Mario Lezoche
email: mario.lezoche@univ-lorraine.fr

Esma Yahia
email: esma.yahia@univ-lorraine.fr

Alexis Aubry
email: alexis.aubry@univ-lorraine.fr

Hervé Panetto
email: herve.panetto@univ-lorraine.fr

Milan Zdravković
email: milan.zdravkovic@gmail.com

Conceptualising and structuring semantics in Cooperative Enterprise Information Systems Models

Keywords: Conceptual modelling, enterprise information systems, semantic interoperability, data model conceptualisation, UML, Fact-Oriented Model, model transformation, transformation rules

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-Introduction

The actual archetype for the Enterprise Information Systems (EISs) involves large number of ISs distributed over large, complex networked architecture. Such cooperative enterprise information systems (CEIS) have access to a large amount of information and have to interoperate to achieve their purpose. CEIS architects and developers have to face a hard problem: interoperability.

While networked systems engineering is more and more focusing on sustainable perspectives, new scientific advances in systems interoperability might contribute to make systems interoperability sustainable. In fact, it can improve sustainability themes on data, semantic, and structural mappings between partner enterprises in the complex network for creating a stable interoperable enterprise operating environment with long term exploitation.

Interoperability can be defined as the ability of two or more systems to share, understand and consume information (IEEE, 1990). (EIF, 2010) has identified three different levels of interoperability: technical, semantic and organisational. Organisational barriers are still an important issue but they are out of scope of this paper. The technological barriers are strongly studied by researchers in computer science and they are, in general, addressed by the models transformation [START_REF] Frankel | Model Driven Architecture: Applying MDA to Enterprise Computing[END_REF].

Our research focuses on the semantic level of interoperability, namely the ability to understand the exchanged information. Information may be defined as data linked to knowledge about this data. It is represented by so-called concepts. A concept is a cognitive unit of meaning [START_REF] Vyvyan | Lexical Concepts, Cognitive Models and Meaning-Construction[END_REF], a mental symbol.

We will contribute to the science foundation of the interoperability domain with a conceptualisation approach for making explicit the finest-grained semantics -the smallest possible piece of information -grouped together into atomic concepts. These so called atoms of semantics are extracted from conceptual models in order to facilitate the semantic matching between two different information systems that have to interoperate. In fact these atoms represent the found smallest possible piece of information to overcome the subjectivity in the modelling activity performed by models architects [START_REF] Lezoche | Formal Fact-Oriented model transformations for Cooperative Information Systems semantic conceptualisation[END_REF].

Moreover a knowledge structuring process is necessary for making explicit the semantic dependencies between the discovered concepts. This structuration is based on identifying semantics aggregates (namely semantic blocks) that represent independent piece of knowledge containing their own minimal semantics (Yahia et al, 2012a).

Linking the works presented in [START_REF] Lezoche | Formal Fact-Oriented model transformations for Cooperative Information Systems semantic conceptualisation[END_REF] and (Yahia et al, 2012a), this paper proposes a complete process of conceptualisation and semantics structuration as a requirement for assessing interoperation capabilities when two or more companies want to cooperate. This modelbased assessment contributes to the sustainability of the interoperability process by tracing, archiving and highlighting core concepts and concept aggregates necessary for improving the collaboration.

The semantic interoperability measure process is not part of this work but has been published in (Yahia et al, 2012b).

Next section presents the general context of our work, namely cooperative enterprise information systems. Then, we will present the knowledge explicitation process that transforms an implemented relational model into a normalised fact-oriented conceptual one. This resulting model makes explicit all atoms of semantics, most of the time hidden into the implemented model. In the fourth section, the semantics structuring process is described. It formalises the definition of semantics aggregates that highlight the structure of the embedded semantics in the conceptual model obtained after the conceptualisation process. Each semantics aggregate (namely, each semantic block) is associated with a concept and defines the minimal mandatory semantics attached to this concept. For validating our proposal, a practical case study is presented in the fifth section. It is based on two applications: an Enterprise Resource Planning (ERP) and a Manufacturing Execution System (MES), involved in a Business to Manufacturing (B2M) interoperation process. Finally, after discussing on the contribution of this work and its limits, we will conclude with some perspectives for future works.

-Cooperative Information systems

Information Systems are systems whose activities are devoted to capture, store and process data and to produce knowledge, used by any stakeholders within an enterprise or among different networked enterprises. It is commonly agreed that Cooperative Information Systems provide a backbone for the Integrated Information Infrastructure [START_REF] Sheth | Changing Focus on Interoperability in Information Systems: From System, Syntax, Structure to Semantics[END_REF]. Although the progress made in Information Technology (IT) considerably improved the efficiency of software development, the models involved in a single application development are numerous and diverse.

Moreover, the components' technologies are diverse, platform-and machine-dependant. The above-mentioned limitations and barriers hinder the development and the maintenance process, significantly.

The main difficulty in analysing the detailed semantics of cooperative information systems models concerns the big amount of concepts and relationships, most of the times "polluted" by implementation constraints. Indeed, deeply studying the semantics embedded into a conceptual model such as the one represented in Figure 1 is really complex and hard to be done manually.

Our proposed approach aims at automatically computing a structured semantic model (Figure 2) that makes easier this analysis. There is a growing demand for integrating cooperative information systems tightly with organizational work so that these information systems can be fully, directly and immediately exploited by the intra and inter-enterprise processes [START_REF] Izza | Integration of industrial information systems: from syntactic to semantic integration approaches[END_REF]. Here, the need of interoperation clearly appears. In fact, to achieve the purpose of the cooperation between the different Information Systems, information must be physically exchanged (technical interoperability), must be understood (conceptual interoperability) and must be used for the purpose for which it has been produced (conceptual and organisational interoperability).

According to [START_REF] Euzenat | Towards a principled approach to semantic interoperability[END_REF], the encoding, lexical and syntactic interoperability levels are the most effective solutions for removing technical barriers for interoperability, but they are not sufficient to achieve a practical interoperability between computerised systems. Enabling a seamless data and model exchange at the semantic level is still a big challenge that needs a conceptual representation of the intended exchanged information and the definition of its pragmatic meaning in the context of the source and destination applications. Aggregates the semantics of Interoperability problems have been classified [START_REF] Panetto | Towards a Classification Framework for Interoperability of Enterprise Applications[END_REF] with regards to a multidimensional perspective emphasising the strong relationship between models abstraction and semantics.

Indeed, conceptualisation of models and its semantics extraction are still an important issue related to contextual understanding of tacit knowledge (thus hidden) embedded into those models. Our work is not only conceptualising EIS models but also it concerns also making assumptions on the mental models of the information systems' designers. The main prerequisite for achieving interoperability of information systems is then to maximise the amount of explicit semantics in the represented models [START_REF] Obrst | Ontologies for semantically interoperable systems[END_REF].

-Semantics enactment in conceptual models

As previously discussed, we focus our interest on the semantic level of interoperability and on enabling different information systems to share and use knowledge models which they represent.

In order to make this possible, we consider in [START_REF] Lezoche | Formal Fact-Oriented model transformations for Cooperative Information Systems semantic conceptualisation[END_REF] two steps that need to be taken: first, we need to understand the conceptual relationships between those models in the context of their use; and second, we need to unhide the tacit knowledge buried inside them, by applying a conceptualisation approach [START_REF] Guarino | Formal Ontology in Information Systems[END_REF]. Conceptual models range in type from the more precise, such as the mental image of a familiar physical object, to the abstractness of mathematical models that cannot be visualized in mind. They can be developed in different levels of abstraction of a single domain (Zdravković et al., 2011). Many conceptualisation approaches have been developed in different knowledge domains (LaOnsgri, 2009). According to [START_REF] Engelbart | Augmenting human intellect: a conceptual framework[END_REF] and (Genesereth and Nilson, 1987), developing conceptual models means specifying the essential objects, or components, of the system to be studied, the relationships of the objects that are recognised, the types of changes in the objects or their relationships which affect the functioning of the system and the types of impact these changes have on the system. These arguments are partially taken into account in our work by interpreting the semantics of the cardinality of relationships and existential constraints (mandatory elements).

Our contribution is to have at our disposal an approach that enables us fragmenting knowledge through the transformation of attributes into entities and relationships. In the proposed approach, presented in Figure 3, different inputs can be used, such as any application model, a data model, or a logical view. In this approach, the initial process (Step 1) is the application of reverse engineering methods, such as [START_REF] Fonkam | An Approach to Eliciting the Semantics of Relational Databases[END_REF] or [START_REF] Chiang Roger | Reverse engineering of relational databases: Extraction of an EER model from a relational database[END_REF]. However, they deliver models without any explicitation of the tacit semantics. The ADM (Architecture-Driven Modernization) initiative (OMG, 2003) from OMG [START_REF] Bézivin | Model-based Technology Integration with the Technical Space Concept[END_REF] is tackling this problem by implementing a common Knowledge Discovery Meta-model to facilitate discovery of the tacit knowledge embedded inside existing software. When information systems are highly generic, the application semantics is actually captured in the populated table rows. For example, in Business Process Management systems, the structure of the enterprise processes, namely activities, associated data structures (messages), compensation and error handling blocks, etc. are defined by a system user and are not expressed by the database schema. In these cases, the intervention of the domain expert in enriching the conceptual model may be useful. Some research paths are tackling this issue by providing the tools to automatically or semi-automatically discover the semantics buried into existing data patterns [START_REF] Astrova | Reverse Engineering of Relational Databases to Ontologies[END_REF]. In our scenario, we are considering that the business knowledge that is embedded in enterprise applications is mainly stored into the DBMS architectural level. We can then extract, from each DB, some knowledge in a form of a conceptual model, by using reverse engineering approaches. Then, knowledge extraction tools and domain experts have to enrich that model with enterprise best practices (knowledge coming from users) in the step 2. These stakeholders know the domain peculiarities and they are capable to express the specific constraints that must be embedded into the conceptual model. However, this phase must follow a structured process, in order to preserve the ontological commitment.

This is particularly important when more experts are involved in the knowledge injection. In such cases, the approaches of setting up a collaborative conceptualisation processes [START_REF] Guo | Collaborative conceptualisation: towards a conceptual foundation of interoperable electronic product catalogue system design[END_REF]) may be useful. Existing tools for knowledge extraction may also be used for this process [START_REF] Bañares-Alcántara | Deliverable 5 -Knowledge Discovery Tools, h-TechSight project[END_REF]. This expert knowledge injection step is detailed in [START_REF] Lezoche | Formal Fact-Oriented model transformations for Cooperative Information Systems semantic conceptualisation[END_REF].

However, the conceptual model resulting from this step is generally strongly modeller-dependent.

In order to avoid semantic misinterpretations of the produced model, the step 3 aims at normalising it by fragmenting the represented knowledge into atoms of semantics. NIAM (Natural-language Information Analysis Method) [START_REF] Nijssen | Conceptual Schema and Relational Database Design[END_REF] proposed to model the world in term of facts (either presenting terms (real things), or representing characteristics (attributes) of these real things), and relationships between facts. NIAM is attribute-free. In the

Step 3, this fact-oriented modelling (FOM) paradigm is adapted for the UML (OMG, 2004) class notation representation of the studied conceptual model. To apply this transformation, a set of modelling rules is presented on Table 1. In the resulting fact-oriented model, adding annotations preserves the semantics. The added annotations concern particular artefacts semantics such as generalisation, association class, aggregation and composite aggregation. Moreover, adapting the definitions from [START_REF] Nijssen | Conceptual Schema and Relational Database Design[END_REF], we define two different concept types:

 "Lexical Concept" (LC) is an object in a certain reality that can be written down. LCs always consist of letters, numbers, symbols or other characters. They can be used as

Cla ss 1 +Attr1[0..1] +Attr2[1] Cla ss2 Cla ss3 * 1 Cla ss4 Cla ss5 * 1 Cla ss 6 +Attr1[1] +Attr2[0..1] Cla ss 7 +Attr3[0..1] Cla ss8 Cla ss9 Cla ss10 * 1 Cla ss 1 <<NLC>> Attr1 <<LC>> Attr2 <<LC>> 1 Attr2 Class1__Attr2 1 Class1 0..1 Attr1 Class1__Attr1 1 Class1 Cla ss4 <<NLC>> Cla ss5 <<NLC>> * 1 {Class4 Aggregates: Class3} Cla ss2 <<NLC>> Cla ss3 <<NLC>> * 1 {Class2 IsComposedOf: Class3} Class7 <<NLC>> Class6 <<NLC>> Attr1 <<LC>> Attr2 <<LC>> Attr3 <<LC>> {Class7 generalizes Class6} 1 Attr1 Class6__Attr1 1 Class6 0..1 Attr2 Class6__Attr2 1 Class6 0..1 Attr3 Class7__Attr3 1 Class7 0..1 Attr2 Class7__Attr2 1 Class7 1 Attr1 Class7__Attr1

Making semantics explicit

We summarise here the activities for making semantics embedded in the models explicit.

After renaming the different concepts and attributes in order to be more semantically explicit, the model is updated by formalising some constraints that came after interviewing experts and users of applications. In fact, even if most of the roles constraints are automatically derived from data schemas, many of them are still hidden inside the application itself. For example, considering a particular attribute a 1 , two possible redefinition cases are identified:

(1) a 1 is a non-mandatory attribute in the conceptual model but, as users are always requested to populate it with a specific value, the enriched model must formalise that this attribute a 1 has to be treated as mandatory;

(2) a 1 is defined as mandatory in the conceptual model but, in practice, the users never care about its value and generally fill it with some dummy one. In such case, the enriched model may formalise that this attribute is not mandatory.

As for the role constraints, the majority of associations are retrieved from the model, but some implicit associations are only defined by enterprise practices and are not expressed in the model itself. The explication process applies also in this context. After this explication process, the enriched conceptual model formalises the whole application semantics (both the explicit one and the users' tacit one).

-A semantics structuring process

After conceptualising and enacting finest-grained semantics embedded into CISs models, resulting with a normalised FOM, a structuring process is carried out for building semantics aggregates (Yahia et al., 2012a). Each of those identified aggregates represents a "semantic molecule", composed of atomic concepts, with its own minimal mandatory semantics.

To build such aggregates, previous work (Yahia et al., 2012a) proposed a recursive approach for analysing the detailed semantics of the IS conceptual models obtained by the conceptualisation approach presented in section 3. We are considering that these models embed the whole explicit semantics of the associated IS. For the sake of self-completeness of this paper, the structuring approach is summarised in the next subsections.

Core and extended semantics

When considering an available fact-oriented conceptual model from one IS (outputs from section 3), we can distinguish the mandatory (constrained) and non-mandatory (non-constrained) association roles, which represent mandatory and non-mandatory concepts (LCs and NLCs) expressing semantics.

The set of mandatory concepts represents all the necessary and sufficient elements that make the conceptual model semantically coherent and understandable. It comprises the non-lexical and lexical concepts linked to constrained association roles with a multiplicity equal to 1 or 1..*. On the contrary, the non-mandatory concepts correspond to the non-mandatory roles (multiplicity equal to 0..1 or *) and are only enriching the semantics of those IS conceptual models.

To some extent, the set of mandatory concepts corresponds to the core semantics that is embedded into a given IS conceptual model. The extended semantics is defined by the set of mandatory and non-mandatory concepts.

Some mathematical definitions

We define, for each IS conceptual model, the following notations.

Definition 1.

is the set of the identified lexical and non-lexical concepts, formally defined by | is a lexical or a non lexical concept from the IS conceptual model Moreover, we define two subsets of as follows:

 is the subset of restricted to the non-lexical concepts and,



is the subset of restricted to the lexical concepts.

We can note that:

∪ and ∩ ∅ Definition 2.
is the set of the identified associations between concepts. Formally, it is defined by  is the subset of restricted to the mandatory non-lexical concepts and,



is the subset of restricted to the mandatory lexical concepts.

We can note that:

∪ , ∩ ∅ ∩ , ∩
Definition 5. For each non-lexical concept , we can define the set of its associated mandatory lexical concepts as follows:

∈ ∃ , ∈ , ∈ 1,1. . * Definition 6.
For each non-lexical concept , we can define the set of its associated mandatory non-lexical concepts as follows:

∈ ∃ , ∈ , ∈ 1,1. . *
If we consider a concept defined in the context of the IS core semantics, we notice that, in order to be semantically effective in the studied domain, this concept needs to be associated on the one hand to its mandatory lexical concepts and on the other hand to other non-lexical concepts. This defines the notion of Semantic Block (SB).

Semantic blocks identification

Definition

Considering a particular non-lexical concept from , a semantic block, denoted as and associated with the concept , represents the set of the concepts necessary for the minimal semantics definition of the non-lexical concept given by the conceptual model.

Formally, is defined as follows:

∪ ∈ 1
This definition suggests that the notion of semantic block is recursive. In the following, the meta-model of the semantic block is given and a procedure for computing all the semantic blocks of a conceptual model is proposed.

Semantic block meta-model

Here we propose to formalise the semantic block architecture through the meta-model represented on Figure 4. A semantic block defines the minimal mandatory semantics of one or several non-lexical concepts such that these concepts are in the same strongly connected component 1 . Moreover, the semantics of one or several concepts can be aggregated into one or several semantic blocks. As the semantic block is a specialisation of the abstract class "Concept", its semantics can be aggregated into one or several semantic blocks of higher levels. The Block System represents the last level of aggregation and contains the minimal mandatory semantics of the studied IS conceptual model.

How to build the Semantic blocks?

Let us consider the conceptual model on Figure 5 and its transformation on Figure 6 obtained by applying the third step presented in section 3. For sake of readability, we have hidden the stereotypes («LC» and «NLC»). Let us build the semantic block of the NLC 2. The intrinsic 1 A strongly connected component of a directed graph is a maximal set of vertices such that for every pair of vertices u and v, there is a directed path from u to v and a directed path from v to u. mandatory semantics of the concept 2 is defined by the semantics of the mandatory lexical concepts that are associated to it, namely 1 2 and 2 2. Moreover, a given instance of the concept 2 exists only if it is associated to at least one instance of the concept 5. That means that 5 is mandatory for expressing the semantics of 2. Moreover, considering the roles of 1 and 3 in their association with 2, we can see that the minimal multiplicity is equal to 0.

That means that the existence of any instance of 2 is not constrained by the existence of one instance of 1 or 3. Finally, we find again 2 2 ∪ 1 2, 2 2 ∪ 5 as in equation ( 1). Recursively, we can demonstrate that the intrinsic mandatory semantics of the concept 5 is defined by the semantics of 1 5 and that a given instance of the concept 5 exists only if it is associated to exactly one instance of the concept 8 and exactly one instance of the concept 2. That means that 5 5 ∪ 1 5 ∪ 2 ∪ 8 .

Applying the same reasoning, we can build 8 as follows: 8 8 ∪ 1 8 .

Finally we can deduce that: 2 2, 5, 8 ∪ 1 2, 2 2 ∪ 1 5 ∪ 1 8 . To simplify the computation of the semantic block of one concept , (Yahia et al, 2012a) propose, first, to identify the set of non-lexical concepts that are included in the semantic block and, second, to add the associated mandatory lexical concepts. That means that is determined as follows:

Figure 5 -An instance of conceptual model

C1 +A1C1[1] +A2C1[0..1] C2 +A1C2[1] +A2C2[1] +A3C2[0..1] C3 +A1C3[1] +A2C3[0..1] C4 +A1C4[1] +A2C4[0..1] 1..* * 1 * 1..* 0..1 C5 +A1C5[1] +A2C5[0..1] 1..* 0..1 1 * C8 +A1C8[1] +A2C8[0..1] 1 * C6 +A1C6[1] +A2C6[0..1] 1..* 1..* C7 +A1C7[1] +A2C7[0..1]
∪ with  ⋃ ∈ and,

 ∈

For instance, 2 2, 5, 8 and 2 1 2, 2 2, 1 5, 1 8 . (Yahia et al, 2012a) propose the following procedure to compute all the semantic blocks of a given conceptual model:

A to compute the semantic blocks

i. Building the associated semantic-dependency graph. ii. Building the graph of the strongly connected components based on the semanticdependency graph.

iii. Computing the semantic blocks associated with each strongly connected component.

iv. Computing, for each , the semantic block by adding all the mandatory lexical concepts associated to each non-lexical concept from .

v. Computing ∪ .

These steps are summarised as follows.

Building the associated semantic-dependency graph

To facilitate the building of the semantic blocks for each from C , the associated set are identified by using graph theory modelling and its associated mathematical tools.

The conceptual model can be associated with what we call a semantic-dependency graph.

Each node represents a non-lexical concept of the conceptual model. Each edge is built from the conceptual model as follows: the edge , exists if (i) there is an association between and in the conceptual model, and (ii) if the minimal multiplicity for the role of is equal to 1 ∈ . That means that the existence of the edge , represents the fact that is mandatory for expressing the semantics of . The Figure 7 shows the semanticdependency graph associated with the conceptual model of the Figure 5. 4.5.2 Building the graph of the strongly connected components (Yahia et al., 2012a) demonstrate that there is one semantic block per strongly connected component of the semantic-dependency graph. That means that for building the semantic blocks, only one concept in a given strongly connected component are considered (the other concepts share the same semantic block). The semantic-dependency graph is thus simplified by considering an equivalent graph where the nodes represent each strongly connected component of the former semantic-dependency graph. On this graph, one of these nodes (e.g.

SCCi

) is connected to another node (e.g. SCCj) if there exists at least one edge from a concept from SCCi to a concept from SCCj. Identifying all the strongly connected components of a graph is a well-known problem in graph theory that can be solved with polynomial effort by using Kosaraju-Sharir's algorithm [START_REF] Sharir | A strong-connectivity algorithm and its applications in data flow analysis[END_REF]. The graph of the strongly connected components related to the semantic-dependency graph of Figure 7 is given on Figure 8. On this graph, the strongly connected components are defined as follows: SCC1 C1 , SCC2 C2, C5 , SCC3 C3, C4, C6, C7 and SCC4 C8 . 4.5.3 Computing associated with each strongly connected component (Yahia et al., 2012a) propose two algorithms for automatically computing SB . These algorithms are based on paths discovery in the graph. In fact, if there exists one path from the node to the node then is included into i . By applying these algorithms, the following semantic blocks are obtained:

 1 1 ∪ 2 ∪ 3 ∪ 4,  2 2 ∪ 4,  3 3 ∪ 4 and  4 4.
And finally, replacing the strongly connected components by their content, the following semantic blocks are obtained: on the instance of Figure 6 we obtain: 1 2,2 2,1 3,1 4,1 5,1 6,1 7,1C8 ,

 1 1, 2,
 C1 1 1,
 C2, C5 1 2, 2 2, 1 5, 1C8 ,  C3, C4, C6, C7 1 3, 1 4, 1 6, 1 7, 1C8 and
 C8 1C8 .

Computing each semantic block

Each semantic block is the union of and . By applying this definition on the instance of Figure 6 we obtain:

 1 1, 2, 3, 4, 5, 6, 7, 8 ∪ 1 1, 1 2, 2 2, 1 3, 1 4, 1 5, 1 6, 1 7, 1 8 ,  C2, C5 2, 5, 8 ∪ 1 2, 2 2, 1 5, 1C8 ,  C3, C4, C6, C7 3, 4, 6, 7, 8 ∪ 1 3, 1 4, 1 6, 1 7, 1C8 and
 C8 8 ∪ 1C8 .
For validating our approach, next section will detail an industrial case study involving two enterprise information systems that need to interoperate: Sage X3 ERP and Flexnet MES. We will also present the prototype of the tool that implements the whole approach for automatizing the model conceptualisation and semantics structuring processes.

Interoperability between organisational and manufacturing activities is crucial in manufacturing enterprises. Production services have to produce, quickly and efficiently, the right volume of the right product at the right moment. For this reason, they need real time information coming from others services, which need in return a precise and updated data from the production. We propose here to study and present the first part of such a Business to Manufacturing (B2M) interoperability issue by studying Sage X3 as an Enterprise Resource Planning (ERP) application and Flexnet as a Manufacturing Execution System (MES). In order to illustrate our approach, we will detail the conceptualisation process applied to a subset of the ERP information system model in section 5.1. Section 5.2 will detail the semantics structuration process (computing semantic blocks) applied to the same subset.

Section 5.3 will present the results coming from Flexnet MES application. Section 5.4 will discuss about the contributions drawing some limits. For sake of readability, in the following, we will name each subset of models by the name of the related enterprise applications.

Conceptualisation of Sage X3 ERP model

The objectives of this case study are (i) to analyse how the manufacturing order process inside the ERP Sage X3 application is modelled, (ii) to use the proposed modelling process for making the implicit knowledge explicit in the model structure.

The model depicted on Figure 9 is the output from the two first steps proposed in (Lezoche et al., 2012). This means that we have already completed the "Reverse Engineering" and the "Expert knowledge injection" steps. The "Manufacturing Order heading" concept represents the management function of production orders and planned activities. This function allows the generation of a manufacturing order by variation of one or more classifications and a single production line. For each manufacturing order, the achievement of the material benefits and sequencing operations is possible. The function captures general information, such as planning and production facility and the status of the order. It allows entering general information about the production order. The availability of components is then checked through the information given by the bill of material related to the launched products. Once the above initial information is determined, the system updates the list of materials and operations of the created or modified orders. We then applied the pattern transformation rules, presented in the previous section, to increase the granularity of the knowledge embedded into the model. Figure 1 shows the resulting FOM after applying our approach to the Sage X3 manufacturing order process. It presents the explicit and mandatory knowledge linked to the Sage X3 process and it contains the semantic annotations that preserve relationships information for assuring the traceability of the sustainability receipts. As can be evinced by the model, in the Figure 1, there are some pivotal concepts in this process like "Product", "Facility", "Manufacturing Order Product", "Manufacturing Order heading" and "Operation route" that concentrate the majority of the relationships and that transmit the core semantics of the described process. At the first glance, it seems that the resulting model is much more complex than the initial one. This may looks true from a visual point of view, but it is false in terms of simplicity to treat the model's semantics. Indeed, the atomic semantics is made explicit, which helps any automatic

computing. An important result is that using the model with such high level of granularity will facilitate automatic computing for semantic gap evaluation.

Semantics structuring of SageX3 ERP model

The reminding of this section will apply our semantics structuring approach to build semantic-dependency graphs for automatically identifying aggregates of semantics (so called semantics blocs) (Figure 2). This simplified model facilitates the identification of semantically self-contained subsystems, and further interoperation analysis, knowledge discovery capabilities and systems adaptations for enhancing sustainability.

1) Building the associated semantic-dependency graph

As presented in section 4.5 the semantic-dependency graph, related to the conceptual model of SageX3, is built by considering each association between two concepts and then building an edge if the minimal multiplicity for the role is equal to 1. The result of this procedure is presented on Figure 10. The subsequent step is the building of the graph of the strongly connected components (Figure 11), related to the semantic-dependency graph of SageX3 ERP (Figure 10). We can note that three merged nodes has been built (namely SCC1, SCC2, SCC3) representing three strongly connected components. manufacturing order process model and their semantics aggregation relationships.

Conceptualising and structuring semantics of Flexnet MES model

Applying the same procedures, we first obtain the enriched fact-oriented model of the purchase order process in Flexnet application (Figure 12). Then implemented tool computes the semantic blocks as shown on Figure 13. The different procedures presented in this paper been implemented in the MEGA Suite environment2 . MEGA Suite supports UML notations and allows building our own metamodel based on its ad-hoc MOF3 meta-model. The meta-model presented on Figure 4 has been implemented. In this implementation, the semantic block is conceptualised as a UML package and concepts are conceptualised as UML classes stereotyped as «LC» or «NLC».

The implemented procedures assist the expert in the conceptualisation process (step 2) and fully automatized the generation of the FOM model and the identification of all the semantic blocks and their relationships.

Discussion

Applying the whole process for conceptualising and structuring the semantics to the Sage X3 and Flexnet applications, we obtain, for each application:

 one normalised conceptual model that embeds the whole semantics (coming directly from the data schema and enriched by expert knowledge injection) and  one structuration of this semantics through the semantic blocks that emphasizes the dependencies between concepts and that highlights independent semantics These simplified semantic models allow a better understanding of each application's functionalities. An engineer can then focus on specific semantically independent components (i.e. the semantic blocks) of these applications when analysing their interoperation capabilities. When defining what information has to be exchanged, the semantic block allows defining priorities related to the complexity of the model or to some initial requirements. As an example, when dealing with manufacturing orders in Sage X3 application, the semantic block ; contains all the concepts that are mandatory for Sage X3 to operate correctly and thus defines the interoperability requirements when such information is picked up from another application.

Those models are normalised, that means that do not contain any modelling patterns introduced by some modellers' practices. Thus, they can be directly used by some engineers or automatized tools without any ambiguity in their interpretation.

The work presented in this paper contributes to new research dimensions related to sustainable interoperability by facilitating knowledge conceptualisation and structuration into a set of discovered semantic blocks, thus improving learning capacity to better take into account changes when adaptation is required. Moreover, this structured model allows deeply analysing interoperability requirements and thus specifying in which way a network node should react in order to enable the system, as well as the entire network, to evolve for the better sustainable interoperable state.

However, we can draw some limits of our approach. One major assumption is necessary for the approach to be practical: the application must expose its implemented data schema and experts are assumed to be able to update the conceptual model with the many constraints and practices that are not implicitly expressed in the schema. Moreover, the size of a real application schema is so huge (more than 800 tables and 600 relationships for Sage X3) that this semi-automatically implemented approach remains complex to apply due to the necessary implication of one expert.

Conclusions

In this paper, we proposed a conceptualisation approach for enacting implicit semantics embedded into Enterprise Information System models by a deep analysis of existing data models enriched by users' and experts' knowledge. This approach is composed of 3 steps, staging from the traditional database reverse engineering process, through a knowledge elicitation and model enrichment by domain experts, to the application of formal fact-oriented modelling rules for externalising tacit semantics. Moreover, in order to structure the whole semantics into independent aggregates that may emphasize subsystems, we defined the concept of semantic (SB) and we developed an automatized procedure to compute these SBs. The resulting semantics architecture allows the identification of semantically selfcontained subsystems, facilitating further interoperation analysis, knowledge discovery capabilities and systems adaptations for enhancing sustainability. The conceptualisation and structuring processes have been validated on a case study involving two industrial Enterprise Applications, demonstrating the applicability of our approach. This approach contributes to the sustainability aspects of the information systems management. In fact, it aims at extracting, formalizing and using the tacit knowledge for facilitating the maintenance of the interoperability between enterprises when major changes occur.

Further works concern using the resulting semantic conceptual model and architecture for facilitating the assessment of the (non)-interoperation barriers between Enterprise Information Systems or some of their subsystems (identified, for instance, by the semantic blocks). The resulting analysis, based on an interoperability measures map, can help information technology consulting companies for parameterising and integrating enterprise applications (ERP, MES…) taking into account interoperability constraints.

Figure 1 -

 1 Figure 1 -ERP Sage X3 manufacturing order process model

Figure 3 -

 3 Figure 3 -Conceptualisation process (Lezoche et al, 2012)

Figure 4 -

 4 Figure 4 -Meta-model of the semantic block structure

  the minima l ma nd a to ry se mantics o f 1Concept (LC) -> forall ( c | c.Is defined by.associationEnd.multiplicity in {"1", "1..*"} AND self->includes ( c.Non Lexical Concept (NLC) ) )

Figure 6 -

 6 Figure 6 -"Fact-oriented modelling" transformation of the model of Figure 5

Figure 7 -

 7 Figure 7 -Semantic-dependency graph associated with the conceptual model of Figure 5

Figure 8 -

 8 Figure 8 -Graph of the strongly connected components related to the graph of Figure 7

Figure 9 -

 9 Figure 9 -Enriched Sage X3 manufacturing order process model

Figure 10 -

 10 Figure 10 -Semantic-dependency graph related to the conceptual model of SageX3 ERP

Figure 11 -

 11 Figure 11 -Graph of the SCCs related to the semantic-dependency graph of SageX3 ERP

Figure 12 -Figure

 12 Figure 12 -Enriched fact-oriented model of the purchase order process in Flexnet application

  names for or references to other concepts. An attribute in UML class notation becomes a class stereotyped «LC» in FOM notation. "Non-Lexical Concept" (NLC), is an object in a certain reality that cannot be written down. NLCs must be named by LCs or referred to by means of LCs. A class in UML class notation becomes a class stereotyped «NLC» in FOM notation.

		1 Class7	<<NLC>>		<<NLC>>
	Class6	Class7	Class8		Cla ss9
	Class7__Class6
			1		1
			{Class10 isTypeOf: AssociationClass(Class8,Class9)}
				<<NLC>>
			*	Class10	1

Table 1 -Fact-Oriented modelling patterns using UML notation (Lezoche et al, 2012)

 1

		Class and Attributes	Composite aggregation
	UML	FOM	UML	FOM
			Aggregation
			UML	FOM
		Generalisation	Association Class
	UML	FOM	UML	FOM

MEGA international, http://www.mega.com

OMG's MetaObject Facility: http://www.omg.org/mof/


J A Aguilar

I Al Samarai

A Albert

M André

M Anghinolfi

G Anton

S Anvar

M Ardid

A C Assis

T Astraatmadja

J J Aubert

R Auer

B Baret

S Basa

M Bazzotti

V Bertin

S Biagi

C Bigongiari

M Bou-Cabo

M C Bouwhuis

A M Brown

J Brunner

J Busto

F Camarena

A Capone

C Cârloganu

G Carminati

J Carr

Ph S Cecchini

T Charvis

M Chiarusi

H Circella

N Costantini

P Cottini

C Coyle

M P Curtil

I Decowski

A Dekeyser

C Deschamps

C Distefano

D Donzaud

D Dornic

T Drouhin

U Eberl

J P Emanuele

S Ernenwein

F Escoffier

V Fehr

U Flaminio

J L Fritsch

S Fuda

P Galata

G Gay

J P Giacomelli

K Gómez-González

G Graf

G Guillard

G Halladjian

H Hallewell

A J Van Haren

Y Heijboer

J J Hello

B Hernández-Rey

J Herold

C C Hö ßl

M Hsu

M De Jong

N Kadler

O Kalantar-Nayestanaki

A Kalekin

U Kappes

P Katz

C Kooijman

A Kopper

V Kouchner

R Kulikovskiy

P Lahmann

G Lamare

D Larosa

G Lefèvre

D Lo Lim

H Presti

S Loehner

F Loucatos

S Lucarelli

M Mangano

A Marcelin

J A Margiotta

A Martinez-Mora

T Mazure

M Montaruli

L Morganti

H Moscoso

C Motz

M Naumann

D Neff

G E Palioselitis

P Păvălaş

J Payre

P Petrovic

N Piattelli

C Picot-Clemente

V Picq

T Popa

E Pradier

C Presani

C Racca

G Reed

C Riccobene

M Richardt

G V Rujoiu

F Russo

P Salesa

F Sapienza

J P Schöck

R Schuller

F Shanidze

A Simeone

M Spies

J J M Spurio

Th Steijger

M Stolarczyk

C Taiuti

L Tamburini

S Tasca

B Toscano

V Vallage

G Van Elewyck

M Vannoni

P Vecchi

G Vernin

E Wijnker

H De Wolf

Yepes

D Zaborov

J D Zornoza
email: zornoza@ific.uv.es

J Zúñiga

Ph Charvis

T Chiarusi

M Circella

H Costantini

N Cottini

P Coyle

C Curtil

M P Decowski

I Dekeyser

A Deschamps

C Donzaud

D Drouhin

T Eberl

U Emanuele

J P Ernenwein

S Escoffier

F Fehr

V Flaminio

U Fritsch

J L Fuda

S Galata

P Gay

G Giacomelli

J P Gómez-González

K Graf

G Hallewell

H Van Haren

A J Heijboer

Y Hello

J J Hernández-Rey

B Herold

J Hößl

C C Hsu

M Kadler Ab

N Kalantar-Nayestanaki

O Kalekin

A Kappes

U Katz

P Kooijman

C Kopper

A Kouchner

V Kulikovskiy

R Lahmann

P Lamare

G Larosa

D Lefèvre

G Lim

D Lo Presti

H Loehner Ac

S Loucatos

F Lucarelli

S Mangano

M Marcelin

A Margiotta

J A Martinez-Mora

A Mazure

T Montaruli

M Morganti

L Moscoso

H Motz

C Naumann

M Neff

D Palioselitis

G E Pȃvȃlaş Ai

P Payre

J Petrovic

P Piattelli

N Picot-Clemente

C Picq

V Popa Ai

T Pradier

E Presani

C Reed

G Riccobene

C Richardt

M Rujoiu Ai

G V Russo Ag

F Salesa

P Sapienza

F Schöck

J P Schuller

R Shanidze

F Simeone

A Spies

M Spurio

J J M Steijger

Th Stolarczyk

M Taiuti

C Tamburini

L Tasca

S Toscano

B Vallage

V Van Elewyck

G Vannoni

M Vecchi

P Vernin

G Wijnker

E De Wolf

H Yepes

D Zaborov Ak

Time Calibration of the ANTARES Neutrino Telescope

Keywords: Time calibration, Neutrino Telescopes, ANTARES

The ANTARES deep-sea neutrino telescope comprises a three-dimensional array of photomultipliers to detect the Cherenkov light induced by upgoing relativistic charged particles originating from neutrino interactions in the vicinity of the detector. The large scattering length of light in the deep sea facilitates an angular resolution of a few tenths of a degree for neutrino energies exceeding 10 TeV. In order to achieve this optimal performance, the time calibration procedures should ensure a relative time calibration between the photomultipliers at the level of ∼1ns. The methods developed to attain this level of precision are described.

The ANTARES Collaboration has constructed a neutrino telescope in the Mediterranean Sea [START_REF] Coyle For The | The ANTARES deep-sea neutrino telescope: status and first results[END_REF]. The main aim of the project is the search for highenergy neutrinos of astrophysical origin. This is achieved by the detection of Cherenkov photons induced by the passage of relativistic charged particles resulting from neutrino interactions in the material surrounding the detector, the most important channel being the charged current interactions producing muons. Other signatures, such as the cascades produced both in charged and neutral currents are also detected. These photons are detected in a large threedimensional array of 885 photomultipliers (PMTs) installed on twelve vertical lines anchored on the sea bed at a depth of 2475 m. First physics results have been published [START_REF] Ageron | Performance of the First ANTARES Detector Line[END_REF][START_REF] Aguilar | Measurement of the atmospheric muon flux with a 4 GeV threshold in the ANTARES neutrino telescope[END_REF][START_REF] Aguilar | Zenith distribution and flux of atmospheric muons measured with the 5-line ANTARES detector[END_REF].

Detailed simulations have shown [START_REF] Heijboer | Track reconstruction and point source searches with ANTARES[END_REF] that the theoretically achievable angular resolution of the telescope (crucial for the search for cosmic point sources) in the muon channel reaches a few tenths of a degree at energies larger than 10 TeV. This sub-degree resolution has been confirmed using data [START_REF] Kouchner | High energy neutrino astronomy[END_REF]. The reconstruction of the tracks is based on the probability density function (PDF) of arrival times of photons at the photomultipliers. A good timing calibration is therefore mandatory to ensure the reliability of the track reconstruction algorithms. The precision required for the relative time calibration system derives from the transit time spread (TTS) of the photomultipliers (σ T T S ∼1.3 ns) and the effect of the chromatic dispersion in water (∼1.5 ns for a typical light path of 40 m). The addition in quadrature of these contributions leads to a best possible time resolution of ∼2 ns per single photon.

The measurement of the detection times of the PMT hits is based on clock signals which are distributed from shore so that a common reference time is used in the whole apparatus, as explained in Section 3. The clock distribution system determines the propagation delays for these signals to reach the different electronics containers offshore with sub-nanosecond precision. The time measurements from individual PMTs have however to be corrected by appropriate offsets, which are determined in situ by means of a calibration system based on LED and laser devices (optical beacons) emitting light flashes at known times [START_REF] Ageron | The ANTARES Optical Beacon system[END_REF]. In order to ensure that the apparatus reaches its maximum pointing accuracy, it is necessary that the accuracy with which all such offsets are determined, in the so-called relative time calibration, remains below 1 ns, so that the resulting systematic error is significantly smaller than the intrinsic event-by-event fluctuations.

The absolute time calibration is less demanding. A precision of a few seconds is sufficient to correlate reconstructed neutrino directions with steady point sources and an accuracy of the order of milliseconds is sufficient for association to transient astrophysical events (GRBs, AGN flares, SGR bursts, etc.) As it will be explained later, the GPS system provides a good enough time stamping.

The structure of this article is as follows. A brief description of the ANTARES detector and its data-acquisition (DAQ) system is given in Section 2. In Section 3, the main characteristics of the master clock of the experiment, used to synchronize all detector elements, are presented. Section 4 describes the calibration of the time offsets specific to each PMT performed in the laboratory before deployment and in situ. In Section 5 independent cross-checks of the system performance are presented.

The ANTARES detector

The ANTARES detector is located in the Mediterranean Sea, about 40 km from Toulon, off the French coast. It consists of 885 10-inch PMTs (model R7081-20 from Hamamatsu) distributed over twelve lines, of 25 triplet PMT storeys each, anchored to the sea bottom (see Figure 1). The total length of each line is 480 m. The lowest storey of each line is located 100 m above the sea bed. The distance between consecutive storeys is 14.5 m and the horizontal separation between lines is 60-80 m. The PMTs [START_REF] Aguilar | Study of large hemispherical photomultiplier tubes for the ANTARES neutrino telescope[END_REF] are coupled with optical gel to the inner surfaces of pressure-resistant glass spheres (optical modules, OMs [START_REF] Amram | The ANTARES Optical Module[END_REF]). A µ-metal cage inside the OM shields the PMT from the Earth magnetic field. Each storey comprises a triplet of OMs and an electronics module (Local Control Module, LCM). Five consecutive storeys along the line are grouped into a "sector" sharing common data and clock distribution elements. One LCM of a sector (Master Local Control Module, MLCM) contains an Ethernet switch and a Dense Wavelength Division Multiplexing transceiver of a specific wavelength to establish data connection from the sector to shore along optical fibres. At the bottom of each line, a String Control Module (SCM) houses the power units and the optical (de)multiplexers. Furthermore, each line incorporates four LED Optical Beacons (OBs) [START_REF] Ageron | The ANTARES Optical Beacon system[END_REF] used for time calibration and studies of the optical properties of the sea water. In addition, two Laser Beacons are located at the bottom of two of the central lines.

The lines are connected to a junction box from where the Main Electro-Optical Cable (MEOC), of a length of 45 km, links the detector to the shore station.

The shore station houses a computer farm for data filtering and storage and the master clock. A more detailed description of the ANTARES DAQ system can be found in [START_REF] Aguilar | The data acquisition system for the ANTARES neutrino telescope[END_REF].

The signals from one PMT are processed in situ by ASICs (named Analogue Ring Samplers or ARSs [START_REF] Aguilar | Performance of the front-end electronics of the ANTARES Neutrino Telescope[END_REF]), located in the LCMs. Two ARSs are used in 2). The clock period of 50 ns covers about 150 channels of the ADC, corresponding to an average bin width of 0.3 ns. The resulting effective time resolution is thus about 0.3 ns/ √ 12. However, differential non-linearities of the ADCs (i.e. not all bins have the same width) result in an effective precision about four times larger, which is still adequate for our requirements to keep time calibration resolution below ∼1 ns.

The fact that the PMT signals are discriminated by the ARSs using a fixed amplitude threshold leads to a walk effect: a PMT signal with high amplitude crosses the threshold earlier than a coincident low amplitude signal. The difference between the threshold crossing times of pulses of different amplitudes can be of the order of a few nanoseconds. This effect can be corrected if the photo-electron pulse shape (PPS) is known: the PPS function is scaled up or down to reproduce the total charge of the hit and the corresponding thresholdcrossing time is calculated. During standard data acquisition the total charge of a PMT hit is integrated by the ARS and the information about its shape is lost. However, the ARSs can be operated in a special acquisition mode which records PMT signals as waveforms sampled into 128 channels over 200 ns and digitized by an ADC. The PPS used to extract the walk correction is computed by fitting the average waveform obtained from single photo-electron events of all the ARSs. The walk effect correction as a function of the pulse amplitude is shown in Figure 3. It is systematically applied before event reconstruction.

The Clock System

The main goal of the clock system is to provide a common signal to synchronize the readout of the OMs. It consists of a 20 MHz generator on shore, a distribution network and a signal transceiver in each LCM. The optical clock signals received from shore are converted and decoded by an electronics board inside the LCM, and are then distributed over an electrical bus to the ARS chips.

The absolute time stamping is performed by interfacing the clock system with a dedicated electronics board to the GPS timing system that provides a time accuracy of ∼100 ns with respect to the Universal Time Coordinated, well within the requirements (a few seconds to provide the direction of the neutrino in celestial coordinates and a few milliseconds to correlate it to astrophysical phenomena).

Track reconstruction requires the knowledge of the relative arrival times of the Cherenkov photons at the PMTs and therefore only their relative time offsets.

The layout of the clock distribution network is shown in Figure 4. It is based on a bi-directional optical communication system. The clock signals are transmitted (received) between shore and the SCMs of the lines using infrared signals of 1534 nm (1549 nm) wavelength, while within each detector line wavelengths of 1550 nm and 1310 nm are used for transmissions in the two opposite directions. In order to measure the time delays for individual storeys due to the propagation time along the cables, special clock signals are addressed to each LCM clock transceiver which responds by sending back a signal to the shore. The corresponding round-trip time is twice the propagation time to each individual LCM. During the standard operation of the telescope, the round-trip times to all the LCMs of the detector are monitored once per hour, which ensures to have at least one measurement per data taking run. An average of many such measurements provides the required precision. Figure 5 shows an example of the time evolution of the measured round-trip time from the shore station to the SCM of a line. Clock delay variations of the order of a few hundreds of picoseconds are observed and found to be correlated with temperature variations in the onshore section of the MEOC.

Figure 6 shows the stability of the round-trip times between an LCM and the SCM of a line. In this case, the delay variations in the common part of the MEOC cable cancel out and the relative uncertainty is reduced to around 16 ps.

OM time offset calibration

The time elapsed between the incidence of a photon on the photocathode of the PMT and the time stamping of the associated signal in the ARS must be determined. This delay depends on the PMT signal transit time, the length of the cable linking the OM to the LCM, the front-end electronics response time and the ARS threshold. The relevant time constants are initially deter- mined with a dedicated calibration set-up in a dark room prior to deployment. These constants could change slightly after deployment due to the temperature changes, stressing of cables during transportation/deployment, etc. Morever, when the high voltage applied to the PMTs change, the time offsets change too. Using the optical beacon system, they are periodically monitored and recomputed when the lines are operated in the sea.

Onshore calibration

Before deployment the functionality of each line is verified and a complete calibration is performed. The onshore time calibration is carried out illuminating simultaneously groups of OMs by short laser pulses. The propagation times from SCM to LCM are known from the clock system calibration. The contribution from the cable that links the LCM to the OM, the PMT transit time and the front-end electronics delay can thus be extracted.

The time calibration is performed in batches of five storeys (a sector) in the dark room (see Figure 7). The light source used is a Q-switched, Nd-YAG laser [12] that emits intense (E∼1 µJ) and short (FWHM∼0.8 ns) pulses of green light (λ=532 nm) externally triggered at a frequency of 1 kHz. The light is split using a 1-to-16 optical splitter and distributed to the 15 OMs of each sector through optical fibres. Each optical fibre is coupled to a Lambertian diffuser which spreads the laser light over the full area of the corresponding PMT photocathode. The output amplitude of the light (equivalent to about 10 12 photons) is attenuated in order to produce a few tens of photoelectrons in the PMTs. The fibre lengths are adjusted such that the corresponding time differences are less than 0.3 ns. Measurements with the optical fibres swapped between OMs are made to cross-check these time differences. The time reference is provided by the laser internal photodiode. A reference LCM digitises this photodiode signal in order to synchronize the time measurements for OMs of different sectors. An example of the distribution of the difference between the time of the signal recorded by an OM and the emission time of the pulse as recorded by the laser photodiode is shown in Figure 8. The mean value of this distribution yields the difference between the laser light signal time measured by the PMT (including the PMT transit time and the electronics delay) and the time measured by the photodiode channel. The sigma of the distribution is 0.5 ns.

The time offsets between each OM of a line and the first OM of its lowest storey, which is chosen as a reference, are computed for each of the 30 ARSs of each sector. An example result is shown in Figure 9. The spread of the time offsets is of the order of a few nanoseconds, and is due to differences in the internal cabling of the OMs to the storey electronics as well as differences in PMT transit times. These time offsets are stored in the ANTARES database and are used as initial time constants in order to analyse data immediately after the installation of the line on the sea bed. The relative time calibration of the monitoring PMTs of the LED optical beacons (used for the in situ calibration described in subsection 4.2.1) is also performed during the onshore calibration. One of the fibres of the optical splitter is used in this case to send the light to the small PMT within each OB. Since this PMT is meant to measure the relatively high intensity of light emitted by the LEDs, the incident laser light intensity is tuned to be about twenty times higher than that provided to the OMs.

In situ calibration

The in situ measurement of the time offsets of all the OMs is performed with the optical beacon system [START_REF] Ageron | The ANTARES Optical Beacon system[END_REF]. This comprises two kinds of complementary devices: LED beacons that emit blue light (λ = 470 nm) and laser beacons emitting green light (λ = 532 nm) (see [START_REF] Amram | The ANTARES Optical Module[END_REF] for a description of the response of the OM as a function of the wavelength). Pictures of both devices before assembly are shown in Figure 10. The LED beacons are used to monitor the relative time offsets among OMs of the same line (intra-line calibration), whereas the laser beacons are used for monitoring the relative time offsets among the lines (inter-line calibration) and the calibration of the lowest storeys. The in situ calibration allows to re-measure the time constants computed onshore and is particularly important in case of a change in the PMT high-voltage and threshold settings.

LED beacons

Four LED optical beacons are located along every line of the detector in storeys 2, 9, 15 and 21 (counted from bottom to top). Each LED OB contains 36 LEDs distributed on six faces forming a hexagonal prism. The LEDs emit blue light with a maximum intensity of ∼160 pJ per flash (∼4×10 8 photons per pulse) and a pulse width of 4 ns (FWHM). The emission time of the LED light is measured by an 8-mm PMT placed inside the frame of the LED OB (see reference [START_REF] Ageron | The ANTARES Optical Beacon system[END_REF] for more details).

Figure 11 shows the distribution of signal time residuals, i.e. the difference between the signal time recorded in the OM and the emission time of the corresponding LED flash, using the time offsets measured in the dark room and once the nominal travel time of the light from the beacon to the OM has been subtracted. The plot on the left shows the distribution corresponding to an OM close to the OB (∼30 m) which receives a high amount of light. The plot on the right shows the distribution for an OM located seven storeys above the OB (∼100 m). In this case, a tail at positive times due to light scattering in water can be observed. A Gaussian fit to the region including the rising edge of the time distribution and the first bin after its maximum is performed. The range of the fit is restricted in order to use mostly the earliest photons, whose delay due to scattering can be neglected.

The position of the time residual peak, i.e. the mean value of the Gaussian best-fit curve described above, as a function of the distance from the OM to one optical beacon is shown in Figure 12, together with the slopes of such fits for all the OBs. The increase of the time residual with distance originates from an "early photon" effect, arising from the duration of the light pulse and the fact that the first photons detected by the PMT determine the recorded time of the pulse [START_REF] Aguilar | Analysis of the Optical Beacon system and search for point-like sources in the ANTARES neutrino telescope[END_REF]. The PMTs closer to the beacon, which detect a higher amount of photons per pulse, tend to trigger on the photons emitted earlier in the flash, whilst for PMTs farther away the probability distribution for the measured time of the signal is determined by the pulse width. The arrival time of the first photon obeys the order statistics [START_REF] Kendall | The advanced theory of Statistics I[END_REF]. A Monte Carlo simulation taking into account this effect as well as the exponential decrease of the intensity caused by the light attenuation shows that a linear increase in the time residual is expected when the number of photons reaching the PMTs is sufficiently high. A straight line is fitted to the time residual peaks ordered by the distance of the optical modules from the optical beacon. If a point deviates more than 2 ns, the fit is redone excluding it. The deviations from the fit are then used to obtain the time offset correction. The distribution of these time offset corrections for all OMs that can be calibrated with the OBs is shown in Figure 13. It is found that 15% of the cases need a correction to the dark room offsets larger than 1 ns.

Seven storeys above each OB, excluding the one just above the beacon (which receives too much light), can be calibrated. The storeys farther away, which do not receive enough light, are monitored with the next OB along the line. The OMs of the first three storeys of each line can not be calibrated with the LED OBs since they are below or just above the lowest OB. For these, the time offsets given by the dark room measurements are used, corrected by the laser beacon and potassium-40 measurements as explained later.

A way to check the validity of a set of time offsets is to calculate the signal time differences for pairs of OMs in the same storey (intra-storey time differences) when illuminated by the optical beacon. In Figure 14, the intra-storey time differences for one of the lines using the time offsets measured onshore and in situ are shown. The time differences become smaller when using the in situ offsets. For a detector configuration when 10 lines were installed, the RMS of the average intra-storey time difference distribution for the OMs which can be re-calibrated decreases from 0.72 ns to 0.48 ns after the application of the in situ calibration. This is a 30% improvement, which is equivalent to a subtraction of 0.54 ns in quadrature. In terms of sigma, the change is from 0.60 ns to 0.33 ns. Initially calibration runs were performed once per week, but after the time offsets were found to be very stable, the frequency has been reduced to once per month. Since each set of calibration runs takes about two hours, the total dead time is about one day per year, which is considered short enough.

Laser beacon

The relative time offsets among lines can be obtained with the laser beacons. This inter-line calibration is needed because the time offsets measured in the dark room are calculated with respect to a reference OM specific to each line.

Being much more powerful than the LED beacons, the lasers can illuminate all detector lines. Given that only distances where the OMs are illuminated below the one-photoelectron level are considered and since the time width of the laser pulse is very narrow (FWHM∼0.8 ns), the early photon effect is negligible. As a consequence, the time residuals do not depend on the distance to the source, as can be seen in Figure 15. The relative time offsets among lines are then computed as the average of the time residual peaks. The calculated inter-line time offsets are shown in Figure 16. In addition to the inter-line calibration, the laser beacon also provides a tool to compute the time offsets of the OMs in the lowest storeys.

Potassium-40

The radioactive potassium-40 ( 40 K) present in sea water can be used for time and efficiency calibration of the detector using the Cherenkov light induced by the electron emitted in the β-decay of potassium [START_REF] Aguilar | Measurement of the atmospheric muon flux with a 4 GeV threshold in the ANTARES neutrino telescope[END_REF][START_REF] Amram | Background light in potential sites for the ANTARES undersea neutrino telescope[END_REF]. If such a decay occurs within a distance of a few meters from a storey, coincident signals can be recorded by two OMs. In Figure 17 beacon calibrations (Figure 17, right). If the time offset of one of the OMs of the pair were incorrect, we would see that the peak is displaced from zero. The RMS of the mean intra-storey time difference distribution determined by the 40 K improves from 0.72 ns to 0.57 ns when using the time offsets calculated in situ rather than those determined from the dark room calibration. It is worth noticing that the 40 K intra-storey calibration is independent of the LED OB system and relies on a completely different light source: the 40 K is a dim, distributed and closeby source, whereas the beacons are powerful, point-like and distant sources.

Internal LEDs

Each optical module also incorporates an internal LED (of the same model as those used in the LED beacons) which is used exclusively to monitor the stability of the PMT transit time. The LED is located on the back of the phototube and illuminates the photocathode from behind. It is triggered by the clock signal at a constant rate. Figure 18 shows the mean time of the internal LED flashes as recorded by the corresponding PMT as a function of time. The values, measured in situ every week, vary less than 0.2 ns (RMS) over an eight month period.

Time resolution of the front-end electronics

The impact of the front-end electronics on the time resolution can be determined during onshore and in situ calibrations. In this section we present three different methods to estimate this front-end electronics contribution.

At low light intensity, the time resolution of an OM measured in the laboratory is dominated by the transit time spread of the PMT (σ high intensity, this contribution decreases as the square root of the number of photoelectrons and therefore the dominant term to the width of this distribution is the constant contribution due to the front-end electronics. This irreducible contribution is found to be ∼0.5 ns in the dark room calibration (see Figure 8).

The in situ estimation of the time resolution of the electronics is obtained from the distribution of the difference in the time measured by an OM close to an OB with respect to the emission time of the OB pulse. The sigma of the time distribution of the signal in an OM is given by

σ 2 OM = σ 2 T T S N pe + σ 2 water N γ + σ 2 OB + σ 2 elec ( 1
)
where σ T T S is the transit time spread of the PMT, σ water is the spread due to the scattering and chromatic dispersion of light in water (∼1.5 ns for a light path of 40 m), σ OB is the uncertainty of the measured emission time of the pulse and σ elec the spread due to the electronics. For an OM close to an OB, N pe and N γ are high and their corresponding contributions become negligible. Due to the fast rise time of the internal PMT of the OB, σ OB can also be neglected. An example of the time difference distribution is given in Figure 19. Measurements with several OMs close to OBs give a time resolution of ∼0.5 ns for the electronics, in agreement with the results obtained during the onshore calibration.

A third way to check this time resolution is given by comparing the times measured by two OMs in the same storey when illuminated at high intensity. In this case, the sigma of the distribution (see Figure 20) is given by σ OM -OM = √ 2σ elec . A front-end electronics time resolution of 0.5 ns is obtained.

These checks indicate that the uncertainty introduced by the readout system is negligible with respect to the irreducible contributions from the chromatic dispersion and TTS.

Conclusion

The completion of the ANTARES telescope has opened a new window to the neutrino Southern sky. Since the main physics goal of ANTARES is the search for cosmic point sources, an important feature is its angular resolution (a few tenths of a degree above 10 TeV), unsurpassed for this kind of instruments. The track reconstruction algorithms are based on the PDF of the photon arrival times to the PMTs. Therefore, in order to ensure an optimal performance, a precise time calibration of the detection system is crucial.

An onshore calibration performed in the laboratory provides a preliminary time calibration. Once the detector is deployed in the sea, time calibrations are performed in situ with a system of optical beacons. Although most of the corrections to the onshore time offsets are small, there are 15% of cases where they are larger than 1 ns. The observation of coincident photons from the decay of 40 K provides a completely independent verification for these measurements.

The adopted calibration systems and methods attain a relative time calibration between detector elements of less than 1 ns, as required.

Fig. 1 .

 1 Fig. 1. Schematic view of the ANTARES detector, consisting of twelve mooring lines connected to the shore station through an electro-optical cable. Laser beacons are located at the bottom of Lines 7 and 8 (central lines). LED beacons are located in storeys 2, 9, 15 and 21 (counted from bottom to top) of each line. alternation on each OM in order to reduce the dead time of the PMT signals close in time. If an analogue PMT signal reaches an amplitude larger than a given threshold (typically 0.3 photo-electrons), its arrival time and charge are digitized by the ARS chip. The coarse signal time (time stamp) is given by a counter which is incremented by a 20 MHz clock synchronized to signals received from shore by the clock system (see next section). A Time-to-Voltage Converter (TVC) read by an 8-bit ADC is used to measure the fine time in the 50 ns period after the time stamp. The dynamic range of the TVC is determined by recording random signals uniformly distributed in time (see Figure2). The clock period of 50 ns covers about 150 channels of the ADC, corresponding to an average bin width of 0.3 ns. The resulting effective time resolution is thus about 0.3 ns/ √ 12. However, differential non-linearities of the ADCs (i.e. not all bins have the same width) result in an effective precision about four times larger, which is still adequate for our requirements to keep time calibration resolution below ∼1 ns.

Fig. 2 .Fig. 3 .

 23 Fig. 2. TVC distribution generated from random PMT signals. The TVC values have been digitized by an ADC. The histogram has been rebinned by a factor 4 to mitigate the effect of differential non-linearities.

Fig. 4 .Fig. 5 .

 45 Fig. 4. Schematic view of the clock system: optical signals are sent from shore and propagated up to the junction box where they are split towards the SCMs of the different lines. From the SCM they are distributed to each LCM, where a transceiver sends the signal back to shore for calibration purposes.

Fig. 6 .

 6 Fig. 6. Left: Time evolution of the difference in the round-trip times between the shore and an SCM and one of the LCMs. Right: Projection of these values, whose distribution has an RMS of about 16 ps.

Fig. 7 .Fig. 8 .

 78 photodiode

Fig. 9 .

 9 Fig. 9. Time offsets measured for all ARSs of one of the line sectors. The time offsets are relative to the first ARS of the first OM of the lowest storey. The ARS id runs from 0 to 5 within each storey.

Fig. 10 .

 10 Fig. 10. Picture of an LED optical beacon (left) and a laser beacon (right).

Fig. 11 .

 11 Fig. 11. Time residual distribution in two different OMs located two storeys (left) and seven storeys (right) above the LED flashing beacon. The curve is the Gaussian fit explained in the text.

Fig. 12 .Fig. 13 .

 1213 Fig.12. Left: Time residual peak position as a function of the OB-OM distance, i.e. the distance between the optical beacon and the different optical modules, for all the ARSs along seven storeys. The six points at each distance correspond to the six ARSs in each storey (two ARSs per OM). The additional delay with distance is due to the early photon effect (see text). Right: Distribution of the slopes of the fits to the time residual peak positions as a function of the OB-OM distance for all the OBs.

Fig. 14 .

 14 Fig.[START_REF] Kendall | The advanced theory of Statistics I[END_REF]. Time differences between OMs in the same storey for one of the lines using the time offsets measured onshore (left) and in situ (right).

Fig. 15 .Fig. 16 .

 1516 Fig.[START_REF] Amram | Background light in potential sites for the ANTARES undersea neutrino telescope[END_REF]. Time residual peak position versus the distance between the laser beacon and the OM. Each point is the average over all the OMs in the same storey.

Fig. 17 .

 17 Fig.17. Left: Distribution of background hit time differences for one pair of OMs in the same storey. The peak is due to single 40 K decays detected in coincidence by two OMs. The data have been fitted to a sum of a Gaussian distribution and a flat background from random coincidences. Right: Comparison of the distributions of mean intra-storey time differences from 40 K using the onshore and in situ time offsets.

Fig. 18 .

 18 Fig. 18. Example of the mean time of the internal LED flashes as recorded by the PMT as a function of the time.

Fig. 19 .Fig. 20 .

 1920 Fig. 19. Example of the time residual distribution for an OM located one storey above the optical beacon. The sigma of the distribution (0.5 ns) is dominated by the contribution from the front-end electronics.

a

  IFIC -Instituto de Física Corpuscular, Edificios Investigación de Paterna, CSIC -Universitat de València, Apdo. de Correos 22085, 46071 Valencia, Spain b CPPM -Centre de Physique des Particules de Marseille, CNRS/IN2P3 et Université de la Méditerranée, 163 Avenue de Luminy, Case 902, 13288 Marseille Cedex 9, France c GRPHE -Institut universitaire de technologie de Colmar, 34 rue du Grillenbreit BP 50568 -68008 Direction des Sciences de la Matière -Institut de recherche sur les lois fondamentales de l'Univers -Service d'Electronique des Détecteurs et d'Informatique, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France

	Colmar, France
	d Technical University of Catalonia,Laboratory of Applied Bioacoustics,Rambla Exposici,08800 Vilanova i
	la Geltr,Barcelona, Spain
	e INFN -Sezione di Genova, Via Dodecaneso 33, 16146 Genova, Italy
	f Friedrich-Alexander-Universität Erlangen-Nürnberg, Erlangen Centre for Astroparticle Physics,
	Erwin-Rommel-Str. 1, 91058 Erlangen, Germany
	g

h Institut d'Investigació per a la Gestió Integrada de Zones Costaneres (IGIC) -Universitat Politècnica de València. C/ Paranimf 1, 46730 Gandia, Spain. i FOM Instituut voor Subatomaire Fysica Nikhef, Science Park 105, 1098 XG Amsterdam, The Netherlands j APC -Laboratoire AstroParticule et Cosmologie, UMR 7164 (CNRS, Université Paris 7 Diderot, CEA, Observatoire de Paris) 10, rue Alice Domon et Léonie Duquet 75205 Paris Cedex 13, France k LAM -Laboratoire d'Astrophysique de Marseille, Pôle de l' Étoile Site de Château-Gombert, rue Frédéric Joliot-Curie 38, 13388 Marseille Cedex 13, France Dipartimento di Fisica dell'Università, Viale Berti Pichat 6/2, 40127 Bologna, Italy m INFN -Sezione di Bologna, Viale Berti Pichat 6/2, 40127 Bologna, Italy n Dipartimento di Fisica dell'Università La Sapienza, P.le Aldo Moro 2, 00185 Roma, Italy o INFN -Sezione di Roma, P.le Aldo Moro 2, 00185 Roma, Italy p Laboratoire de Physique Corpusculaire, IN2P3-CNRS, Université Blaise Pascal, Clermont-Ferrand, France q INAF-IASF, via P. Gobetti 101, 40129 Bologna, Italy r Géoazur -Université de Nice Sophia-Antipolis, CNRS/INSU, IRD, Observatoire de la Côte d'Azur and Université Pierre et Marie Curie, BP 48, 06235 Villefranche-sur-mer, France s INFN -Sezione di Bari, Via E. Orabona 4, 70126 Bari, Italy t Direction des Sciences de la Matière -Institut de recherche sur les lois fondamentales de l'Univers -Service de Physique des Particules, CEA Saclay, 91191 Gif-sur-Yvette Cedex, France u COM -Centre d'Océanologie de Marseille, CNRS/INSU et Université de la Méditerranée, 163 Avenue de Luminy, Case 901, 13288 Marseille Cedex 9, France v INFN -Laboratori Nazionali del Sud (LNS), Via S. Sofia 62, 95123 Catania, Italy w Université Paris-Sud 11 -Département de Physique, 91403 Orsay Cedex, France

mm/yy] 10/06 11/06 12/06 01/07 02/07 03/07 04/07 05/07 06/07 mean time [ns]

T T S ∼ 1.3 ns). At date [

Acknowledgments

The authors acknowledge the financial support of the funding agencies: Centre National de la Recherche Scientifique (CNRS), Commissariat à l'énergie atomique et aux énergies alternatives (CEA), Agence National de la Recherche (ANR), Commission Européenne (FEDER fund and Marie Curie Program), Région Alsace (contrat CPER), Région Provence-Alpes-Côte d'Azur, Département du Var and Ville de La Seyne-sur-Mer, France; Bundesministerium für Bildung und Forschung (BMBF), Germany; Istituto Nazionale di Fisica Nucleare (INFN), Italy; Stichting voor Fundamenteel Onderzoek der Materie (FOM), Nederlandse organisatie voor Wetenschappelijk Onderzoek (NWO), the Netherlands; Council of the President of the Russian Federation for young scientists and leading scientific schools supporting grants, Russia; National Authority for Scientific Research (ANCS), Romania; Ministerio de Ciencia e Innovación (MICINN), Prometeo of Generalitat Valenciana (GVA) and Multi-Dark, Spain. We also acknowledge the technical support of Ifremer, AIM and 21 Foselev Marine for the sea operation and the CC-IN2P3 for the computing facilities.