Cheikh Tidiane Dieng

Tao-Yuan Jen

Dominique Laurent

An Efficient Computation of Frequent Queries in a Star Schema

Keywords: Frequent Queries, Functional Dependencies, Inclusion Dependencies, Query Comparison, Star Schemas

Although the problem of computing frequent queries in relational databases is known to be intractable, it has been argued in our previous work that using functional and inclusion dependencies, computing frequent conjunctive queries becomes feasible for databases operating over a star schema. However, the implementation considered in this previous work showed severe limitations for large fact tables. The main contribution of this paper is to overcome these limitations using appropriate auxiliary tables. We thus introduce a novel algorithm, called Frequent Query Finder (FQF), and we report on experiments showing that our algorithm allows for an effective and efficient computation of frequent queries.

Introduction

The problem of discovering frequent patterns in a (relational) database is one of a main topics in data mining. However, even when patterns are restricted to conjunctive queries, this problem is known to be intractable, because the size of the search space is exponential in the size of the database. Nonetheless, it is argued in [START_REF] Jen | Mining all frequent selection-projection queries from a relational table[END_REF][START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] that mining all frequent conjunctive queries (i.e., conjunctive queries whose answers have a cardinality greater than or equal to a predefined threshold) becomes tractable if the underlying database operates over a star schema, and if constraints such as functional and inclusion dependencies, are taken into account.

Indeed, it has been shown in [START_REF] Jen | Mining all frequent selection-projection queries from a relational table[END_REF][START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] that such dependencies allow for comparing queries according to a pre-ordering with respect to which the support measure is anti-monotonic (the support of a query being the number of tuples in the answer of that query). As a consequence, a levelwise algorithm such as Apriori ( [START_REF] Agrawal | Fast discovery of association rules[END_REF]) can be used, with the basic additional feature that the considered pre-ordering induces an equivalence relation for which two equivalent queries have the same support. Consequently, one computation per equivalence class allows to determine the support of all queries of this class.

In the present paper, similarly to [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], we consider a relational database operating over a star schema and we follow the approach of [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] for mining frequent projection-selection-join queries in which joins are performed along keys and foreign keys. In this setting, our contribution is to provide an efficient computation of such frequent queries.

Indeed, it is shown in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] that the number of scans of the database in our algorithms is in O(N × |U |) (where N is the number of dimensions of the underlying star schema and |U | is the number of attributes in this schema), and that, in order to have an efficient implementation, an appropriate indexing technique should be used to count the supports safely. The problem to solve is finding an at most linear technique for counting only once the duplicates occurring in the answers to projection queries; a problem which basically requires a quadratic scan of the table. Unfortunately, as such an indexing technique must work for all possible attribute sets, no solution could be found. In fact, in the implementation of [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], auxiliary data are stored in main memory, so as to keep track of the tuples computed so far for a given query. Therefore, this technique is somehow still quadratic (since duplicates are still checked against the auxiliary data), and more importantly, experiments result in main memory overflow for large fact tables.

In order to cope with this important limitation, we propose a novel efficient and scalable algorithm, called Frequent Query Finder (FQF), for the computation of frequent queries. According to FQF, every table r to be mined is associated with an auxiliary table AUX(r), whose role is to associate every tuple t of r with all attribute sets S such that t.S = t ′ .S for some tuple t ′ occurring in r before t, with respect to the scanning order of r. Assuming that these auxiliary tables are computed, it turns out that counting the supports becomes linear in the size of the table to be mined. We are thus provided with an efficient and scalable implementation, in the sense that runtime keeps very low and that no main memory overflow occurs, even for large datasets (up to 100,000 tuples in our experiments). We refer to Section 5 for experiments.

We also emphasize that, although the computation of an auxiliary table AUX(r) is still quadratic in the size of r, our experiments show that our new implementation, even when involving the computation of the auxiliary tables, outperforms that of [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] (when the comparison is possible). Moreover, it is also argued in the end of the paper that the computation of the auxiliary tables can be seen as a pre-processing phase, when mining frequent queries.

The paper is organized as follows: In Section 2, we briefly overview related work, and in Section 3, we recall from [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] the basic definitions and properties of our approach. Then, in Section 4, we present our algorithm FQF for mining conjunctive queries and in Section 5, we report on experiments showing that our algorithms are efficient. Section 6 concludes the paper and discusses future work.

Related Work

Early approaches dealing with frequent queries [START_REF] Dehaspe | Mining association rules in multiple relations[END_REF][START_REF] Diop | Composition of mining contexts for efficient extraction of association rules[END_REF][START_REF] Han | Dmql : A data mining query language for relational databases[END_REF][START_REF] Meo | An extension to sql for mining association rules[END_REF] consider a fixed set of "objects" to be counted when computing supports, meaning that in these approaches, all queries of interest are projections over a fixed attribute set. Moreover, apart from [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF], none of these approaches consider constraints on the data, such as functional dependencies, in order to optimize the computation. In [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF], equivalent attribute sets with respect to functional dependencies are used for query optimization, based on materialized views, which is not the case in our approach.

To the best of our knowledge, [START_REF] Goethals | Relational association rules: getting warmer[END_REF] is the first approach for mining frequent queries in the general context where the set of objects to be counted is not fixed. However, in [START_REF] Goethals | Relational association rules: getting warmer[END_REF], equivalent queries are generated, which can not be tested efficiently (a problem that does not exist in our approach); and moreover, data dependencies are not taken into account.

The work of [START_REF] Goethals | Mining tree queries in a graph[END_REF], dealing with mining tree queries in a graph, is also closely related to ours. Indeed, in [START_REF] Goethals | Mining tree queries in a graph[END_REF], a graph is seen as a binary relation, and frequent tree queries are expressed as SQL projection-selection-join queries. This work is somehow generalized in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF] to the case of projectionselection-join queries, with the restriction that a given relation cannot occur more than once in the joins. Queries considered in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF] are more general than ours, since (i) all possible joins in which base relations occur at most once are considered in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], whereas we only consider such joins along keys and foreign keys, and (ii) selection conditions of the form (Y = Y ′ ) where Y and Y ′ are relation schemas are allowed in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], which is not the case in our approach. However, in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], dependencies are not taken into account, thus resulting in redundant computations.

In our previous work [START_REF] Jen | Mining all frequent selection-projection queries from a relational table[END_REF][START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF][START_REF] Jen | Towards mining frequent queries in star schemes[END_REF], we have considered conjunctive query mining in a star schema, focussing successively on projection queries ( [START_REF] Jen | Towards mining frequent queries in star schemes[END_REF]), projection-selection queries ( [START_REF] Jen | Mining all frequent selection-projection queries from a relational table[END_REF]), and projection-selection-join queries ( [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]). The main contribution of this previous work is to show that taking dependencies into account in query comparison results in an efficient computation of frequent conjunctive queries. In particular, in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], it is shown that if the database schema is a star schema, then the problem of mining frequent projection-selection-join queries where joins are performed along keys and foreign keys becomes tractable. However as previously mentioned, in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], experiments show severe limitations, and the contribution of this paper is to propose an efficient and scalable implementation that overcomes these limitations.

Formal Model

Queries

We first recall that a database ∆ over a star schema consists of a distinguished table ϕ with schema F , called the fact table, together with a set of other tables δ1, . . . , δN with schemas D1, . . . , DN , called the dimension tables, such that:

1. If K1, . . . , KN are the (primary) keys of δ1, . . . , δN , respectively, then, denoting by K the union of these keys (i.e., K = K1 . . . KN ), K is the key of ϕ. In other words, for every i = 1, . . . , N , δi satisfies Ki → Di and ϕ satisfies K → F . We denote by F the set of these functional dependencies.

2. For every i = 1, . . . , N , πK i (ϕ) ⊆ πK i (δi) (thus each Ki is a foreign key in the fact table ϕ). The attribute set M = F \ K is called the measure of the star schema. As usual, we denote by F + the set of all functional dependencies that can be inferred from F, using the Armstrong's axioms, and we denote by X + the set of all attributes A such that X → A is in F + ( [START_REF] Ullman | Principles of Databases and Knowledge-Base Systems[END_REF]).

In what follows, we consider a fixed database ∆ = (δ1, . . . , δN , ϕ), along with projection-selection-join queries with the following specificities:

-the tuple in selection condition is either the empty tuple, denoted by ⊤ (in which case all tuples are selected), or a tuple y over Y (in which case all tuples t such that t.Y = y are selected); -the joins are performed along keys and foreign keys, that is, either the join is reduced to a single table, or it involves the fact table ϕ.

Definition 1. Let ∆ = (δ1, . . . , δN , ϕ) be a database over a star schema.

The considered set of queries, denoted by Q, is the set of all queries of the form q = πX (σy(r)), or more simply πX σy(r), such that XY ⊆ R (R denotes the schema of r), and where:

-r is either a table in ∆ or a join of such tables containing ϕ; -y is either the empty tuple ⊤or a tuple over relation schema Y . For every query q in Q, the support of q in ∆, denoted by sup(q), is the cardinality of the answer to q. Given a support threshold min-sup, a query q is said to be frequent if sup(q) ≥ min-sup.

We illustrate our approach using the following example, borrowed from [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], and that we shall use as a running example throughout the paper.

Example 1. Consider the database ∆ consisting of three tables and a set of functional and inclusion dependencies, as shown in Figure 1. The meaning of the attributes is as follows:

-Cid, Cname and Caddr stand for Customer Identifier, Customer Name and Customer Address, -P id and P type stand for Product Identifier and Product Type, -Qty stands for Quantity (i.e., number of products sold). The schema of ∆ is clearly a star schema, with Sales as its fact table, and Cust and P rod as its dimensional tables.

The queries q1 = π Cid σParis(Cust) and q2 = π Cid σParis beer(C ust ⋊ ⋉ P rod ⋊ ⋉ Sales) are in Q, the answers of which being {c1, c2, c3} and {c1, c2}, respectively. Thus, if min-sup = 2, these queries are frequent.

On the other hand, π Cid (Cust) and π Cid (Cust ⋊ ⋉ Sales) are also in Q, and are written as π Cid σ ⊤ (Cust) and π Cid σ ⊤ (Cust ⋊ ⋉ Sales), respectively. Their answers are respectively {c1, c2, c3, c4} and {c1, c2}.

Query Comparison

Definition 2. Let q = πX σy(r) and q1 = πX 1 σy 1 (r1) be queries in Q. Then q1 is said to be more specific than q in ∆, denoted by q q1, if one of the following holds: It has been shown in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] that the relation is indeed a pre-ordering (i.e., reflexive and transitive), with respect to which the support is antimonotonic, i.e., (∀q, q1 ∈ Q)(q q1 ⇒ sup(q1) ≤ sup(q)).

1. y1 ∈ πY 1 (r1) 2. y ∈ πY (r), y1 ∈ πY 1 (r1
Clearly, this property is required when mining patterns according to a level-wise algorithm, such as Apriori ( [START_REF] Agrawal | Fast discovery of association rules[END_REF]). Moreover, the pre-ordering induces an equivalence relation defined as follows: two queries q and q1 in Q are said to be equivalent, denoted by q ≡ q1, if q q1 and q1 q hold. The equivalence class of a query q is denoted by [q]. Referring back to Example 2, the queries q3 and q ′ 3 are equivalent, since it has been seen that q3 q ′ 3 and q ′ 3 q3 both hold. As a consequence of the anti-monotonicity property mentioned above, it turns out that equivalent queries have the same support. Therefore, instead of computing the supports of individual queries, we consider only one query per equivalence class.

The pre-ordering is extended to the set of equivalence classes C, and then becomes an ordering (i.e., reflexive, anti-symmetric and transitive) over C. Moreover, a class [q] is said to be frequent if its support (i.e., the support of all queries in [q]) is greater than or equal to min-sup.

It is easy to see that all queries q = πX σy(r) in Q such that y ∈ πY (r) are equivalent and have a support equal to 0, a value meant to be less than the support threshold min-sup. Similarly, all queries q = πX σy(r) in Q such that y ∈ πY (r) and Y → X ∈ F + are equivalent, and have a support equal to 1, another value meant to be less than min-sup. Thus, these equivalence classes, respectively denoted by C0 and C1, are not considered in the computation of frequent queries.

Equivalence classes different than C0 and C1, whose set is denoted by C * , have been characterized in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]. We simply recall that, given a query q = πX σy(r) such that [q] is in C * , we consider the representative

q + = π X ′ σ y ′ (r ′ ) of [q] such that: 1. X ′ = (XY ) + and Y ′ = Y + , 2. r ′ = r if r is a dimension table, otherwise, r ′ = J
where J is the join of all tables in ∆, 3. y ′ is the tuple over Y + such that y is a subtuple of y ′ and y ′ ∈ π Y + (r ′ ). In the remainder of the paper, all considered queries are assumed to satisfy the properties above, and stand for their equivalence classes.

Example 3. In Example 1, we have J = (Cust ⋊ ⋉ P rod ⋊ ⋉ Sales). As seen in Example 2, q3 = π Cid Cname σ ⊤ (Cust ⋊ ⋉ Sales) and q ′ 3 = π Cid Cname Caddr σ ⊤ (J) are equivalent. As (Cid Cname) + = (Cid Cname Caddr) and ∅ + = ∅, [q3] is represented by q ′ 3 . It can be seen that [q3] is the set of all queries πX σ ⊤ (r) such that Cid ⊆ X ⊆ (Cid Cname Caddr), and either r = J or r = (Cust ⋊ ⋉ Sales). For q = πCname P typeσp 2 (J), we have (Cname P id P type) + = (Cname P id P type), P id + = (P id P type), and p2 beer ∈ π P id P type (J). Thus, [q] is represented by π Cname P id P type σp 2 beer(J ), and this class is the set of all queries πX σy(r) such that Cname ⊆ X ⊆ (Cname P id P type), and either y = p2 and r = (Cust ⋊ ⋉ Sales) or r = J or y = p2 beer and r = J.

Algorithms

Main Algorithm: FQF

As in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], frequent classes in C * are computed by a level-wise algorithm, called Frequent Query Finder (FQF), whose main steps are shown in Figure 2: all dimension tables are first mined, and then the join J of all tables in ∆ is mined. Moreover, as in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], we define the notion of generic class to avoid generating classes that are processed in the same way.

Algorithm FQF

Input: The database ∆ associated to an N -dimensional star schema and a support threshold min-sup. Output: The set F req of all frequent classes. Method:

F req = ∅ for i = 1, . . . , N do mine(δi, F req(δi)) F req = F req ∪ F req(δi) compute J = δ1 ⋊ ⋉ . . . ⋊ ⋉ δN ⋊ ⋉ ϕ mine(J, F req(J)) F req = F req ∪ F req(J) return F req Fig. 2.
The main algorithm FQF Definition 3. Given a class q = πX σy(r) in C * , the generic class associated to q, denoted by X, Y, r , is the set of all classes πX σ y ′ (r) in C * such that y ′ is a tuple in πY (r), i.e., X, Y, r

= {πX σ y ′ (r) ∈ C * | y ′ ∈ πY (r)}.
Algorithm mine, shown in Figure 3, follows a level-wise strategy ( [START_REF] Agrawal | Fast discovery of association rules[END_REF]). Namely, starting with the less specific generic class, that is r, the following steps are iterated until no frequent classes are generated:

1. Generate and prune the set C of candidate generic classes, based on the current set L of frequent generic classes (see [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]); 2. Compute the supports of all classes associated with the remaining candidate generic classes in C; 3. Discard all classes whose support is less than the support threshold; 4. Assign L to the set of all generic classes that contain at least one frequent class. However, the steps above require more attention than in Apriori, because (i) we are dealing with equivalence classes, instead of individual itemsets, (ii) the ordering over C * is more difficult to handle than set inclusion, and (iii) computing the supports requires to efficiently scan the database.

Consequently, the main difficulties are first, generating and pruning generic classes, and second, computing efficiently the supports of classes in C * . The first point has been addressed in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] (see Proposition 7 in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]), but not the second one, which is the main contribution of the present paper, and which we address below.

Algorithm scan

When scanning a given table r, the main difficulty is that every tuple in the answer to a query must be counted only once, whereas, due to projection, it might occur several times when scanning r. In order to cope with this difficulty, it is argued in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] that indexing techniques are required. Unfortunately, considering such indexing techniques, which have to work for all possible attribute sets, is not realistic. In order to cope with this problem, in [START_REF] Jen | Mining all frequent selection-projection queries from a relational table[END_REF][START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], each scan is associated with huge

Algorithm mine

Input: A table r (either a dimension table δi or the join J) defined over R. Output: The set F req(r) of all frequent classes in C * of the form πX σy(r). Method: if |r| < min-sup then //no computation since, for every q in C * of the form πX σy(r), |r| ≥ sup(q) F req(r) = ∅ else //the computation starts with the generic class R, ∅, r

L = { R, ∅, r } ; F req(r) = {πRσ ⊤ (r)} while L = ∅ do //L is the set of frequent generic classes from the previous level C = generate(L, r) C = prune(C, L, r) scan(C, AUX(r), L, LF req (r))
//L contains all frequent generic classes of the current level, and //LF req (r) is the corresponding set of frequent classes F req(r) = F req(r) ∪ LF req (r) return F req(r) Fig. 3. Computing frequent queries on a table r volumes of auxiliary data, resulting in main memory overflow for large fact tables.

Instead, in the present paper, before scanning r, we build an auxiliary table, denoted by AUX(r), as follows. Assuming that r contains n tuples t1, . . . , tn, the first row AUX(r) [START_REF] Agrawal | Fast discovery of association rules[END_REF] of AUX(r) is set to the empty set, and for every i = 2, . . . , n, the ith element of AUX(r), denoted by AUX(r)[i], contains all maximal (with respect to set inclusion) attribute sets S for which there exists j < i such that tj.S = ti.S. Therefore, when considering ti during a scan of r, knowing that S is in AUX(r)[i] ensures that for every X ⊆ S, ti.X has already been processed.

The corresponding algorithm is shown in Figure 4, where match(ti, tj) stands for the set of all attributes A such that ti.A = tj.A. We note that computing match(ti, tj) amounts to compare ti and tj, which does not require using any index.

Example 4. We illustrate the construction of the auxiliary table AUX(J) in the context of Example 1, for J = Cust ⋊ ⋉ P rod ⋊ ⋉ Sales. The tables J and AUX(J) are shown in Figure 5.

Since match(t2, t1) = Caddr, we obtain AUX(J) [START_REF] Dehaspe | Mining association rules in multiple relations[END_REF] = Caddr. Similarly, since match(t3, t1) = (P id Caddr P type) and match(t3, t2) = (Cid Cname Caddr), AUX(J) [START_REF] Diop | Composition of mining contexts for efficient extraction of association rules[END_REF] is the set of these two attribute sets.

The computation for AUX(J) [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF] is similar, but although match(t4, t3) = Caddr, this schema does not appear in AUX(J) [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF]. This is so because Caddr is a subset of (Cid Cname Caddr Qty) and (P id Caddr P type) that both belong to AUX(J) [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF]. Now, given a table r and assuming that AUX(r) has been computed, the supports of equivalence classes over r are computed through parallel scans of r and AUX(r). The corresponding algorithm scan is shown in Figure 8 shows the runtimes of FQF compared to those presented in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] for db2D12TtM1, with t between 50 and 5000. Clearly, FQF outperforms our previous implementation presented in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]: the reduction of runtime between the implementation in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] and FQF is always greater than 33%. In should also be noticed from Figure 8 that the runtime for only mining frequent classes is very low, since less than 40 seconds.

Similarly, as shown in Figure 9, the time spent in mining the frequent classes for the databases db2D12TtM1 with t between 10,000 and 90,000 is very low compared to that for calculating the auxiliary tables. Moreover, this runtime increases slowly with the size of the fact table. We also emphasize that, in these experiments, we had no main memory overflow, contrary to what happened with the previous implementation presented in [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF], when t exceeds 5000.

Figure 10 reports on runtime over the number of dimensions, for the databases dbdD12TtM1 where d ranges from 2 to 5 and for t equal to 2000, 5000 and 10,000. This figure clearly shows that the time spent for mining frequent classes decreases significantly when the number of dimensions increases. This is so because, given a number of attributes (12 in our case), when d increases, more functional dependencies are available, and so, less classes have to be processed. It is important to note that, according to our previous statement that the number of scans of the database is in O(N × |U |) (where N is the number of dimensions and |U | the total number of attributes), one would rather expect an increase of runtime when N increases. However, what these experiments show is that, although the increase of the number of dimension tables entails more scans, this is compensated by a drastic reduction of the number of generic classes.

Figure 11 shows the runtime over the support threshold (expressed as a ratio of the size of the fact table), for databases db5D25TtM1 with t equal to 2000, 5000 and 10,000. Clearly, runtime decreases rapidly when the support threshold increases.

We recall from Section 2 that the only other work aiming at mining all frequent queries from a relational database is that in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], and thus, we could compare our algorithm only to the Conqueror algorithm ( [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF]). This has been done using the IMDB database (http://www.imdb.com), for various support thresholds (expressed in numbers of tuples). To do so, we first transformed the IMDB database into a star schema having 3 dimensions, 6 attributes and no measure. In this experiment, the fact table contains 158,441 tuples.

As shown in Figure 12, our algorithm performs better than the Conqueror algorithm. This is so because, in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], functional and inclusion dependencies are not taken into account, as we do in our approach. However, we recall in this respect that selection conditions of the form Y = Y ′ (where Y and Y ′ are attribute sets) are considered in [START_REF] Goethals | Mining association rules of simple conjunctive queries[END_REF], which is not the case in our approach.

We end this section by two important remarks regarding the computation of the auxiliary tables.

1. The computation of auxiliary tables can be seen as a pre-processing, because it has to be computed only once for all runs of FQF, provided that, meanwhile, the database has not been updated. This remark is very important regarding runtime, because, as shown in Figures 8 and9, assuming that auxiliary tables are available, the runtime of FQF is very low even for large fact tables. 2. When a database table r is updated, maintaining up to date the associated auxiliary table AUX(r) can be achieved efficiently. Indeed, in the case of insertion of a new tuple t in r, and assuming that t becomes the last tuple of r, a new row is added to AUX(r) and the associated schemas are obtained through one scan of r. If a tuple ti is deleted from r, then AUX(r)[i] must be deleted from AUX(r), and only the rows AUX(r)[j] such that j > i and match(tj, ti) ∈ AUX(r)[j] have to be updated.

Conclusion and Further Work

We presented new algorithms for mining frequent queries in databases over a star schema, based on theoretical results introduced in our previous work [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF]. We showed through experiments that, in this particular case, mining frequent conjunctive queries becomes tractable. Our approach relies on the computation of auxiliary tables that can be seen as a pre-processing phase. An important point in this respect is that, assuming these auxiliary tables are available, the time for mining frequent queries becomes very low, as shown in our experiments. Future work consists in processing further tests and optimizing our algorithms. We also plan to generalize our approach to database schemas other than star schemas, and to study the possible rules that can be obtained based on frequent queries.

Fig. 9 .

 9 Fig. 9. Runtime over the size of the fact table.

Fig. 10 .

 10 Fig. 10. Runtime over the number of dimensions.

Fig. 11 .

 11 Fig. 11. Runtime over support.

Fig. 12 .

 12 Fig. 12. FQF versus Conqueror.

  ), and Y1 → X1 ∈ F + 3. All of the following hold: Cid (Sales) ⊆ π Cid (Cust) π P id (Sales) ⊆ π P id (P rod) Cid Caddr P type → Cid ∈ F + , Caddr P type → Caddr ∈ F + , and (d) Indeed, by Definition 2.2, Paris ∈ π Caddr (Cust), beer 5 ∈ πP type Qty (P rod ⋊ ⋉ Sales) and P type Qty → Qty is in F + . Notice that, by Definition 2.1, we also have q5 q4.

	Cust Cid Cname Caddr
	c1	John Paris		P rod P id P type
	c2	Mary Paris		p1 milk
	c3	Jane Paris		p2 beer
	c4	Anne Tours
	Sales Cid P id Qty c1 p1 10 c2 p2 5 c2 p1 1		F : Cid → CnameCaddr P id → P type CidP id → Qty
	c1 p2 10 I : π Paris beer ∈ π Caddr P type (Cust ⋊ ⋉ P rod ⋊ ⋉ Sales). Therefore, q1 q2.
		Consider now q ′ 2 = πCnameσc 2 beer(C ust ⋊ ⋉ P rod ⋊ ⋉ Sales). Then,
	by Definition 2.2, q1	q ′
		For q3 = π Cid Cname σ ⊤ (Cust ⋊ ⋉ Sales), as above, q3	q2 holds. For
	q ′ 3 = π Cid Cname Caddr σ ⊤ (Cust ⋊ ⋉ P rod ⋊ ⋉ Sales), applying again Defini-
	tion 2.3, it can be seen that q3 q ′ 3 and q ′ 3	q3 hold.
		For q4 = πQtyσbeer 15(P rod ⋊ ⋉ Sales), by Definition 2.1, we find q1 q4,
	q2 q4 and q3 q4, because beer 15 ∈ πP type Qty (P rod ⋊ ⋉ Sales).
		For q5 = πQtyσbeer 5(P rod ⋊ ⋉ Sales), we have q1	q5, q2	q5 and
	q3	q5.

Fig. 1. The database of the running example (a) either r = r1 or r1 involves the fact table ϕ

, (b) y ∈ πY (r), y1 ∈ πY (r1), Y1 → X1 ∈ F + , (c) XY1 → X1 ∈ F + and Y1 → Y ∈ F + , (d) yy1 ∈ πY Y 1 (r ⋊ ⋉ r1).

Example 2. In the context of Example 1, consider again the queries q1 = π Cid σParis(Cust) and q2 = π Cid σParis beer(C ust ⋊ ⋉ P rod ⋊ ⋉ Sales). Referring to Definition 2.3, we have: (a) Cust ⋊ ⋉ P rod ⋊ ⋉ Sales involves the fact table Sales, (b) Paris ∈ π Caddr (Cust), Paris beer ∈ π Caddr P type (Cust ⋊ ⋉ P rod ⋊ ⋉ Sales) and Caddr P type → Cid ∈ F + , (c) 2 , because Paris ∈ π Caddr (Cust), c2 beer ∈ π Cid P type (Cust ⋊ ⋉ P rod ⋊ ⋉ Sales) and Cid P type → Cname ∈ F + .

Algorithm aux

Input: A table r to be scanned containing tuples t1, . . . , tn. Output: The table AUX(r). Method: AUX [START_REF] Agrawal | Fast discovery of association rules[END_REF] = ∅ for each i = 2, . . . , n do AUX(r)[i] = ∅ for each j = 1, . . . , i -1 do compute match(ti, tj) if AUX(r) [i] contains no super set of match(ti, tj) then AUX(r)[i] = AUX(r)[i] ∪ match(ti, tj) return AUX(r) Fig. [START_REF] Esposito | Answering constraint-based mining queries on itemsets using previous materialized results[END_REF]. Computing the auxiliary table AUX(r) J Cid P id Cname Caddr P type Qty t1 c1 p1 John Paris milk 10 t2 c2 p2 Mary Paris beer 5 t3 c2 p1 Mary Paris milk 1 t4 c1 p2 John Paris beer 10

(P id Caddr P type), (Cid Cname Caddr) 4 (Cid Cname Caddr Qty), (P id Caddr P type) Fig. 5. The table J and the associated table AUX(J) of Example 1 Figure 6. The input of Algorithm scan is a set C of candidate generic classes of the form X, Y, r for which r contains the tuples t1, . . . , tn. All frequent classes associated with all generic candidate classes in C are computed as follows: For every i = 1, . . . , n, the following actions are performed, for every X, Y, r in C:

1. If AUX(r)[i] contains a super schema of X, then ti.X has been encountered for some j < i. Thus ti.X has already been processed for all classes with a projection over X. Otherwise, ti.X is encountered for the first time, and thus, has to be processed. 2. In the latter case, ti.X has to be counted for the support of q = πX σt i .Y (r). Two cases are then possible: (a) If AUX(r)[i] contains a super schema of Y then q has been processed previously, and thus is already associated with X, Y, r . In this case, the support of q is incremented. (b) Otherwise, q is processed for the first time, and so, is not associated with X, Y, r . In this case, we check if q can be pruned (see below), and if not, its support is initialized to 1 and q is associated with X, Y, r .

Algorithm scan

Input: The set C of candidate generic classes, the table AUX(r).

Output: The set L of frequent generic classes in C, and the associated frequent classes LF req (r).

Method: Once these actions are performed, all supports of all classes that have to be computed are known. All classes whose support is greater than or equal to min-sup are put in LF req (r) and the set L of frequent generic classes is output.

In our algorithms, pruning is performed at two distinct levels: for generic classes in Algorithm mine, and for classes in Algorithm scan. In Algorithm mine, a generic class X, Y, r is pruned if at least one of its predecessors (according to ) contains no frequent classes, which entails that no class in X, Y, r can be frequent. However, if X, Y, r is not pruned, it may happen that a particular class πX σy(r) of X, Y, r can be pruned. This is checked in Algorithm scan as mentioned in item 2(b) above, according to Algorithm pruneQuery shown in Figure 7.

It is important to note that Proposition 7 of [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF] shows that this latter pruning is partial, in the sense that not all predecessors of the class πX σy(r) are tested. We opted for such a partial pruning for efficiency reasons, as processing a complete pruning would damage performance.

Algorithm pruneQuery

Input: A class q = πX σy(r). Output: boolean. Method: if there exist A ∈ Y and a ∈ dom(A) such that q = πX σ y ′ (r) / ∈ LF req (r) and y = y ′ a then return true; return false; Fig. 7. Class Pruning Fig. 8. Runtime over the size of the fact table for FQF and the implementation of [START_REF] Jen | Mining Frequent Queries in Relational Databases[END_REF].

Experiments

We performed experiments on an Pentium Duo Core with 2Go main memory running on Ubuntu Linux 2.6. The algorithms are implemented in Java using JDBC to communicate with MySql. Datasets have been generated using our own generator, adapted from the IBM data generator (www.almaden.ibm.com).

The generated databases over star schemas are denoted by dbdDaTtMm where d is the number of dimensions, a is the total number of attributes, t is the number of tuples in the fact table, and m is the number of measure attributes. In all our experiments, except those reported in Figures 11 and12, the support threshold is set to 0.6 times the number of tuples in the fact table, that is 0.6 × t. We also mention that all runtimes reported below include the computation time of the construction of auxiliary tables. Moreover, in Figures 8 and9, the runtimes excluding the computation of the auxiliary tables are also shown.


Dr Sandra Ribes
email: sribes@med.uni-goettingen.de

Maria Eugenia Pachón-Ibáñez

M A Domínguez

Raúl Fernández

Fe Tubau

Javier Ariza

Francesc Gudiol

Carmen Cabellos

Maria Ángeles Domínguez

Definition of combination effects: the definition is probably based on the end-point (24h) readings; this needs to be clearly defined

Keywords: GISA, heteroresistance, linezolid, peritonitis, experimental infections GISA, heteroresistance, linezolid, peritonitis, experimental infections

In vitro and in vivo activities of linezolid alone and combined with vancomycin and imipenem against with

reduced susceptibility to glycopeptides

Yes, the definition is based on the 24 h readings. A sentence has been added clarifying this point (page 5).

3. Antibiotic assay: Imipenem was analysed microbiologically. It is well documented that imipenem is rather unstable -has this been considered in the course of sampling, storage, and bioassay? -Please specify stability. Detection limits are given for vancomycin (quantitated chemically), but not for imipenem and linezolid -has to be done. How were the standards handled? Throughout the entire course of experimentation in parallel to treatment, sampling etc, etc? How high was the loss in imipenem-activity during this procedure and were some measures taken to adjust for the loss in activity?

Standard curves were constructed with mouse plasma; For imipenem, assay validation indicated linearity, r2 value of 0.9709 and for linezolid 0.9887. The detection limit for imipenem was 0.5 mg/ml and for linezolid was 2 mg/ml. Two sentences have been added with these details, page 7, (antibiotic assay). There were no special measures with imipenem. Samples were immediately centrifugated and frozen.

PK:

The PK-parameters should be reported, not only the PK/PD surrogates.

Table 1 has been deleted as suggested in point 8.

5. Protein binding is specified for linezolid + vancomycin, but not for imipenem, although free drug levels are reported. Furthermore, protein binding quoted refer to binding to human serum-proteins; binding to animal serum-proteins is quite often different. In this case, the authors are lucky, as the values differ not too much -but there are slight discrepancies which should be corrected and the "correct" references have to be be quoted:

Vanco Knudsen JD et al., AAC 1997;41: 1910-1915 The references about protein binding in rodents have been added. Also the corrected data have been added, including a correction of the original calculation that had a mistake. A protein binding of imipenem of 13-20% has been reported in human serum.

There is no report concerning the protein binding of imipenem in murine serum but we have found data on rats where the protein binding was considered as "limited" and "negligible": Therefore, free imipenem concentrations were considered to be the same as detected in the bioassay method.

6. Peritonitis model: statistical analysis has to be done on the same basis as for the bacteraemia model, i.e. comparison of the various treatment groups -which may very likely show that there are no differences.

We think that ANOVA is a correct test for comparison of the various treatment groups and we have analyzed by this test the results and published in several journals. 7. Appearance of resistance: this important and clinically relevant aspect is just mentioned in the discussion chapter; however, the authors have had the chance to generate corresponding data themselves. As the authors missed this chance, they should not discuss this aspect.

We have deleted the paragraph. 8. Table 1: PK/PD surrogates are presented -without using them or explaing their use in somewhat greater depth. The authors write that regimens have been selected mimicking human kinetics, i.e. serum conc similar to those found in humans. But these data are not presented, so that the reader has no impression how similar the concentrations were in the end. On page 11, lines 9-14 the authors refer very briefly and totally speculative to this table. But there is no basis for such a speculation. Others have provided PK/PD rationales for the clinical use of e.g. imi + line (Ong CT et al., Surgical Infections 2005; 6:419-426 and several others; Gentry-Nielsen quoted above for line). These publications should have been used as a baseline for the interpretation of the results generated in this study -please re-write this para -or delete any reference to PK/PD surrogates. The reviewer strongly recommends to shorten the manuscript by deleting e.g. the resistance-and PK/PD discussion etc, so that the manuscript should be shortened to the format of a concise article.

The paragraphs and Table 1 have been deleted.

Last but not least I'd like to draw the attention of the investigators to a phenomenon which is most frequently not considered at all: chronobiology. PK of almost every agent is strongly dependent from the circadian rhythm of the animals, which is disturbed anyway due to handling of the animals during the "human working hours" -it is a 12h difference + experimental stress. This results in an approx 50% variation of imi-kinetics in the rat, for example, leading to a marked variability of exposure during the day-and night-time. Again, this is not considered when PK data are generated during the lab-working hours only, which has very likely been the case in the course of this study, too. This comment is just food for thought.

Thank you very much for this interesting comment.

Reviewer #3: The paper is well-written and deals with the potential use of the new antimicrobial agent linezolid in combination with either imipenem or vancomycin in an era of increasing antibiotic resistance. It analyzes data and presents concise results from both laboratory and animal studies and concludes that linezolid, either alone or in combination with the other agents, is a promising antimicrobial for the therapy of infections by S. aureus strain with reduced glycopeptide susceptibility. In my opinion, there are three major and two minor points the authors should address to:

Major comments

*

The authors should comment on their selection of the peritonitis model, since peritonitis is usually mixed aerobic/anaerobic infection with predominantly Gram negative bacteria. In particular, why is this model a simulation of a Gram positive infection in humans? A reference to a previous experimental study conducted with that model should also be included.

The election of this particular peritonitis model was based on the previous experience of our working group to study therapeutic options in the management of infections caused by multiresistant Gram positive bacteria. Moreover, it is an interesting model to use as screening model in a small animal.

We have added a reference about the model and a sentence in the text (page 6, reference number 23). On page 6 ln 10 of the "mouse peritonitis model", it is stated that "at a given time point, mice were anaesthetised.". That time point is not given, thus its relation to the last administration of antimicrobials is unknown, in order to assess the results and, consecutively, the efficacy of the drugs. Moreover, it is inferred, although not stated, that the total number of doses administered to the sacrificed mice is 5. Is that correct? "At a given time point, mice were anaesthetized" this time points refers to 25 hours after start of therapy. We have added a sentence clarifying this point page 6, ln 10 of the "mouse peritonitis model".

Yes, we administered a total number of 5 doses: at hours 0, 5, 10, 15 and 20, covering 25 hours of therapy.

•

Why were concentrations of linezolid and imipenem not determined using an HPLC method? HPLC is the method of choice for the free (ie active) fraction of an antibiotic in serum and concentrations of the present study should be measured and reported with that methodology.

The HPLC technique is an expensive method that requires specialized equipment, high cost solvents and experience to adjust the most suitable chromatographic conditions. On the other hand, the bioassay method is clearly a less expensive method, ease of handling and requires no specialized equipment. In a study where linezolid concentrations in human serum and urine were determined, both techniques produced comparable results (Borner K, Borner E, Lode H. Determination of linezolid in human serum and urine by high-performance liquid chromatography. Int J Antimicrob Agents. 2001 Sep;18(3):253-8).

•

In addition, references 22 and 23 refer to protein binding in humans, who might be different in mice; thus, the murine pharmacodynamics should be recalculated accordingly.

Please see point 5 reviewer 1.

Minor comments

*

The abstract should be structured.

The abstract has been structured.

The volume of the journal is missing from reference #3.

The volume of reference 3 has been added. Reduced vancomycin and teicoplanin activities against hGISA and GISA isolates have been reported in experimental studies [START_REF] Climo | Combinations of vancomycin and beta-lactams are synergistic against staphylococci with reduced susceptibilities to vancomycin[END_REF][START_REF] Domenech | A mouse peritonitis model for the study of glycopeptide efficacy in GISA infections[END_REF][START_REF] Moore | Vancomycin treatment failure associated with heterogeneous vancomycin-intermediate Staphylococcus aureus in a patient with endocarditis and in the rabbit model of endocarditis[END_REF], while in the clinical setting vancomycin has appeared to be sub-optimal in deep-seated and difficultto-treat infections caused by these strains [START_REF] Moore | Vancomycin treatment failure associated with heterogeneous vancomycin-intermediate Staphylococcus aureus in a patient with endocarditis and in the rabbit model of endocarditis[END_REF][START_REF] Ariza | Vancomycin in surgical infections due to methicillin-resistant Staphylococcus aureus with heterogeneous resistance to vancomycin[END_REF]. Furthermore, the antagonistic effect or false synergy showed by in vitro studies with the combination of glycopeptides and β-lactams refuses its use as a potentially promising alternative to glycopeptide monotherapy [START_REF] Aritaka | Combination effect of vancomycin and beta-lactams against a Staphylococcus aureus strain, Mu3, with heterogeneous resistance to vancomycin[END_REF][START_REF] Goldstein | False synergy between vancomycin and beta-lactams against glycopeptide-intermediate Staphylococcus aureus (GISA) caused by inappropriate testing methods[END_REF]. The oxazolidinone linezolid, one of the new treatment options for multidrug-resistant Gram-positive bacteria [START_REF] Drew | Emerging options for treatment of invasive, multidrugresistant Staphylococcus aureus infections[END_REF][START_REF] Lentino | New antimicrobial agents as therapy for resistant gram-positive cocci[END_REF][START_REF] Rybak | In vitro activities of daptomycin, vancomycin, linezolid, and quinupristindalfopristin against Staphylococci and Enterococci, including vancomycin-intermediate and -resistant strains[END_REF], shows high in vitro activity against resistant staphylococcal strains [START_REF] Rybak | In vitro activities of daptomycin, vancomycin, linezolid, and quinupristindalfopristin against Staphylococci and Enterococci, including vancomycin-intermediate and -resistant strains[END_REF][START_REF] Perry | Linezolid: a review of its use in the management of serious gram-positive infections[END_REF].

In vitro and in vivo activities of linezolid alone and combined with vancomycin and imipenem against

In patients with MRSA infections, linezolid has shown comparable efficacy to vancomycin [START_REF] Rubinstein | Linezolid (PNU-100766) versus vancomycin in the treatment of hospitalized patients with nosocomial pneumonia: a randomized, double-blind, multicenter study[END_REF][START_REF] Stevens | Linezolid versus vancomycin for the treatment of methicillin-resistant Staphylococcus aureus infections[END_REF]. Moreover, it shows excellent oral bioavailability and does not require dose adjustment for renal insufficiency [START_REF] Perry | Linezolid: a review of its use in the management of serious gram-positive infections[END_REF]. Its unique mechanism of action by inhibiting ribosomal protein synthesis at an early stage of bacterial replication leads to the absence of cross resistance with other antimicrobials [START_REF] Rubinstein | Linezolid (PNU-100766) versus vancomycin in the treatment of hospitalized patients with nosocomial pneumonia: a randomized, double-blind, multicenter study[END_REF]. Although linezolid-nonsusceptible strains are unusual [START_REF] Jones | Zyvox Annual Appraisal of Potency and Spectrum Program Results for 2006: an activity and spectrum analysis of linezolid using clinical isolates from 16 countries[END_REF], long courses of oxazolidinone therapy could select resistant mutants [START_REF] Wilson | Linezolid resistance in clinical isolates of Staphylococcus aureus[END_REF], hence the use of a combined strategy might be considered in clinical practice. To date, the efficacy of linezolid as part of a combination has been studied against MRSA strains but very few data has been reported against hGISA or GISA strains [START_REF] Jacqueline | In vivo efficacy of ceftaroline (PPI-0903), a new broad-spectrum cephalosporin, compared with linezolid and vancomycin against methicillin-resistant and vancomycin-intermediate Staphylococcus aureus in a rabbit endocarditis model[END_REF][START_REF] Sacar | Linezolid alone and in combination with rifampicin prevents experimental vascular graft infection due to methicillin-resistant Staphylococcus aureus and Staphylococcus epidermidis[END_REF].

Linezolid plus β-lactams exhibited bactericidal and synergistic activity against MRSA and hGISA strains in experimental models of endocarditis and meningitis [START_REF] Jacqueline | In vivo efficacy of ceftaroline (PPI-0903), a new broad-spectrum cephalosporin, compared with linezolid and vancomycin against methicillin-resistant and vancomycin-intermediate Staphylococcus aureus in a rabbit endocarditis model[END_REF]. Linezolid plus rifampicin was an effective prophylactic regimen for preventing staphylococcal prosthetic vascular graft infection, although the combination did not show higher efficacy than linezolid monotherapy [START_REF] Sacar | Linezolid alone and in combination with rifampicin prevents experimental vascular graft infection due to methicillin-resistant Staphylococcus aureus and Staphylococcus epidermidis[END_REF].

We aimed to evaluate and compare the efficacies of linezolid alone and in combination with either vancomycin or imipenem against two S. aureus strains with reduced susceptibility to glycopeptides.

MATERIALS AND METHODS

Bacterial strains

Two clinical isolates of S. aureus with different degrees of resistance to glycopeptides were included: a hGISA strain isolated in our hospital and belonging to the Iberian clone, growing on 4 mg/l vancomycin Mueller-Hinton plates with a sub-population frequency of 3.6 x 10 -6 CFU/ml (this strain was equivalent to the Mu3 heteroresistant strain) [START_REF] Ariza | Vancomycin in surgical infections due to methicillin-resistant Staphylococcus aureus with heterogeneous resistance to vancomycin[END_REF]; and a GISA strain (Mu50, ATCC 700699) reported as the first GISA strain [START_REF] Hiramatsu | Methicillin-resistant Staphylococcus aureus clinical strain with reduced vancomycin susceptibility[END_REF]. MICs (mg/l), determined using the Etest and the macrodilution method [START_REF]Methods for dilution antimicrobial susceptibility test for bacteria that grow aerobically[END_REF], were for the hGISA strain: cloxacillin, 1024; cefotaxime, 1024; teicoplanin 8; vancomycin (VAN), 2; linezolid (LZD), 1; and imipenem (IMP), 32. MICs for the GISA strain were: cloxacillin, 1024; cefotaxime, 2048; teicoplanin, 16; VAN, 8; LZD, 2; and IMP, 64.

In vitro time-kill studies

The bactericidal activities of the drugs were tested in glass tubes containing Mueller-Hinton broth and a final inoculum of 1 x 10 5 to 1 x 10 6 CFU/ml [START_REF]Methods for dilution antimicrobial susceptibility test for bacteria that grow aerobically[END_REF]. sheep blood agar plates (SBA) at 37ºC for 24 h. Experiments were performed in duplicate. The following effects were studied in combinations after 24 h of incubation: a bactericidal effect was defined as a decrease in the initial inoculum of ≥ 3 log 10 CFU/ml. Synergy of a combination was defined as a > 2 log 10 CFU/ml reduction over the most active agent alone, with one of the drugs at subinhibitory concentration. An indifferent effect was defined as < 1 log (increase or decrease) in killing.

Pharmacokinetics

Pharmacokinetic studies were performed to select dose regimens that result in serum concentrations similar to those found in humans [START_REF] Domenech | A mouse peritonitis model for the study of glycopeptide efficacy in GISA infections[END_REF][START_REF] Macgowan | Pharmacokinetic and pharmacodynamic profile of linezolid in healthy volunteers and patients with Gram-positive infections[END_REF]. Groups of 21 healthy mice were used for each pharmacokinetic study. A single weightadjusted antibiotic dose was administered subcutaneously (sc) to each animal.

At different time points, sets of three animals were anaesthetised intraperitoneally (ip), and blood samples (0.5 ml) were obtained by an intracardiac puncture. Blood was centrifuged and serum stored at -80°C.

Pharmacokinetic and pharmacodynamic parameters were obtained by a computer-assisted method (PK Functions for Microsoft Excel. Usansky, Desai and Tang-Liu, Pharmacokinetics and Drug Metabolism Dept, Allergan, Irvine, CA 92606) after determination of antibiotic concentrations over the time. Based on the obtained parameters the final selected doses were: vancomycin 60 mg/kg every 5 h (300 mg/kg/day), linezolid 35 mg/kg every 5 h (175 mg/kg/day) and imipenem 30 mg/kg every 5 h (150 mg/kg/day).

Mouse peritonitis model

This mouse peritonitis model has been previously characterized in our laboratory [START_REF] Domenech | A mouse peritonitis model for the study of glycopeptide efficacy in GISA infections[END_REF][START_REF] Domenech | Experimental study on the efficacy of the combinations of glycopeptides and Β-lactams against Staphylococcus aureus with reduced susceptibility to glycopeptides[END_REF]. Inbred, female C57BL/6 mice (6 weeks; 14-16 g) were used (Harlan Int. Ibérica, S.A., Barcelona, Spain). Inoculation was performed via a 26-gauge syringe by ip injection of 0.5 ml of the inoculum consisting of a 5 x 10 8 CFU/ml staphylococcal suspension with 5% (w/v) mucin in sterile saline. A group of control mice (n ≥ 18) were killed 4 h after inoculation (hour 0) and antibiotic sc therapy was initiated. The rest of the mice were randomized to the control group receiving saline (n ≥ 25) or to one of the following therapeutic schedules (n ≥ 10 per therapy): Linezolid, vancomycin, imipenem, linezolid+vancomycin, linezolid+imipenem and vancomycin+imipenem receiving sc treatment over 25 h. At 25 h of therapy (5 h after the last antibiotic dose), mice were anaesthetised ip with ketamine/xylazine and peritoneal washes were performed by injecting 2 ml of sterile saline ip followed by a massage of the abdomen. Immediately, 0.1 ml of blood was withdrawn by cardiac puncture and animals were then sacrificed by cervical dislocation. Next, the abdomen was opened and 0.2 ml of peritoneal fluid (PF) was recovered from peritoneum.

Undiluted and ten-fold diluted PF samples (0.1 ml) were plated on SBA plates to perform bacterial determinations. Mortality was recorded after 25 h of therapy.

Blood samples were grown in TSB at 37ºC for 24 h and then 0.1 ml of broth was cultured on SBA plates to assess S. aureus bacteraemia.

Antibiotic assays

Vancomycin serum concentrations were determined by fluorescent polarization immunoassay using a TDx analyzer (ABBOTT CIENTIFICA, S.A., Diagnostics Division, Costa Brava 13, 28034 Madrid, Spain) with a detection limit of 2.0 µg/ml. Serum concentrations of linezolid and imipenem were measured using the agar disc diffusion method and Bacillus subtilis ATCC 12432 and Escherichia coli ATCC 25922, respectively, as assay organisms. Standard curves were constructed using mouse plasma. Assay validation indicated linearity (r 2 value) of 0.9709 for imipenem and 0.9887 for linezolid. The detection limit was 0.5 g/ml and 2 g/ml for imipenem and lnezolid, respectively.

Statistics

Statistical analysis was performed with SPSS 12.0. ANOVA with Dunnett's posthoc tests was used to analyse multiple bacterial count comparisons between therapeutic and control groups. Two-tailed Fisher's exact test was used for analyse survival and bacteraemia data. A P value of < 0.05 was considered statistically significant.

RESULTS

In vitro time-kill studies

Linezolid achieved a bacterial decrease up to 2 log CFU/ml when tested at 4-16 mg/l against both strains. Vancomycin achieved a bacterial decrease of 2 log CFU/ml when studied at 2 and 8 mg/l against the hGISA and the GISA strain, respectively. Imipenem failed to inhibit bacterial growth at any tested concentration (8-64 mg/l).

In killing curves with the hGISA strain, linezolid combined with vancomycin showed lower activity than vancomycin alone. Vancomycin activity was decreased between 1-1.5 log 10 CFU/ml at 24 h. The same combination improved the activities of antibiotics tested alone against the GISA strain (Figure 1).

The combination of linezolid at concentrations above the MIC and imipenem did not improve upon the activity of linezolid tested alone against either strain. The addition of sub-MIC concentrations of linezolid to imipenem produced a synergistic effect against both strains (Figure 2).

The combination of vancomycin with imipenem was bactericidal and synergistic against the hGISA strain. Vancomycin tested at 2 mg/l in combination with imipenem (8-64 mg/l) was also bactericidal and improved upon the activity of vancomycin alone against the GISA strain.

Pharmacokinetics.

Linezolid and vancomycin free maximum concentrations in serum were 18.16 and 37.73 mg/l, respectively (with a protein binding of 26 % for linezolid and 25 % for vancomycin [START_REF] Gentry-Nielsen | Pharmacodynamic activity and efficacy of linezolid in a rat model of pneumococcal pneumonia[END_REF][START_REF] Knudsen | Activity of vancomycin and teicoplanin against penicillin resistant pneumococci in vitro and in vivo and correlation to pharmacokinetic parameters in the mouse peritonitis model[END_REF]) Imipenem free maximum concentration found in serum was 38.26 mg/l. Drug serum concentrations in humans are 12-15 mg/l for linezolid (dose 600 mg/12 h), 30-40 mg/l for vancomycin (dose 1 g/12 h) [START_REF] Murillo | Efficacy of high doses of levofloxacin in experimental foreign-body infection by methicillin susceptible Staphylococcus aureus[END_REF] and 32.1 mg/L (dose 500 mg/6 h) for imipenem [START_REF] Paradis | Comparative study of pharmacokinetic and serum bactericidal activities of cefpirome, ceftazidime, ceftiaxone, imipenem and ciprofloxacin[END_REF] Mortality and bacteraemia rates. In control mice, mortality rates were 90% and 69% after 25 h of infection with the hGISA and GISA strains, respectively.

At the same time point, mortality in mice infected with the hGISA strain was 0% in all therapeutic groups except for the imipenem (20%, 2/10) and the vancomycin plus imipenem (7%, 1/14) groups. In mice infected with the GISA strain, mortality was 0% in all treated animals except for those receiving imipenem monotherapy (45.5%, 5/11). Data from GISA-infected animals treated with imipenem monotherapy were not considered for any statistical analysis because of the low number of animals that survived after 25 h of therapy (n=6).

Bacteremia in control animals at 0 h, expressed as percentage of positive blood cultures, was 100% for each strain. Bacteraemia rates in control and therapeutic groups after 25 h of therapy are shown in Table 1. Imipenem alone and in combination with vancomcycin failed in blood bacterial clearance.

Llinezolid alone and its combinations significantly reduced the bacteraemia rates achieved by the control group in hGISA-infected mice (P < 0.04). Mice treated with linezolid combinations also showed lower number of positive blood cultures than imipenem-treated group (P < 0.04). In GISA-infected mice, linezolid alone and in combination with imipenem significantly reduced the bacteraemia rates reached by the control (P ≤ 0.02) and the vancomycin plus imipenem (P < 0.05) groups.

Murine peritonitis model. Therapeutic efficacy. Bacterial counts in PF (mean log 10 CFU/ml ± SD) of control animals at hour 0 were 8.17 ± 0.81 for the hGISA strain (n = 25) and 7.82 ± 0.57 for the GISA strain (n = 18). Bacterial counts in PF of control and treated mice after 25 h are shown in Table 2. Efficacy of an antibiotic therapy was defined as the decrease in the number of CFU (Δlog CFU/ml) in PF between 0 and 25 h. All regimens were statistically more effective than the control group for both strains (P < 0.001). Linezolid monotherapy produced similar bacterial decreases against both isolates.

Linezolid was as effective as vancomycin against the hGISA strain but slightly improved vancomycin activity against the GISA strain.

Linezolid combinations showed comparable efficacies to linezolid monotherapy against both strains. The association of linezolid with vancomycin was more active reducing bacterial counts than vancomycin alone in mice infected with the GISA strain. The addition of linezolid to imipenem showed enhanced activity upon imipenem alone against both strains. The association of linezolid with either vancomycin or imipenem showed higher activity than vancomycin plus imipenem against both strains (P = 0.048, linezolid plus vancomycin vs vancomycin plus imipenem against the GISA strain).

DISCUSSION

The increasing incidence of nosocomial infections due to S. aureus antibioticresistant strains and the report of therapeutic failures associated with standard glycopeptide therapy highlight the importance of identifying new synergistic drug combinations [START_REF] Naimi | Comparison of community-and health careassociated methicillin-resistant Staphylococcus aureus infection[END_REF][START_REF] Moore | Vancomycin treatment failure associated with heterogeneous vancomycin-intermediate Staphylococcus aureus in a patient with endocarditis and in the rabbit model of endocarditis[END_REF][START_REF] Ariza | Vancomycin in surgical infections due to methicillin-resistant Staphylococcus aureus with heterogeneous resistance to vancomycin[END_REF]. Linezolid has demonstrated good activity against most staphylococci, including methicillin-resistant strains [START_REF] Lentino | New antimicrobial agents as therapy for resistant gram-positive cocci[END_REF][START_REF] Rybak | In vitro activities of daptomycin, vancomycin, linezolid, and quinupristindalfopristin against Staphylococci and Enterococci, including vancomycin-intermediate and -resistant strains[END_REF].

Linezolid was tested in vitro at achievable concentrations in human serum after oral administration of 500 and 600 mg regimens [START_REF] Macgowan | Pharmacokinetic and pharmacodynamic profile of linezolid in healthy volunteers and patients with Gram-positive infections[END_REF]. At 4-16 mg/l linezolid was effective against both hGISA and GISA strains. Its association with different drugs exerted distinct effects. Linezolid combined to imipenem was synergistic against both strains. The synergistic interaction between low concentrations of linezolid and imipenem has been previously reported against MRSA strains [START_REF] Jacqueline | In vitro and in vivo synergistic activities of linezolid combined with subinhibitory concentrations of imipenem against methicillin-resistant Staphylococcus aureus[END_REF]. An indifferent effect was the most common result achieved with the interaction between linezolid and vancomycin accordingly to previous studies involving MRSA and hGISA strains [START_REF] Jacqueline | In vitro activity of linezolid alone and in combination with gentamicin, vancomycin or rifampicin against methicillin-resistant Staphylococcus aureus by time-kill curve methods[END_REF][START_REF] Arce | In vitro activity of linezolid in combination with doxycycline, fosfomycin, levofloxacin, rifampicin and vancomycin against methicillin-susceptible Staphylococcus aureus[END_REF]. Of particular interest was our finding of a synergistic killing with sub-MIC concentrations of both antibiotics in combination against the GISA strain. This enhanced effect has been reported on another GISA strain in an in vitro pharmacodynamic model [START_REF] Allen | In vitro activities of quinupristindalfopristin and cefepime, alone and in combination with various antimicrobials, against multidrug-resistant staphylococci and enterococci in an in vitro pharmacodynamic model[END_REF].

In the murine peritonitis model caused by the hGISA strain no differences were found between linezolid and vancomycin monotherapies in terms of bacterial counts in peritoneal fluid and survival. In contrast, in GISA-infected mice linezolid showed a slightly higher activity than vancomycin, although this did not reach statistical significance. Moreover, linezolid achieved higher percentages of blood culture sterilization in comparison to vancomycin against both isolates.

The use of combined regimens would be a good approach to improve the effectiveness of linezolid in the management of drug-resistant infections. In our experimental setting, the addition of linezolid to vancomycin showed similar efficacy but decreased the bacteraemia rates in comparison to vancomycin and linezolid monotherapies against the hGISA strain. The same combination enhanced vancomycin activity against the GISA strain but did not improve the rates of blood sterilisation achieved with monotherapy regimens.

Even though β-lactam antibiotics do not show any activity against MRSA and hGISA strains, their use in combination with linezolid has been shown to be highly effective against MRSA strains in vitro and in experimental endocarditis [START_REF] Jacqueline | In vitro and in vivo synergistic activities of linezolid combined with subinhibitory concentrations of imipenem against methicillin-resistant Staphylococcus aureus[END_REF]. In our study, linezolid combined to imipenem was an effective therapy in mice infected with hGISA/GISA strains in terms of bacterial and bacteraemia reduction.

Our study found some discrepancies between in vitro and in vivo results. It should be emphasized that in vitro interaction may not translate into clinical efficacy, mainly because of the diversity of mechanisms involved in in vivo antibiotic interactions which can not be analyze by the use of in vitro techniques [START_REF] Fantin | In vivo antibiotic synergism: contribution of animal models[END_REF]. In deed, experts recommend to use the in vivo efficacy more than the in vitro data when selecting an antistaphylococcal drug as a therapeutic option [START_REF] Cunha | Methicillin-resistant Staphylococcus aureus: clinical manifestations and antimicrobial therapy[END_REF].

To date, few studies have addressed the role of linezolid combinations against glycopeptide-resistant S. aureus. The present study confirms the antistaphylococcal activity of linezolid in association with vancomycin or imipenem indicating that linezolid combinations preserves the activity of linezolid alone and might be considered as therapeutic options in the management of infections caused by S. aureus strains with reduced susceptibility to glycopeptides. Fig. 2

  = 25% in mice Line: Gentry-Nielsen MJ et al., AAC 2002; 46: 1345-1351 = 26% in rats Imi: has to searched by the authors

  Lefeuvre S, Marchand S, Lamarche I, Mimoz O, Couet W. Microdialysis study of imipenem distribution in the intraperitoneal fluid of rats with or without experimental peritonitis. Antimicrob Agents Chemother. 2006; 50:34-37. Lefeuvre S, Marchand S, Pariat C, Lamarche I, Couet W. Microdialysis study of imipenem distribution in the peritoneal fluid of rats with experimental pancreatitis. Antimicrob Agents Chemother. 2008; 52:1516-18

  Domenech A, Ribes S, Cabellos C, Domínguez MA, Montero A, Liñares J, Ariza J and Gudiol F.A mouse peritonitis model for the study of glycopeptide efficacy in GISA infections. Microbial Drug Resístanse 2004;10: 346-53. Domenech A. Ribes S, Cabellos C, Taberner F, Tubau F, Dominguez MA, Montero A, Liñares F, Ariza J, Gudiol F. Experimental study on the efficacy of the combinations of glycopeptides and Β-lactams against Staphylococcus aureus with reduced susceptibility to glycopeptides. J. Antimicrob. Chemother. 2005; 56: 709-716 *

  Staphylococcus aureus with reduced susceptibility to glycopeptides Sandra Ribes a, *, Maria Eugenia Pachón-Ibáñez a, *, Maria Ángeles Domínguez b , Raúl Fernández b , Fe Tubau b , Javier Ariza a , Francesc Gudiol a , and Carmen Cabellos a . * Both authors equally contributed to this work. a Laboratory of Experimental Infection, Infectious Diseases Department, IDIBELL-Hospital Universitari de Bellvitge, Feixa Llarga s/n, 08907 L'Hospitalet de Llobregat, Barcelona, Spain. INTRODUCTION Methicillin-resistant Staphylococcus aureus (MRSA) is the most important cause of antibiotic-resistant healthcare-associated infections [1]. In addition, clinical isolates of S. aureus with heterogeneous resistance to vancomycin (hGISA) and, more rarely, glycopeptide-intermediate resistant strains (GISA) have emerged worldwide over the past years [2-4].

  Linezolid (Pfizer, Madrid, Spain), imipenem-cilastatin (Merck, Sharp & Dohme, Madrid, Spain) and vancomycin (Normon, Madrid, Spain) were provided by the manufacturers. Antibiotics were tested for a range of concentrations according to their MICs and their achievable levels in human serum: linezolid concentrations ranging from 1/4 x to 8 x MIC, vancomycin concentrations ranging from 1/4 x to 1 x MIC, imipenem levels from 1/8 x to 1 x MIC, as well as concentrations of 1/4 x, 1/2 x and 1x MIC of each drug in combination. In all experiments, growth control was assessed using an extra tube without antibiotic. At 0, 6 and 24 h of incubation, aliquots of 100 μl were taken from each tube to perform direct and 10-fold dilutions, and were cultured onto 5%

Table 1

 1 has been deleted. Human concentrations have been added to mice concentrations. Page 8.

Table 1 .

 1 Bacteraemia rates of control and therapeutic groups of infected mice after 25 h of subcutaneous therapy. Data are expressed as percentages of positive blood cultures (n≥ 10 mice/group except for imipenem against the GISA strain where n = 6).

	LZD, linezolid; VAN, vancomcyin; IMP, imipenem
		% Positive blood cultures
	Therapy (25h)
		hGISA strain	GISA strain
	Control	100	100
	LZD 35 mg/kg/5 h	73 a	67 a, c
	VAN 60 mg/kg/5 h	93	81
	IMP 30 mg/kg/5 h	100	81*
	LZD + VAN	64 a, b	79
	LZD + IMP	64 a, b	67 a, c
	VAN + IMP	93	100

a P < 0.04 vs. Control group b P < 0.04 vs. IMP group c P < 0.05 vs. VAN + IMP group * Small "n"; this group was excluded from statistical studies.

Table

Table 2 .

 2 Bacterial counts in peritoneal fluid (PF) for therapeutic and control groups after 25 h of subcutaneous therapy.

		PF bacterial counts ± SD (log CFU/ml) [n]
	Therapy (25h)
		hGISA strain	GISA strain
	Control	8.19 ± 0.57 [29]	8.29 ± 0.9 [29]
	LZD 35 mg/kg/5 h	5.88 ± 0.61 [15] a	5.60 ± 0.61 [18] a, b
	VAN 60 mg/kg/5 h	5.90 ± 0.31 [14] a	6.02 ± 0.56 [16] a
	IMP 30 mg/kg/5 h	6.40 ± 0.80 [10] a	7.38 ± 1.38 [6]*
	LZD + VAN	5.94 ± 0.30 [14] a	5.61 ± 0.56 [14] a, b
	LZD + IMP	5.81 ± 0.41 [14] a	5.74 ± 0.52 [15] a
	VAN + IMP	6.15 ± 0.68 [14] a	6.28 ± 0.49 [14] a

a P < 0.001 vs. Control group b P < 0.05 vs. VAN + IMP group * Small "n"; this group was excluded from statistical analysis.

Table Figure 1

 Figure . Time-kill curves of the combinations of linezolid plus vancomycin that improved the activities of both monotherapies against the GISA strain. LZD, linezolid; VAN, vancomycin. Time-kill curves with synergistic activity for linezolid in combination with imipenem against hGISA and GISA strains.

	Fig.1
	Figure 2. LZD, linezolid; IMP, imipenem
	10
		9 9			hGISA strain
							Control
	Log cfu/mL Log cfu/mL	5 6 7 8 8 6 7					LZD 1x Control VAN 1x LZD 1x LZD 1x + VAN 1x LZD 1/2x + VAN 1x LZD 1/4x + VAN 1x IMP 1x LZD 1x + IMP 1/2x LZD 1x + IMP 1/4x LZD 1x + IMP 1/8x LZD 1/2x + IMP 1x
		4 5
		3 4
			0	6	12	18	24
		3	0	6	hours 12	18	24
	10			hours
		9					Control
	4 5 6 7 10 8 8 9 Log cfu/mL 6 7 Log cfu/mL			GISA strain		LZD 1x LZD 1/2x VAN 1/2x VAN 1/4x LZD 1x + VAN 1/2x Control LZD 1x IMP 1/2x LZD 1x + VAN 1/4x LZD 1/2x + VAN 1/2x LZD 1x + IMP 1/2x LZD 1x + IMP 1/4x LZD 1/2x + IMP 1/2x LZD 1/2x + IMP 1/4x LZD 1/4x + IMP 1/2x
		5
		3
		4	0	6	12	18	24
		3			hours
			0	6	12	18	24
					hours

ACKNOWLEDGEMENTS

Part of this work was presented at the 47 th Interscience Conference on Antimicrobial Agents and Chemotherapy, Chicago, Ill., 17-20 September 2007. Funding: This work was partially supported by the Spanish Network for Infectious Diseases Research (REIPI RD06/0008/0022) and by a grant from Pfizer (Spain). M.P-I was supported by a grant from REIPI.


Maxime Mikikian
email: maxime.mikikian@univ-orleans.fr

Yves Tessier

Laïfa Boufendi

Lénaïc Couëdel

Carousel Instability in a Capacitively-Coupled RF Dusty Plasma

Rotating plasma spheroids are observed in a capacitively-coupled radio-frequency (ccrf) discharge containing grown dust particles. These plasma spheroids are regions of slightly enhanced emission that rotate along the electrodes circumference. This effect is not systematically observed and when it occurs, the number and speed of the spheroids can vary with the discharge parameters. These spheroids have been by using high speed-imaging.

particles can be grown inside a plasma by gas phase reactions [START_REF] Berndt | Aspects of Reactive Complex Plasmas[END_REF][START_REF] Mikikian | Dust particles in low-pressure plasmas: Formation and induced phenomena[END_REF][START_REF] Massereau-Guilbaud | Influence of the power on the particles generated in a low pressure radio frequency nitrogen-rich methane discharge[END_REF] that lead to high densities of submicron dust particles. These particles acquire a negative charge and when the global charge they represent is no more negligible compared with the electron density, a wide variety of low frequency instabilities are observed. They follow the dust particle growth [START_REF] Mikikian | Low Frequency Instabilities during Dust Particle Growth in a Radiofrequency Plasma[END_REF][START_REF] Mikikian | Plasma Emission Modifications and Instabilities Induced by the Presence of Growing Dust Particles[END_REF][START_REF] Samsonov | Instabilities in a dusty plasma with drag and ionization[END_REF] or concern the void region often present in the center of dust clouds. In this last case, the void size oscillates with a strong nonlinear behavior (heartbeat [START_REF] Mikikian | Mixed-Mode Oscillations in Complex Plasma Instabilities[END_REF][START_REF] Mikikian | Threshold phenomena in a throbbing complex plasma[END_REF][START_REF] Zhdanov | Auto-oscillations in complex plasmas[END_REF]). Another type of instability connects these two effects and corresponds to void size oscillations induced directly by the growth of a new dust generation inside the void [START_REF] Cavarroc | Instabilities during the growth of dust successive generations in silane-based plasmas[END_REF][START_REF] Couëdel | Self-excited void instability during dust particle growth in a dusty plasma[END_REF].

In this paper, we report on the observation of another kind of plasma instability consisting in the rotation of plasma spheroids along the circumference of the electrodes in a capacitively-coupled RF discharge. Due to this characteristic motion, we named this behavior the "carousel instability".

Experiments are performed in the PKE-Nefedov reactor where a low-pressure (~ 1 mbar) argon plasma is produced in a ccrf discharge (electrode diameter 4 cm, separation 3 cm). The plasma sputters a polymer layer deposited on the electrodes, injecting molecular precursors in the gas phase. It gives birth to the growth of dust particles with a final size of about a few hundreds of nanometers after several minutes. The typical instability frequency is around a few tens of Hz and in order to analyze the dust cloud dynamics or the plasma emission, a high-speed camera is required.

The images shown in Fig. 1 have been obtained by recording the plasma emission at 1789 frames per second during dust particle growth. Fig. 1(a) is the raw image with a poor contrast but plasma spheroids can be detected close to both electrodes (one of them is marked). In order to better reveal these plasma spheroids, the image has been filtered notably by subtracting a reference image and by using false The number of spheroids and their speed can vary with the applied rf power. This dependence is currently under investigation. In the present case, a typical speed of about a few meters per second has been measured. It gives a typical frequency of about 45 Hz and a spheroid needs around 22 ms for completing its rotation around the electrode. The spheroids of the bottom electrode are not exactly in front of those of the top electrode and some small discrepancies in their respective motion have also been observed. In some conditions, spheroids are only present above the bottom electrode. The exact nature and origin of these spheroids are currently undetermined. It is not possible to conclude if they are only constituted of plasma or of plasma and dust particles, even if the last hypothesis is highly probable. The influence of the dust cloud on the existence and characteristics (number speed) of these spheroids still needs to be clarified.

In this paper, we evidenced an instability occurring in a dusty ccrf discharge and consisting in the rotation of plasma spheroids. The study of this carousel instability can reveal new aspects of the dust-plasma interaction. On the esthetical point of view, this motion transforms the discharge into a carousel of light.

  colors [Fig 1(b)]. Five plasma spheroids are thus clearly evidenced in front of each electrode and the position of one of them is marked. They seem to follow the electrode edges and rotate clockwise. Figs. 1(c)-(e) follow Fig. 1(b) and they evidence the successive positions of the plasma spheroids. In these figures, positions 2, 3 and 4 of the spheroid marked in Fig. 1(b) are indicated. In Fig. 1(e) the 5 plasma spheroids are well evidenced as the ones in the foreground are not hiding those in the background. Each plasma spheroid is indicated by a letter. Fig. 1(f) is the superimposition of 8 successive frames [the first four positions are the ones shown in Figs. 1(b)-(e)]. A different color is used for each frame and positions 1 and 8 of the spheroid labeled c are indicated.

4 Fig. 1 .

 41 Fig. 1. Carousel instability in a ccrf argon plasma containing grown dust particles. Images of the plasma emission have been obtained with a high-speed camera. (a) Raw image of the plasma emission. The two disk-shaped electrodes are observed on the top and bottom parts. (b) Same image in false colors after filtering and subtracting a reference frame. Five plasma spheroids are observed near each electrode. They are labeled in (e). Position 1 of spheroid c is marked. (c)-(e) Successive frames revealing the clockwise rotation of the spheroids. Successive positions (2, 3, 4) of the spheroid c are marked. (f) Superimposition of 8 frames using a different color for each frame. 1 st (red) and 8 th (pink) positions of spheroid c are indicated.

The PKE-Nefedov chamber has been made available by the Max-Planck-Institute for Extraterrestrial Physics, Germany, under the funding of DLR/BMBF under grants No.50WM9852.