectives and plan

their actions (e.g., suggesting to the student to search

for help from other users).

A personal agent (the one that represents the user

in the virtual environment) knows about the current

objective (or preferences) and the user’s resources

level (knowledge), when it is evaluated by some

diagnostic component specific of the application, or

interface based on the task. In AMPLIA, such

diagnostic application is represented by an expert

agent (DomainAgent) and the personal agent

(LearnerAgent) that may negotiate beliefs about

knowledge. If the student argumentation skill is not

enough to convince the diagnostic application, the

personal agent asks for help of a pedagogical agent

(MediatorAgent), able along the negotiation process.

This pedagogical agent could search and contact a

specific agent from the application domain (in order

to make support material available to the user) or

even contact an expert user to provide a description

of the problem and to give help to the learner.

Once the user’s objective and cognitive

resources status (the Bayesian model of the case

study proposed and the log of the user actions) are

diagnosed, the LearnerAgent decides how to help

the user to reach his/her objectives. Let’s suppose

that the LearnerAgent finds that the user it

represents is trying to reach an objective (modelling

a case study) using an incorrect tactics, for example,

a cyclic graph (this means that the user lacks some

resource, in this case, knowledge about the Bayesian

network definition). The LearnerAgent may decide

to teach the student using the pedagogical support

the MediatorAgent has suggested.

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The MediatorAgent could send a message to the

DomainAgent, or to the intelligent search of web-

based material agent, or can suggest a visit to a FAQ

directory (or to a discussion forum) or contacting the

personal agent of other user to ask for human help.

The LearnerAgent decides to ask for pedagogic

advice about which is the best pedagogic strategy.

For that end, it contacts the MediatorAgent that

helps in the pedagogic negotiation process between

the user and the DomainAgent.

In AMPLIA environment, besides real students,

there are the following artificial agents that are

essential to the pedagogic negotiation:

• LearnerAgent, responsible for representing the

student within the system, and acting in favour

of its interests. This agent undertakes the

student's role in the setting that is being

discussed up to now.

• DomainAgent, responsible for representing the

expert in the domain. This agent has the

knowledge the student must study.

• MediatorAgent, responsible for mediating the

teaching and learning process between the

Domain agent and Learner agent. This agent

partially undertakes the teacher's role, within

the scenario that has been being discussed.

In terms of pedagogical negotiation the

LearnerAgent represents the student, gathering all

concrete evidences about the status of its learning

process, registering the self-confidence level

declared and trying to infer its confidence with

relation to other agents of the system.

The DomainAgent and MediatorAgent share the

teacher's role. The DomainAgent incorporates the

knowledge base on the theme to be studied and,

therefore, it has the higher confidence level about

the topic. The MediatorAgent incorporates

negotiation mechanisms needed to solve conflicts of

this process, that is, teaching pedagogical strategies

that can be used in pedagogical negotiation.

There are two major aspects in the

accomplishment of such multi-agent system: (1)

implementing the interaction between student and

LearnerAgent, and (2) implementing the interaction

among other agents.

2.1 The Interaction between the

Student and the LearnerAgent

In AMPLIA, the student makes its argumentation by

modelling a Bayesian network. (Rolf & Magnusson,

2002) affirms that the practice and teaching of

reasoning and argumentation are adequate for the

use of schemas. The student's manner of expressing

him/herself occur through a graphic editor, where

arguments are formed by nodes and links among

them. Rolf & Magnusson classifies three levels of

software that can express arguments through graphic

structures. This classification takes into account the

calculus used. Belvedere system, for example, does

not have any calculus, constituting the first level;

Athenas and Reason!Able systems are in an

intermediate level, having some numerical naming

and rules for filtering the best arguments. AMPLIA

is at the third level, having an advanced

mathematical theory, based on Bayesian inference.

All these systems, except AMPLIA, do not present a

mediator in the learning process.

The procedures analysis of the student’s during

the network building is also a function of the

LearnerAgent, which infers the credibility

(expectation) that the system has on the student. A

high expectation or credibility is computed, if the

student effectively demonstrates autonomy and

confidence in his/her actions.

Three credibility degrees are defined.

• Low Credit: attributed in indecision and low

confidence cases, for example, when the

student constantly erases and puts nodes again.

• Medium Credit: when the student uses the

system help spontaneously, or when he/she

builds a network model which is less efficient

than the previous one.

• High Credit: when the student builds his/her

model autonomously, using even resources out

of the environment, as for example, web-search

mechanisms.

The credibility that the LearnerAgent infers is

translated, by the MediatorAgent point of view, with

more or less autonomy to the student, not directly

interfering in the strategy, but in the tactics that

leads the student to a more active or passive action.

2.2 The Interaction among Agents

The negotiation process follows the following

protocol.

(1) The DomainAgent presents a case study for the

student. The LearnerAgent only takes notes on

the example and passes it to the student.

(2) The DomainAgent made available the case

studies from where the student models the

diagnostic hypothesis. The student models the

diagnostic hypothesis, and sends (through the

LearnerAgent) his/her model to the

DomainAgent to be evaluated. This evaluation

refers to the importance of each area in the

model (trigger, essential, complementary...).

(3) Based on the result of the DomainAgent analysis

and on the confidence level (declared by the

student) supplied by the LearnerAgent, the

MediatorAgent chooses the best pedagogic

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281

strategy, activating the tactics suitable to a

particular situation.

(4) The student evaluates the message received from

the MediatorAgent and tries to discuss the topics

which considers important, by changing its

model. At this stage, the student may also decide

to give up the learning process.

The AMPLIA's negotiation process occurs in a

dynamic choice of strategies. The parameters

considered are linked to student's beliefs, to the

evaluation carried out by the DomainAgent and to

the observations registered by the LearnerAgent.

In this negotiation process, both the student and

the DomainAgent have the possibility of giving up

the interaction. The DomainAgent only leaves the

negotiation process when the student presents a

solution, whose performance is equivalent or better

than its model. The DomainAgent may come to

accept the student's modelling, although it does not

correspond exactly to its model, but the student uses

the arguments to solve the study case problem

presented to him.

3 PEDAGOGICAL NEGOTIATION

Pedagogical negotiation requires we know its key

role along a teaching-learning process, namely

which are the final objectives of this process and

how negotiation may help to reach them.

In traditional negotiation processes, based on the

Economic Theory, the result is the maximisation of

gains expected by the agents. We expect to find a

solution that maximises gains of agents in relation to

all possibilities of solutions to the current

negotiation. Gains are measured through a utility

function known by the agents The problem lies

exactly on the presupposition that an agent knows

how to determine the utility in a given situation, as

well as in situations derived from its actions

(Sandholm, 1999). This does not happen in a

teaching and learning process, because, it is difficult

to realise how a student generates all his/her

preferences.

The same is valid for the teacher. Simply, it is

not reasonable to presuppose that the teacher has

total knowledge on all situations that may happen in

a teaching-learning process. Students can present

results so that, even they are not in accordance with

the teacher's expectations, they can be perfectly

acceptable in terms of teaching objectives intended.

We observe that results of a pedagogical

negotiation should be related to the final objectives

of teaching-learning process, as well as the concept

of preference or utility for an agent are not enough

to characterise results expected in the pedagogical

negotiation. As a solution for these problems, we

adopted some simplifying presuppositions, based on

the common sense, with which we expect to

contribute to elicit more this issue.

A primarily presupposition is not to approach the

teaching-learning process directly as a knowledge

transference process. Characterising the process in

this way implies to consider the need for solving

classical epistemological issues that do not have

concrete answers: what is knowledge? How could it

be transferred to another person? How to measure a

person's knowledge? To this claim we add the

discourse of pedagogical models supported in the

Piaget's genetic epistemology (Piaget, 1970), where

the subject builds knowledge through interactions.

We will use the notion of confidence that an

agent can have in relation to another (or about itself)

analysed aiming at maximising this relationship as

the process evolves. We will adopt the notion of

confidence based on the expectation of future

behaviour of an agent in relation to another (or to

itself). The idea is that the "expectation of future

behaviour" may be evaluated more precisely than

the perception of "how much this agent knows on

theme".

Considering the teacher-student learning

scenario, a first step in the characterisation of the

teaching-learning process is to attribute distinct

objectives for each role. In a constructivist point of

view, the teacher role is to mediate the interaction

process in such a way that the student can explore

and ask questions about facts, think about them and

formulate hypotheses. In this case, certification can

be translated through the confidence level that the

teacher has on the student, when he/she is in known,

and mainly new, situations, where knowledge

assimilated and already set or new reasoning and

hypotheses are required.

Relating to the teacher's role, as a mediator of

the teaching and learning process, it should be

considered not only the relationship of confidence

between teacher and student, but it is required an

inverse analysis, that is, the relationship of

confidence between student and teacher. Thus, there

are two important characteristics to outline in the

student's behaviour. (1) The student is confident on

the teacher's appraisal capacities during the

development of contents. This statement does not

imply necessarily that the confidence level is

complete, i.e., that the student should blindly trust

the teacher. What is said is that there should be a

reasonable level of confidence, and that it should be

undertaken so that the teaching and learning process

can be accomplished. (2) Definition of what the

student expects as a result of the teaching and

learning process. The simplifying presuppositions is

to undertake that the student expects to reach a level

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of knowledge that makes possible to understand and

solve situations or problems within the area or

discipline that is being studied. The point is not

exactly what the student intends, but how we could

have concrete evidences that this objective was

reached.

The teaching-learning process could be seen as a

way of reducing the initial asymmetry of the

confidence relation between teacher and student and

the topic studied, maximising the confidence of all.

Putting this into a scheme:

• Beginning of the teaching and learning process:

Teacher:

(IP.1) High level of confidence in the capacity of

value the topic approached.

(IP.2) Low level of confidence in the student's

capacities to deal with this topic.

Student:

(IA.1) Low level of confidence in the capacity of

value the topic approached

(IA.2) High level of confidence in the capacity of

value the topic approached.

• End (expected) of the teaching and learning

process:

Teacher:

(FP.1) High level of confidence in the capacity of

value the topic approached

(FP.2) High level of confidence in the capacity of

value the topic approached.

Student:

(FA.1) High level of confidence in the capacity of

value the topic approached.

(FA.2) High level of confidence in the capacity of

value the topic approached.

Conditions (IP.1) and (FP.1), as well as (IA.2)

and (FA.2) should not change, being only bases for

an adequate beginning, development and end of the

process. The effective result of the process would be

the increase in the confidence level of the teacher in

the student: (IP.2) for (FP.2), and of the student in

himself/herself: (IA.1) for (FA.1).

3.1 Formalising these objectives

There are several ways of analysing the confidence

among agents, and it is possible to characterise

several important aspects of this notion. According

to (Castelfranchi & Falconi, 1998), trust relations

among agents depend on mental states and,

therefore, only agents with mental attitudes (beliefs,

desires, intentions, etc.) can trust one another. We

assume a weaker notion of trust towards an

expectation of future actions of an agent, similar to

the confidence notion defined by (Fischer &

Ghidini, 2002). Their notion of confidence is based

on a modal logic of beliefs and abilities, which is

intuitive, according to the idea that we trust

somebody when we know how this person will

behave in certain situations.

Some comments should be made, comparing

modelling outlined above for the teaching and

learning process and the formal notion of confidence

defined in the work by (Fischer & Ghidini, 2002),

which is given in the formula Bi ◊j ϕ. In this formal

expression, there is not space for a "level of

confidence", or the agent i believes that j will

eventually make ϕ, or not. A possible approach to

deal formally with this incongruous feature is to

undertake this kind of belief, everything or nothing,

and try to structure the belief object, formula ϕ,

splitting it into sub-formulas ϕ1, ϕ2, ..., ϕn logically

related to ϕ, in a way that ϕ1, ϕ2, ..., ϕn necessarily

imply ϕ. Another way would be to deal with

probabilities linked to a logic formula explicitly,

using, for example, the PROB(ϕ) operator, defined

in the work (Rao & Georgeff, 1991), which

attributes a probability PROB(ϕ) = α that the

formula ϕ is true in a certain possible world.

In the present work, the last approach will be

used having in mind the notorious drawbacks of

defining a generic method of structuring some

formula in terms of its most important components

(a problem similar to the knowledge structuring).

For example, supposing a scenario composed of an

agent p professor, an agent a student and a

proposition ϕ, that states the answer to be required.

When facing a questioning on the theme being

studied, we have that propositions (IP.2) and (FP.2)

may be formalised as:

(IP.2) B

PROB( ◊

ϕ ) = α

(FP.2) B

PROB( ◊

ϕ ) = β where α ≤ β.

Coefficients α and β are probabilities used to

indicate the confidence level or expectation that the

student a eventually hits the answers asked in ϕ (or

that he/she states the entire proposition ϕ complete,

which is the same). In the beginning of the teaching-

learning process, the teacher has a low expectation α

that the student gives the correct answer. After this

process, the expectation should increase to a new

coefficient β. It is important to highlight that, from

the formal point of view, effects of negotiation in a

teaching-learning process can bring two kinds of

changes in the formulas given above: they may both

change the logic proposition ϕ related to the topic

approached or change the final expectation β (or

even the α initial value) of this process.

3.2 The role of pedagogical

negotiation

Although the teaching-learning activity can be

considered a process of "equalising" confidence

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283

levels, we can not presuppose that it has a linear,

monotonic and continually increasing behaviour,

also, we can not guarantee that this process will

increase a certain confidence level step-by-step

(linear), without interruptions (monotonic) or

drawbacks (continually increasing) until it reaches

the required level. Evaluation conflicts between

teacher and student are common, and so it is needed

to adopt a negotiation process in order to solve them

through argumentation mechanisms, with the aim of

strengthening the confidence relation between

teacher and student. The expected result will be to

increase the confidence level among all agents.

Another important issue is the definition of with

teaching and learning strategy should be selected.

The present work undertakes the constructivist

approach, which is being introduced into AMPLIA

system (Seixas et al, 2002), where the student will

have an active role in the learning process and the

teacher will be the mediator and motivator of this

process proposing reflection strategies in problem

solving. The main pedagogical strategies adopted are

positive strategies turned towards student's

motivation, and not only negative ones to identify

student's "mistakes" and "problems".

3.3 A hypothetical pedagogical

negotiation process

The Figure 2 above intends to represent a

hypothetical pedagogical negotiation process, step

by step, in AMPLIA.

The vertical axis represents the confidence level

the student declares (self-confidence). (Just for

representation reasons, three confidence levels are

shown). The system understands this as the students

attitude towards the negotiation process. So, if the

student declares a high confidence, the system

interprets that the student feels him/herself very

secure and he/she doesn’t want to do meaningful

changes in the model. On the other side, in a low

confidence situation, the system believes the student

will be open to receive help, because he/she feels

secure about his/her model. So the second student

will be more ready for a negotiation process than the

first one.

The horizontal axis represents the students

network evaluation results, carried out by the

DomainAgent. The network is tested for its

qualitative and quantitative aspects and according to

it, the DomainAgent classifies the network as not

feasible (the network has cycles or not oriented

nodes), incorrect (there is an excluder node),

incomplete (absence of important nodes), feasible (it

is not the same as the specialists model, but it

satisfies the study case) or complete (it is identical

with the specialist model).

The size of the circles on the graphic represents

the credibility (expectation) the LearnerAgent infers,

based on the students actions during the network

construction process. Three credibility degrees are

defined, presented in the section 2.1.

The graphic represents five steps of a negotiation

process. At first, the student has informed a low

confidence in his/her model. This model was

evaluated as incorrect, and the credibility the system

has inferred is medium. The negotiation process is

directed to the network construction and to the

students self confidence. Now, in the second step,

the student declares a medium self confidence level,

and the model, although it is not incorrect, is not

feasible. The credibility the system has inferred

remains as a medium value. The negotiation process

is once more directed to the network construction

and to the students confidence. After that, now being

the third step, the student declares his/her confidence

as medium level, the network is incomplete and the

credibility the system has inferred is very low. So

the negotiation process is carried out, involving the

network construction, the students self-confidence

and the students autonomy too. At the fourth step,

the student still states medium confidence in his/her

network, but it is evaluated as feasible and the

system infers a high credibility. At this moment, the

negotiation process is focused on the student’s self

confidence, which has to be enlarged. At the fifth

and last step, the student’s confidence is high, the

network is evaluated as feasible, and the system has

a high credibility in the student’s actions. At this

moment the system considers the negotiation

process is finished, because the confidence degrees

between the student and the system were levelled,

the student’s model is feasible and the system

believes the student can act autonomously.

AMPLIA

0123456

Network

Confidence

Credibilidade

momento1

momento2

momento3

momento4

momento5

Credibility

Step

Figure 2: Hypothetical pedagogical negotiation process

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4 FINAL CONSIDERATIONS

In intelligent teaching and learning environments

pedagogical agents take different kind of roles.

These agents adapt the environment to the needs of

the student, based on the student profile that is

composed by information provided by the student or

inferred by the agent, as in (Souto et al., 2002).

Pedagogical agents can also assume the role of

“tutors” that, based on the observation of the student

activity, show hints or make suggestions to the

student, attempting to conduce his/her actions

toward the solution of some problem, like ADELE

(Johnson & Shaw, 1997), ANDES (Gertner et al

1998) or SE-Coach (Conati, & VanLehn, 2000).

In AMPLIA, the pedagogical agent works like a

mediator in the knowledge construction process,

acting directly in the interaction between subject and

object, through a “dialogical” relationship that can

be called “negotiation”. Negotiation is directly

linked to the pedagogical way of how to make a

student to develop his diagnostic reasoning, refining

his/her learning ability

The set of ideas described until now, show our

point of view of how to analyse, interpret and model

the complex phenomena that occurs in the teaching-

learning process, at least in some very restricted

domains of graduate level medical education. The

validation of these ideas and the generalisation of

them to new educational domains or other areas can

only occur with time and with real world application

and testing. So we need to set-up experimental

evaluation courses and effectively use AMPLIA in

these courses.

We have taken a two-level evolutionary strategy

to project and build the AMPLIA environment. In

the basic level, we first develop prototypes for our

three types of agents, then we specify an initial

model for their communication and finally

implement the communication tasks in each kind of

agent, extending their abilities to cope with new

needs derived from communication (that is create

new prototypes of the agents). At this point we can

return to the specification of the communication

modelling adding new elements to it and returning to

the prototyping phase or we can proceed to the next

level. The following level takes place in a real

teaching environment, that is, in this level we

proceed with one experimental course, evaluating at

the same time the positive (and negative) effects of

the AMPLIA environment and taking note on any

lack of feature or resource of the environment and

also trying to figure out how it can be improved.

Currently we are in the final phase of

development of the individual agents and already

have made the initial modelling of the

communication. Indeed we are starting to implement

the communication acts in some of the agents. To

this purpose we have assumed a strong commitment

to current standards of communication languages

and protocols between agents, that is, we are

committed to restrict the communication of our

agents to FIPA standards, provided that they exist to

the application we need. For example, currently all

communication is carried by standard query-ref,

query-if, request, propose and similar acts, following

standard query, request, propose and other

interaction protocols. The content language adopted

to exchange information and knowledge between

agents is FIPA-SL.

However, we already have detected an important

problem in FIPA content language standard. Simply

there is no support to represent probabilistic

information. So as it can be easily seem in sections 2

and 3 our agents do not only exchange probabilistic

information but they need to negotiate, argue and

discuss intentionally over probabilistic propositions.

To solve this problem we have taken an pragmatic

approach, by extending FIPA-SL to support

Bayesian networks contents and incorporating an

operational semantics to these inserted probabilistic

propositions in the agents.

To easily integrate AMPLIA with current

Internet infrastructure, we have chosen to use only

HTTP protocol to transport FIPA communicative

acts. This kind of transport solution is not only

completely sanctioned by FIPA, but has the

beneficial effect of allowing the communication

between agents pass through firewalls, filters,

routers and other network devices, which is a

important advantage when we start to use AMPLIA

in a WAN environment as distance learning tool.

We intend to start to evaluate the AMPLIA with

experimental courses in the second quarter of 2004.

The first courses will occur in a LAN environment,

to allow the direct observation of the effects and

results of the application of the environment on the

subjects (students) and the fine-tuning of the

AMPLIA. Only after these first local and carefully

observed tests we have the intention to evolve our

environment to work in a WAN (distance learning)

context.

ACKNOWLEDGEMENTS

The authors gratefully acknowledge the Brazilian

agencies CAPES and CNPq for the partial support to

this research project.

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