Olivier Carton
email: olivier.carton@liafa.jussieu.fr

Olivier Finkel
email: olivier.finkel@ens-lyon.fr

Pierre Simonnet
email: simonnet@univ-corse.fr.

On the Continuity Set of an omega Rational Function

Keywords: 1991 Mathematics Subject Classification. 68Q05, 68Q45, 03D05. LIP Research Report RR 2008-04 Infinitary rational relations, omega rational functions, topology, points of continuity, decision problems, omega rational languages, omega context-free languages

In this paper, we study the continuity of rational functions realized by Büchi finite state transducers. It has been shown by Prieur that it can be decided whether such a function is continuous. We prove here that surprisingly, it cannot be decided whether such a function f has at least one point of continuity and that its continuity set C(f ) cannot be computed.

In the case of a synchronous rational function, we show that its continuity set is rational and that it can be computed. Furthermore we prove that any rational Π 0 2 -subset of Σ ω for some alphabet Σ is the continuity set C(f ) of an ω-rational synchronous function f defined on Σ ω .

Introduction

Acceptance of infinite words by finite automata was firstly considered in the sixties by Büchi in order to study decidability of the monadic second order theory of one successor over the integers [START_REF] Büchi | On a Decision Method in Restricted Second Order Arithmetic[END_REF]. Then the so called ω-regular languages have been intensively studied and many applications have been found. We refer the reader to [START_REF] Thomas | Automata on Infinite Objects[END_REF][START_REF] Staiger | ω-Languages, Chapter of the Handbook of Formal languages[END_REF][START_REF] Perrin | Infinite Words, Automata, Semigroups, Logic and Games[END_REF] for many results and references.

Gire and Nivat studied infinitary rational relations accepted by Büchi transducers in [START_REF] Gire | Relations Rationnelles Infinitaires[END_REF]GN84]. Infinitary rational relations are subsets of Σ ω × Γ ω , where Σ and Γ are finite alphabets, which are accepted by 2-tape finite Büchi automata with two asynchronous reading heads. They have been much studied, in particular in connection with the rational functions they may define, see for example [START_REF] Choffrut | Uniformization of Rational Relations, Jewels are Forever[END_REF][START_REF] Béal | Squaring Transducers: An Efficient Procedure for Deciding Functionality and Sequentiality[END_REF][START_REF] Simonnet | Automates et Théorie Descriptive[END_REF][START_REF] Staiger | ω-Languages, Chapter of the Handbook of Formal languages[END_REF][START_REF] Prieur | Fonctions Rationnelles de Mots Infinis et Continuité[END_REF].

Gire proved in [START_REF] Gire | Une Extension aux Mots Infinis de la Notion de Transduction Rationnelle[END_REF] that one can decide whether an infinitary rational relation R ⊆ Σ ω × Γ ω recognized by a given Büchi transducer T is the graph of a function f : Σ ω → Γ ω , (respectively, is the graph of a function f : Σ ω → Γ ω recognized by a synchronous Büchi transducer). Such a function is called an ω-rational function (respectively, a synchronous ω-rational function).

The continuity of ω-rational functions is an important issue since it is related to many aspects. Let us mention two of them. First, sequential functions that may be realized by input deterministic automata are continuous but the converse is not true. Second, continuous functions define a reduction between subsets of a topological space that yields a hierarchy called the Wadge hierarchy. The restriction of this hierarchy to rational sets gives the Wagner hierarchy.

This paper is focused on the continuity sets of rational functions. Prieur proved in [START_REF] Prieur | Fonctions Rationnelles de Mots Infinis et Continuité[END_REF][START_REF] Prieur | How to Decide Continuity of Rational Functions on Infinite Words[END_REF] that it can be decided whether a given ω-rational function is continuous. This means that it can be decided whether the continuity set is equal to the domain of the function. We show however that it cannot be decided whether a rational function has at least one point of continuity. We show that in general the continuity set of a rational function is not rational and even not context-free. Furthermore, we prove that it cannot be decided whether this continuity set is rational.

We pursue this study with synchronous rational functions. These functions are accepted by Büchi transducers in which the two heads move synchronously. Contrary to the general case, the continuity set of synchronous rational function is always rational and it can be effectively computed. We also give a characterization of continuity sets of synchronous functions. It is well known that a continuity set is a Π 0 2 -set. We prove conversely that any rational Π 0 2 -set is the continuity set of some synchronous rational function.

The paper is organized as follows. In section 2 we recall the notions of infinitary rational relation, of ω-rational function, of synchronous or asynchronous ω-rational function, of topology and continuity; we recall also some recent results on the topological complexity of infinitary rational relations. In section 3 we study the continuity sets of ω-rational functions in the general case, stating some undecidability results. Finally we study the case of synchronous ω-rational functions in section 4.

2.

Recall on ω-rational functions and topology 2.1. Infinitary rational relations and ω-rational functions Let Σ be a finite alphabet whose elements are called letters. A non-empty finite word over Σ is a finite sequence of letters: x = a 1 a 2 . . . a n where ∀i ∈ [1; n] a i ∈ Σ. We shall denote x(i) = a i the i th letter of x and x[i] = x(1) . . . x(i) for i ≤ n. The length of x is |x| = n. The empty word will be denoted by λ and has 0 letter. Its length is 0. The set of finite words over Σ is denoted Σ ⋆ . Σ + = Σ ⋆ -{λ} is the set of non empty words over Σ. A (finitary) language L over Σ is a subset of Σ ⋆ . The usual concatenation product of u and v will be denoted by u.v or just uv. For V ⊆ Σ ⋆ , we denote by

V ⋆ the set R = {v 1 . . . v n | n ∈ N and ∀i ∈ [1; n] v i ∈ V }.
The first infinite ordinal is ω. An ω-word over Σ is an ω -sequence a 1 a 2 . . . a n . . ., where for all integers i ≥ 1 a i ∈ Σ. When σ is an ω-word over Σ, we write σ = σ(1)σ(2) . . . σ(n) . . . and σ[n] = σ(1)σ(2) . . . σ(n) the finite word of length n, prefix of σ. The set of ω-words over the alphabet Σ is denoted by Σ ω . An ω-language over an alphabet Σ is a subset of Σ ω . For

V ⊆ Σ ⋆ , V ω = {σ = u 1 . . . u n . . . ∈ Σ ω | ∀i ≥ 1 u i ∈ V } is the ω-power of V .
The concatenation product is extended to the product of a finite word u and an ω-word v: the infinite word u.v is then the ω-word such that:

(u.v)(k) = u(k) if k ≤ |u| , and (u.v)(k) = v(k -|u|) if k > |u|.
We assume the reader to be familiar with the theory of formal languages and of ω-regular languages, see [Büc62, Tho90, EH93, Sta97, PP04] for many results and references. We recall that ω-regular languages form the class of ω-languages accepted by finite automata with a Büchi acceptance condition and this class, denoted by RAT , is the omega Kleene closure of the class of regular finitary languages.

We are going now to recall the notion of infinitary rational relation which extends the notion of ω-regular language, via definition by Büchi transducers: Definition 2.1. A Büchi transducer is a sextuple T = (K, Σ, Γ, ∆, q 0 , F ), where K is a finite set of states, Σ and Γ are finite sets called the input and the output alphabets, ∆ is a finite subset of K × Σ ⋆ × Γ ⋆ × K called the set of transitions, q 0 is the initial state, and F ⊆ K is the set of accepting states. A computation C of the transducer T is an infinite sequence of consecutive transitions (q 0 , u 1 , v 1 , q 1 ), (q 1 , u 2 , v 2 , q 2 ), . . . (q i-1 , u i , v i , q i ), (q i , u i+1 , v i+1 , q i+1 ), . . . The computation is said to be successful iff there exists a final state q f ∈ F and infinitely many integers i ≥ 0 such that q i = q f . The input word and output word of the computation are respectively u = u 1 .u 2 .u 3 . . . and v = v 1 .v 2 .v 3 . . . The input and the output words may be finite or infinite. The infinitary rational relation R(T ) ⊆ Σ ω × Γ ω accepted by the Büchi transducer T is the set of couples (u, v) ∈ Σ ω × Γ ω such that u and v are the input and the output words of some successful computation C of T . The set of infinitary rational relations will be denoted RAT 2 .

If R(T ) ⊆ Σ ω × Γ ω is an infinitary rational relation recognized by the Büchi transducer T then we denote Dom(R(T )

) = {u ∈ Σ ω | ∃v ∈ Γ ω (u, v) ∈ R(T )} and Im(R(T )) = {v ∈ Γ ω | ∃u ∈ Σ ω (u, v) ∈ R(T )}.
It is well known that, for each infinitary rational relation R(T ) ⊆ Σ ω × Γ ω , the sets Dom(R(T )) and Im(R(T )) are regular ω-languages.

The Büchi transducer T = (K, Σ, Γ, ∆, q 0 , F ) is said to be synchronous if the set of transitions ∆ is a finite subset of K × Σ × Γ × K, i.e. if each transition is labelled with a pair (a, b) ∈ Σ × Γ. An infinitary rational relation recognized by a synchronous Büchi transducer is in fact an ω-language over the product alphabet Σ×Γ which is accepted by a Büchi automaton. It is called a synchronous infinitary rational relation. An infinitary rational relation is said to be asynchronous if it can not be recognized by any synchronous Büchi transducer. Recall now the following undecidability result of C. Frougny and J. Sakarovitch.

Theorem 2.2 ( [FS93]

). One cannot decide whether a given infinitary rational relation is synchronous.

A Büchi transducer T = (K, Σ, Γ, ∆, q 0 , F ) is said to be functional if for each u ∈ Dom(R(T )) there is a unique v ∈ Im(R(T )) such that (u, v) ∈ R(T ). The infinitary rational relation recognized by T is then a functional relation and it defines an ω-rational (partial) function f T : Dom(R(T )) ⊆ Σ ω → Γ ω by: for each u ∈ Dom(R(T )), f T (u) is the unique v ∈ Γ ω such that (u, v) ∈ R(T ). An ω-rational (partial) function f : Σ ω → Γ ω is said to be synchronous if there is a synchronous Büchi transducer T such that f = f T . An ω-rational (partial) function f : Σ ω → Γ ω is said to be asynchronous if there is no synchronous Büchi transducer T such that f = f T .

Theorem 2.3 ( [Gir83]

). One can decide whether an infinitary rational relation recognized by a given Büchi transducer T is a functional infinitary rational relation (respectively, a synchronous functional infinitary rational relation).

Topology

We assume the reader to be familiar with basic notions of topology which may be found in [Mos80, Kec95, LT94, Sta97, PP04]. There is a natural metric on the set Σ ω of infinite words over a finite alphabet Σ which is called the prefix metric and defined as follows. For u, v ∈ Σ ω and u v) where l pref (u,v) is the least integer n such that the (n + 1) th letter of u is different from the (n + 1) th letter of v. This metric induces on Σ ω the usual Cantor topology for which open subsets of Σ ω are in the form W.Σ ω , where W ⊆ Σ ⋆ . Recall that a set L ⊆ Σ ω is a closed set iff its complement Σ ω -L is an open set. We define now the next classes of the Borel Hierarchy:

= v let d(u, v) = 2 -l pref (u,
Definition 2.4. The classes Σ 0 n and Π 0 n of the Borel Hierarchy on the topological space Σ ω are defined as follows:

-

Σ 0 1 is the class of open sets of Σ ω . -Π 0
1 is the class of closed sets of Σ ω . And for any integer n ≥ 1:

-

Σ 0 n+1 is the class of countable unions of Π 0 n -subsets of Σ ω . -Π 0
n+1 is the class of countable intersections of Σ 0 n -subsets of Σ ω . The Borel Hierarchy is also defined for transfinite levels: The classes Σ 0 α and Π 0 α , for a non-null countable ordinal α, are defined in the following way.

-

Σ 0 α is the class of countable unions of subsets of Σ ω in ∪ γ<α Π 0 γ . -Π 0
α is the class of countable intersections of subsets of Σ ω in ∪ γ<α Σ 0 γ . Let us recall the characterization of rational Π 0 2 -subsets of Σ ω , due to Landweber [START_REF] Landweber | Decision Problems for ω-Automata[END_REF]. This characterization will be used in the proof that any rational Π 0 2 -subset is the continuity set of some rational synchronous function. Theorem 2.5 (Landweber). A rational subset of Σ ω is Π 0 2 if and only if it can be recognized by a deterministic Büchi automaton.

There are some subsets of the Cantor set, (hence also of the topological space Σ ω , for a finite alphabet Σ having at least two elements) which are not Borel sets. There exists another hierarchy beyond the Borel hierarchy, called the projective hierarchy. The first class of the projective hierarchy is the class Σ 1 1 of analytic sets. A set A ⊆ Σ ω is analytic iff there exists a Borel set B ⊆ (Σ × Y ) ω , with Y a finite alphabet, such that x ∈ A ↔ ∃y ∈ Y ω such that (x, y) ∈ B, where (x, y) ∈ (Σ × Y ) ω is defined by: (x, y)(i) = (x(i), y(i)) for all integers i ≥ 1.

Remark 2.6. An infinitary rational relation is a subset of Σ ω × Γ ω for two finite alphabets Σ and Γ. One can also consider that it is an ω-language over the finite alphabet Σ × Γ. If (u, v) ∈ Σ ω × Γ ω , one can consider this couple of infinite words as a single infinite word (u(1), v(1)).(u(2), v(2)).(u(3), v(3)) . . . over the alphabet Σ × Γ. Since the set (Σ × Γ) ω of infinite words over the finite alphabet Σ × Γ is naturally equipped with the Cantor topology, it is natural to investigate the topological complexity of infinitary rational relations as ω-languages, and to locate them with regard to the Borel and projective hierarchies. Every infinitary rational relation is an analytic set and there exist some Σ 1 1 -complete, hence non-Borel, infinitary rational relations [START_REF] Finkel | On the Topological Complexity of Infinitary Rational Relations[END_REF]. The second author has recently proved the following very surprising result: infinitary rational relations have the same topological complexity as ω-languages accepted by Büchi Turing machines [START_REF] Finkel | Borel Ranks and Wadge Degrees of Omega Context Free Languages[END_REF][START_REF] Finkel | On the Accepting Power of 2-Tape Büchi Automata[END_REF]. In particular, for every recursive non-null ordinal α there exist some Π 0 αcomplete and some Σ 0 α -complete infinitary rational relations, and the supremum of the set of Borel ranks of infinitary rational relations is the ordinal γ 1 2 . This ordinal is defined by A.S. Kechris, D. Marker, and R.L. Sami in [START_REF] Kechris | 1 1 Borel Sets[END_REF] and it is proved to be strictly greater than the ordinal δ 1 2 which is the first non ∆ 1 2 ordinal. Thus the ordinal γ 1 2 is also strictly greater than the first non-recursive ordinal ω CK 1 , usually called the Church-kleene ordinal. Notice that amazingly the exact value of the ordinal γ 1 2 may depend on axioms of set theory, see [START_REF] Kechris | 1 1 Borel Sets[END_REF][START_REF] Finkel | Borel Ranks and Wadge Degrees of Omega Context Free Languages[END_REF]. Remark 2.7. Infinitary rational relations recognized by synchronous Büchi transducers are regular ω-languages thus they are boolean combinations of Π 0 2 -sets hence ∆ 0 3 -sets [START_REF] Perrin | Infinite Words, Automata, Semigroups, Logic and Games[END_REF]. So we can see that there is a great difference between the cases of synchronous and of asynchronous infinitary rational relations. We shall see in the sequel that these two cases are also very different when we investigate the continuity sets of ω-rational functions.

Continuity

We have already seen that the Cantor topology of a space Σ ω can be defined by a distance d. We recall that a function f :

Dom(f ) ⊆ Σ ω → Γ ω , whose domain is Dom(f ), is said to be continuous at point x ∈ Dom(f ) if : ∀n ≥ 1 ∃k ≥ 1 ∀y ∈ Dom(f ) [ d(x, y) < 2 -k ⇒ d(f (x), f (y)) < 2 -n ]
The function f is said to be continuous if it is continuous at every point x ∈ Σ ω . The continuity set C(f ) of the function f is the set of points of continuity of f . Recall that if X is a subset of Σ ω , it is also a topological space whose topology is induced by the topology of Σ ω . Open sets of X are traces on X of open sets of Σ ω and the same result holds for closed sets. Then one can easily show by induction that for every integer n ≥ 1, Π 0 n -subsets (resp. Σ 0 n -subsets) of X are traces on X of Π 0 n -subsets (resp. Σ 0 n -subsets) of Σ ω , i.e. are intersections with X of Π 0 n -subsets (resp. Σ 0 n -subsets) of Σ ω . We recall now the following well known result.

Theorem 2.8 (see [START_REF] Kechris | Classical Descriptive Set Theory[END_REF]). Let f be a function from Dom(f ) ⊆ Σ ω into Γ ω . Then the continuity set C(f ) of f is always a Π 0 2 -subset of Dom(f ). Proof. Let f be a function from Dom(f ) ⊆ Σ ω into Γ ω . For some integers n, k ≥ 1, we consider the set

X k,n = {x ∈ Dom(f ) | ∀y ∈ Dom(f ) [ d(x, y) < 2 -k ⇒ d(f (x), f (y)) < 2 -n ]}
We know, from the definition of the distance d, that for two ω-words x and y over Σ, the inequality d(x, y) < 2 -k simply means that x and y have the same (k + 1) first letters. Then it is easy to see that the set X k,n is an open subset of Dom(f ), because for each x ∈ X k,n , the set X k,n contains the open ball (in Dom(f )) of all y ∈ Dom(f ) such that d(x, y) < 2 -k .

By union we can infer that X n = k≥1 X k,n is an open subset of Dom(f ) and then the countable intersection

C(f ) = n≥1 X n is a Π 0 2 -subset of Dom(f ).
In the sequel we are going to investigate the continuity sets of ω-rational functions, firstly in the general case and next in the case of synchronous ω-rational functions.

Continuity set of ω-rational functions

Recall that C. Prieur proved the following result.

Theorem 3.1 ( [Pri00,Pri01]). One can decide whether a given ω-rational function is continuous.

Prieur showed that the closure (in the topological sense) of the graph of a rational relation is still a rational relation that can be effectively computed. From this closure, it is quite easy to decide whether a given ω-rational function is continuous.

So one can decide whether the continuity set of an ω-rational function f is equal to its domain Dom(f ). We shall prove below some undecidability results, using the undecidability of the Post Correspondence Problem which we now recall.

Theorem 3.2 (Post). Let Γ be an alphabet having at least two elements . Then it is undecidable to determine, for arbitrary n-tuples (u 1 , . . . , u n ) and (v 1 , . . . , v n ) of non-empty words in Γ ⋆ , whether there exists a non-empty sequence of indices i 1 , . . . , i k such that u i1 . . .

u i k = v i1 . . . v i k .
We now state our first undecidability result.

Theorem 3.3. One cannot decide whether the continuity set C(f ) of a given ω-rational function f is empty.

Proof. Let Γ be an alphabet having at least two elements and (u 1 , . . . , u n ) and (v 1 , . . . , v n ) be two sequences of n non-empty words in Γ ⋆ . Let A = {a, b} and

C = {c 1 , . . . , c n } such that A ∩ C = ∅ and A ∩ Γ = ∅.
We define the ω-rational function f of domain Dom(f ) = C + .A ω by:

• f (x) = u i1 . . . u i k .z if x = c i1 . . . c i k .z and z ∈ (A ⋆ .a) ω . • f (x) = v i1 . . . v i k .z if x = c i1 . . . c i k .z and z ∈ A ⋆ .b ω . Notice that (A ⋆ .a) ω
is simply the set of ω-words over the alphabet A having an infinite number of occurrences of the letter a. And A ⋆ .b ω is the complement of (A ⋆ .a) ω in A ω , i.e. it is the set of ω-words over the alphabet A containing only a finite number of letters a.

The two ω-languages (A ⋆ .a) ω and A ⋆ .b ω are ω-regular, so they are accepted by Büchi automata. It is then easy to see that the function f is ω-rational and we can construct a Büchi transducer T that accepts the graph of f . We are going to prove firstly that if x = c i1 . . . c i k .z ∈ C + .A ω is a point of continuity of the function f then the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ) would have a solution i 1 , . . . , i k such that u i1 . . .

u i k = v i1 . . . v i k .
We distinguish two cases. First Case. Assume firstly that z ∈ (A ⋆ .a) ω . Then by definition of f it holds that f (x) = u i1 . . . u i k .z. Notice that there is a sequence of elements z n ∈ A ⋆ .b ω , n ≥ 1, such that the sequence (z n ) n≥1 is convergent and lim(z n ) = z. This is due to the fact that A ⋆ .b ω is dense in A ω . We set x n = c i1 . . . c i k .z n . So we have also lim

(x n ) = x. By definition of f , it holds that f (x n ) = f (c i1 . . . c i k .z n ) = v i1 . . . v i k .z n . If x = c i1 . . . c i k .z is a point of continuity of f then we must have lim(f (x n )) = f (x) = u i1 . . . u i k .z. But f (x n ) = v i1 . . . v i k .z n converges to v i1 . . . v i k .z.
Thus this would imply that u i1 . . . u i k = v i1 . . . v i k and the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ) would have a solution. Second Case. Assume now that z ∈ A ⋆ .b ω . Notice that (A ⋆ .a) ω is also dense in A ω . Then reasoning as in the case of z ∈ (A ⋆ .a) ω , we can prove that if x = c i1 . . . c i k .z is a point of continuity of f then u i1 . . . u i k = v i1 . . . v i k so the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ) would have a solution.

Conversely assume that the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ) has a solution, i.e. a non-empty sequence of indices i 1 , . . . , i k such that u i1 . . .

u i k = v i1 . . . v i k .
Consider now the function f defined above. We have:

f (c i1 . . . c i k .z) = u i1 . . . u i k .z = v i1 . . . v i k .z for every z ∈ A ω
So it is easy to see that the function f is continuous at point c i1 . . . c i k .z for every z ∈ A ω .

Finally we have proved that the function f is continuous at point c i1 . . . c i k .z, for z ∈ A ω , if and only if the non-empty sequence of indices i 1 , . . . , i k is a solution of the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ). Thus one cannot decide whether the function f has (at least) one point of continuity.

Theorem 3.4. One cannot decide whether the continuity set C(f ) of a given ωrational function f is a regular ω-language (respectively, a context-free ω-language).

Proof. We shall use a particular instance of Post Correspondence Problem. For two letters c, d, let PCP 1 be the Post Correspondence Problem of instances (t 1 , t 2 , t 3 ) and (w 1 , w 2 , w 3 ), where t 1 = c 2 , t 2 = t 3 = d and w 1 = w 2 = c, w 3 = d 2 . It is easy to see that its solutions are the sequences of indices in

{1 i .2 i .3 i | i ≥ 1} ∪ {3 i .2 i .1 i | i ≥ 1}.
In particular this language over the alphabet {1, 2, 3} is not context-free and this will be useful in the sequel. Let now Γ be an alphabet having at least two elements such that Γ ∩ {c, d} = ∅, and (u 1 , . . . , u n ) and (v 1 , . . . , v n ) be two sequences of n non-empty words in Γ ⋆ . Let PCP be the Post Correspondence Problem of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ).

Let A = {a, b} and C = {c 1 , . . . , c n } and D = {d 1 , d 2 , d 3 } be three alphabets two by two disjoints. We assume also that A ∩ {c, d} = ∅.

We define the ω-rational function f of domain Dom(f ) = C + .D + .A ω by :

• f (x) = u i1 . . . u i k .t j1 . . . t jp .z if x = c i1 . . . c i k .d j1 . . . d jp .z and z ∈ (A ⋆ .a) ω . • f (x) = v i1 . . . v i k .w j1 . . . w jp .z if x = c i1 . . . c i k .d j1 .
. . d jp .z and z ∈ A ⋆ .b ω . Reasoning as in the preceding proof and using the fact that (A ⋆ .a) ω and A ⋆ .b ω are both dense in A ω , we can prove that the function f is continuous at point x = c i1 . . . c i k .d j1 . . . d jp .z, where z ∈ A ω , if and only if the sequence i 1 , . . . , i k is a solution of the Post Correspondence Problem PCP of instances (u 1 , . . . , u n ) and (v 1 , . . . , v n ) and the sequence j 1 , . . . , j p is a solution of the Post Correspondence Problem PCP 1 . There are now two cases. First Case. The Post Correspondence Problem PCP has not any solution. Thus the function f has no points of continuity, i.e. C(f ) = ∅. Second Case. The Post Correspondence Problem PCP has at least one solution i 1 , . . . , i k . We now prove that in that case the continuity set C(f ) is not a context-free ω-language, i.e. is not accepted by any Büchi pushdown automaton. Towards a contradiction, assume on the contrary that C(f ) is a context-free ω-language. Consider now the intersection

C(f ) ∩ R where R is the regular ω- language c i1 . . . c i k .(d + 1 .d + 2 .d + 3 ).A ω .
The class CF ω of context-free ω-languages is closed under intersection with regular ω-languages, [START_REF] Staiger | ω-Languages, Chapter of the Handbook of Formal languages[END_REF], thus the language

C(f ) ∩ R would be also context-free. But C(f ) ∩ R = c i1 . . . c i k .{d i 1 .d i 2 .d i 3 | i ≥ 1}.
A ω and this ω-language is not context-free because the finitary language

{d i 1 .d i 2 .d i 3 | i ≥ 1} is not context-free. So we have proved that C(f ) is not a context-free ω-language.
In the first case C(f ) = ∅ so C(f ) is a regular hence also context-free ω-language. In the second case C(f ) is not a context-free ω-language so it is not ω-regular. But one cannot decide which case holds because one cannot decide whether the Post Correspondence Problem PCP has at least one solution i 1 , . . . , i k .

Continuity set of synchronous ω-rational functions

We have shown that for non-synchronous rational functions, the continuity set can be very complex. In this section, we show that the landscape is quite different for synchronous rational functions. Their continuity set is always rational. Furthermore we show that any Π 0 2 rational set is the continuity set of some rational function.

Theorem 4.1. Let f : A ω → B ω be a rational synchronous function. The continuity set C(f ) of f is rational.

Proof. We actually prove that the complement A ω \ C(f ) is rational. Since the inclusion C(f ) ⊆ Dom(f ) holds and the set Dom(f ) is rational, it suffices to prove that Dom(f ) \ C(f ) is rational.

Suppose that f is realized by the synchronous transducer T . Without loss of generality, it may be assumed that T is trim, that is, any state q appears in an accepting path. Let x be an element of the domain of f . We claim that f is not continuous at x if there are two infinite paths γ and γ ′ in T such that the following properties hold, i) the path γ is accepting and y = f (x).

ii) the labels of γ and γ ′ are (x, y) and (x, y ′ ) with y = y ′ . The path γ exists since x belongs to the domain of f . Remark that the path γ ′ cannot be accepting since T realizes a function. It is clear that if such a path γ ′ exists, the function f cannot be continuous at x.

Suppose that f is not continuous at x. There is a sequence (x n ) n≥0 of elements from the domain of f converging to x such that d(f (x), f (x n )) > 2 -k for some integer k. Since each x n belongs to the domain of f , there is a path γ n whose label is the pair (x n , f (x n )). Since the set of infinite paths is a compact space, it can be extracted from the sequence (x n ) n≥0 another sequence (x s(n) ) n≥0 such that the sequence (γ s(n) ) n≥0 converges to a path γ ′ . Let (x ′ , y ′ ) be the label of this path γ ′ . Since (x n ) n≥0 converges to x, x ′ is equal to x and since d(f (x), f (x n )) > 2 -k , y ′ is different from y. This proves the claim.

From the claim, it is easy to build an automaton that accepts infinite words x such that f is not continuous at x. Roughly speaking, the automaton checks whether there are two paths γ and γ ′ as above. Let T be the transducer (Q, A, B, E, q 0 , F ). We build a non deterministic Büchi automaton A. The state set of A is Q × Q × {0, 1}. The initial state is (q 0 , q 0 , 0) and the set of final states is F × Q × {1}. The set of transitions of this automaton is

G = {(p, p ′ , 0) a → (q, q ′ , 0) | ∃b ∈ B p a|b → q ∈ E and p ′ a|b → q ′ ∈ E} ∪ {(p, p ′ , 0) a → (q, q ′ , 1) | ∃b, b ′ ∈ B p a|b → q ∈ E, p ′ a|b ′ → q ′ ∈ E and b = b ′ } ∪ {(p, p ′ , 1) a → (q, q ′ , 1) | ∃b, b ′ ∈ B p a|b → q ∈ E and p ′ a|b ′ → q ′ ∈ E} Theorem 4.2.
Let X be a rational Π 0 2 subset of A ω . Then X is the continuity set C(f ) of some rational synchronous function f of domain A ω .

Proof. If A only contains one symbol a, the result is trivial since A ω only contains the infinite word a ω . We now assume that A contains at least two symbols. Let b be a distinguished symbol in A let c a new symbol not belonging to A.

We define a synchronous function f that is of the following form :

f (x) =          x if x ∈ X wc ω for some prefix w of x if x ∈ X \ X wb ω for some prefix w of x if x ∈ (A * b) ω \ X wc ω for some prefix w of x otherwise,
where w is a word precised below. By Theorem 2.5, there is a deterministic Büchi automaton A = (Q, A, E, {q 0 }, F ) accepting X. We assume that A is trim.

The function f is now defined as follows. If x belongs to X, then f (x) is equal to x. If x belongs to the closure X of X but not to X, let w be the longest prefix of x which is the label of a path in A from q 0 to a final state. Then f (x) is equal to wc ω . If x does not belong to the closure of X, let w be the longest prefix which is the label of a path in A from q 0 . Then f (x) is equal to wb ω if b occurs infinitely many times in x and it is equal to wc ω otherwise. It is easy to verify that the continuity set of f is exactly X.

We now give a synchronous transducer T realizing the function f . Let R be the set of pairs (q, a) such that there is no transition

q a → p in A. The state set of T is Q × {0} ∪ (Q \ F ) × {1} ∪ {q 1 , q 2 ,
q 3 , q 4 }. The initial state is q 0 and the set of final states is F × {0} ∪ (Q \ F ) × {1} ∪ {q 2 , q 4 }. The set of transitions is defined as follows.

G = {(p, 0) a|a → (q, 0) | p a → q ∈ E} ∪ {(p, 0) a|c → (q, 1) | p a → q ∈ E and q / ∈ F } ∪ {(p, 1) a|c → (q, 1) | p a → q ∈ E and p, q / ∈ F } ∪ {(p, 0) a|b → q 1 | (p, a) ∈ R} ∪ {(p, 0) a|c → q 3 | (p, a) ∈ R} ∪ {p a|b → q 1 | p ∈ {q 1 , q 2 } and a = b} ∪ {p b|b → q 2 | p ∈ {q 1 , q 2 }} ∪ {q 3 a|c → q 3 | a ∈ A} ∪ {p a|c → q 4 | p ∈ {q 3 , q 4 } and a = b}
Recall that a point x of a subset D of a topological space X is isolated if there is a neighborhood of x whose intersection with D is equal to {x}. Isolated points have the following property with regard to continuity. Any function from a domain D is continuous at any isolated point of D. Therefore, if X is the continuity set of some function of domain D, X must contain all isolated points of D. The following theorem states that for rational Π 0 2 sets, this condition is also sufficient.

Theorem 4.3. Let D and X be two rational subsets of A ω such that X ⊆ D.

If there exists a rational Π 0 2 -subset X ′ of A ω such that X = X ′ ∩ D, and if X contains all isolated points of D, then it is the continuity set C(f ) of some synchronous rational function f of domain D.

In the proof of Theorem 4.2, the complement of the set X has been partitioned into two dense sets. The following lemma extends this result to any rational set of infinite words.

Lemma 4.4. Let X be a rational set containing no isolated points. Then, the set X can be partitioned into two rational sets X ′ and X ′′ such that both X ′ and X ′′ are dense in X.

Proof. Let X be a rational set of infinite words with no isolated points and let A be a deterministic and trim Muller automaton accepting X. We refer the reader for instance to [START_REF] Thomas | Automata on Infinite Objects[END_REF][START_REF] Perrin | Infinite Words, Automata, Semigroups, Logic and Games[END_REF] for the definition and properties of Muller automata. From any state q, either there is no accepting path starting in q or there are at least two accepting paths with different labels starting from q.

We first consider the case where the table T of A only contains one accepting set F . Since the automaton is trim, all states of F belong to the same strongly connected component of A. We consider two cases depending on whether the set F contains all states of its connected component.

Suppose first that the state q does not belong to F but is in the same strongly connected component as F . Let X ′ and X ′′ the sets of words which respectively label an accepting path which goes an odd or an even number of times through the state q. It is clear that X ′ and X ′′ have the required property.

Suppose now that F contains all the states in its strongly connected component. Since X has no isolated point, there must be a state q of F with two outgoing edges e and e ′ . Let X ′ be the set of words which label a path of the following form. The trace of this path over the two edges e and e ′ is an infinite sequence of the form (e + e ′ ) * (ee ′ ) ω .

We now come back to the general case where the table T of A may contain several accepting sets {F 1 , . . . , F n }. Let X i be the set of words accepted by the table {F i }. Note first that if the both sets X i and X j can be partitioned into dense rational sets into X ′ i , X ′′ i , X ′ j and X ′′ j , the both sets X ′ i ∪ X ′ j and X ′′ i ∪ X ′′ j are dense in X i ∪ X j . Note also that if F i is accessible from F j , then any set dense in X i is also dense in X j and therefore in X i ∪ X j . It follows that if the set X i can be partitioned into two dense rational sets X ′ i and X ′′ i , the set X i ∪ X j can be partitioned into X ′ i ∪ X j and X ′′ i . From the previous two remarks, it suffices to partition independently each X i such that the corresponding F i is maximal for accessibility. By maximal, we mean that F i is maximal whenever if F j is accessible from F i , then F i is also accessible from F j and both sets F i and F j are in the same strongly connected component. This can be done using the method described above.

We now come to the proof of the previous theorem.

Proof. The proof is similar to the proof of Theorem 4.2 but the domain D has to be taken into account. By hypothesis there exists a rational Π 0 2 -subset X ′ of A ω such that X = X ′ ∩ D. Let A a trim and deterministic Büchi automaton accepting X ′ .

We define the function f of domain D as follows. For any x in X, f (x) is still equal to x. If x belongs to X ∩ D \ X, f (x) is equal to wc ω where w is the longest prefix of x which is the label in A of a path form the initial state to a final state.

By Lemma 4.4, the set Z = D \ X can be partitioned into two rational subsets Z 1 and Z 2 such that both Z 1 and Z 2 are dense into Z. If x belongs to D \ X, then f (x) is defined as follows. Let w be the longest prefix of x which is the label in A of a path from the initial state. Then f (x) is equal to wb ω if x ∈ Z 1 and f (x) = wc ω if x ∈ Z 2 .

The following corollary provides a complete characterization of sets of continuity of synchronous rational functions of domain D ⊆ A ω when D is the intersection of a rational Σ 0 2 -subset and of a Π 0 2 -subset of A ω . This is in particular the case if D is simply a Σ 0 2 -subset or a Π 0 2 -subset of A ω . Corollary 4.5. Let D and X be two rational subsets of A ω such that X is a Π 0 2subset of D and D = Y 1 ∩ Y 2 , where Y 1 is a rational Σ 0 2 -subset of A ω and Y 2 is a Π 0 2 -subset of A ω . If X contains all isolated points of D, then it is the continuity set C(f ) of some synchronous rational function f of domain D.

Proof. Let D and X satisfying the hypotheses of the corollary.

Assume firstly that D = Y 1 is a Σ 0 2 -subset of A ω . Then it is easy to see that X ′ = X ∪ (A ω -D) is a rational Π 0 2 -subset of A ω such that X = X ′ ∩ D. Thus in this case Corollary 4.5 follows from Theorem 4.3.

Assume now that D = Y 1 ∩ Y 2 , where Y 1 is a rational Σ 0 2 -subset of A ω and Y 2 is a Π 0 2 -subset of A ω . By hypothesis X is a Π 0 2 -subset of D thus there is a Π

0 2 -subset X 1 of A ω such that X = X 1 ∩ D = X 1 ∩ (Y 1 ∩ Y 2 ) = (X 1 ∩ Y 2 ) ∩ Y 1 .
This implies that X is also a Π 0 2 -subset of Y 1 because X 1 ∩ Y 2 is a Π 0 2 -subset of A ω as intersection of two Π 0 2 -subsets of A ω . From the first case we can infer that there is a rational Π 0 2 -subset X ′ of A ω such that X = X ′ ∩ Y 1 . Now we have also X = X ′ ∩ (Y 1 ∩ Y 2 ) = X ′ ∩ D because X ⊆ Y 2 . Thus in this case again Corollary 4.5 follows from Theorem 4.3.


Florjan Bombaj
email: florjan.bombaj@supagro.inra.fr

Dominique Barjolle

Theodosia Anthopoulou

Gabriel Michaud

Family Farming in the Albanian Mountainous Areas: Local Agro Pastoral Farming Systems and Market Integration Perspectives

Keywords: family farming, livestock systems, mountainous area, Albania

Introduction

Albania is a Balkan country located in the Mediterranean part of Europe but a potential candidate country to enter the European Union. This country was communist until 1991, when the transition into a market economy began. The agrarian reform and this transition have led to the deconstruction of the old economic regime which was characterized by state planning and centralized productive resource management (652 farm units with an average of 1,050 ha per unit).

Today, according to MAFCP (2014) around 352,315 farm households still have a high level of land fragmentation (1.16 ha/farm with an average of 4.8 parcels). According to the FAO definition of family farming a family farm is managed and operated by a family and relies predominantly on family labor, including both women's and men's. According to MAFCP (2014) a small farm is managed by a family, relies predominantly on family labor and is characterized by a small area of arable land, lower or equal to the national average (1.16 ha/ land area per farm) as well as a high level of land fragmentation. The agricultural sector is strongly centered on family farming. More than 90 percent of the 352,315 farms in Albania are below 2 hectares and account for about 95 percent of the land used, being the only country in Europe to rely largely on extensive small-scale domestic production (MAFCP, 2014). According to [START_REF] Cochet | Origine et actualité du "Système agraire": Retour sur un concept[END_REF] the farming system is an operating mode using the current

The objectives of this paper are to understand the evolution of family farming in a mountainous area of Southern Albania after the fall of communism in 1991 and to identify the socio-economic developments that characterize this territory in very last years. According to primary or secondary historical data, there is a recent increasing demand for dairy and meat products due to the rapid growth of urban markets. This has pushed for an increase in livestock production. Simultaneously new moving breeders from southern Albania are renting vast good pastures and the management reform of public pastures have put more pressure on common pastures. At the end, the paper discusses the perspectives of improving livestock farming systems in that context. Major changes in the agricultural sector have led to an increase in livestock production, which provides about 57% of the total value of agri-food production, followed by the arable crops with 26% and fruit production with 17% (MAFCP, 2014). At the national level this increase is more accentuated during the period 2012-2014 when small ruminants increased by 22%.

The dairy industry holds an important place in the Albanian agri-food sector (MAFCP, 2014).

According to official statistics, domestic production of milk reached 1,1 million tons in 2012 marking an increase of 9% since 2007.

Regarding mountainous areas, between 1991 and 2014, the population migrated massively to the lowlands or abroad. The farming systems have deeply changed but without significant land concentration phenomena.

The natural landscapes and typical Mediterranean pastures mainly explain the predominance of small ruminants in the mountainous area of Albania. As farm size is very small and the alpine pastures quite rich, family livestock farming is one of the main sources of family income in these territories. It is therefore considered as a key resource for local development (Bernard et al., 2014; Garnier, 2013). Yet, the long economic transition and demographic fall [START_REF] Lerin | Mobilités spatiales et développement en Albanie : enseignement de la transition post-communiste et enjeux d'avenir. 17 p. 4[END_REF] This concerns the selected municipality of Vithkuq (see figure 1) which has a long agro-pastoral tradition. The recent evolution of this municipality is very similar to the one of the country: along with to the demographic desertification of the municipality after the fall of communism, data show a sharp increase in herd size, new dynamics in terms of modernization of the local dairies and issues in natural resources use (Çili et al. 2013).

Research context and questions

In the mountain areas, changes and unsteadiness caused by depopulation and globalization impact local economies and societies. According to Wymann von Dach et al. (2013), these changes contribute to higher pressure on local resources [START_REF] Peeters | Importance, evolution, environmental impact and future challenges of grasslands and grasslandbased systems in Europe[END_REF], unsustainable practices in land use, Farming activity in mountainous areas is mainly family-based (Crowley, 2013; Varotto & Lodatti, 2014; Wymann von Dach et al. 2013). Family farming in its various forms around the world reflects the heterogeneity of economies and societies (Thirion et al. 2015).

According to Manoli et al. (2011) understanding the diversity of production systems in a given territory is key for analyzing the territory as a space where society and institutions interact locally A farming system deals with two important issues: a) natural resource management; b) market integration perspectives. Since livestock production is dominant in mountain areas, their analysis in terms of natural resource management and market integration is crucial.

The principal activity of all farmers in Vithkuq is livestock production; therefore they are all breeders.

The management of mountain pastures and resource use access affect the farming systems of these breeders (Bombaj et al. 2015; Çili et al. 2013).

The paper aims to discuss two hypotheses: First: after the collectivization period, the local agro pastoral farming systems have gradually adapted to the new political and economic context. Some groups of family farmers have increased their herds causing some changes in the management and in the intensity of the use of pastures. In consequence the lack of specific policies has harmed natural resource management.

Methodological approach

Given the extent of the area (with a surface of 243 km 2 ) and the difficulty of access to some very remote villages, we have chosen a limited number of communities. We studied 3 communities in 3 spatial organizational units, crossing an area of milk collection where the dairies are located with an area of their related summer pastures (see table 3 and4).

Combining secondary data (statistics and documents) and primary data (interviews with local actors and specialists), the final delimitation of the 3 units selected for our research was done according to the number of families in each village, the number of animals, and the proximity and ties to the identified dairies. An important criterion was also the significance of traditions and sources available on the history of the village, and the official written sources on the evolution of the population and livestock production. The sampling for interviews was done with consideration to a balance between large and specialized farmers, medium-sized farmers and very small subsistence farmers according to their respective importance of their pasture use.

The purpose of the sampling was to investigate different breeders with different experiences and perspectives, different strategies and their different relationships to resource use helping us understand the pastoral system. Using this approach, it was possible to get a global and detailed description of the farming system and its specificities in the considered municipality.

Our approach was conducted in four steps: According to the subsidies policy of the Ministry of Agriculture a large specialized farm must have more than 100 sheep or 10 cows to benefit from subsidies. This was taken in account in our sample characterization to define a large specialized farm.

In the studied area (the 3 units), we identified in total 131 small subsistence farms, 142 mediumsized farms and 53 large specialized farms.

The small subsistence farms are characterized by self-consumption and very occasional or even no sale (see table 1).

Results

1 Context of Family farming in Albania

In Albania, since the fall of communism, family farming has been a major contributor to national food security by producing food for self-consumption as well as for the market. The

2 Recent evolution of the value chains of milk and meat in the municipality of Vithkuq

The municipality of Vithkuq numbers 11,500 dairy sheep out of a total of 18,549 ruminants.

In fact sheep breeding is ideally adapted to the topographic and climatic conditions of the local natural resources. Breeding was practiced in the area during the communist period, and the knowhow around its milk production persists today.

Sheep herd represent 86% of total herds on the territory.

The population of the municipality of Vithkuq The total capacity of milk transformation into cheese of these 3 dairies is rather smaller than the ability of the local breeders to commercialize milk.

Price was decreasing in constant price (see figure 4). The determinant factors of this market power are the location and the transport costs. Breeders don't have the possibility to sell their milk to other nearby dairies.

Therefore, the price is set by the buyers, who really pressure the breeders. The low price is certainly linked to the dominant position of the dairies in that area, because in other parts of Albania, the price of milk is much better and is has been increased in the same period of time [START_REF] Gontard | Diagnostic agraire du massif pastoral de Rrungaja. Région de Korçë-Sud-Est de l'Albanie. Mise en valeur des pâturages-principale ressource de ces territoires de montagnes-par les systèmes d'élevage[END_REF].

The meat value chain is almost totally informal and even almost illegal. The farmers can sell the animals to local slaughterhouses and butchers for better prices compared with milk (see figure 5).

Milk does not always cover the production costs and meat production generates more income than milk production. The price for lambs in kg/live/weight in 2016 is lower than in 2000, but lamb production is more economically profitable for the breeders in terms of income. The first two ways cover 80% of total sales of animals in the area.

T h e v a l u e c h a i n i s t o t a l l y i n f o r m a l a n d There is only one public slaughterhouse in the region which works at low capacity because nobody forces traders and butchers to slaughter the animals according to the law. Therefore, the food safety standards are not met, the value chain is poorly organized and the possibility to buy and the prices are very unstable.

With regards to the influence of these two value chains' structure on the evolution of production in the territory; it is worth noting that in 2014, the total milk production had decreased by 9% compared with 2005 while the meat production had increased by 55%. This trend is clearly linked to the extremely low price of milk, which does not always cover the production costs (see table 4 andfigure 4) According to the sample characterization we have calculated the incomes for three categories of farms.

For the first category, we calculated the income for a typical self-consumption farm which does not do transhumance. For the second category we calculated the income for a typical medium-sized farm which does transhumance and for the third category, we calculated the income for a typical capitalist large specialized farm. This type of farm was identified this year in the territory because they have large herds which graze on the summer pastures of the Municipality.

In figure 6 we can see the big difference in incomes between a local transhumant breeder having a medium size farm and a big transhumant breeder. This can be explained by two reasons:

(1) the herd size of the first breeder is between 300-400 sheep and for the second between 700-1000.

(2) they have different strategies in terms of meat production. The local transhumant breeder has a double orientation milk/meat but the big transhumant breeder has purely a meat orientation strategy.

3 Pastures management

The municipality of Vithkuq has 5,350 ha of summer pastures over 1200 m. They are spread over the whole territory. For breeders, access to summer pastures is really key for their survival and This property right was given to this owner during the first decade after the fall of communism in 1991.

(2) Communal pastures: Common pastures managed by each village: these communal pastures Recently, the large and specialized local breeders have been in competition with "big" transhumants coming from Vlora, Tepelena and Delvina (Southern Albania) over the state summer pastures.

The private summer pastures, according to historical data, were always used by the big transhumants coming from southern Albania. They usually pay for the totality of the summer pastures owned by the "bey" because their herds are between 500-1500 sheep.

With the new territorial reform in 2016 the status of pastures is changing right now. The communal and state pastures will be public pastures and should be allocated on priority basis to local breeders.

Only if the local breeders are not willing to pay to access the pastures, will the public authorities of the Region offer the land to breeders from outside the municipality.

To sum up: all public pastures will be managed by the public authorities of the Region of Korca and the unique very large private owner (descendant from the "bey") will be the only manager of the private pastures. Therefore, local breeders will need to pay for the communal pastures which were free to access before the reform.

The impact of this change could be profitable With the reform, more pastures should be available to transhumant breeders since some communal pastures, reserved for villagers, were undergrazed.

But some challenges were identified as well during the interviews:

For the non-transhumant local breeders the reform could be complicated, they will have to be organized to rent all parcels of pastures used before as commons. In the villages where this is not possible, "big" transhumants or other transhumants coming from the region may use them. This year only one village has done this. Breeders of this village have chosen the chief of village to represent them and he can rent the public pastures that were communal pastures belonging to the village before the reform.

For the "big" transhumants the challenge will be to obtain the same state pastures they had obtained before the reform. Public pastures will be allocated with priority to local transhumant breeders. This can be an opportunity for them to federate in associations and build new strategies for valorizing their animal products.

Conclusion

The municipality of Vithkuq is a mountainous territory with a long tradition and know-how, especially in livestock farming systems.

The family farming model is adapted to the topographic and climatic conditions of the environment but also to the new current dynamics of the urban markets. The farming system has evolved and adapted to the governmental structural changes that occurred during the transition period. Indeed, breeders specialize according to their physical abilities for livestock production, the availability of the young labor force and the economical and physical environment in which they are located.

Our research shows that this territory has suffered Recently, the dynamics of expansion and specialization have involved the reorganization of the pastoral space. This has created an increasing demand for greater pastures that are managed in an unclear way, generating conflict between the local farmers and the "big" transhumants who obtain contracts to exploit this resource during summer.

Although farmers have increased their herd size, they do not really have a favorable bargaining power with the dairies. The bargaining power in the milk and meat value chains is asymmetric and the current dynamics of the value chain do not position the products in a niche market capable of engaging a virtuous circle for the good remuneration of the producers and for the reproduction of the natural resources.

Suggestions

The chaotic economic transition of the Albanian At the international level the needs for investing in facilities respecting modern technology, and the enforcement of existing regulations regarding food safety are key to stabilizing access to the urban markets under the European Union legal regime.

Access to markets will be profitable to the family farms if there is enough competition within the value chain in order for the breeders to obtain fair prices that compensate them for costs of production.

Those costs are quite high due to the natural conditions of a rigorous climate and harsh slopes that are typical in all mountainous area.

If the products are well priced, an increase in production will follow, with the consolidation of medium-sized to large farms, able to invest in better buildings and to modernize their facilities. If these farms can increase their production capacities they will be able to benefit from public support such as subsidies.

But the increase in herds needs to be accompanied by a common management strategy of the pastures.

This will depend not only on the ability of the regional authorities to effectively implement the recent reform of State and common land management but also on the collective action of local breeders to cooperate for a successful management strategy of their pastures.

Notes 1 )http://paza-albania.eu/web/PAZA_Project_1_1.php

  natural, technical, and socio-economic factors, closely related to the evolution history of a given territory. The agrarian reforms towards a market economy have pushed farmers to change their farming systems adapting their production to market demand.

  have nowadays created a binding context to trigger local economic development dynamics.Albania is organized in 15 regions, which are divided in 36 districts. There are overall 309 rural municipalities and 2,980 villages which are the smallest administrative units in the country.Our study area is located in the region of Korca, which is one of the most developed economic regions in southeastern Albania. For this region, the development of the urban area of the city of Korca and the agricultural development of the plain surrounding the city take a much more important place than the mountainous area of our study area.

Fig 1 .

 1 Fig 1. The municipality of Vithkuq Source: Elaboration on GIS by Florjan Bombaj

  Second: the lack of public support has led to a weak development of the milk and meat value chain. Based on fieldwork in the municipality of Vithkuq this paper aims to respond to the following research questions: a) what is the evolution of the family farming model and the specificities of the local agro pastoral farming system in the territories under consideration after the fall of communism in 1991? b) Which are the market integration perspectives of the local livestock production and the pastoral resource management issues?

  system development dynamics. At the national level we used several documents, including reports, papers and other data. At the local level we studied the municipality of Vithkuq.

- 2 .

 2 Characterization of the whole reference population of breeders. The interviewed breeders were described by age, herd size, herd type (cattle/ sheep/goat), according to an existing database of the Albanian Ministry of Agriculture and the European project "PAZA". (The "improving consumer protection against zoonotic disease -Albania"). This project 1 aims to promote the sustainable control of zoonotic diseases and strengthen institutional and administrative capacity.

- 3 .

 3 Fieldwork phase based on semi-structured interviews with key informants, questionnaires addressed to producers, personal field observations, in two phases; first, structured interviews, semistructured and informal observations collected directly from the breeders; second, interviews and personal observations on the wholesale and the retail market in Korca and stores in Tirana.

- 4 .

 4 Results analysis and discussion. The "PAZA" project database, the herd size per farm in the municipality, and the subsidies policy of the Ministry of Agriculture determined our sample characterization for all the local breeders of the municipality of Vithkuq. Consequently in this municipality we considered a farm to be one of self-consumption with 1-10 sheep/goats and / or 1-4 bovine animals; medium-sized farms with 11-99 sheep / goats and / or 5-9 bovine animals; large specialized farms with more than 100 sheep / goats or more than 10 bovine animals.

Fig 2 .

 2 Fig 2. Sample survey (step 3) Source: Author's field data collection

Fig 3 .

 3 Fig 3. Distribution of local (municipality of Vithkuq) breeders surveys according to the type of farming Source: Author's field data collection

  reconstruction of the family farming system has faced constant challenges like emigration, the very small size of farms, access to urban markets, the irrigation and drainage systems, the low standard of technologies, the weak organization of farmers, and the low development level of agrifood processing, among others, more general, like the lack of infrastructure, weak educational and medical services and the poor human and financial resources of the public administration.In 1991, the collectivist system collapsed, the cooperative of the municipality disappeared and some massive and brutal privatization took place. In the context of the land reform(law 7501, in 1991) at the national level, each family has recovered land and some livestock heads. The distribution was not the same in all the villages, ranging from 0,1 ha to almost half a hectare per capita. Until 2000, many villages in the municipality were massively desertified. Those who remained, the most employable members, have often migrated mainly to Greece. In general, during the first decade after the fall of communism, the majority of farms underwent unimportant changes and remained within the subsistence model though some farms have slightly enlarged. Irrigation and mechanization systems were abandoned. The infrastructure of the cooperatives was largely destroyed, many wanting to recover its share of materials. The farming system evolution depends from the pastures available in the municipality, especially during summer. Large specialized farms demand more pastures during summer which creates competition among breeders for this resource. The use of pastures is a major resource for the breeders. In fact, during the summer, severe droughts affect the availability of grass under 1200m altitude and a vast majority of the animals go to summer pastures over 1200m. In the winter, the snow and the rigorous climate impose the feeding of the herds with forage based on grass cut over the summer. In fact, the availability of summer pastures and the quantity of forage for passing the winter are actually the main limiting factor both at individual farm level (size of each herd), and at municipal level (total number of animals). In 2014 in Albania only 51% of the total milk produced was sold to the wholesale market which is equivalent to 530.4 tons of milk sold in 2014 in Albania or exported. Annual consumption of milk by FAOSTAT is 303.72 kg / capita in 2013. Despite the fact that milk production has increased rapidly in the recent years, opportunities for export of these products remain limited. This is due to a number of factors throughout the value chain of these products such as the lack of quality standards, appropriate technology, marketing, etc. The current national agricultural policy subsidizes the dairy and small ruminants sectors. Subsidies for milk production are given to the farmers who deliver their milk to dairies. Support for dairy cows and sheep is given per animal, support for transhumance of sheep is paid per farm. The subsidies are precisely 9 € per ewe/per year and 37 € per cow/per year. They are paid only to breeders with more than 100 sheep and / or more than 10 cows. The alignment of Albania's agriculture and rural development policy with the Common Agricultural Policy demands new strategies to transform and adapt Albanian family farms to European policies, laws and standards. This transition tends to smoothly transform the fragmented structures of the agricultural sector to become competitive while protecting and valorizing local products and developing the disadvantageous territories.

  has a long history in livestock production and pasture management. It corresponds to a coherent agro-pastoral zone with a rich flora and fauna of pastures producing dairy products of high flavor and quality that are well known by local and Albanian consumers.From the year 1997 to 2000 a severe financial and political crisis stopped the evolution of livestock production in the country. Since the year 2000 some herds have begun to really grow, boosted by the human investment returns from emigration and the support activities of some NGOs in the region. The specialization was mainly oriented towards sheep "because it's the tradition" -mentioned a young farmer who recently took over the family herd after a few years working in Greece -and because they are adapted to local systems. During the same period many pluriactive breeders, having already more or less moved in this direction, have adapted their livestock system either by reducing the importance of other activities, or by reducing their herds to free up their time (oriented to other activities).

There

  are three ways in which the lambs/calves/ kids are sold: a) the breeders go to the wholesale animal market in Korca a precise day every week. This is expensive for the majority of farmers who do not have means of transport. They are forced to organize in groups and pay for conveyance. b) via the wholesale traders in the region. This way of selling animals is very usual. The coordination is done by phone and the merchant comes in person to purchase the animals on site, on a live weight basis; c) via the retail traders of Tirana. These are mostly former inhabitants of the area who buy animals in the area and who sell to the wholesale market in Tirana.

Fig 4 .

 4 Fig 4. Constant prices of animal products in the municipality of Vithkuq between 2000 and 2016 -price index of 2000 = 100 (indexed with the annual national inflation rate)

  their capacity to invest. Three ways of managing pastures exist. (1) Private pastures: The majority of private pastures are owned by local breeders, who may use and cultivate these pastures. More than 1000 ha summer pastures are owned by a unique very large private owner (descendant from the "bey" (ottoman honor title of land owners during the Ottoman Empire regime in Albania: 1463-1912).

Fig 6 .

 6 Fig 6. Farms incomes for three types of farms in

  to the quality of pasture management. For the local transhumant breeders this change can be an incentive to invest in bigger herds and could be a way to organize them and work together. If local breeders have to organize themselves together to rent pastures, this could be a first step in the creation of cooperatives or organization to promote their products together.

  from a desertification of the population after the fall of communism in 1991. The reduction of the population has been accompanied by a recent sharp increase in herd size and new dynamics in the local production systems. Livestock breeding, as a tradition and know-how, remains an important economic source for people in this marginalized territory. Market demand for animal products, especially for meat, has increased sharply in recent years. Products "Origin Vithkuq" are highly demanded by the market despite the fact that they have no logo or other brand. The demand for these local products explains the expansion of herds in the area and many farmers see the need to produce in large quantities to flourish economically. Mountain pastures are an important resource for the breeders of Vithkuq. The exploitation of this resource is a major challenge for the management of both farming systems and the landscape. The large specialized farms need to respect the governmental rules to benefit from the subsidy policy. The medium-size farms are adapting their herds to benefit from public support.

  mountainous territories nowadays demands new strategies in terms of rural development. The Municipality of Vithkuq in particular needs a lot of adjustments and structural changes to support the local breeders. Indeed, the need for agricultural development and pasture management strategies are numerous. From the value chain perspective, the adjustments needed to upgrade to reach the European standards regarding food quality and safety is high. The milk and the meat sectors worth the development because the taste and flavor of the cheeses and the meat produced in that mountainous area are wellknown and meet the expectations of the Albanian consumers as well on the urban markets. These consumers have a high preference for the local milk and meat products but the safety food standards and quality labels still remain rare.

Table 3 .

 3 Dairies income for the year 2014

		DAIRY	DAIRY	DAIRY
		VITHKUQ	LUBONJE	PANARIT
	DAIRY
	PROD
	CHEESE
	(Q 2 )	170	100	72
	DAIRY
	CAP 3
	(Q/DAY)	23	10	7
	DAIRY
	INCOMES
	EUROS
	/YEAR	45, 955	25,735	18,529
	Source: Author's calculation
	2) Q is in quintals
	3) CAP is capacity

Table 4 .

 4 Pastoral dynamics of Vithkuq (326 families)

				TOT	TOT
	YEAR	TOT POP	HERD SIZE	MILK PROD	MEAT PROD
				(q)	(q)
	2005	2,939	17,920	27,500	1,605
	2014	1,660	18,549	25,200	2,497
	Diff
	in %	-56%	+4%	-9%	+55
	Source: (Çili et al, 2013); (Matka 2015) and author's calculation
	TOT =Total PROD=Production

Florjan BOMBAJ, Dominique BARJOLLE, Theodosia ANTHOPOULOU, Gabriel MICHAUD : Family Farming in the Albanian Mountainous Areas: Local Agro Pastoral Farming Systems and Market Integration Perspectives

Source:[START_REF] Gontard | Diagnostic agraire du massif pastoral de Rrungaja. Région de Korçë-Sud-Est de l'Albanie. Mise en valeur des pâturages-principale ressource de ces territoires de montagnes-par les systèmes d'élevage[END_REF]


Florjan Bombaj
email: florjan.bombaj@supagro.fr

In which way the governmental and institutional changes in the resource use of a common good affect the local communities? Evolution and perspectives from Southeast Albania

Keywords: Communal pastures, mountain territory, common good, Albania

In which way the governmental and institutional changes in the resource use of a common good affect the local communities? Evolution and perspectives from Southeast Albania F. Bombaj, D. Barjolle, François Casabianca, T.

One of the most well-known mountain territories for the dairy products in Albania is the municipality of Vithkuq, Southern Albania. The last years the increase of the livestock production [START_REF] Bombaj | Family Farming in the Albanian Mountainous Areas: Local Agro Pastoral Farming Systems and Market Integration Perspectives[END_REF] has created an increasing demand for greater pastures. The pastures that are in common use are recognized as communal pastures. The recent territorial reform implemented by the government in 2016 has changed the rules of the common use of these pastures. Local breeders need to pay for a resource which was free before. Consequently, our research question is to analyse in which way the territorial reform affect the local communities in the considered study area.

According to (Hardin, 1968) when a resource is open access, each user can use without limit this resource, leading to his disappearance. As a possible solution to this tragedy, as highlighted by (Ostrom, 2014), the communities can find adequate ways to manage their common resource. Ostrom underlines the fact that expectations of rising resource prices encourage better management Séance 3-Le foncier comme bien commun 78 by the users. In a community when a free resource becomes a paid resource the local users may be not able to cope with the new situation and the common resource can be useless to them.

The objective of this paper is to analyze the dynamics of the pastures management in a mountainous area of Southern Albania after the fall of communism in 1991 and to identify the recent management issues of the pastures that are in common use. We rely on the original example of the municipality of Vithkuq in the Southeast of Albania, to discuss how local breeders use the pastures as a common, and how the recent governmental and institutional changes in the resource use affect the pasture management at the local level.

Methodology and sources used

The method uses two approaches. The first is the agrarian diagnostic approach as an effective way to characterize the farming system of a given territory [START_REF] Cochet | Origine et actualité du "Système agraire": Retour sur un concept[END_REF]. The second is the Likert method to analyse the current dynamics of the pasture management after the institutional changes in the resource use.

Our method was conducted in four stages:

Stage 1.Literature research and landscape analysis to determine the villages that use and contribute to the common management of the pastures.Fieldwork7 based on personal field observations, in two phases; first, structured and semi-structured interviews addressed to regional authorities; second; structured and semi-structured interviews with key members of the selected villages. Stage 3.Questionnaires8 regarding the current dynamics and possible perspectives after the governmental and institutional changes in the resource use. The two set of six questions dedicated to the reactions and the future pastures use by the breeders were based on the different situations observed in different villages. The breeders (see chart 2) have been chosen according to three criteria: First, the production system that uses communal pastures. Precisely the non-transhumant sheep system and the non-transhumant cow system. This choice has been made respecting a representativeness of the livestock systems. Second: villages concerned by the collective management of the communal pastures. Villages concerned by the collective management of the communal pastures (Vithkuq and Shtyllë). Third: villages not concerned by the collective management of the communal pastures. In these villages have been chosen breeders who are affected by the reform and who will have to pay what was previously free.

Stage 4.Analysis of the results and discussion. Having a global and detailed description of the nature of the pastoral management system in the selected villages the results allow discussing contemporary developments which affect the pastures as a common good and the local breeders as concerned actors.

Conclusion

The local production system depends from the pastures available in the municipality, especially during summer. Large specialized farms demand more pastures during summer which creates competition among breeders for this resource. The "massif of Rrungaja" is one of the rarest cases when a single owner has more than 1000 ha of pastures in a massif where communal pastures and private pastures intersect. There is a collective organization at the village level where breeders organize to manage the communal pastures. These are small herd size breeders. Therefore the guarding of their small herds is regularly organized in collected herds. Only two villages (Vithkuq and Shtyllë), made use of the communal pastures (625 ha) from March to November.

In these villages two different types of collected herds using the communal pastures coexist:

(1) The non-transhumant sheep system. Being the most common system it includes families having double activity or retired breeders who keep a small herd and a plot of land. The breeders gather their herds in collected herds to take them together to the pasture. The breeders being in the non transhumant sheep system have 12 to 50 sheep. Their collected herds range from 150 to 200 sheep and corresponding on average to 15-20 families. There is a rotation for the guarding according to the number of animals per breeding: one day of guarding for 10 head of sheep. (2) The non-transhumant cow system.It is the equivalent of the non-transhumant sheep system but specialized in cattle. The breeders being in the non transhumant cow system have 1 to 2 cows. They gather their herds in collected herds to take the cows together to the communal pastures every day.

For the bovine herd is one day of guarding for one cow.

The two main villages (Vithkuq and Shtyllë) where the communal pastures are located are more interested in the short term to a collective way of renting pastures but only in one village a group has been created. In this village the major factor explaining the immediate creation of the group is the competition with the big transhumants coming from southern Albania demanding pastures that are located close by to their communal pastures.

Table 1. Reaction of local breeders after the reform You are of the opinion that this reform will have positive effects on the common management of the pastures, that is to say it allows a better management of this resource in association with your breeding colleagues 1 2 7 6

The reform has prompted you to regroup with your fellow breeders to rent pastures together 1 5 7 5

The reform has positive effects on the maintenance of mountain pastures, and on the number of animals you can grow there

8 1

The district of Korça is the most efficient institution to manage the common pasture on which you are used to go to your animals 5 7 6

The reform allows a better cohesion between the breeders to share the estives 2 4 7 5

In total = 18 Breeders In conclusion, communal pastures are important for breeders who have small herds and do not perform transhumance. The new rules create barriers for them for the use of the communal pastures. The changes affect the farming system of the breeders that need to adapt their production strategies and pasture management plans. Nevertheless, the recent changes can be a way for breeders to organize themselves not only to collectively manage the communal pastures but also to promote their products together. The Ostrom grid for collective common goods management analysis will clarify the breeder"s behaviour for the new rules of pastures access.

  Chart 1. Sample survey Chart 2. Breeders interviewed for the territorial reform Source: Authors survey Stage 2.Historical analysis and characterization of the local production systems. Using this approach, it was possible to get a global and detailed description of the pastures management system and production systems specificities in the selected villages. Difference in pasture use byFONCIMED. Réseau CIHEAM-INRA de recherche et d"échange sur le foncier méditerranéen. 10ème Séminaire Annuel "Le foncier, un actif du développement territorial et de la durabilité des communautés rurales?", Thessaloniki, 2-4 Novembre 2017 FONCIMED. Network CIHEAM-INRA for research and exchange on Mediterranean land tenure. 10th Annual Seminar "Land tenure as an asset for territorial development and the sustainability of rural communities?", Thessaloniki, 2-4 November 2017 Séance 3-Le foncier comme bien commun 79 different villages was observed. Villages having the same livestock systems have different pasture use access.

FONCIMED.

  Réseau CIHEAM-INRA de recherche et d"échange sur le foncier méditerranéen. 10ème Séminaire Annuel "Le foncier, un actif du développement territorial et de la durabilité des communautés rurales?", Thessaloniki, 2-4 Novembre 2017 FONCIMED. Network CIHEAM-INRA for research and exchange on Mediterranean land tenure. 10th Annual Seminar "Land tenureas an asset for territorial development and the sustainability of rural communitiesLocal breeders, who do not transhumance, from March to November, bring their flocks daily to pasture closer to the villages and return them to their stable at night. The big transhumants coming from southern Albania settle on the private pastures of « Bey » (shown in red) and partially on the state pastures (shown in blue), located far away from the villages (see figure2). The local summer transhumants settled mainly on the state pastures located as close as possible to their village. Some use the highest communal pastures.

Figure 1 .

 1 Figure 1.The study area (5 villages) and the territorial identification of the different pastures" governance types.

Figure 2 .

 2 Figure 2. Movements of herds represented on a topographic section

foncier, un actif du développement territorial et de la durabilité des communautés rurales?",

  Réseau CIHEAM-INRA de recherche et d"échange sur le foncier méditerranéen. 10ème Séminaire Annuel "Le Thessaloniki, 2-4 Novembre 2017 FONCIMED. Network CIHEAM-INRA for research and exchange on Mediterranean land tenure. 10th Annual Seminar "Land tenure

FONCIMED.

as an asset for territorial development and the sustainability of rural communities?",

  Thessaloniki, 2-4 November 2017

un actif du développement territorial et de la durabilité des communautés rurales?",

  FONCIMED. Réseau CIHEAM-INRA de recherche et d"échange sur le foncier méditerranéen. 10ème Séminaire Annuel "Le foncier, Thessaloniki, 2-4 Novembre 2017 FONCIMED. Network CIHEAM-INRA for research and exchange on Mediterranean land tenure. 10th Annual Seminar "Land tenure

as an asset for territorial development and the sustainability of rural communities?",

  Thessaloniki, 2-4 November 2017

Séance 3-Le foncier comme bien commun 82Table 2 .

 2 Resource use plan for the future

	Source: Authors survey

See chart 1.

Applying the Likert method, see chart 2.

Conflicts between locals and transhumants are lower if renting is done by a group of farmers than by a single one

1 12

The group helps to a better coordination between breeders and local and regional institutions 3 1 13 1

Renting pastures together cements confidence among the breeders to take care of the problems of management of the pasture of the zone

Without ensuring the use of pastures the future of livestock is threatened 18

It will be possible to organize in spite of the conflicts between my family and the neighbor (or neighbors).

2 10 5

In total = 18 Breeders


Pierre Joseph

Marianne Elias

Fabien Mesnilgrente

Adrian Laborde

Debora Berti

Costanza Montis

Lucrezia Caselli

Barbara Lonetti

Chiara Magnani

Anne-Françoise Mingotaud

Microfluidics to fabricate and probe vesicles mimicking cells

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

Microfluidics to fabricate and probe vesicles mimicking cells

Being the base element of cell membranes, lipid bilayers are an essential ingredient of many biological processes. In order to understand mechanisms at play for example in molecule translocation through membrane proteins, or interaction of the cell with nanoparticles (NPs), artificial, biomimetic membranes have been developed: supported or suspended bilayers, Giant Unilamellar Vesicles (GUV) which are micron-sized compartments. They constitute simplified models to decompose the elementary events (biochemical, physical, and chemical) at stake in real biological situations [START_REF] Montis | Interaction of Nanoparticles with Lipid Membranes: A Multiscale Perspective[END_REF] . Existing Methods to work with these artificial membranes do not permit reproducible properties or complex configurations (size, chemical composition of the membrane). Microfluidics, the handling of fluids in microfabricated chips, offers new and versatile tools, both to fabricate more elaborated "artificial cells" [START_REF] Swaay | Microfluidic Methods for Forming Liposomes[END_REF] and to manipulate and study them [START_REF] Robinson | Microfluidic Trapping of Giant Unilamellar Vesicles to Study Transport through a Membrane Pore[END_REF] . We propose to combine microfluidics (LAAS team, https://www.laas.fr/public/en/mile), physico-chemistry with biological relevance (Italian team), and polymeric self-assemblies for nanomedicine (IMRCP team) in order to decipher biological processes occurring at cell membranes, particularly as regards nanoparticles/membrane interaction. Two applications are targeted: nanoparticles toxicity and nanomedicine.

A few results (more or less preliminary) will be discussed: Chips designed to characterize vesicle mechanical properties, in the spirit of on-chip micropipettes [START_REF] Guo | Microfluidic Micropipette Aspiration for Measuring the Deformability of Single Cells[END_REF] , show significant stiffening of GUV after their incubation with gold NP. They also permit to test hybrid vesicles, composed of mixtures of lipids and copolymers, promising in particular for nanomedicine [START_REF] Magnani | Hybrid Vesicles from Lipids and Block Copolymers: Phase Behavior from the Micro-to the Nano-Scale[END_REF] . The effects of photoactive drugs included in polymeric nanocarriers are also characterized in real-time on vesicles sensitive to oxidation, thanks to a microfluidic architecture permitting to switch inlet solution. Droplet-based configurations to fabricate GUV are also implemented.

On-going work aims at extracting quantitative information: improving designs, understanding how intrinsic properties (membrane bending modulus) relate to measured properties (such as the critical pressure to release a vesicle), as function of nanoparticles surface chemistry, membrane composition, flow conditions.

  Joseph P, Elias M, Mesnilgrente F, Laborde A, [LAAS-CNRS, Université de Toulouse] Berti D, Montis C, Caselli L [CSGI, Departement of Chemistry, Florence University] Lonetti B, Magnani C, Mingotaud AF [Lab des IMRCP, Université Toulouse III PS]


Florjan Bombaj

Dominique Barjolle

Jean-Marc Touzard

Myslym Osmani

Materials and Methods Conclusions Meat value chain dynamics in the Albanian mountains areas. What issues prevent the development of the traditional mountains products?

Combining statistics and preparatory discussions with local actors and regional specialists, the selection of villages was done according to the number of families in each village, herd size evolution, proximity and ties with the three dairies in the territory. Different publications and diagnostic results on a mountain territory in northern Albania were consulted for the comparison between the two territories.

Introduction Results

Stage 1 -National value chain analysis. At the national level we used several documents, including reports, databases, papers and other scientific data.

No market information system in place

The majority of meat producers are small subsistence farms. The national meat value chain it is not profitable to them.

High production costs and no technical improvements that boost the productivity.

The very poor structuring of the two value chains for the two territories gives very little market power to the farmers.

Bad markets' functioning may prevent positive effect of any setting-up and registration of GI for these local products.

"XV EAAE Congress -Towards Sustainable Agri-Food Systems: Balancing between Markets and Society"

Stage 2 -

 2 Vithkuq value chains analysis in several steps: a) exploratory phase with literature research and choice of the study area; b) sample characterization. c) fieldwork phase Stage 3. Results analysis and workshop with the local actors and breeders. The results were discussed during a workshop with the concerned actors. Stage 4 -Meat value chain analysis of the Hasi district in northern Albania.

•

  chain SWOT analysis of the Hasi district The meat value chain SWOT analysis of Vithkuq In the Albanian mountains' territories the livestock production is dominant. They have strong potential for developing GI for their products. Since 2012, great efforts are made to better valorise a few local products in northern Albania in the Hasi region.Another PhD-project has developed participative research in a mountain territory with a strong past and present pastoral activity. Vithkuq is well known for a high reputation of its dairy and meat products. The meat production is increasing constantly.• Meat consumption in Albania is already 43.4 kilograms per capita.VC Links• Local meat is limited and expensive.• No link between the Albanian farmers and the meat processing industry.Imports• In the value chain of meat there are also slaughtering and processing enterprises. • The majority of raw meat is imported. of slaughtered animals is often much too low resulting in low profitability; the reasons are the demand for very young animals and the unavailability of cheap feed


Florent Laroche

Mehdi Chayani

Xavier Granier

A scientific network serving the uses of 3D humanities

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

A SCIENTIFIC NETWORK SERVING THE USES OF 3D HUMANITIES

The 3D Consortium of the TGIR Huma-Num has been created based on the observation that there are many initiatives around 3D for the Digital Humanities without real coordination between them. The proliferation of initiatives makes the task difficult and only a consortium-type organization can bring together forces in order to define standardized solutions. The difficulty is increased by the fact that we are dealing with multiple domains, combining science and technology with the humanities. The aim of the consortium is to facilitate discussions by putting together a maximum of research groups that integrate the use of 3D digital data in their scientific practice, to develops tools for acquisition, visualization, interpretation and preservation of data for the Humanities. The consortium is therefore willing to develop synergies between national Humanities and 3D disciplines in order to: (i) share experiences; (ii) edit recommendations in terms of methodology, standards and formats; (iv) identify the specific needs of Digital Humanities and link them to the rapid evolution of 3D technologies; (v) develop common tools and platforms; (vi) bring French experiences into international networks (Parthenos, Dariah, ARIADNE); (vii) disseminate all this information as widely as possible, among academics, industry and administrations.

WHO WE ARE

CREATION, SCIENTIFIC USE AND ARCHIVING OF 3D DATA FOR HUMANITIES AND SOCIAL SCIENCE

The 3D Consortium of the TGIR Huma-Num has been created based on the observation that there are many initiatives around 3D for the Digital Humanities without real coordination between them. The proliferation of initiatives makes the task difficult and only a consortium-type organization can bring together forces in order to define standardized solutions. The difficulty is increased by the fact that we are dealing with multiple domains, combining science and technology with the humanities. The aim of the consortium is to facilitate discussions by putting together a maximum of research groups that integrate the use of 3D digital data in their scientific practice, to develops tools for acquisition, visualization, interpretation and preservation of data for the Humanities. The consortium is therefore willing to develop synergies between national Humanities and 3D disciplines in order to: (i) share experiences; (ii) edit recommendations in terms of methodology, standards and formats; (iv) identify the specific needs of Digital Humanities and link them to the rapid evolution of 3D technologies; (v) develop common tools and platforms; (vi) bring French experiences into international networks (Parthenos, Dariah, ARIADNE); (vii) disseminate all this information as widely as possible, among academics, industry and administrations.

WHAT WE DO

DISSEMINATE GOOD PRACTICES

Publications of several reports with recommendations on long term archiving 3D project, 3D softwares inventory, 3D glossary, and specifications and needs for a project with 3D models of Cultural Heritage.

The 3D Consortium of the TGIR Huma-Num has been created based on the observation that there are many initiatives around 3D for the Digital Humanities without real coordination between them. The proliferation of initiatives makes the task difficult and only a consortium-type organization can bring together forces in order to define standardized solutions. The difficulty is increased by the fact that we are dealing with multiple domains, combining science and technology with the humanities. The aim of the consortium is to facilitate discussions by putting together a maximum of research groups that integrate the use of 3D digital data in their scientific practice, to develops tools for acquisition, visualization, interpretation and preservation of data for the Humanities. The consortium is therefore willing to develop synergies between national Humanities and 3D disciplines in order to: (i) share experiences; (ii) edit recommendations in terms of methodology, standards and formats; (iv) identify the specific needs of Digital Humanities and link them to the rapid evolution of 3D technologies; (v) develop common tools and platforms; (vi) bring French experiences into international networks (Parthenos, ARIADNE); (vii) disseminate all this information as widely as possible, among academics, industry and administrations.

LIFE CYCLE OF 3D DATA FOR CULTURAL HERITAGE

A FRENCH NATIONAL 3D REPOSITORY

French National Repository of 3D Data for researchers in digital humanities, with a secured backup environment. The data stored in the repository is accompanied by standardized metadata giving information on the scientific context of the project.

STANDARDIZATION SURVIVAL KIT (SSK)

In collaboration with the Parthenos Project, we have published use case scenarios for the production and processing of 3D objects and also for the preservation 3D of digital objects.

consortium3d-coordination@services.cnrs.fr CONTACT http://www.conservatoire3d.fr/ http://ssk.huma-num.fr/#/ The 3D Consortium of the TGIR Huma-Num has been created based on the observation that there are many initiatives around 3D for the Digital Humanities without real coordination between them. The proliferation of initiatives makes the task difficult and only a consortium-type organization can bring together forces in order to define standardized solutions. The difficulty is increased by the fact that we are dealing with multiple domains, combining science and technology with the humanities. The aim of the consortium is to facilitate discussions by putting together a maximum of research groups that integrate the use of 3D digital data in their scientific practice, to develops tools for acquisition, visualization, interpretation and preservation of data for the Humanities. The consortium is therefore willing to develop synergies between national Humanities and 3D disciplines in order to: (i) share experiences; (ii) edit recommendations in terms of methodology, standards and formats; (iv) identify the specific needs of Digital Humanities and link them to the rapid evolution of 3D technologies; (v) develop common tools and platforms; (vi) bring French experiences into international networks (Parthenos, Dariah, ARIADNE); (vii) disseminate all this information as widely as possible, among academics, industry and administrations.

KEYWORDS

https://shs3d.hypotheses.org/

The 3D Consortium of the TGIR Huma-Num has been created based on the observation that there are many initiatives around 3D for the Digital Humanities without real coordination between them. The proliferation of initiatives makes the task difficult and only a consortiumtype organization can bring together forces in order to define standardized solutions. The difficulty is increased by the fact that we are dealing with multiple domains, combining science and technology with the humanities. The aim of the consortium is to facilitate discussions by putting together a maximum of research groups that integrate the use of 3D digital data in their scientific practices, to develops tools for acquisition, visualization, interpretation and preservation of data for the Humanities. The consortium is therefore willing to develop synergies between national Humanities and 3D disciplines in order to: share experiences; edit recommendations in terms of methodology, standards and formats; identify the specific needs of Digital Humanities and link them to the rapid evolution of 3D technologies; develop common tools and platforms; bring French experiences into international works (Parthenos, Dariah, ARIADNE); (vii) disseminate all this information as widely as possible, among academics, industry and administrations.

  aLTAG 3D: open source software to document the metadata of a scientific 3D project. This software is suitable with the French archiving service of CINES (National Computing Center for Higher Education) Store 3D data and metadata in CINES data center STANDARDIZED SOLUTIONS

  http://altag3d.huma-num.fr F. Laroche (Epotec LS2N) -M. Chayani (Archeovision) -X. Granier ( Institut d'Optique Graduate School, LP2N)