Gilles Sérasset
email: gilles.serasset@imag.fr

A Generic Collaborative Platform for Multilingual Lexical Database Development

The motivation of the Papillon project is to encourage the development of freely accessible Multilingual Lexical Resources by way of online collaborative work on the Internet. For this, we developed a generic community website originally dedicated to the diffusion and the development of a particular acception based multilingual lexical database.

The generic aspect of our platform allows its use for the development of other lexical databases. Adapting it to a new lexical database is a matter of description of its structures and interfaces by way of XML files. In this paper, we show how we already adapted it to other very different lexical databases. We also show what future developments should be done in order to gather several lexical databases developers in a common network.

Introduction

In order to cope with information available in many languages, modern information systems need large, high quality and multilingual lexical resources. Building such a resource is very expensive. To reduce these costs, we chose to use the "collaborative" development paradigm already used with LINUX and other open source developments.

In order to develop such a specific multilingual lexical database, we built a Web platform to gather an Internet community around lexical services (accessing many online dictionaries, contributing to a rich lexical database, validating contributions from others, sharing documents, . . . ). Initially built for the Papillon project, this platform is generic and allows for the collaborative development of other lexical resources (monolingual, bilingual or multilingual) provided that such resources are described to the platform.

After presenting the Papillon project and platform, we will show how we may give access to many existing dictionaries, using an unified interface. Then, we will present the edition service, and detail how it may be customised to handle other very different dictionaries.

The Papillon project

Motivations

Initially launched in 2000 by a French-Japanese consortium, the Papillon project1 [START_REF] Sérasset | Papillon lexical database project: Monolingual dictionaries and interlingual links[END_REF] rapidly extended its original goal -the development of a rich French Japanese lexical database -to its actual goalthe development of an Acception based Multilingual Lexical Database (currently tackling Chinese, English , French, German, Japanese, Lao, Malay, Thai and Vietnamese).

This evolution was motivated in order to:

• reuse many existing lexical resources even the ones that do not directly involve both initial languages,

• be reusable by many people on the Internet, hence raising the interest of others in its development,

• allow for external people (translator, native speakers, teachers. . . ) to contribute to its development,

For this project, we chose to adopt as much as possible the development paradigm of LINUX and GNU software2 , as we believe that the lack of high level, rich and freely accessible multilingual lexical data is one of the most crucial obstacle for the development of a truly multilingual information society3 .

Papillon acception based multilingual database

The Papillon multilingual database has been designed independently of its usage(s). It consists in several monolingual volumes linked by way of a single interlingual volume called the interlingual acception dictionary. Each monolingual volume consists in a set of word senses (lexies), each lexie being described using a structure derived from the Explanatory and Combinatory Dictionary (Mel'čuk et al., 1995;[START_REF] Mel'čuk | Dictionnaire Explicatif et Combinatoire du français contemporain, recherches lexico-sémantiques, volumes I, II, III et IV[END_REF][START_REF] Mel'čuk | Dictionnaire Explicatif et Combinatoire du français contemporain, recherches lexico-sémantiques, volumes I, II, III et IV[END_REF]Mel'čuk et al., 1995[START_REF] Mel'čuk | Dictionnaire Explicatif et Combinatoire du français contemporain, recherches lexico-sémantiques, volumes I, II, III et IV[END_REF].

The interlingual acception dictionary consists in a set of interlingual acceptions (axies) as defined in [START_REF] Sérasset | Interlingual lexical organisation for multilingual lexical databases in nadia[END_REF]). An interlingual acception serves as a placeholder bearing links to lexies and links between axies4 . This simple mechanism allows for the coding of translations. As an example, figure 1 shows how we can represent a quadrilingual database with contrastive problems (on the well known "rice" example).

Development methodology

The development of the Papillon multilingual dictionary gathers voluntary contributors and trusted language specialist involved in different tasks (as shown in figure 2).

• First, an automatic process creates a draft acception based multilingual lexical database from existing monolingual and bilingual lexical resources as shown in [START_REF] Teeraparseree | Jeminie: A flexible system for the automatic creation of interlingual databases[END_REF][START_REF] Mathieu Mangeot-Lerebours | Construction collaborative dune base lexicale multilingue, le projet Papillon[END_REF]. This step is called the bootstrapping process. • Then, contributions may be performed by volunteers or trusted language specialists. A contribution is either the modification of an entry, its creation or its deletion. Each contribution is stored and immediately available to others.

• Volunteers or language specialist may validate these contributions by ranking them.

• Finally, trusted language specalists will integrate the contribution and apply them to the master MLDB. Rejected contributions won't be available anymore.

The Papillon Platform

The Papillon platform is a community web site specifically developed for this project. This platform is entirely written in Java using the "Enhydra5 " web development Framework. All XML data is stored in a standard relational database (Postgres). This community web site proposes several services:

• a unified interface to simultaneously access the Papillon MLDB and several other monolingual and bilingual dictionaries;

• a specific edition interface to contribute to the Papillon MLDB,

• an open document repository where registered users may share writings related to the project; among these documents, one may find all the papers presented in the different Papillon workshops organized each year by the project partners;

• a mailing list archive, Sections 3 and 4 present the first and second services.

3 Unified access to existing dictionaries To encourage volunteers, we think that it is important to give a real service to attract as many Internet users as possible. As a result, we began our development with a service to allow users to access to many dictionaries in a unified way. This service currently gives access to twelve (12) bilingual and monolingual dictionaries, totalizing a little less than 1 million entries, as detailled in table 1.

Strong points

The unified access interface allows the user to access simultaneously to several dictionaries with different structures. All available dictionary will be queried according to its own structure. Moreover, all results will be displayed in a form that fits its own structure.

Any monolingual, bilingual or multilingual dictionary may be added in this collection, provided that it is available in XML format.

With the Papillon platform, giving access to a new, unknown, dictionary is a matter of writing 2 XML files: a dictionary description and an

Implementation

It is possible to give access to any XML dictionary, regardless of its structure. For this, you have to identify a minimum set of information in the dictionary's XML structure.

The Papillon platform defines a standard structure of an abstract dictionary containing the most frequent subset of information found in most dictionaries. This abstract structure is called the Common Dictionary Markup [START_REF] Mangeot | Frameworks, implementation and open problems for the collaborative building of a multilingual lexical database[END_REF]. To describe a new dictionary, one has to write an XML file that associate CDM element to pointers in the original dictionary structure.

As an example, the French English Malay FeM dictionary [START_REF] Gut | Kamus Perancis-Melayu Dewan, Dictionnaire francais-malais[END_REF] has a specific structure, illustrated by figure 4.

Figure 5 gives the XML code associating elements of the FeM dictionary with elements of the CDM.

Along with this description, one has to de- <cdm-elements> <cdm-volume element="volume"/> <cdm-entry element="HFEM"/> <cdm-headword element="HW-FRE"/> <cdm-pronunciation element="PRNC"/> <cdm-pos element="CAT-STAR"/> <cdm-definition element="FRE"/> <cdm-translation d:lang="eng" element="ENG-STAR"/> <cdm-translation d:lang="msa" element="MAL-STAR"/> <cdm-example d:lang="fra" element="FRE"/> <cdm-example d:lang="eng" element="ENG"/> <cdm-example d:lang="msa" element="MAL"/> <cdm-key1 element="HOM"/> </cdm-elements> fine an XSL style sheet that will be applied on requested dictionary elements to produce the HTML code that defines the final form of the result. If such a style sheet is not provided, the Papillon platform will itself transform the dictionary structure into a CDM structure (using the aforementioned description) and apply a generic style sheet on this structure.

Editing dictionaries entries

Presentation

As the main purpose of the Papillon platform is to gather a community around the development of a dictionary, we also developed a service for the edition of dictionary entries.

Figure 6: The edition interface is a standard HTML interface Any user, who is registered and logged in to the Papillon web site, may contribute to the Papillon dictionary6 by creating or editing7 an entry. Moreover, when a user asks for an unknown word, he is encouraged to contribute it to the dictionary.

Contribution is made through a standard HTML interface (see figure 6). This interface is rather crude and raises several problems. For instance, there is no way to copy/paste part of an existing entry into the edition window. Moreover, editing has to be done on-line8 . However, as the interface uses only standard HTML elements with minimal javascript functionality, it may be used with any Internet browser on any platform (provided that the browser/platform correctly handles unicode forms).

Strong points

From the beginning, we wanted this interface to be fully customizable by Papillon members without relying on the availability of a computer science specialist. our reasons are:

• the fact that we wanted the structure of the Papillon dictionary to be adaptable along with the evolution of the project, without implying a full revisit of the web site implementation;

• the fact that each language may slightly adapt the Papillon structure to fit its own needs (specific set of part of speech, language levels, etc.), hence adding a new dictionary implies adding a new custom interface;

Hence, we chose to develop a system capable of generating a usable interface from a) a description of the dictionary structure (an XML Schema) and b) a description of the mapping between element of the XML structure and standard HTML inputs.

For this, we used the ARTStudio tool described by [START_REF] Calvary | A unifying reference framework for the development of plastic user interfaces[END_REF]. Using a tool that allows for the development of plastic user interfaces allows us to generate not only one, but several interfaces on different devices. Hence, as we are now able to generate an HTML interface usable with any standard web browser supporting Unicode, we may, in the future, generate interfaces for Java applications (that can be used offline) or interfaces for portable devices like pocket PCs or Palm computers.

Implementation 4.3.1 Definition of the dictionary

structure To provide an edition interface, the Papillon platform needs to know the exact dictionary structure. The structure has to be defined as a standard XML schema. We chose to use XML schema because it allows for a finer description compared to DTDs (for instance, we may define the set of valid values of the textual content of an XML element). Moreover XML schemata provides a simple inheritance mechanism that is useful for the definition of a dictionary. For instance, we defined a general structure for the Papillon dictionary (figure 7) and used the inheritance mechanism to refine this general structure for each language (as in figure 8).

Description of the interface

Describing the interface is currently the most delicate required operation. The first step is to define the set of elements that will appear in the <element name="lexie"> <complexType> <sequence> <element ref="d:headword" minOccurs="1" macOccurs="1" /> <element ref="d:writing" ... /> <element ref="d:reading" ... /> <element ref="d:pronunciation" ... /> <element ref="d:pos" ... /> <element ref="d:language-levels" ... /> <element ref="d:semantic-formula" ... /> <element ref="d:government-pattern" .../> <element ref="d:lexical-functions" ... /> <element ref="d:examples" ... /> <element ref="d:full-idioms" ... /> <element ref="d:more-info" ... /> </sequence> <attribute ref="d:id" use="required" /> </complexType> </element> ... <element name="pos" type="d:posType" /> <simpleType name="posType"> <restriction base="string" /> </simpleType> ... interface and their relation with the dictionary structure. Each such element is given a unique ID. This step defines an abstract interface where all elements are known, but not their layout, nor their kind.

This step allows for the definition of several different tasks for the edition of a single dictionary.

The second step is to define the concrete realization and the position of all these elements.

For instance, in this step, we specify the POS element to be rendered as a menu. Several kind of widgets are defined by ARTStudio. Among them, we find simple HTML inputs like text boxes, menus, check-boxs, radio buttons, labels. . . , but we also find several high level elements like generic lists of complex elements.

As an simple example, we will see how the pos (part of speech) element is rendered in the Papillon interface. First, there will be an interface element (called S.364) related to the pos element (figure 9). Second, this element will be realized in our interface as a comboBox (figure 10).

<Instance type="element" id="S.364"> <InstanceKind value="static"/> <InstanceBuildKind value="regular"/> <Name value="pos"/> <ClassNameSpace value=""/> <ClassName value="posType"/> <TaskOwnerID value="S.360"/> <TaskRangeID list="S.360"/> </Instance> Figure 9: Definition of the abstract interface element associated to the pos element. This element will display/edit value of type posType defined in the aforementioned schema.

<Interactor type="element" class="GraphicInteractor" id="i2008"> <Type value="presentation"/> <TaskID value="S.363"/> <InteractorID value="ComboBox"/> <InstanceID value="S.364"/> <Width value="10"/> <Height value="20"/> </Interactor> Using this technique is rather tricky as there is currently no simple interface to generate these rather complex descriptions. However, using these separate description allows the definition of several edition tasks (depending on the user profile) and also allows, for a single task, to generate several concrete interfaces, depending on the device that will be used for edition (size of the screen, methods of interactions, etc.).

Interface generation

Using the describe structure of the dictionary, we are able to generate an empty dictionary entry containing all mandatory elements. Then, we walk this structure and instantiate all associated widgets (in our case HTML input elements), as defined in the interface description. This way, we are able to generate the corresponding HTML form.

When the user validates a modification, values of the HTML input elements are associated to the corresponding parts of the edited dictionary structure (this is also the case if the user asks for the addition/suppression of an element in the structure). Then, we are able to regenerate the interface for the modified structure. We iterate this step until the user saves the modified structure.

Conclusions

The Papillon platform is still under development. However, it already proves useful for the diffusion of a little less than 1 million entries from 12 very different dictionaries. This is possible as, from the very beginning, we designed the platform to be as a generic as possible.

This genericity also allows for its use for the on-line development of the Papillon database. It is also used for the development of the Estonian French GDEF dictionary, managed by Antoine Chalvin from INALCO, Paris. Moreover, we developed an interface for the japanese German WadokujiTen [START_REF] Apel | WaDokuJT -A Japanese-German Dictionary Database[END_REF]. This proves that our platform may be useful in a general context.

Our future activities will follow 3 axis:

• improving the definition of edition interfaces; currently, we have no tool to simplify this definition and its complexity makes it difficult for a linguist to use it without help from computer science specialists;

• generating different interfaces from the same descriptions; currently, we only generate on-line HTML interfaces, but the tools we use allows for the development of interfaces in other contexts; hence with the same approach, we will develop java applets or java applications to be used either on-line or off-line;

• developing network cooperation modules between several instances of the Papillon platform; this will allow the deployment of the platform on several sites; we will address two aspects of such a deployment; first, duplication of identical instances providing access and edition services on the same dictionaries; second the deployment of several instances providing access and edition services on different dictionaries (where dictionaries edited on a site may be accessed on another site).

Figure 1 :

 1 Figure 1: Macrostructure of the Papillon MLDB, showing the handling of contractive problems.

Figure 2 :

 2 Figure 2: Methodology for the development of the Papillon database.

Figure 3 :

 3 Figure 3: The unified access interface and results from three different dictionaries

Figure 4 :

 4 Figure 4: A simplified example entry from the French English Malay FeM dictionary.

Figure 5 :

 5 Figure 5: Associations between elements of the FeM dictionary and elements of the CDM.

Figure 7 :Figure 8 :

 78 Figure 7: General structure shared by all volumes of the Papillon dictionary; showing the part of speech element pos defined as a textual element.

Figure 10 :

 10 Figure 10: Definition of the effective widget for the pos element.

Table 1 :

 1

Dictionaries available through the unified access interface XSL stylesheet. For currently available dictionaries, this took an average of about one hour per dictionary.

http://www.papillon-dictionary.org/

i.e. allowing and encouraging external users to access and contribute to the database.

3 i.e. an Information Society with no linguistic domination and where everybody will be able to access any content in its own mother tongue.

Note that these links are not interpreted semantically, but only reflect the fact that translation is possible

see http://www.enhydra.org/

And, for now, only to this particular dictionary.

Removal of an entry is not yet implemented.

In fact, entries may be edited off-line and uploaded on the server, but there is currently no specialized interface for off-line edition, meaning that users will have to use standard text/XML editor for this.

Acknowledgements

Developments on the Papillon project could not have taken place without support from CNRS (France) and JSPS (Japan). We would like to warmly thank François Brown de Colstoun who supports this project since its very beginning. Developments of the platform and especially the editing part has been mainly done by Mathieu Mangeot and David Thevenin during their Post Doctoral fellowship at NII (National Institue of Informatics), Tokyo. Finally the Papillon platform would not be useful without partners who agreed to give free access to their superb dictionaries.


Christian Boitet
email: christian.boitet@imag.fr

Mangeot Mathieu
email: mathieu.mangeot@imag.fr

Sérasset Gilles

The PAPILLON project: cooperatively building a multilingual lexical data-base to derive open source dictionaries & lexicons

The PAPILLON project aims at creating a cooperative, free, permanent, web-oriented and personalizable environment for the development and the consultation of a multilingual lexical database. The initial motivation is the lack of dictionaries, both for humans and machines, between French and many Asian languages. In particular, although there are large F-J paper usage dictionaries, they are usable only by Japanese literates, as they never contain both original (kanji/kana) and romaji writing. This applies as well to Thai, Vietnamese, Lao, etc.

Introduction

The project was initiated in 2000 and launched with the support of the French Embassy and NII (Tokyo) in July 2000, and took really shape in 2001, with a technical seminar in July 2001 at Grenoble, and concrete work (data gathering, tool building, etc.). The macrostructure of Papillon is a set of monolingual dictionaries (one for each language) of word senses, called "lexies", linked through a central set of interlingual links, called "axies". This pivot macrostructure has been defined by [START_REF] Sérasset | Interlingual Lexical Organisation for Multilingual Lexical Databases[END_REF] and experimented by [START_REF] Blanc | Designing an Acception-Based Multilingual Lexical Data Base under HyperCard: PARAX[END_REF] in the PARAX mockup. The microstructure of the monolingual dictionaries is the "DiCo" structure, which is a simplification of Mel'tchuk's (1981;1987;1995) DEC (Explanatory and Combinatory Dictionary) designed by [START_REF] Polguère | Towards a theoretically-motivated general public dictionary of semantic derivations and collocations for French[END_REF] & Mel'tchuk to make it possible to construct large, detailed and principled dictionaries in tractable time.

Languages included in the project

In 2000, the initial languages of the Papillon project were English, French, Japanese and Thai. Thai was included because there had been a successful project, SAIKAM (Ampornaramveth et al. 1998;2000), supported by NII and NECTEC, of building a Japanese-Thai lexicon by volunteers on the web. Lao, Vietnamese, and Malay have been added in 2001 because of active interest of labs and individuals.

The star-like macrostructure of Papillon makes it easy to add a new language. Also, the DiCo microstructure of each monolingual dictionary is defined by an XML schema, containing a large common core and a small specialization part (morphosyntactic categories, language usage).

Interlingual links

Axies, also called "interlingual acceptions", are not concepts, but simply interlingual links between lexies, motivated by translations found in existing dictionaries or proposed by the contributors. In case of discrepancies, 1 axie may be linked with lexies of some languages only, e.g. FR(mur#1), EN(wall#1), RU(stena#1), and to other axies by refinement links:

Example: Axie#234 --lg--> FR(mur#1), EN(wall#1), RU(stena#1) --rf--> Axie#235, Axie#236 Axie#235 --lg--> DE(Wand#2), IT(muro#1), ES(muro#1) Axie#236 --lg--> DE(Mauer#2),
IT(parete#1), ES(pared#1) It is also possible to have 2 axies for the same "concept" at a certain stage in the life of the database, because the monolingual information is not yet detailed enough. Suppose the level of language (usual, specialized, vulgar, familiar…) is not yet given for FR(maladie#1), FR(affection#2), EN(disease#1), EN(affection#3). Then we might have, for translational reasons: Axie#456 --lg--> FR(maladie#1), EN(disease#1) Axie#457 --lg--> FR(affection#2), EN(affection#3) When this information will be put in each of the above 4 monolingual entries, we may merge the 2 axies and get: Axie#500 --lg--> FR(maladie#1, affection#2), EN(disease#1, affection#3) Axies may also be linked to "external" systems of semantic description. Each axie contains a (possibly empty) list for each such system, and the list of systems is open. The following are included at this stage; UNL UWs (universal words), ONTOS concepts, WordNet synsets, NTT semantic categories.

Building the content

Recuperating existing resources

Building the content of the data base has several aspects. To initiate it, the project starts from open source computerized data, called "raw dictionaries", which may be monolingual (4,000 French DiCo entries from UdM, 10,000 Thai entries from Kasetsart Univ.), bilingual (70,000 Japanese-English entries and 10,000 Japanese-French entries in J.Breen's JDICT XML format, 8000 Japanese-Thai entries in SAIKAM XML format, 120,000 English-Japanese entries in KDD-KATE LISP format), or multilingual (50,000 French-English-Malay entries in FEM XML format).

Integrating the data into Papillon

In the second phase, the "raw dictionaries" are transformed into a "lexical soup" in M. [START_REF] Mangeot-Lerebours | Environnements centralisés et distribués pour lexicographes et lexicologues en contexte multilingue[END_REF] intermediary DML format (an XML schema and namespace). The transformation into almost empty DiCo entries and the creation of axies for the translational equivalences is semi-automatic. A tool has been programmed at NII for that task.

Enriching the data with contributions

After that, it is hoped that many contributors will "fill in" the missing information. The basis for that third and continuous phase is a server for cooperative building of the data base, where each contributor has his/her own space, so that contributions can be validated and integrated into the DB by a group experts. Users can establish user groups with specific read and write access rights on their spaces.

Consultation of the resulting data

Online consultation

Consultation is meant to be free for anybody, and open source. Requests produce personalizable views of the data base, the most classical of which are fragments of bilingual dictionaries. However, it is also possible to produce multitarget entries, on the fly and offline. Users (consumers) are encouraged to become contributors. To contribute, one may propose a new word sense, a definition, an example of use, a translation, the translation of an example, a correction, etc., or an annotation on any accessible information: Every user can contribute with his own knowledge level.

Download of entire files

Users can also retrieve files, and can contribute to define new output formats. The files retrieved can contain structural, content-oriented tags. This open source orientation contrasts with the current usage of allowing users to retrieve files containing only presentation-oriented tags.

Coverage of the dictionary

An interesting point is that the project wants to cover both general terms and terminological terms.

Another one is that it contains a translation subproject, because definitions, examples, citations, etc. have to be translated into all languages of the collection. For this, the notion of complex lexie, already present to account for lexical collocations such as compound predicates (e.g. "to kick the bucket"), is extended to cover full sentences. Axies relating them are special because they can't in general relate them to external semantic systems such as WordNet. An exception is UNL: the UNL list for an axie may contain one UNL graph, produced automatically, manually, or semi-automatically. This graph may be automatically sent to available UNL "deconverters" to get draft translations.

Project organisation

In the current stage, the project has no legal implementation as a fundation, association, company, etc., although many participants have already established official MOUs and other types of agreements on which to base their cooperative work. There is a steering committee of about 10-12 members, who represent Papillon where they are, and not the converse. There is a set of tasks, and for each task a working group and an advisory committee. One of the tasks is the management of the project. In between, there is a coordinating group containing the heads of the tasks and chaired by the head of the management task. Sponsors may not donate money to the project, which has no bank account. Rather, they are encouraged to donate data, to assign personal part time to the project, and to fund participating organizations and persons as they see fit.

Conclusion

The theoretical frameworks for the whole database, the macrostructure and the microstructure are very well defined. It constitutes a solid basis for the implementation.

A lot of open problems still have to be addressed for the Papillon project to be a success. In this respect, the Papillon project appears to be a very interesting experimentation platform for a lot of NLP research as data acquisition or human access to lexical data, among others. All these research will improve the attraction of such a project to the Internet users. This attraction is necessary for the project to go on, as it is highly dependent on its users motivations. This way, we will be able to provide a very interesting multilingual lexical database that we hope useful for a lot of persons.


Mathieu Mangeot-Lerebours

Sérasset Gilles
email: gilles.serasset@imag.fr

Frédéric Andrès
email: andres@nii.ac.jp

Frameworks, Implementation and Open Problems for the Collaborative Building of a Multilingual Lexical Database

Many NLP systems are based on lexical data. The development costs of such data are a major drawback in such NLP systems. In order to cut these costs, we adopt a strategy inspired from "opensource" projects to allow volunteers to collaborate in the creation of a multilingual lexical database. For this, we had to specify and develop tools to manage a lexical database containing information complete and detailed enough to be usable for a wide range of applications. This paper presents our project and details the tools, frameworks and structures used to manage such a database. We will also show some research problems still to be addressed in this context.

Résumé

La connaissance linguistique reste une constituante importante de nombreux systèmes de traitement automatique des langues (TAL). Le coût de création d'un dictionnaire est l'un des freins majeurs dans le développement de ces systèmes. Afin de réduire les coûts de création de cette connaissance lexicale, nous adoptons une méthode inspirée des projets "opensource" afin de créer une base lexicale multilingue.

Pour cela, nous avons spécifié et développé des outils de gestion d'une base lexicale contenant des informations suffisamment complètes et détaillées pour êtres utilisées dans de nombreuses applications différentes. Cet article présente notre projet et détaille les outils, les cadres et les structures utilisées pour la gestion de cette base. Nous montrons aussi certains problèmes de recherche ouverts qu'il nous faut aborder dans ce contexte.

Introduction

Many NLP systems are based on lexical data. The development costs of such data are a major drawback in such NLP systems. Furthermore, the existing lexical data have generally been developed for a specific purpose and can't be reused easily in other applications. The Papillon project applies some tools and methods to develop multipurpose, multilingual lexical data collaboratively on Internet. This data is complete and detailed enough to be eventually used either by NLP systems (MT engines for example) or by human users (language learners, translators…). After presenting the motivations of the Papillon project, we will show the management of existing data. Then we will describe the structure of the Papillon dictionary, and the tools that are used to allow contributions from Internet volunteers.

1

The Papillon Project

Motivations

The Papillon project is the result of the gathering of different people sharing common problems and solutions.

A Lack of Resources

On the Internet, a lot of free dictionaries are available but very few of them imply more than 2 languages. Most of these dictionaries include English as one of their languages. Furthermore, the existing dictionaries often lack information essential for beginners or NLP systems. Another point contributing to this lack: the high costs of development of large lexical resources for NLP involves also a high price, dissuasive for the end-user.

Existing Structures and Tools for Multilingual Dictionaries

Some partners of the Papillon project have been involved in research on the definition of structures and tools to handle multilingual lexical databases. They were looking for an opportunity to apply their research results on real scale lexical data.

Collaborative Development on the Internet

Most partners were participating, as computer scientists, in the development of open source products. With the democratisation of Internet access in a lot of countries, came the opportunity to apply the open source principles to the development of a multipurpose, multilingual lexical database. Cooperation projects for bilingual dictionaries are already going on such as EDICT, a Japanese-English dictionary lead by Jim [START_REF] Breen | A WWW Dictionary and Word Translator: Threat or Aid to Language Acquisition?[END_REF] for more than 10 years and more recently, SAIKAM, a Japanese-Thai dictionary (see [START_REF] Vutichai Ampornaramveth | An Internet-Based Collaborative Dictionary Development Project: SAIKAM[END_REF]). With the Papillon project, the dictionary is extended to a multilingual lexical database. Volunteers will find lexicons developed by others and some tools to complete or correct the Papillon multilingual dictionary. Users will also be able to define their own personal views of the database.

Dictionary Markup Language Framework

Mathieu Mangeot-Lerebours (2001) defines a complete framework for the consultation and the construction of dictionaries. The framework is completely generic in order to manage heterogeneous dictionaries with their own proper structures. This framework is extensively used in Papillon project.

Dictionary Markup Language (DML)

The framework consists in the definition of an XML namespace 1 called DML (Dictionary Markup Language). All lexical data of a lexical database can be described with DML elements. The entire hierarchy of the XML files, elements and attributes is described using XML schemata and grouped into the DML namespace. Figure 1 describes the organisation of the main DML elements. The XML schemata are available online. This allows users to edit and validate their files online with an XML schema validator.

Common Dictionary Markup (CDM)

The DML framework may be used to encode many different dictionary structures. Indeed, two dictionary structures can be radically different. In order to handle such heterogeneous structures with the same tools, we have defined a subset of DML element and attributes that are used to identify which part of the different structures represent the same lexical information. This subset is called Common Dictionary Markup (CDM). This set is in constant evolution. If the same kind of information is found in several dictionaries then a new element representing this piece of information is added to the CDM set. It allows tools to have access to common information in heterogeneous dictionaries by way of pointers into the structures of the dictionaries.

Three Layers for the Lexical Data

The lexical data repository of the Papillon project is divided into 4 subdirectories:

• Administration contains guidelines and administrative files

• Hell (data in original format) • Purgatory (data in XML & UTF-8) • Paradise (data in Papillon format)
The name of the files and directories is normalised in order to allow easy navigation into the repository. All lexical data stored in the repository is free of rights or protected by a GPL-like licence.

Hell Directory

This directory contains lexical data in their original format. When a dictionary is received, it is first stored there while waiting to be "recycled". For each dictionary, we create a metadata file containing all available information concerning the dictionary (name, languages covered, creation date, size, authors, domain, etc.). It is then used to evaluate the quality of the dictionary and to guide the recycling process. These dicitonaries are freely downloadable as they are.

Purgatory Directory

The Purgatory directory receives the lexical data once the recuperation process is over. This process consists in converting the lexical data from its original format into XML encoded in UTF-8. To perform this task, we use the RECUPDIC methodology described in Doan-Nguyen (1998) regular expression tools like Perl scripts.

If a dictionary is already encoded in XML, the recuperation process consists in mapping the elements of information into CDM elements and storing the correspondence into the metadata file. Internet users access these dictionaries as classical online dictionaries, retrieving individual entries by way of requests on the Papillon web site.

Paradise Directory

The Paradise directory contains only one dictionary often called the "Papillon dictionary". This dictionary has a particular DML structure. Internet users access entries of this dictionary by way of requests to the Papillon web site. It is possible to retrieve only one entry, or any subset of entries in any available output format. The "native" format is the Papillon textual XML DML format in UTF-8. Users also have ways to add new entries or correct existing ones online. Other purgatory dictionaries may be integrated into the Papillon dictionary with the help of the CDM elements.

2

The Papillon Multilingual Dictionary

Macrostructure

The architecture of the Papillon multilingual dictionary is based on Gilles [START_REF] Sérasset | Interlingual Lexical Organisation for Multilingual Lexical Databases in NADIA[END_REF] and has been prototyped by [START_REF] Blanc | PARAX-UNL: a Large Scale Hypertextual Multilingual Lexical Database[END_REF]. This architecture uses a pivot structure based on multiple monolingual volumes linked to an interlingual acception volume.

Each entry of a monolingual volume represents a word sense. In this document, we use the term of "lexie" as in the Explanatory and Combinatory Dictionary to name a monolingual entry. The meaning of "lexie" is not the same as "lexeme". A lexie is a complete monolingual entry. The interlingual volume gathers all the interlingual acceptions. An interlingual acception represents the union of word-senses or "lexies" considered as "equivalent" among different monolingual volumes. This equivalence is calculated from translation links. In this document, we use the term of "axie" to name an interlingual acception. Real contrastive problems in lexical equivalence (not to be confused with monolingual polysemy, homonymy or synonymy as clearly explained in Mel'cuk and Wanner ( 2001) are handled by way of a special kind of link between axies. Figure 2 illustrates this architecture using a classical example involving "Rice" in 4 languages. In this example, we used the word senses as given by the "Petit Robert" dictionary for French and the "Longman Dictionary of Contemporary English" for English. As shown, the French and English dictionaries do not make any word sense distinction between cooked and uncooked rice seeds. However, this distinction is clearly made in Japanese and Malay. No axie may be used to denote the union of the word senses for Malay "nasi" and "beras" unless we want to consider them as true synonyms in Malay (which would be false). Hence, we have to create 3 different axies: one for the union of "nasi" and 御飯 (gohan), the other for the union of "beras" and 米 (kome) and one for the union of "rice" and "riz". A link (noncontinuous line in Figure 1 has to be added between the third axies and the others in order to keep the translation equivalence between the word-senses. Note that the links between axies do not bear any particular semantics and should not be confused with some kind of ontological links.

Bilingual dictionaries can be obtained from the multilingual dictionary.

Microstructure

The structure of the lexies (units of the monolingual dictionaries) is based on [START_REF] Polguère | Towards a theoreticallymotivated general public dictionary of semantic derivations and collocations for French[END_REF] and Mel'cuk's work on the combinatorial and explanatory lexicography, a part of the meaning-text theory. An XML schema using the DML framework has been defined to represent this structure as accurately as possible.

This structure is common to all the monolingual dictionaries. In order to cope with language differences, small variations are authorised for each monolingual lexicon. Up to now, these variations have been used to define the parts of speech for each language and to add information specific to each language, such as level of politeness and counters for Japanese. Figure 3 presents an excerpt of the XML encoding of the French entry "meurtre" (murder) and Figure 4 shows a DEC-like view. The general schema has been presented in detail in Gilles [START_REF] Sérasset | Papillon Lexical Database Project: Monolingual Dictionaries & Interlingual Links[END_REF].

Implementation of the Collaborative Web Site

For the external user, the Papillon project is viewed as a dynamic web site providing access the existing dictionaries and giving ways to contribute to the Papillon dictionary.

General Architecture

The Papillon web site is built with a Java based open source framework called Enhydra 2 . It is designed around a standard 3-tier architecture • a presentation layer in charge of the interface with the user. We currently use classical HTML/CSS rendering, but plan to integrate WML access to the dictionaries (for mobile phones), • a business layer in charge of data manipulation and transformation. We currently use XML data (in UTF-8) and XSL transformations for data manipulation, • a data layer in charge of the communication with the database via a JDBC driver. The data layer should be managed by an XML database allowing language dependent sorting. For the moment, XML databases are still in an early stage. In order to advance in the project, a mapping system for DML has been defined in order to store the XML data into conventional relational databases. PostgreSQL is used at this point.

Particular features

As different users may have different needs (translators, learners…) we define different views of the Papillon dictionary. Each view is 2 available at www.enhydra.org encoded as a XSL stylesheet that is applied on the result of each user query. In the future, we will also allow users to define their own custom views and store them on the server. All these transformations are done on the server in order to allow users to use their preferred browser (even if it is not XML aware). Figure 4 shows an example of the French entry "MEURTRE" (murder) viewed as in Mel'cuk's DEC dictionary. To avoid the unintentional pollution of the database by erroneous data, the contributions of a user are to be validated by a central group of trusted users. In the mean time, the contributions are stored as XSL stylesheets in the cntributor's private space. Each time a user requests a corresponding entry, the request is performed in the main database and in the user space. The results from the user space are used to modify results from the main database. This way, the contribution is immediately visible to the user exactly as if it had been integrated into the main database. While contributions are waiting to be validated and integrated into the common space, The contributors may choose to share them with other users or groups of users.

Every user can contribute at his/her level. For example, a linguist specialist of lexical functions will enter values of lexico-semantic functions, a phonologist pronunciations and a professional bilingual translator will enter new interlingual links or check the semi-automatically generated ones. For this, different interfaces will be developed to accommodate the various user profiles.

Annex Tools

As the web site hosts a rather complex collaborative work, we have added some tools that are not related to lexicography, but that have to work in a multilingual context. First, there is a tool to archive our Papillon mailing list. Such a tool is very common on Internet sites. However, as we found out, these tools may not be used in our multilingual context, where mails may contain discussion in different languages, written with different tools, and encoded using different standards. Hence we patched an existing tool so that it archives all mail in UTF-8, regardless of its original encoding.

To avoid the considerable work of the webmaster and to facilitate the communication and the exchange of informations between the users of the database, we are developing tools to facilitate the use of a document repository.

After registration and login, users can easily upload online a file in whatever format. It will immediately be stored into the document repository and made accessible online on the web.

Actual Research and Development Directions

The Papillon project is a extremely interesting experimentation platform. We are currently working on validation of monolingual data, management of axies and acquisition of new data.

Validation of the Monolingual Data

A team of trusted lexicographers validates user contributions before they are integrated into the main database. This validation is a time consuming process and implies a good level in linguistics and lexicography. Moreover, we may not find enough specialists volunteering for such a work and we may have to pay a core team for this. This task is essential and should be conducted as quickly as possible lest the users will be discouraged by the delays implied by the central team.

Hence, even in this validation process, we wish to enroll users as much as possible. For this task, we plan to implement tools for indirect validation of information using vote mechanisms and generating questions answerable without any special knowledge in linguistics.

As a first experiment, we will use a French generator in order to produce a lot of examples using the word to be validated and a set of known words (already validated). These examples will be presented to native speakers and they will simply have to accept or reject them. This strategy is very interesting in our context, as it will help validating the lexical functions.

Management of the Interlingual Links

The use of a pivot dictionary to represent translation equivalence is challenging. This macrostructure is very satisfying on a theoretical level, but introduces a high complexity of management.

In [START_REF] Sérasset | Interlingual Lexical Organisation for Multilingual Lexical Databases in NADIA[END_REF], we envisaged that these interlingual acceptions would be created and managed by hand by a team of specialists, helped by tools that would detect inconsistencies and propagate decisions among the different languages. This appeared to be unrealistic. However, we now have means to manage these acceptions automatically. For this, we use the fact that the interlingual acceptions volume does not, in any way, represent a semantic pivot. It is not related to an ontology. In fact, the only relevant purpose of this interlingual volume is to factorise the bilingual links we find in classical bilingual dictionaries (or the ones that will be specified by the users). Hence, given a set of translation equivalences between monolingual acceptions of different languages, it is possible to compute a minimal set of acceptions (and their links) that conforms to a set of well-formedness criteria. One of the difficult tasks is to obtain bilingual translation equivalences between monolingual acceptions when bilingual dictionaries often provide bilingual links between mere lemmas. For this, we will use aligned corpora and translations memories to add contextual information to the translation pairs.

Acquisition of new data

To depend entirely on volunteer work is of course unrealistic, especially while beginning to build the lexical database. That is why we first reuse existing dictionaries in order to build the kernelof the database. Contributors will come in later, filling in missing informationin existing entries and creating partial or complete new entries as well as links. However, as we are using a rather complex structure which require some skills that are not shared by all Internet users, we will have to help them help us.

In particular, we are beginning to use corpusbased techniques to extract lemmas that will be candidates as a value of a lexical function.

Determining the appropriate lexical function is one of the jobs of our contributors, but they will be helped in this task by tools that will provide them with questions and candidate paraphrases. For a complement of information or to help the contributors in their task, the database should also propose the consultation of other dictionaries stored locally or available online on the web. Moreover, to be really useful for the reader, and especially to the learners, the examples found in the dictionaries will be translated in other languages literally and semantically. Some of these translations will be extracted from aligned corpora.

Conclusion

The theoretical frameworks for the whole database, the macrostructure and the microstructure are very well defined. It constitutes a solid basis for the implementation.

A lot of open problems still have to be addressed for the Papillon project to be a success. In this respect, the Papillon project appears to be a very interesting experimentation platform for a lot of NLP research as data acquisition or human access to lexical data, among others. All this research will improve the attraction of such a project to the Internet users. This attraction is necessary for the project to go on, as it is highly dependent on its users motivations. This way, we will be able to provide a very interesting multilingual lexical database that we hope useful for a lot of persons.

Figure 2 .

 2 Figure 2. Illustration of Papillon's macrostructure.

Figure 4 .

 4 Figure 4. French entry "meurtre" dynamically displayed using Mel'cuk's classical view


Gilles Sérasset
email: gilles.serasset@imag.fr

Current Status of the Papillon Server Development

Keywords: Papillon multilingual database, dynamic web server, Enhydra Résumé Base de données lexicale multilingue Papillon, serveur web dynamique, Enhydra

This paper gives an overview of the current Papillon web server and the services it provides.

Introduction

One of the main Papillon project's objectives is to provide a web server where Papillon contributor will find different services. After an intensive work, the developers (mainly Mathieu Mangeot-Lerebours and Gilles Sérasset) have finally achieved the core of this dynamic web server.

Most of the services are now unimplemented and the implemented ones are currently in a beta version, but we finally succeeded in opening the first version of the Papillon web server. This server is accessible through the URL: «! http://www.papillon-dictionary.org/! ». This paper presents the current state of this server. We will first give an external overview of the server, then we will discuss and present it's implementation. We will describe the implemented services give some perspectives on the services that are planned.

External view of the Papillon web server

When entering the Papillon web site, the user is welcomed by a page summarizing the main objectives of the Papillon project. Like every other page of the Papillon web site, this page is composed of 3 parts:

• A header, used to navigate inside the main sections of the web site (Part I). All pages share this header.

• A menu, that provides a quick access to different links (Part II). This menu is always present, but the links may vary depending on the section or the user.

"Information" section

The information section is the central place where any user should find any information concerning the Papillon project, from its objectives to its current implementation. It currently offers 2 services:

• A mailing list archive.

• A document repository.

The mailing list archive provides a searchable archive of all mails exchanged by Ppillon partners through the official papillon mailing list. The Information repository offers a searchable repository of different documents providing information about the Papillon project. Here, the user can find different documents containing:

• Some general information about the papillon project These services are detailed in section 3.

"Consultation" section

The consultation section is the place where the user has access to the lexical data available on the Papillon server. This section currently offers a unique general interface giving access to all the dictionaries (as in [START_REF] Mangeot-Lerebours | Accès unique à des dictionnaires hétérogènes[END_REF]).

This integrated interface gives access to the dictionaries belonging to the "Purgatory layer" (as defined in [START_REF] Mangeot-Lerebours | Environnements centralisés et distribués pour lexicographes et lexicologues en contexte multilingue[END_REF]) as well as to the Papillon multilingual dictionary itself (Paradise layer, see [START_REF] Sérasset | Papillon Lexical Database Project: Monolingual Dictionaries & Interlingual Links[END_REF][START_REF] Tomokiyo | Papillon : a Project of Lexical Database for English, French and Japanese, using Interlingual Links[END_REF]).

Purgatory layer

This interface will require more development as the general interface is not informative enough to be used by general users (number of entries available for each dictionary, macrostructure of each dictionary…). However, it is currently functional. Hence, if I am looking at the Headword "meurtre" (murder) in the French Vietnamese dictionary, I'll get the following result:

This output is a formatted view of the data stored in the Papillon web site. This view may be customized easily, however, in the current implementation, this customization cannot be done directly by a user, as the customization interface is not implemented yet.

Several views are available for each dictionary. Among these views, the XML view faithfully reflects the structure of each dictionary (every dictionary is stored in XML format).

Paradise layer

Asking for the same headword ("meurtre") in the Papillon dictionary will lead to the following result (see [START_REF] Mel | Meaning-Text models: a recent trend in Soviet linguistics[END_REF][START_REF] Mel | A Formal Lexicon in the Meaning-Text Theory: or How to do Lexica with Words[END_REF][START_REF] Mel | Introduction à la lexicologie explicative et combinatoire[END_REF]. As see above, the result is presented in a customizable form. But, when dealing with entries of the Paradise layer (of the Papillon dictionary per se), we are also able to present entries from other languages that correspond to the same interlingual acception as defined in [START_REF] Sérasset | Interlingual Lexical Organisation for Multilingual Lexical Databases[END_REF][START_REF] Sérasset | SUBLIM, un système universel de bases lexicales multilingues; et NADIA, sa spécialisation aux bases lexicales interlingues par acceptions[END_REF] and prototyped in [START_REF] Blanc | Visite guidée de PARAX, une base lexicale pentalingue par acceptions sous HyperCard[END_REF] (in our example, in Japanese and Malay).

"Edition" section

The "Edition" section is the place where the user will be able to contribute to the Papillon dictionary. He will be able to correct existing entries and add new ones in the dictionary. This section is not implemented yet as it require a lot of development (management of private user spaces, interface to the Papillon dictionary's microstructure…).

Until now, users willing to contribute entries to the dictionary may use his favorite XML editor to produce a valid Papillon entry. Then send it to the Papillon web site maintainer who will add it to the web site. You should send an email to the Papillon web site maintainer to get an example of a Papillon entry.

"Contacts" section

This section gives addresses of persons in charge of the Papillon project.

"Help" section

This section will contain documents describing the Papillon web site and giving simple help on the web site organization.

Software architecture

Papillon web site is a dynamic web site built with the "Enhydra" framework (an open source Java Application Server). This framework provides different tools and managers that are extensively used by the Papillon application.

The Papillon application features a 3-tier architecture:

• The presentation layer contains code that specifies the graphical user interface (GUI) of this application. In our context, this GUI is implemented through a standard web browser. Hence, contains HTML templates and JAVA classes that implement the GUI behavior. • The business layer contains the classes that are specific to the Papillon application.

• The data layer contains the persistent classes and the methods that perform the database requests.

With this architecture, it will be easy to adapt the Papillon application to a different context. To adapt it to be used on cellular phone, we will only modify the presentation layer and provide HTML data (for I-mode phones) or WML file for WAP phones. It will also be relatively easy to adapt the data layer to a XML database.

All requests to the Papillon application are served through a load balancer that distributes requests among different machines. Hence, it will be easy to handle more and more requests without involving any additional development.

The Enhydra framework allows a clear separation between the presentation code (that implements the behavior of the GUI) and the HTML templates (that specify the appearance of the GUI). Hence, the appearance may be modified by graphic designers with no particular knowledge of any programming language (unlike PHP or ASP pages).

Implemented services

Among the services currently provided by the Papillon application, the user will find an information repository and a mailing list archive.

Information documents repository

The Papillon application is organized to allow contributive work from Internet users. In our context, users are not only able to provide lexical data. They are also able to provide additional information that has to be integrated to the Papillon web site.

For that purpose, users having the sufficient privileges will be able to easily upload documents that will be integrated to the Papillon web site. When uploading such a document, users will provide its title, its author and the section in which he want it to appear (for a list of available sections, see paragraph 1.1).

In this repository, we accept PDF documents, DOC or RTF (word) files, GIF or JPG images or a simple HTML file. In addition to these kinds of files, we also accept a ZIP or TAR archive containing a whole HTML document (consisting in different HTML and GIF/JPG files linked together) that will be integrated to the site.

When submitting a HTML document, the user only has to focus on its content. The Papillon server will automatically add the header and menu composing the standard Papillon layout. The following figure shows such a HTML document, as seen by any Papillon user after its addition in the repository.

Current Status of the Papillon Server Development 6/7

Mailing list archive

The Papillon project currently maintains a mailing list gathering all participants. This mailing list is a very valuable resource for information. Hence an archive of this mailing list is really useful.

However, the Papillon mailing list is particular as it gathers participants from a lot of countries speaking about languages. This fact leads to mails that use different encodings. None of the currently available mailing list tools we know are able to correctly handle such different encodings. Hence, we had to patch one of them (MhonArc) to handle these encodings.

Mails sent to the mailing list are converted to UTF-8, then uploaded into the Papillon database where they are immediately available to be viewed by Papillon web site users.

This archive is searchable.

Conclusion and perspectives

The first beta release of the Papillon application is now available on the web. It provides some of the services that are planned by the Papillon project. This release is a good starting point for the future developments of the Papillon project.

We chose to first implement the tools that will allow Papillon partners to communicate easily. With a mailing list archive and a document repository the partners will be able to complete the current phase that involves a lot of specification and training. Moreover, the "Purgatory" layer (as defined in Mathieu Mangeot's PhD Thesis) is implemented, allowing users to get an integrated access to many dictionaries.

After a short debugging phase, we will be able to add new features to the Papillon application:

• Manage private user spaces in order to allow users to annotate (correct) the available entries • Implement a simple specialized GUI to edit new Papillon entries (as in [START_REF] Sérasset | Informatisation du Dictionnaire Explicatif et Combinatoire! : le projet NADIA-DEC[END_REF][START_REF] Sérasset | Outils pour lexicographes! : application à la lexicographie explicative et combinatoire[END_REF][START_REF] Sérasset | Le projet NADIA-DEC! : vers un dictionnaire explicatif et combinatoire informatisé! ?[END_REF][START_REF] Sérasset | L'édition lexicographique dans un système générique de gestion de bases lexicales multilingues[END_REF] • Implement a clean architecture to ease the application localization and provide versions in a lot of languages • Experiment a WML access to the Papillon database (for cellular phones)

• Integrate tools to check the coherence and ease the management of the Papillon data • Experiment with XML databases on the data layer.

• …

As Papillon is an opened project, this list of extensions will evolve in the time as users will get involved in the specification of the project.

  • A content (Part III) that is specific to the page.

•

  Published articles related to the Papillon project • Information about the development of Papillon's server and tools • The description of the different dictionaries available on the server • Some simple "How To" recipes on tasks involved by the Papillon project • Other miscellaneous information


Enguerrand Couka

François Willot

Dominique Jeulin

Mona Ben Achour

Anthony Chesnaud

Alain Thorel

M Ben Achour

Modeling of the multiscale dispersion of nanoparticles in a hematite coating

Keywords: Microstructure optimization, Random media, Nanomaterials, Granulometry, Coating

come   L'archive ouverte pluridisciplinaire

Introduction

Hematite nanoparticles of various aspherical shapes have been synthesized and characterized for use in optical materials [START_REF] Spuch-Calvar | Hematite spindles with optical functionalities: Growth of gold nanoshells and assembly of gold nanorods[END_REF][START_REF] Xu | Uniform hematite α -Fe 2 O 3 nanoparticles: Morphology, size-controlled hydrothermal synthesis and formation mechanism[END_REF] or for magnetic properties [START_REF] Tadic | Synthesis, morphology and microstructure of pomegranate-like hematite (α -Fe 2 O 3 ) superstructure with high coercivity[END_REF], ranging from pseudo-cubic [START_REF] Park | Internal Structure Analysis of Monodispersed Pseudocubic Hematite Particles by Electron Microscopy[END_REF] to cigar-like hematite particles [START_REF] Manickavasagam | Characterization of colloidal hematite particle shape and dispersion behavior[END_REF]. At a higher length scale, the dispersion of hematite particles is most often heterogeneous [START_REF] Huang | Flower-like porous hematite nanoarchitectures achieved by complexation-mediated oxidation-hydrolysis reaction[END_REF]. However, the multiscale distribution of nanoparticles, embedded in a resin, has not been studied to the same extent. Some microstructure models have been proposed in other contexts. Jean et al. [START_REF] Jean | A multiscale microstructure model of carbon black distribution in rubber[END_REF] devised a multiscale Boolean models to represent the dispersion of carbon black in rubber. Azzimonti et al. [START_REF] Azzimonti | Optical properties of deposit models for paints: fullfields FFT computations and representative volume element[END_REF] introduced deposit models to simulate the dispersion of nanoparticles in optical materials. Such models are important to predict the behavior of nanomaterials. The multiscale dispersion strongly influences their effective (i.e. macroscopic) properties. For linear conducting materials, numerical computations have shown that the presence of aggregates of highly-conducting inclusions increase the overall properties as compared to more homogeneous dispersions [START_REF] Willot | Elastic and electrical behavior of some random multiscale highly-contrasted composites[END_REF]. In nanomaterials, the typical length scales of the particles's spatial distribution is often much larger than the inclusions themselves but of the same order as wavelength of light. Accordingly, taking dispersion into account is especially important for predicting the optical properties of composites [START_REF] Jeulin | Random structures in physics[END_REF].

This work is devoted to the numerical modeling of the spatial distribution of nanoparticles of hematite in a epoxy matrix. We present the material and segment greylevel SEM microstructure images in Sec. [START_REF] Xu | Uniform hematite α -Fe 2 O 3 nanoparticles: Morphology, size-controlled hydrothermal synthesis and formation mechanism[END_REF]. In Sec. [START_REF] Tadic | Synthesis, morphology and microstructure of pomegranate-like hematite (α -Fe 2 O 3 ) superstructure with high coercivity[END_REF] we extract the correlation function and granulometry of the nanoparticles and of the epoxy. In Sec. (4) we introduce a simple two-scales microstructure model to represent the microstructure. The parameters of our model are optimized according to correlation function and granulometry criteria, as defined in Sec. [START_REF] Tadic | Synthesis, morphology and microstructure of pomegranate-like hematite (α -Fe 2 O 3 ) superstructure with high coercivity[END_REF]. Results are presented in Sec. [START_REF] Manickavasagam | Characterization of colloidal hematite particle shape and dispersion behavior[END_REF]. We conclude in Sec. [START_REF] Huang | Flower-like porous hematite nanoarchitectures achieved by complexation-mediated oxidation-hydrolysis reaction[END_REF].

Hematite nanocubes coating

Dispersion of nanoparticles

In this work, we consider Fe 2 O 3 iron oxide (hematite) nanoparticles embedded in a epoxy resin. The hematite particles, shown at high resolution in Fig. [START_REF] Spuch-Calvar | Hematite spindles with optical functionalities: Growth of gold nanoshells and assembly of gold nanorods[END_REF], were specifically synthesized to resemble cubes [START_REF] Ben Achour | Dielectric properties of hematite nanoparticles with various morphologies[END_REF].

The hematite nanoparticles were blended in an epoxy resin with a concentration of 10% in mass. The nanoparticles and resin were first mixed to-gether in a mortar until the resulting paint becomes homogeneous. Using a bar coater technology, the mixture was then spread onto a thick and flexible shrink-wrap support in order to obtain a thin coating. For that purpose, an Elcometer 4340 motorised film applicator was used. This versatile, rugged and precise manufacturing process ensures a smooth, reproducible and consistent application of coatings, such as paint, varnish, cosmetics, glue and ceramics, without any ridge associated with such a technique. The bar coater is indeed equipped with a highly-engineered aluminium table, much smoother than a glass support, and heating element, if suited. It was accurately calibrated using a coordinate measuring machine to reach a high level of flatness. The average variation of coating thickness on the Elcometer table is about ±2.3 µm while it is equal to ±12.0 µm on glass of some low-cost tables. During the deposition, the roller translates towards the coating direction but does not spin round. The deposition speed may be set up from 0.5 to 10 cm per second and coating as thin as 5 µm may be fabricated. In this work, 150 µm thick coatings were fabricated.

As seen in Fig. [START_REF] Spuch-Calvar | Hematite spindles with optical functionalities: Growth of gold nanoshells and assembly of gold nanorods[END_REF], the particles shape are similar to dice with rounded edges and corners.

The length of the diagonal of the cubes's faces, measured from the SEM images, is about 300 nm. The SEM image in Fig. (1a) shows the spatial dispersion of nanoparticles at higher length scales. Hematite particles aggregate around "empty regions" almost entirely made of epoxy. Around those areas, they form curved "channels" (surfaces in 3D) and some clusters of particles in regions where the channels join. Along channels, Hematite particles are quite closely packed as shown in Fig. (1b). Clearly, the dispersion exhibits a multi-scale microstructure with at least two scales: the particles average length and the typical size of the channels.

The rest of this work is devoted to the analysis and modelling of the nanoparticles spatial arrangements. The formation of the channels and their physical interpretation, beyond the scope of this work, is not investigated.

Image segmentation

Hereafter, we focus on 4 randomly-selected SEM images of 950 × 950 pixels, representing a region of area 30 µm×30 µm. The images's resolution is 31 nm per pixel. We segment them according to a three-steps process illustrated in Fig. [START_REF] Xu | Uniform hematite α -Fe 2 O 3 nanoparticles: Morphology, size-controlled hydrothermal synthesis and formation mechanism[END_REF]. We first apply a gaussian filter to erase noise and smoothen the background. Second, we separate nanoparticles from the resin by maximization of the interclass variance [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF], an automatic segmentation method that does not need any parameter. Third, we apply an alternate sequential filter (Fig. 2). As seen in Fig.

Morphological measurements

In this section, we use correlation functions and granulometry distributions to quantify the dispersion of nanoparticles in the resin.

Correlation function

We define the covariance function as the probability:

C(r) = P{x ∈ H, x + r ∈ H}, ( 1
)
where H is the union of hematite nanoparticles in the microstructure, and x is a point. At large distances |r| ≫ 1 the two events x ∈ H and x + r ∈ H become uncorrelated and C(r = ∞) ≈ C(0) 2 . Thus, we define the normalized covariance, or correlation function, as:

C(r) = C(r) -C(0) 2 C(0) [1 -C(0)] . (2)
Taking vectors r = re 1 (r ≥ 0) aligned with the horizontal axis e 1 , we observe nearly identical correlation functions for each sample, as shown in the inset of Fig. [START_REF] Park | Internal Structure Analysis of Monodispersed Pseudocubic Hematite Particles by Electron Microscopy[END_REF]. We also observe little difference along the vertical and horizontal axis, shown in Fig. [START_REF] Park | Internal Structure Analysis of Monodispersed Pseudocubic Hematite Particles by Electron Microscopy[END_REF] as well, so that the microstructure is almost isotropic as far as correlation functions are concerned. Hereafter, we note C(r) the correlation function C(r) irrespective of the orientation of the vector r. The average over samples and over the horizontal and vertical directions of the correlation functions is referred to hereafter as "correlation of the SEM images". In Fig. ( 4), the tangent slope at the origin r = 0, shown in brown, cuts the abscissa at r ≈ 155 nm. This length is to be interpreted as the mean chord length of nanoparticles. It is consistent with the length of the diagonal of the nanocubes faces, of about 300 nm, measured from Fig. [START_REF] Spuch-Calvar | Hematite spindles with optical functionalities: Growth of gold nanoshells and assembly of gold nanorods[END_REF].

Granulometry

We define the cumulative granulometry by openings of the epoxy phase as the conditional proba- bility:

G(s) = P{x ∈ E} -P{x ∈ E(S ; s)} P{x ∈ E} (3)
where x is a point in the image, E is the epoxy phase (complementary of H) and E(S ; s) is the morphological opening of E by the structural element S dilated by size s. We use the first and second neighbors, i.e. a square of 3 × 3 pixels, as structural element S whereas s take on values that are multiples of the pixel size. The granulometry defined above is a measure of the cumulative size distribution in E. We compute G(s) independently for each of the 4 samples. The resulting curves, shown in Fig. [START_REF] Manickavasagam | Characterization of colloidal hematite particle shape and dispersion behavior[END_REF] are close to each other, except at large sizes s > 700 nm. The granulometry of sample 2 is slightly higher than the others in this domain. We hereafter neglect these variations and take the mean of all four curves, referred to as "granulometry of the SEM images" (Fig. 5). We emphasize our use of the epoxy phase E rather than H in the granulometry. The former only is sensible to the spatial dispersion of nanoparticles. Indeed, the granulometry of the nanoparticles is zero for sizes larger than 4 voxels and contains little information (not shown). By contrast, the granulometry G(s) is non null for s ≤ s 0 with s 0 ≈ 2.5 µm. The value s 0 is an estimate of the maximum diameter of regions without hematite. Similarly, the granulometry G(s) gives the mean diameter of these regions, estimated to 1.05 µm.

Microstructure model

We now introduce a random 3D microstructure model to represent the nanoparticles dispersion in the epoxy. In our model, we assume that all nanoparticles are identical (perfect) cubes with uniformly-oriented random orientations. This simplification allows us to focus on the modeling of the spatial dispersion of particles, which is our main interest. More evolved models involving size or shape distributions of particles are straightforward extensions of this work. Regions without hematite particles (or with little of them) will be hereafter referred to as "exclusion zones" in our model, which is described according to the three steps below.

First, we generate exclusion zones by a set of hard-core spheres, determined by the spheres volume fraction f , their diameter a and a repulsion distance ∆. When generating sphere centers, points closer to ∆ from another point are skipped. We add spheres until the volume fraction f of exclusion zones is obtained. Accordingly, a portion of exclusion zones intersect whenever ∆ < a.

In a second step, we place nanocubes according to a deposit model that simulates an isotropic packing of hematite particles [START_REF] Willot | Microstructure-induced hotspots in the thermal and elastic responses of granular media[END_REF]. The total number of nanocubes is determined as a random variable following Poisson's law. Their average number is deduced from the volume fraction of nanocubes, measured from SEM images. We start by inserting the fraction 1f ′ of nanocubes lying outside exclusion zones. The center of each nanocube is, initially, generated randomly in the domain, and moved in a random, isotropicallydistributed direction until a certain criterion is met. There are two possibilities. If the cube initially cuts a previously-inserted nanocube, or an exclusion zone, we move it and insert it as soon as it is entirely out of the exclusion zones and of other nanocubes. Conversely, if the cube initially does not cut a previously-inserted nanocube nor an exclusion zone, we move it until it touches either one. We insert it at the last position before the intersection occurred.

In a third step, the fraction f ′ of cubes lying inside exclusion zones are inserted. We use a similar packing method: if the cube center is inside an exclusion zone and the cube does not cut a previously-inserted nanocube, it is moved in a ran- dom direction until it touches a nanocube or its center is out of exclusion zones. Conversely, if the cube initially is out of an exclusion zone or intersects an already-inserted cube, we move it until its center is inside an exclusion zone and the cube does not intersect any other cube.

We emphasize that nanoparticles never intersect each other, but, instead, are "packed" together. An example of the generation of a microstructure with ∆ = f ′ = 0 is shown in Fig. As predicted, the volume fraction f of excluding zones has an important effect on the granulometry as shown in Fig. 8 (bottom) for f ′ = 0, a = 1550 nm and ∆ = 775 nm. When a is small, this effect is less (not shown). For the same values of the three parameters f ′ = 0, a = 1550 nm and ∆ = 775 nm, the effect of f on the granulometry is small. A similar strong effect of the diameter a is observed on the granulometry but also, as expected, on the correlation function (Fig. 9). This effect occurres whether at high or low volume fractions f (not shown).

The included volume fraction f ′ and the repulsion distance ∆ have little influence on the correlation (not shown). The former predictably influences the granulometry, whereas the repulsion distance ∆ only marginally changes it (Fig. 10).

Microstruture optimization and representative volume element

We hereafter optimize the microstructure model parameters by minimizing crostructure models whereas C M (r) and G M (s) refer to the known SEM correlation functions and granulometry, resp. The criterion above allows us to optimize on both the correlation function and on the granulometry. Both quantities are comprised between 0 and 1. The weights η 1 > 0 and η 2 > 0 are used to favor one over the other. Hereafter we make the arbitrary choice

η 1 h dr C M (r) -C SEM (r) 2 + η 2 h ds G M (s) -G SEM (s) 2 (4
η 1 = 1, η 2 = 1 -f 0 ≈ 0.91.
We use the standard gradient descent and Levenberg-Marquardt methods [START_REF] Press | Numerical Recipes Third Edition: The art of scientific computing[END_REF]. The latter has been successfully used for optimizing multiscale microstructure models [START_REF] Jean | A multiscale microstructure model of carbon black distribution in rubber[END_REF]. Numerical optimization is undertaken on 3D microstructures containing 800 × 800 × 200 voxels. Random 2D cuts normal to the third axis, containing 800 × 800 pixels, are used to compute criterion [START_REF] Park | Internal Structure Analysis of Monodispersed Pseudocubic Hematite Particles by Electron Microscopy[END_REF] The granulometry and correlation functions of the optimized microstructure model and of the SEM images are shown in Fig. [START_REF] Otsu | A threshold selection method from gray-level histograms[END_REF]. In terms of these two criteria, the optimized model is very close to the SEM images. Finally, as a complementary examination, we compute the representative volume element (RVE) related to the nanoparticules dispersion. Let D 2 (S ) be the variance of the surface fraction of nanoparticles measured over independent 2D domains of area S in the material. For large areas S , the following asymptotic behavior is recovered [START_REF] Matheron | The Theory of Regionalized Variables and its Applications[END_REF]:

D 2 (S ) ∼ f 0 (1 -f 0 )S 0 S , S ≫ S 0 (5)
where S 0 is the integral range and f 0 ≈ 10% is the surface fraction of nanoparticles (Sec. 2.2). The integral range S 0 is determined by the covariance C(r) [START_REF] Kanit | Determination of the size of the representative volume element for random composites: statistical and numerical approach[END_REF]. The quantity D(S ) gives the confidence interval for the estimation of the surface fraction of nanoparticles on N domains of area S [START_REF] Kanit | Apparent and effective physical properties of heterogeneous materials: representativity of samples of two materials from food industry[END_REF]. The absolute error of such estimate is:

ǫ abs = 2D(S ) √ N (6)
To compute numerically D 2 (S ), we divide one SEM image into n × n non-overlapping squares of area S and compute the surface fraction of nanoparticles over each subdomain. We approximate D 2 (S ) as the variance of the obtained set of surface fractions. The same computation is undertaken along a random 2D cut of our optimized microstructure model. The two curves are represented in Fig. [START_REF] Willot | Microstructure-induced hotspots in the thermal and elastic responses of granular media[END_REF]. Overall, the standard deviation function of our optimized model is close to that of the SEM images, although this quantity is not (explicitly) involved in criterion [START_REF] Park | Internal Structure Analysis of Monodispersed Pseudocubic Hematite Particles by Electron Microscopy[END_REF]. A region of interest S > 1.50 µm 2 is selected. Powerlaw fits on the SEM and optimized models give D 2 (S ) ∼ 3.14 10 -3 S -0.96 and D 2 (S ) ∼ 3.58 10 -3 S -0.97 , respectively, consistently with Eq. ( 5). The former is represented in Fig. 13 (solid black line).

From this fit, we deduce the integral range S 0 ≈ 3.52 10 -2 µm 2 . At the scale of the SEM images (S = 153 µm 2 ) the absolute error in Eq. ( 5) is ǫ abs ≈ 1.1% so that f 0 ≈ 9.4 ± 1.1%.

Conclusion

The spatial dispersion of hematite nanoparticles in a epoxy resin is accurately modeled by a two-scales microstructure made of spherical "exclusion zones" containing few hematite particles. Use of the granulometry of the embedding (epoxy) phase as criterion is crucial to describe the spatial dispersion of particles. The model's parameters are efficiently optimized using either standard gradient method or the Levenberg-Marquardt method.

Parametrized microstructure models are a first step towards designing materials with improved physical properties. 3D microstructure models are conveniently coupled with Fourier numerical methods [START_REF] Willot | Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields[END_REF] for solving PDEs on images of complex materials, without meshing. These tools predict the electric [START_REF] Willot | Fourier-based schemes with modified Green operator for computing the electrical response of heterogeneous media with accurate local fields[END_REF], elastic [START_REF] Willot | Elastic and electrical behavior of some random multiscale highly-contrasted composites[END_REF] or optical [START_REF] Azzimonti | Optical properties of deposit models for paints: fullfields FFT computations and representative volume element[END_REF] responses of composites. Applied to the present work, these methods should allow one to determine how the peculiar multiscale dispersion of nanoparticles affects the material's overall properties. In previous numerical investigations [START_REF] Willot | Elastic and electrical behavior of some random multiscale highly-contrasted composites[END_REF], multiscale dispersions have been shown to strongly influence the physical properties of inclusion-matrix coatings.

Fig. 1 :

 1 Fig. 1: Nanocubes of hematite (bright) in a epoxy resin (dark) (a); same material with scale magnified 10 times (b).

Fig. 2 :

 2 Fig. 2: Segmentation of SEM images (enlargement): original grayscale image (a), noise-filtering and thresholding (b), removing of small inclusions (c).

Fig. 3 :

 3 Fig. 3: Two of the four segmented SEM images, shown at the same scale.

Fig. 4 :

 4 Fig. 4: Symbols: mean over all samples of the correlation functions C(r) of segmented SEM images in the horizontal and vertical directions. Black solid line: mean over the two directions (brown: tangent at r = 0, see text). Inset: correlation function C(r) for r ≤ 62 nm in the horizontal direction, for each sample.

Fig. 5 :

 5 Fig. 5: Cumulative granulometry G(s) of the complementary of SEM images (symbols) as a function of the size s in nanometers. Solid line: average over all 4 samples. Inset: granulometry distribution function dG(s)/ds .

Fig. 6 :Fig. 7 :

 67 Fig. 6: 2D cut of a realization of the two-scale microstructure model (a); same image with exclusion zones shown in yellow (b).

Fig. 8 :

 8 Fig. 8: Effect of the volume fraction f of exclusion zones on the correlation function (a) and granulometry (b) with other parameters fixed.

  [START_REF] Huang | Flower-like porous hematite nanoarchitectures achieved by complexation-mediated oxidation-hydrolysis reaction[END_REF].Exclusion zones are represented in yellow (right), the final microstructure is shown left. Examples of microstructures with ∆ = f ′ = 0, and exclusion zones volume fraction f = 10% are shown in Fig. (7) with small (left) and large (right) exclusion zones diameters a.

Fig. 9 :

 9 Fig. 9: Effect of the diameter a of exclusion zones on the correlation function (a) and granulometry (b) with other parameters fixed.

Fig. 10 :

 10 Fig. 10: Effect of the volume fraction f ′ of hematite in exclusion zones (a) and of the hardcore parameter ∆ (b) on the granulometry, with the other 3 parameters fixed.

Fig. 11 :

 11 Fig. 11: Optimized numerical microstructure (a) and one segmented SEM image sample (b) observed at the same scale. Each image represents a square of size 24.8 µm with resolution 31 nm per pixel. The parameters of the optimized model are f = 25%, a = 1862 nm, f ′ = 20%, ∆ = 620 nm.

Fig. 12 :

 12 Fig. 12: Granulometry of the optimized numerical microstructure and of SEM images. Inset: correlation function.

Fig. 13 :

 13 Fig. 13: Variance D 2 (S ) of the apparent surface fraction of nanoparticles computed over a domain of surface area S : comparison between SEM images and optimized microstructure model. Solid black line: fit of the variance D 2 (S ) for S ≫ S 0 . Black arrow: integral range S 0 .

Acknowledgement This study was made with the support of A.N.R. (Agence Nationale de la Recherche) under grant 20284 (LIMA project).