Julie Giovacchini
email: julie.giovacchini@cnrs.fr

Laurent Capron

Publishing open-access bibliographical data on Ancient Greek and Latin texts: challenges, constraints, progression 1

Keywords: database, open access, bibliography, Sciences of Antiquity, semantic web, Nakala

INTRODUCTION

The publication of bibliographical data on Classical and Late Antiquity 2 has a considerable history already, since it dates back to the early twentieth century with the publication in 1927 of the two volumes of an important retrospective bibliography entitled Dix Années de Bibliographie Classique (1914-1924) [Ten years of Classical bibliography, 1914-1924], by Jules Marouzeau 3 . In keeping with the evolving needs specific to each discipline with regard to Antiquity, a number of specialised bibliographies have flourished with the intention of providing a comprehensive list of works published in their respective fields. Some of these bibliographies have since made use of electronic media for their circulation, continuing to maintain the paper version as their reference, while others have been digital from the outset. Thus each has its own classification scheme and indexing system, and sometimes even its own canonical forms of authority. Since most of these resources are proprietary, it is not their natural vocation to be mutually compatible: at best, certain practices tend towards a standardisation of formats and classification schemes. The work required in terms of referencing the data to make it interoperable has not yet been completed, although numerous initiatives demonstrate a desire to use common repositories. The IPhiS-CIRIS project ('Information Philologique -Savoirs Antiques' [philological information -ancient knowledge], Centre Jean Pépin, CNRS-ENS) is participating more particularly in defining a set of reference data of names of authors and titles of ancient works to be fed into a database of editions of ancient texts. When drawing up these files we come up against a number of difficulties: concurrent forms for the same entry, inexistent forms of the state of certain works in the existing repositories, duplicates, homonymic forms of titles or authors, dubious attributions of works to a particular author, controversial attributions to various authors, etc. Deciding on the forms of these tables and the links between them created a number of technical difficulties from the outset; these are characteristic of Antiquity and have not yet been fully dealt with in the computer modelling.

I STATE OF PLAY 1.1 A blossoming of initiatives

There is today a large quantity of bibliographical resources in the field of Classical and Late Antiquity that is available -partly or fully -on the Internet. Mention may be made of L'Année Philologique, published annually since 2017 by Brepols, after having for a long time been distributed by Les Belles-Lettres: not only is this bibliography the only one to attempt to cover the group of disciplines encompassing Classical and Late Antiquity -it is also the oldest and largest bibliography listing studies on these authors and editions of texts, and a fee is charged for access. The other resources are specialised bibliographies in the form of regularly updated databases. There are many examples 4 , but we may mention here:

• Base d'Information Bibliographique en Patristique (free access) 5 ;

• Bibliographie papyrologique en ligne (free access) 6 ; • L'Année épigraphique (paywall) 7 ; • Syri.ac: An annotated bibliography of Syriac resources online (free access) 8 ;

• Répertoire des sources philosophiques antiques (free access) 9 ;

• Droits Antiques (free access) 10 . New formats of shared bibliographical resources are springing up all the time, using software specifically designed for organising bibliographies. It is now possible, for example, to share collections and libraries in Zotero 11 . In addition, we are also seeing the appearance of digital libraries of ancient editions and manuscripts: each library has its own criteria for managing its collections of manuscripts and ancient editions, developing tools in-house that not only allow consultation but also, more often than not, prevent or restrict the downloading of data.

Mention should also be made of the massive but disorganised (and of very uneven quality) digitalisation work carried out by GoogleBooks / GoogleScholars, archive.org, HathiTrust (with restrictions on access from outside the US) projects, and the development of academic networks (such as academia.edu) for following up topics and researchers. These are new approaches to the publication and circulation of bibliographical data that -whatever we think of themcorrespond to new uses or new expectations in academic circles. Thus there is a host of initiatives in this field, but we are still at an experimental stage in terms of digitalising and structuring bibliographical data. There are a number of problems: firstly the large number of proprietary resources, and secondly the fact that the good quality open resources are still not well known outside digital humanities circles. Demand for the production of open data in fact involves producing data that meets not only the required technical standards but also scientific demands, always seeking to deliver data that is accessible to a wide public, whether or not its members are technologically informed. Thus it is necessary to bind together the political and scientific issue of access with the technical issues. This demands that we do not compromise on excellent scientific quality, ergonomics, ease of use, and good practices ensuring the continued existence of the tools, and it is sometimes difficult to maintain our stand.

The inexistent common portal for bibliography on Antiquity

In an ideal world, we might imagine that all these databases could be compiled into one vast bibliography of Antiquity, but so far there is very little interoperability among them. The problem is firstly one of quality, because of the absence of convergence among the strictly bibliographical structuring systems, such as the Dublin Core, which is used more than extensively in describing standardised bibliographical data, and the systems that describe ancient sources which use specific and sometimes contradictory characters. True interoperability among bibliographical databases would require a standardisation not only of the choices applied in describing the bibliographical resources themselves (articles, monographs, editions) but also of their material sources (manuscripts, papyri, inscriptions) and their textual sources (standardisation of titles and authors). It is important to underline the effort made by the Project Biblissima12 to work on interoperability of a large variety of databases concerning history of books and libraries in the Middle Age and the Renaissance, including research tools for ancient authors and texts. We shall see below more specifically why true operability remains on a distant horizon with regard to the Sciences of Antiquity, and how we, for our part, have broached the issue. The problem is also one of quantity. Recent years have seen an inflation in both the bibliographical mass and the number of initiatives to make use of it, an immediate consequence of the bibliometric evaluation systems set up by the academic institutions. This burgeoning of scientific literature, even though it is a sign of the vitality of the research work being carried out, eventually wilts when faced with the defective referencing system that is in use. There is no longer any single bibliographical undertaking capable of coping with the entire quantity of scientific production13 . We should also add that recent years have seen a renewal of scientific approaches in the field of Antiquity, with the emergence of areas of study devoted to cultures other than those of the Greco-Roman world in its strictest sense, and this in turn has led to numerous studies on the transmission and exchange of textual, literary, technical and philosophico-religious productions. However, the bibliographical tools that include these aspects are not yet particularly developed, and researchers are often faced with a fragmentation of resources, with access to each specialised bibliography creating yet another obstacle that needs to be overcome.

"Back to the source"

Rather than bemoaning the fact that we are not able to embrace the galaxy of scientific publications related to Classical Antiquity, we have, with the IPhiS-CIRIS project, opted for developing a tool in phase with these new methods, in terms of both content and ergonomics14 . The first stage therefore involved refining this abundance of material in order to concentrate our efforts on a homogenous part of the publications. We chose to concentrate first on the editions of texts and then on those studies whose prime object is to identify authors and establish texts and their tradition. In doing so we introduced a new methodology: we chose to consider the text as the starting point for the architecture of our bibliographical database. However, there is nothing self-evident about identifying and referencing texts: there is no fixed form of titles15 in Antiquity; many texts, in fragmentary form, have come down to us without any title, and others have been reworked and the various versions need to be differentiated, while others are no longer attributed with any certainty to a particular author, or were for a certain amount of time before scientific progress challenged their attribution, and so on. Our aim -on a small yet ambitious scale -was therefore reformulated at the start of the IPhiS project in 2014 as being: 1) to supply as complete as possible a bibliography of the editions of Greek and Latin texts from the time printing began up to the present day, including in the different states in which they are known (in their original language or in translation; in partial or complete form; treated as part of a larger set; etc.); 2) to supply this bibliography in a structured format that would allow the exchange of data with other bibliographical databases, whether specialised in any particular discipline or not; 3) to provide, as far as possible, access to the resource by indicating the link to an open-access digitalisation of the edition or, if it exists, to the manuscripts used as the basis for the edition, to make it easier for our users to find their way around the global landscape of digital resources concerning Antiquity16 . The project has given rise to a working database, IPhiS, which is not open to the public, and to a web interface for published data once it has been validated by the CIRIS17 team.

II CLASSICAL BIBLIOGRAPHY AND ITS PARTICULARITIES

What constitutes an ancient text

Ancient texts, which form the core of our project, are above all shifting realities: between the initial form of a text published as the work of a given author and the form in which it has come down to us there are quantities of intermediate forms which we lump together in the reference title of the text 18 . There are any number of possible causes for an early text being deformed into the version of it we know today: the text may have been reworked by its original author and we are in possession of several concurrent versions; the author of the text may be uncertain or under debate; the text may not have reached us in its original or complete form, either by choice (quoted by another author, for example) or by accident (a fragmentary, defective or badly copied manuscript), etc. However, all these forms refer to a single ideal conceptual philological object, which contains in it all the forms it has already been able to take and could still take in the future. The task of referencing these objects is ongoing, and no catalogue today can claim to be exhaustive or complete. Developments in the field of research also mean that this referencing cannot, by its very nature, be definitive, even if we seek to establish sustainable data: anyone could be caught out by an unexpected discovery that challenges an attribution or a title, or by the rediscovery of a text for which we thought we had reliable, constant information.

The problem of title

The question of the title of the ancient text is in itself a problem: in our efforts to draw up a list of titles we had to consider a number of realities that corresponded to the expression 'title'. Some texts -such as plays and novels -really do have a title. It is less evident when we are dealing with scientific, philosophical or religious treatises, since they would be qualified as '(treatise) on a particular subject', sometimes with a sub-title. This is then an explanatory title, but its form is not fixed and it may evolve, in copies that are made of it, by abbreviation, or by extension. Other texts have no other title than that given by a subsequent publisher according to their genre ('oration', 'speech', 'homily', etc.): these texts are often passed down to us in a corpus, within which they are numbered; this order becomes 'canonical' until new manuscripts are discovered, challenging the order by adding new texts or removing others, and we are then faced with duplicate or triplicate numberings. Most of the poetry that comes down to us from Antiquity is only known in anthologies and collections within which the poems are numbered, but the same poem, since it is included in several collections, is given several identifiers: we then choose to consider the compilation as the reference text, and the poem as a constituent part rather than as a text in its own right. Lastly, an incalculable number of texts have come down to us with no title at all, in isolation, sometimes only as a fragment: if their content is deemed important, they are given a title that quickly becomes the reference title. However, some of these titles are no more than designations of the accident as a result of which the text has come down to us: for example, what is designated as the 'Palatine Anthology' is a collection of poems which has come down to us via a manuscript found in the Palatine Library in Heidelberg19 . We have sometimes chosen to propose a new, more meaningful title for a text which has a relatively meaningless title 20 . It is thus this multiplicity of situations that the field "title" covers. In our database we have made room for 'aliases' that retain the history of the titles, when they vary from one publisher to another, or from one piece of manuscript evidence to another, or simply because we give Greek texts a working title in Latin even though we are fully aware that the original title is the Greek one. Since we always provide for each text a cross-reference towards other repertories of texts, we often notice that these repertories don't use the same exact title for the same text. If there is no reason to reject all of these variant titles, we tend to keep the title given in the Thesaurus Linguae Graecae Canon 21 of texts or in the Library of Latin Texts 22 for classical texts, and the title given in the Clavis Clavium 23 for Christian texts.

Linking a text to an author

Another difficulty with referencing is that of creating a link between a text and an author. Two specific situations had to be taken into account in our bibliographical database: texts with no identified author, and texts whose presumed author is or has been disputed. In both cases, we must report the lack of precision or the ambiguity in our knowledge, without hiding anything.

Texts with no author

This first case appears simple, since it is possible to attribute a text with no author to an 'anonymous' author. However, the entry 'anonymous' in the table of authors would refer to just one person whose name has been lost! Our approach has therefore been to use collective headings in the 'creator author' field, making it possible to classify our texts in categories without concealing the loss of the name of their author, and providing the possibility of finding the text by means of a themed search. The headings and number of these collective entries are left completely up to us, but there is a tendency in academic circles to adopt common practices, and so we have tried to harmonise our headings with those used in other databases, particularly the Pinakes database24 developed by the Greek section at the IRHT (CNRS -UPR 841) 25 . Thus these collective headings function as "supra-authors" and it would have been perfectly logical for us to attribute to each text, whether its author was known or not, a collective heading in addition to its possible author, in the same way as one would use markers or labels when organising index cards. We decided to only use this option in the case of unknown authors or for certain large-scale groupings in mainly early editions. Initially, we chose to use these names only in the case of texts without a known author, that is to say as an alternative generic author name. But we do not rule out modifying this parameter later and systematically assigning each text one or more of these names to allow a thematic search in the database.

Disputed attribution

The other situation is when texts have come down to us under the name of an author that subsequently proves to be incorrect, either specifically and deliberately -for example the many cases of religious authors whose work was banned but some of their texts continued to be copied under the name of another author who was authorised -, or as the result of an error in transmission caused by homonymy or confusion. Sometimes modern publishers of ancient texts took up such problems of attribution a while ago, and in some cases they have come up with a solution. Thus some texts no longer circulate under the wrong author's name, and once the controversy has been deemed closed for several decades, we make no mention of this other than in a comment on the text. But much doubt still remains about many texts, and we felt it was necessary to report on this as a stage in academic research.

We therefore opted for creating the notion of 'disputed attribution' by mentioning specifically the bibliography involved in the controversy. It is therefore possible, in our database, to list a text under several authors and to mention which authors are accepted or rejected by modern publishers, with the corresponding bibliography. Apart from the fact that this provides additional access to the bibliographical data concerned, our solution makes use of the state of research and the importance of considering the uncertainty that sometimes surrounds the texts that have come down to us from Antiquity, by presenting such texts to the user on both the page for the author (Figure 1) and the page for the corresponding text (Figure 2).

Geographical data

It is usual to designate certain Ancient authors by adding to their name that of a town or country to which they are attached by birth or the place of their main activity, particularly in cases of homonymy. Wherever possible we have preferred sequencing these two items of information, the one prosopographic and the other toponymic. However, this obviously supposes that the geographical data has been checked and crossed-referenced against the historical geography repositories. Where this was known, we linked each author to one or more places, possibly specifying the event associated with the place (birth, education, activity, death). Here again we made it possible to weight the reliability of the historical data by adding an indication of whether the data is certain or disputed. This specific data is displayed in an extension of the CIRIS application in a cartographic format 26 that we felt was more pertinent. For the time being, only the geographical data of the philosophical authors are being published; ultimately we hope to be able to provide this data for all the Ancient authors in the database 27 .

26 https://ciris.huma-num.fr/cartographie.php?langue=fr; consulted on 23 April 2021. See also Fig. 12 supra. The specific publication of this geographical data has constituted an appendix to the project which we present in the report [Giovacchini et al., 2020]. 27 We have chosen to display our biographic data in a modern map, with contemporaneous place names. This choice is a pedagogical one, and is directly focused on the accessibility of our tool for non-scholar users and particularly high school students.

A bibliography in its environment

For the files of both titles and authors, we rely systematically whenever possible on repositories that have already been checked and found reliable, to which we direct users (Pinakes, VIAF, DataBNF, etc), but if appropriate we also propose our own repository, which has our own structuring. Once we had opted for acknowledging the rightful place of uncertain data on bibliographical and philological objects with rather complex contours, presenting a classification meant both respecting the standards without which it is impossible to share data as well as making decisions reaching well beyond straightforward indexing or alignment, and therefore supposed a degree of scientific risk-taking. In the history of the IPhiS-CIRIS project, accessibility has played a structuring role. Initially, the project was constructed on the basis of an ambition to offer full open access, in reaction to the idiosyncratic and extremely constricting proprietary model of the Année Philologique28 . Thus the notion of open access was directly correlated to the question of the structuring and display of the data. Opening up data is not simply the unequivocal gesture of lifting a barrier: rather it means from the outset thinking of the data as an element that may be shared or potentially improved or altered within a complex environment -what is often nowadays called a 'data ecosystem'. Which is tantamount to saying that accessibility is necessarily free of charge, but that is not its only feature. The project therefore exploits a dimension of structuring that is in fact already historically consubstantial with the Classical sources. Since the time of the very first publishers, Greco-Latin literary texts -because of their often incomplete or fragmentary state and the existence of successive versions that form overlays rather than replacements -possess systems of unique identifiers of varying complexity.

Many non-classicists from academia and beyond still express surprise that classicists have been aggressively integrating computerized tools into their field for a generation. The study of Greco-Roman antiquity is, however, a data-intensive enterprise. Classicists have for thousands of years been developing lexica, encyclopedias, commentaries, critical editions, and other elements of scholarly infrastructure that are best suited to an electronic environment. Classicists have placed great emphasis on systematic knowledge management and engineering. The adoption of electronic methods thus reflects a very old impulse within the field of classics. The paper knowledge based on Greco-Roman antiquity is immense and well organized; classicists, for example, established standard, persistent citations schemes for most major authors, thus allowing us to convert nineteenth-century reference tools into useful electronic databases. Classicists are thus well prepared to exploit emerging digital systems. For many classicists, electronic media are interesting not (only) because they are new and exciting but because they allow us to pursue more effectively intellectual avenues than had been feasible with paper29 .

Since the time of the monuments of German erudition in the eighteenth and nineteenth centuries, Classicists have always considered manipulation of the corpora as constituting a consultation, far beyond cursive continuous reading. Consultation supposes transversality and navigation; the corpora are explored and refer back to each other in an inchoative method that can never end. This mode of appropriation is necessary in as much as ancient texts are not units that are closed in on themselves but rather are open samples that are always subject to revision and rereading and above all that serve as sources for other texts. By its very nature, one Greco-Latin literary text refers to other texts in the present state of transmission: one text transmits other texts and is itself transmitted by others. (By 'source' we mean here the material source as well as the historical and literary source, both meanings mingling fairly imperceptibly in the case of texts of the Greco-Latin Antiquity period 30 .) Thus the very first step towards accessibility consists, as we have seen, of modelling this network of inter-generating texts, and making the text as a source the pivotal point or central table of the database. The second stage supposes adding to this central table a sufficient number of controlled identifiers to allow unambiguous navigation both inside and outside the database. These two gestures suppose a distancing from the usual structuring of a bibliography: departing from the traditional documentary model which constructs the reference around the modern edition and is not affected by fine granularity (fragment, extract, etc), considering the modern edition as the culminating point of a long historical process, one state of the text among others, neither the latest nor the 'best', and focusing attention on the source text identified as a sort of bibliographical invariable in its ideal form, whose actual occurrences are so many versions. This involves no more or less than applying the Lachmannian notion of archetype to the bibliography, albeit by shedding any naively realist posture 31 . It is supposed that a text was produced in a given period by a given author on a given subject; if the text in its empiric form is no longer accessible today, it has produced a certain number of historical avatars which all have in common a desire to be reproductions or indirect representations of the text, which must then be taken seriously as the focus, raison d'être and true purpose of these avatars. This is truly a matter of accessibility, since it is the only modelling that actually meets the expectations of the users of a bibliographical database; these users are primarily readers, as they read and carry out research on texts, but they are also authors who produce texts themselves. This departure from the usual bibliographical frame is also an interesting way of converging towards other schemes that are less strictly disciplinary and more generalist, with a view to strengthening the navigability of the data.

III TOWARDS GLOBAL INTEROPERABILITY: OPENING UP DATA

Semanticizing IPhiS

In 2019, the IPhiS database and its public web version (CIRIS) migrated from a local server on the Villejuif site to Huma-Num's Very Large Research Infrastructure (TGIR). The conditions for this migration were excellent, offering guarantees of incomparable permanence compared with the constraints of local hosting. The operation, although highly beneficial for the project, was dependent on one medium-term condition: it had to be possible for the Isidore 32 search engine to harvest the essential CIRIS data. Since Isidore functions according to the principles of the web of linked data, we had to 'translate' our traditional relational database in such a way as to make it compatible with a number of semantic constraints, which meant converting the main IPhiS data into searchable resources meeting the semantic standards accepted by Isidore 33 . 30 This is a problem that justifies the title of our job at the CNRS: the analysis of source, many examples of which are to be found in our team's research logbook; see for example [Capron, 2016c] and [Grignon, 2016.]. 31 An expression of this type of realism forms a common theme running through recent experiments carried out on citing Ancient sources; all the models proposed are based on historical breakdowns and undisputed nomenclatures that are deemed historical fact, whereas they are actually no more than reconstructions. Thus the most advanced tool available to date in terms of citation, the CapiTainS environment (presented for example in [Clérice, 2017]), proposes alignments that are technically extremely advanced, constructed on the basis of the CTS (Canonical Text Services) model, which in turn uses a text identification system that does not dispute the pertinence of the titles being aligned. Although in theory this system is indeed able to allow title variants to be taken into account by distinguishing works from versions of works, in fact it only does so marginally, as it excludes for example the possibility of fuzzy matches, variable divisions, and intertextual conversion. 32 https://isidore.science/ ; consulted on 23 April 2021. 33 There is nothing original in this process of semanticisation on our part. Indeed it is a process that has become banal: items of digital data are adapted to the constraints of the data web so that they will comply with the Isidore is a harvester and a tool of enrichment, but to be able to harvest and enrich it first needs to be able to recognise, identify and link. It is therefore necessary to propose data set out in a format it is able to interpret, and for the actual items of data to be described using metadata Isidore recognises. The Isidore documentation offers two options for preparing databases:

• Propose data using an XML flow of standardised metadata using the OAI-PMH protocol associated with metadata in Dublin Core format. This method is suitable for use with documentary databases, corpora, scientific archives and document/data libraries. For example, a tool such as Omeka offers OAI-PMH via a module. 34 • Propose data using an XML sitemap flow pointing to webpages containing RDFa metadata. This method is suitable for research programme websites presenting corpora of documents or data, scientific blogs (but not Hypotheses.org), and webpages in general. 35 We 36 selected the first option, specifically adapted to our case, and decided to do so by making use of another tool proposed by the Huma-Num grid of services: a Nakala 37 depository. This solution supplied us with an OAI-PMH depository generated automatically by our posting in Nakala without having to incorporate the data directly in a database that was already substantial enough; it also enabled us to select more closely which sets of data were most pertinent for harvesting purposes. This option nevertheless raised other problems, and not all of them have as yet been completely resolved. The principle of a Nakala depository is relatively simple: it is an autonomous uploading area in which items of data are associated either manually or using an API with metadata standardised according to the grids of Dublin Core vocabulary, which is currently the most frequently used model for producing bibliographical metadata38 . The first question that had to be asked was therefore whether the fields in the various IPhiS tables matched those of the Dublin Core vocabulary, with a view to being able to establish an equivalence between the two, this being a prerequisite for the possibility of interoperability between IPhiS and Nakala. If we compare the IPhiS data model with the Dublin Core vocabulary, we can see straight away that there are considerable convergences -which is perfectly natural and to be expected of a bibliographical database. The most important of these convergences is the adaptation in IPhiS of an important distinction, namely differentiating between the creator of a resource and a contributor to a resource. It is a particular feature of ancient texts that their transmission involves a number of participants who, although they are not all authors strictly speaking, have nevertheless made a not inconsiderable contribution to the elaboration of a given text up to its final state: these participants include publishers, printers, translators and commentators. The distinction between creator and contributor was from the outset an elegant solution in the data model for differentiating sufficiently clearly the various stages in the transmission of the text; we preferred this to the more traditional distinction between ancient and modern authors which is based on a vague and relatively inoperative temporal difference as we wish to distinguish not between periods but between interventions requirements of search engines, in a frame that is often institutional. We may note, for example, that the tool SKOS Play allowing the conversion of data into RDF/SKOS from an Excel spreadsheet was developed with funding from the Luxembourg State in order to produce public data in a semantic format (cf. [Francart, 2017]). 34 http://info.omeka.net/build-a-website/manage-plugins/oai-pmh-repository/; consulted on 23 April 2021. 35 https://documentation.huma-num.fr/isidore/; consulted on 23 April 2021. 36 The development and implementation work described in this section was carried out mainly by Bernard Weiss and Julie Giovacchini (ontology and mapping with the DCMI by Julie Giovacchini, scripts for automated supply to the Nakala API by Bernard Weiss); the tests were devised jointly by both these researchers. 37 https://www.nakala.fr/ consulted on 23 April 2021.

on the texts. Thus the IPhiS data model allows the entry of an 'ancient' author as a contributor to a text on a par with a humanist or contemporary publisher.

Using Nakala to semanticize a database: limits and advantages

Adapting to Nakala

For the actual uploading in Nakala, we had to overcome a number of relatively substantial technical constraints, which obliged us to delimit very clearly both what we wanted to display and our choice of metadata to accompany the display.

In the first place, Nakala is mainly intended to be used for uploading data in the form of files attached to metadata, and the main working interface is a visual interface that only allows the individual uploading of file after file. But our situation is very different: we want to post large sets of data in an automated way, by supplying the depository directly so that it updates itself at the same time as the database, which is designed to continue to receive data indefinitely. We therefore concentrated firstly on uploading the records of editions in the presentation proposed by CIRIS, as these constitute the most important and complete IPhiS data, leaving aside temporarily the direct display of the thesauruses of Ancient authors and texts. Our Nakala depository is envisaged as a place for displaying edition records which are considered as so many separate files, each comprising an image (PDF or screen capture of the page of the record in CIRIS) and a set of metadata (Figures 3 and4 39 ). Also, in order to automate the process and upload large quantities, we had to access Nakala via its API 40 . Using a script, we recuperated the necessary files and metadata in IPhiS and then uploaded them in the API by using a 'post' request. This is the only way the depository can be updated automatically. The script, first developed in PHP, is still experimental, but once it has been stabilised, the next stage of the work will consist of proposing an open version in PHP and Python that can be adapted for use in other projects similar to ours. The Nakala API requires a particular formalism for the presentation of metadata, requiring us to adapt our requests to convert the fields in the IPhiS database in such a way as to produce metadata in JSON format, which is compatible with Nakala. This part of the work was relatively delicate and called for a number of arbitrations that were at times somewhat frustrating. For a very straightforward record, limited for example to very little metadata in addition to the compulsory metadata, we arrive at the following form: { "status": "published", "metas": [{ "value": "Ermarco -Frammenti", "lang": "it", "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://nakala.fr/terms#title },{ "value": { "givenname": "Hermarchus", "surname": "Philosophus", "orcid": null }, "propertyUri": http://nakala.fr/terms#creator },{ "value": null, "lang": null, "propertyUri": http://nakala.fr/terms#created },{ "value": "CC-BY-4.0", "lang": null, "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://nakala.fr/terms#license },{ "value": "http://purl.org/coar/resource_type/c_c513", "lang": null, "typeUri": "http://www.w3.org/2001/XMLSchema#anyURI", "propertyUri": http://nakala.fr/terms#type },{ "value": "Francesca Longo Auricchio -éd. (VIAF -7280456)", "lang": "it", "typeUri": "http://www.w3.org/2001/XMLSchema#string", "propertyUri": http://purl.org/dc/terms/contributor },{ "value": "https://ciris.huma-num.fr/noticeedition.php?langue=fr&id=54", "lang": "fr", "typeUri": "http://www.w3.org/2001/XMLSchema#anyURI", "propertyUri": http://purl.org/dc/terms/relation }] } Injecting this form into the API via a 'post' request produces the following display (Figure 5): Nakala relies mainly on two controlled vocabularies, Dublin Core and FOAF, and adds five compulsory metadata (type, license, creator, created, title) in its own namespace. As indicated above, it is theoretically possible to translate all the metadata for our bibliographic records using qualified Dublin Core -including relationships between texts, external sources and references, using the notion of relationship. Our initial mapping was organised as follows: In practice we nevertheless came up against certain consistency issues, connected with the different intents of our database and the Nakala environment, and we had to partly adapt this mapping.

Thus the compulsory metadata in Nakala includes the notions of creator and created in respect of the date of creation. But these notions, in Nakala's internal logic as expressed in the API, apply not to the content of the data but to the data itself: the creator is the person who posted the data, and the date is the date of posting. If we maintain this idea in our display, the metadata then proves to be very poor, and harvesting is likely to prove of little pertinence, even though it is always possible to add further layers of metadata subsequently. For our type of bibliographical data, creating the possibility of carrying out a search on the basis of the name of the person uploading an item of data merely results in the creation of unnecessary noise and is probably a nuisance for users of both Nakala and Isidore.

We therefore decided to circumvent this constraint and indicate as creator the creator of the intellectual content -so, as far as we are concerned, still a creator author, but an ancient author. However, in this case it is impossible to associate a creation date with this creator. This is because the date format for an Ancient work cannot be expressed as D/M/YYYY as required by Nakala's API. At the time of posting we therefore systematically need to associate a zero value to the compulsory created item of metadata. These constraints are offset by the possibility of incorporating a clickable link in the metadata items leading directly to the record in the database. Thus whether by visiting the depository directly or as a result of harvesting by Isidore, the user will always have the possibility of rapid access to the full record in its original place of publication, as the last metadata item visible in Figure 5 shows.

What we display in Nakala, and why

This obviously raises the question of the necessary redundancy of accesses to an item of digital data. The purpose of conversion is to produce a display which will, we hope, increase the visibility of the database -but which cannot take the place of direct consultation of the database if full information is required. Therein lies all the ambiguity of the application of semantic technologies to digital objects that are already natively relational: the overlay of relational logic, thought out as navigation or an explicit path from one resource to another, by an object logic in which the fine description provides the key but does not set out the entire path; thus the description increases the visibility of the resource in certain search tools, but does not take the place of direct exploration of the resource itself. In other words, full display in Nakala would require the construction of a semantic clone of our database, and that would be pointless. Nakala is therefore used like a magnifying glass, with the intention of making it possible for Isidore to harvest certain strategic metadata in order to increase in fine the flow of visits not to the Nakala depository but to the database itself. It is in this logic that the date of creation of the data or its creator becomes a useless item of information, which must be replaced by the creator of the intellectual content likely to be of interest to the user. These choices, summed up in Figure 6, which are still being implemented, are the final stage in a lengthy thinking process; before accepting these compromises it was necessary to start by exploring the hypothesis of systematicity. Would we have been able to display the complete set of IPhiS data directly in Nakala if we had wanted to? The answer is no, for the time being, because firstly if we had wanted to display not only the records for editions but also all the connected data in the IPhiS thesaurus, we would have fairly quickly reached the limit of the vocabularies accepted by the API, and secondly Nakala does not natively recognise the SKOS vocabulary. If we compare for example the IPhiS data and a set that is close not in terms of quantity but of type of object listed -the BNF data -we can see fairly well how DataBNF compensates for the shortcomings of qualified Dublin Core and FOAF with on the one hand certain elements of SKOS for the data in its thesauruses and on the other a specific ontology describing relations and objects specific to its resources and its display 41 . Similarly, a full IPhiS semantic display would suppose the creation of a specific ontology to express certain traits which, as far as we know, are not currently taken into account by the standard bibliographical ontologies. This is more particularly the case for the matter of incomplete texts, noted as fragments or pieces, or collections of texts, anthologies or corpora; it is also, and perhaps even more so, the case for describing the complex progression in order to distinguish between a text's creator, copyist, translator and publisher throughout its history. It is possible to construct this ontology, and we are able to propose an overview of it here, produced using Protégé software 42 (Figures 7 to 11). Implementation of this ontology is not immediately desirable, since it would lead to a very significant technical constraint by causing, apart from the creation of one or more namespaces, the need to attribute a considerable number of URI because of the growing size of the database and manage the negotiation of content between the HTML and RDF versions for each item of data. This is a very real constraint, and one to which experts in the bibliographical semantic web have been drawing attention for quite some time 43 .

Conclusion

As we see it, it is not pertinent, because of the nature of our data on ancient texts, to only use tools such as Nakala to make sure that they are displayed and harvested. Our philological aims are as varied as they are complex; there is therefore always a constraint to either force their harmonisation so that it is not necessary to draw up over-heavy sharing schemas, or simplify them artificially so that they fit into categories that were not designed to accommodate them.

43 "The attribution of URI specific to your set of data for secondary entities is thus an additional burden since you will have to maintain them; however, it is also a security feature in terms of the consistency of your set of data. It all depends on how much you trust the sets of data whose URI you re-use, and the ease of discerning which entities you are manipulating within these external artefacts. Happily, there are other less ponderous solutions for displaying data such as ours in the best possible way. Some are already virtually in place, as a result of our initial choice to cross our own data with as many external repositories as possible. The alignment work carried out with the VIAF, the Pinakes database authorities, dataBNF, or even, in the case of our cartographic extension, several geographical repositories, may ultimately make it possible to envisage entering IPhiS data via channels that are not strictly philological, either via a general bibliography or by using access paths that cease to have anything to do with the base material and are semantic by nature from the outset -or at least readily convertible into a semantic logic.

What is more, we have long given CIRIS users the possibility of downloading a large part of the data in open format for their personal use. This is the case not only for the thesauruses of texts by ancient authors, which are directly downloadable in *.csv format in CIRIS, but also for the edition records that can be exported in RIS format, thereby making them compatible with most bibliographical management software. In the cartographic extension carried out using the open application uMap44 , all the data for the maps can also be downloaded (Figure 12). Diversifying the ways of displaying our data does not in any way mean having to renounce full interoperability; quite the contrary, in fact: it means optimising this sharing by selecting, for each aspect of the items of data, the tool best suited to their display. It is important to take care in determining which item of data should be entrusted to which tool. Doing so takes advantage of the specific features of the items -their transmission is complex, they are charged with a scientific uncertainty that it is our duty to make known, and they represent a wealth of variety of types that it would be wrong to attempt to standardise. An effort still needs to be made regarding the data contained in thesauruses. Here we feel the choice to retain a firm barrier between back-and front-office remains pertinent, since this is checked data that must be subjected to tight editorial control, under an expert eye. That is why, while contributions to the IPhiS database are allowed, in order to enable external users to

Figure 1 :

 1 Figure 1 : Reporting disputed attribution to an author (here, Epicurus). (https://ciris.huma-num.fr/noticeauthor.php?langue=fr&id=785, consulted on 21 April 2021).

Figure 2 :

 2 Figure 2: Reporting disputed attribution for a text. (https://ciris.huma-num.fr/noticetext.php?langue=fr&id=382, consulted on 21 April 2021).

Figure 4 :

 4 Figure 4 : Example of metadata -CIRIS record 45

Figure 5 :

 5 Figure 5: Example of metadata -CIRIS record 54.

Figure 6 :

 6 Figure 6: Complete process of publication and display.

Figure 7 :

 7 Figure 7: Hierarchy of classes in IPhiS ontology in Protégé.

Figure 8 :

 8 Figure 8: Hierarchy of properties of IPhiS ontology in Protégé.

Figure 9 :

 9 Figure 9: IPhiS ontology, extracted from the description in RDF: semantics of Texts.

Figure 10 :

 10 Figure 10: IPhiS ontology, extracted from the description in RDF: semantics of Editions.

Figure 11 :

 11 Figure 11: Partial graph of IPhiS ontology.

Figure 12 :

 12 Figure 12: Access to geographical data in CIRIS.

  If you create your own URI for secondary entities, you can always link them to the others at a later stage (see A.7)." [trans.] [Bermès, Isaac & Poupeau, 2013 paragraph 49].

See: https://www.cairn.info/le-web-semantique-en-bibliotheque--9782765414179-page-69.htm; consulted on 23 April 2021.

https://biblissima.fr/; consulted on 23 April 2021.

While we cannot entirely subscribe to the political hypotheses put forward by Claude Calame in[START_REF] Calame | Les sciences de l'Antiquité. Entre néolibéralisme et culture de supermarché : inflation bibliographique et désarroi méthodologique[END_REF], we cannot but subscribe to his visionary description, set out as early as 1999, of the editorial frenzy that took hold of the academic world in general and the Sciences of Antiquity in particular and produced a situation in which no researcher is now able to claim to have knowledge of the entire annual production in his/her disciplinary field, however confident he/she may be.

Journal of Data Mining and Digital Humanities http://jdmdh.episciences.org

We shall not set out again in detail here in the following pages the entire genesis of the project, which is well documented already. It was presented in detail at the Digit-Hum workshop in 2020 (https://hdl.handle.net/10670/1.dpif0n; consulted on 23 April 2021). We shall merely recall in this footnote all the active members of the project, all of whom contributed to the results presented in this text: Laurent Capron, Julie Giovacchini, Sébastien Grignon and Juliette Lemaire of the Centre Jean Pépin, and Bernard Weiss of the ARDIS unit (UPS2259) for implementing the computerised development of the various models.

See our description of the data model selected and choice of text as the principal node in[Giovacchini et al., 2017 p. 6].

It has to be underlined that, although our goal is to provide bibliographical data about editions of texts, we also try to give a direct link to open access databases of texts like Perseus (http://www.perseus.tufts.edu/hopper/collection?collection=Perseus:collection:Greco-Roman; consulted on 23 April 2021).

https://ciris.huma-num.fr/ consulted on 23 April 2021. The public interface is available in four languages (French, English, German and Latin). Since the data are bibliographical data, they cannot be translated and remain in their original language. The content block reproduces most of the time the table of contents of the book. In some cases, we provide some comments about the edition; these comments are always in French.

See for example[Giovacchini, 2016 1 and 2].

[Capron,

2016a] 20[Capron, 2016b] 21 http://stephanus.tlg.uci.edu/canon.php; consulted on 23 April 2021. 22 http://clt.brepolis.net/llta/public/About.aspx?what=all; consulted on 23 April 2021. 23 https://clavis.brepols.net/clacla/Default.aspx; consulted on 23 April 2021.. This database is a common portal for the previously only printed catalogues of texts Clauis Patrum Graecorum, Clauis Patrum Latinorum, Bibliotheca Hagiographica Graeca and Bibliotheca Hagiographica Latina: it is not a unified repository and every text keeps its former catalogue number.

http://jdmdh.episciences.org

https://pinakes.irht.cnrs.fr/; consulted on 21 April 2021.

List of our headings in the internal documentation for the database, produced by Juliette Lemaire: available at https://ciris.huma-num.fr/manuel/doku.php?id=manuelciris:anonymes&do=login; consulted on 21 April 2021. Collective headings in Pinakes are listed at: https://pinakes.irht.cnrs.fr/mode-d-emploi.html; consulted on 21 April 2021.

The general policy of CIRIS is readable online (https://ciris.huma-num.fr/mentionslegales.php?langue=fr; consulted on 23 April 2021) ; the model is one of a CC-BY-SA license.

[START_REF] Crane | Classics and the Computer: An End of the History[END_REF]

This vocabulary is described and documented on the website of the Dublin Core Metadata Initiative: https://www.dublincore.org/specifications/dublin-core/dcmi-terms/; consulted on 23 April 2021.

The screen captures were generated at the time of the stage in the test of the procedure described in these pages, as the Nakala depository whose development we describe is not yet public. Figure 3 : Example of file -CIRIS record 45

https://api.nakala.fr/doc; consulted on 23 April 2021.

Cf. the full outline of DataBNF at https://data.bnf.fr/images/modele_donnees_2018_02.pdf; consulted on 23 April 2021.

https://ciris.huma-num.fr/cartographie.php; consulted on 23 April 2021.

Documentation is in fact currently being drafted within the general documentation, to help contributors: https://ciris.huma-num.fr/manuel/doku.php?id=manuelciris:contribuer ; consulted on 23 April 2021.


Mietton Flore

Aditya K Sengupta

Molla Annie

Picchi Gisele

Barral Sophie

Heliot Laurent

Grange Thierry

Wutz Anton

Dimitrov Stefan
email: <stefan.dimitrov@ujf-grenoble.fr>

Monod

Stefan Dimitrov

Weak but uniform enrichment of the histone variant macroH2A1 along the inactive X chromosome

Keywords: Animals, Cell Line, Chickens, Chromatin Immunoprecipitation, Female, Fluorescent Antibody Technique, Histones, metabolism, Humans, Liver, metabolism, Male, Mice, Nucleosomes, metabolism, Promoter Regions, Genetic, genetics, Protein Transport, X Chromosome, metabolism, X Chromosome Inactivation

In this work we have studied the enrichment and distribution of the histone variant mH2A1 in the condensed inactive X chromosome (Xi).

By using highly specific antibodies against mH2A1 and stable HEK 293 cell lines expressing either GFP-mH2A1 or GFP-H2A, we found that the inactive X chromosome contains ~1.5 fold more of mH2A1 compared to the autosomes. To determine the distribution of in vivo mH2A1 along the X chromosome we used native ChIP on Chip technique. DNA, isolated from mH2A1 immunoprecipitated nucleosomes from either male or female mouse liver were hybridized to tiling microarrays covering either 5 kb around most promoters or the entire X chromosome. The data show that mH2A1 is uniformly distributed across the entire Xi. Interestingly, a stronger mH2A1 enrichment along the pseudoautosomal X chromosome region was observed in both sexes. Our results indicate a potential role for macroH2A in large scale chromosome structure and genome stability.

Introduction

In the eukaryotic cell nucleus DNA is packaged into chromatin. Chromatin exhibits a repetitive structure and its basic unit, the nucleosome, consists of an octamer of core histones (two each of H2A, H2B, H3 and H4) around which two superhelical turns of DNA are wrapped ( ). 35

In addition to the conventional core histones, cells express histone variants. Such histone variants are non-allelic forms of the conventional histones and are expressed in a very low amount within the cell. The histone variants display varying degrees of similarity to their normal counterparts ( , ). The most studied histone variants belong to the H2A and H3 families ( , , ). When inserted into the histone octamer, 34 35 7 21 30 variants may build nucleosomes with a different architecture and specialized functions ( , ). For example, the crystal structure of the variant 5 7 histone H2A.Z shows specific local molecular changes, which could affect the stability of the H2A.Z nucleosome particle ( ). This could 32 explain, in turn, the reported distinct properties of H2A.Z nucleosomal arrays in solution ( , , , ). Recent data demonstrated that a novel 1 15 16 32 histone variant, H2A.Bbd, is less tightly bound both and in the nucleosome compared to H2A ( , ). The easier exchange and in vitro in vivo 6 17 transfer of H2A.Bbd to a H3-H4 tetrameric particle could reflect the lower stability of the H2A.Bbd nucleosome ( , ). 4 17 The histone variants play an important role in numerous vital cell processes as well as in several diseases (reviewed in , , , ). For 7 21 30 37 example, H2A.Z seems to be implicated in both activation and repression of transcription ( , , , ). The reported data suggested that 13 20 22 31 H2A.Z is also involved in chromosome segregation ( ). 29

MacroH2A (mH2A) is an unusual histone variant, which consists of a domain similar to conventional H2A (H2A-like domain) fused to a large Non Histone Region (NHR) ( ). mH2A reconstituted nucleosomes exhibit a modified structure with major alterations observed close to 26 the dyad axis ( ). These alterations interfere with the binding of the transcription factor NF-B to its cognate sequence ( ). In addition, 3 κ 3 SWI/SNF was unable to both remodel and mobilize mH2A variant nucleosomes. experiments showed that the presence of mH2A In vitro repressed Pol II transcription ( ). It has also been reported that the presence of mH2A in the promoter results in a repression of transcription 14 ( , ). In agreement with this, mH2A.1 is depleted on active genes and experiments with mH2A.1 ( / ) mice have shown that it is ex vivo 2 25 -implicated in silencing of endogenous murine leukemia viruses ( , ) Several reports using immunofluorescence approaches have claimed that the inactive X chromosome (Xi) is enriched with the histone variant mH2A ( , , , ). However, the specificity of the association of mH2A with the Xi was challenged since, by using the same 8 11 12 23 immunofluorescence approach combined with GFP-mH2A localization and FRAP analysis, it was shown that the enrichment of mH2A may " " reflect the higher chromatin concentration within the inactive highly condensed X chromosome ( ). 27

In order to solve this disagreement in the literature, we have studied the distribution of mH2A on Xi by using quantitative immunofluorescence and ChIP on Chip techniques. We found that the inactive X chromosome contains ~ 1.5 fold more mH2A1 compared to the autosomes. Intriguingly, mH2A1 shows uniform distribution all along the Xi.

MATERIALS AND METHODS

Cell culture and nuclei preparation

The human embryonic kidney HEK 293 cells were grown on Dulbecco s modified Eagle s medium. Media were supplemented with 10

Mononucleosome and oligosome preparation

Nuclei were isolated from mouse livers. After appropriate digestion of nuclei with micrococcal nuclease, linker histone-depleted chromatin (containing either mono-or oligosomes) was purified by centrifugation through sucrose gradients containing 0,6M NaCl. Then, the collected fractions were dialysed overnight against 50mM NaCl, 1mM EDTA, 10 mM Tris-HCl, pH 7.5 and if necessary concentrated on Centricon (DO varying from 2 to 6).

260

MacroH2A1 ChIP

Immunoprecipitation were carried out as follow: the linker histone depleted samples were incubated for 8h, at 4 C, with immunopurified °macroH2A antibodies. Protein A-sepharose beads were first saturated with chicken erythrocyte nucleosomes (the anti-mH2A1 antibody we used does not recognize the chicken mH2A1) and then added to the mixture. The incubation lasted 1 hour under mild agitation, at room temperature. Then, beads were washed five times in 50mM NaCl, 1mM EDTA, 10 mM Tris-HCl, pH 7.5 and finally recovered for protein or DNA extractions. Mononucleosomes represent the input, the first IP wash corresponds to the unbound fraction while beads contain the bound material. An amount of each fraction was loaded onto a 12 18 gradient SDS-PAGE and analysed by western blot. Successively histones %-% macroH2A1 and H2A were detected on the same membrane. Nucleosomal DNA of each fraction was extracted from beads with a classical proteinase K digestion protocol.

Genome-wide mouse promoter DNA microarrays hybrydization

Genomic profiling was done by NimbleGen Systems as part of a Chromatin Immunoprecipitation Array Service. We used a mouse promoter tiling microarray set of two 385K arrays covering 5kb (about 4000 to 1000) of 24,939 promoters with a minimum spacing of 110

- +
bp between probes excluding repeated sequences. Probes were 45 to 85 nucleotide-long with an isothermal design (target Tm: 76 C). We °provided non-amplified DNA from input and pull-down (5 g each) samples to NimbleGen Systems for differential labeling by random μ priming using a Cy3/Cy5-coupled 9mer oligonucleotide and hybridization to oligonucleotide arrays. For each experiment, input and pull-down channel signal intensities and scaled log ratios were provided by NimbleGen Systems. We then divided for each probe the immunoprecipitated 2 over input ratio from the female liver chromatin with that from the male liver chromatin, and compared with t-tests the significance of the difference between the female to male ratio obtained with the X chromosome to that obtained with any autosome or the combination of all autosomes.

Hybridization on microarrays covering the whole mouse X chromosome

Microarray Design

Custom tiling microarrays were manufactured by NimbleGen Systems, Inc, based on a probe selection across provided by NimbleGen Systems Inc. The probes were selected to be unique within the mouse genome, at a median resolution of 306bp across the entire X chromosome and at a median resolution of 227bp for a part of chromosome 17 (4657287-19251247, NCBI m36). The microarray had 335514 probes from chromosome X and 52486 from chromosome 17. Note that repeated sequences were not present in the microarrays.

Hybridization

DNA was purified from macroH2A-enriched chromatin and input chromatin. Labeling (ChIP-red, input-green), hybridization to microarrays and data collection was performed by RZPD/ImaGenes.

Data Analysis

Signals from chromosome 17 were used for normalization and scaling within and across microarrays on the assumption that macroH2A distribution on chromosome 17 would be similar between males and females, unlike the X chromosomes. Tukey s biweight function was respectively. In order to detect patterns within the data, the combined datasets were then transformed using wavelet smoothening to generate continuous wavelet transform heatmaps ( ). Wavelet smoothened data at the 64-kb scale was obtained using maximal overlap discrete wavelet 33 transform (MODWT) and used for analyses ( ).

33

RESULTS

Quantitative immunofluorescence studies on the distribution of mH2A1

To study the association of mH2A with the inactive X chromosome we first developed a highly specific polyclonal antibody to mH2A1 ( ). The antibody was generated against the NHR of mH2A1. In whole HEK 293 cell extracts the immunopurified antibody figures 1-3 recognizes a single polypeptide with a molecular mass of 42 kD, corresponding to mH2A1 (

). We then used this antibody to study Figure 1A the distribution of mH2A1 in HEK 293 cells containing several inactive X chromosomes. The immunofluorescence analysis demonstrated that the antibody stained preferentially several dense regions of the interphase HEK 293 cell nucleus, called Barr Bodies, and corresponding to the inactive X chromosomes territories (

). These observations are in agreement with the reported immunofluorescence data ( , ). Figure 1B 8 11 However, an enhanced DAPI staining of the Xi was also observed ( and ). Since the enhanced DAPI staining is associated with a Figures 1B 2A

higher degree of compaction of Xi, even if mH2A1 is uniformly distributed all over the nucleus, one would expect a higher signal intensity with the anti-mH2A1 antibody of the Xi, which would reflect simply the higher degree of compaction (higher chromatin concentration) of Xi (for detail see ). In agreement with this, in normal human female fibroblasts, all anti-conventional histone antibodies, as well as the 27 anti-mH2A antibody, preferentially stained the inactive X chromosome (results not shown and ( ). Moreover, both ectopically expressed 27 GFP-mH2A and GFP-H2A were found concentrated on the inactive X chromosome ( ). Thus, the observed preferential staining might reflect 27 either an enrichment of mH2A1 or a higher chromatin concentration or both in the Xi.

To differentiate between these possibilities, we have carried out quantitative analysis of the amount of mH2A1 associated with Xi by using fluorescence microscopy and stable HEK 293 cell lines expressing either GFP-mH2A or GFP-H2A or na ve HEK 293 ( ). Note that ï

these cells commonly exhibit several inactive X chromosomes ( ). mH2A1 in the na ve cells was detected by using the anti-mH2A1 antibody ( 8

ï
). The intensity of the fluorescence signals of the GFP and the anti-mH2A1 staining for the three types of cells was measured. The Figure 2A same measurements were also carried out for a randomly chosen region with the same dimensions as these of the Xi. The ratio of the two signals was then calculated and the same was done for the DAPI signals in the respective nucleus (

). The data clearly show that this Figure 2B ratio for the DAPI staining is close to 1.5 in the three types of cells (

). This demonstrates that in somatic cells the concentration of Figure 2B chromatin in the Xi is ~50 higher than that of autosomes. The ratio of the GFP fluorescence signals in the cells expressing GFP-H2A was % also determined to 1.5, which further confirms, as expected, the higher concentration of chromatin in Xi and the accuracy of the DAPI measurements. The picture was different when we measured cells expressing green fluorescent protein tagged mH2A1. The ratio of the mH2A fluorescence signals from the Xi compared to autosomes in these cells was determined close to 2 (

). Similarly, immunofluorescence Figure 2B staining of naive 293 cells with our mH2A antibody gave a nearly twofold higher signal intensity on the Xi compared to autosomes (Figure 2B ). Therefore, mH2A shows higher enrichment on the Xi than would be expected from the calculated chromatin concentration. We conclude that the preferential staining of the Xi has two components; first an enrichment of mH2A1 and secondly it reflects a higher concentration of chromatin. Our data show that both components contribute essentially to similar extent to the observed signal over the Xi.

Distribution of mH2A1 on the promoters reveals uniform enrichment on the X chromosome in the liver of female mouse Since mH2A1 might be involved in the repression of transcription, we first sought to detect whether enrichment on specific promoters could be detected. To test this we have carried out ChIp on Chip experiments by using DNA tiling microarrays covering 5 kb around the transcription start site of 25,000 mouse promoters (NimbleGen System Inc.) and oligonucleosomes prepared from male or female mouse liver that were immunoprecipitated with anti-mH2A antibody. DNA from the input and immunoprecipitated (bound) fraction was isolated and used " "

for hybridization. We immunoprecipitated sufficient material to avoid amplification of the bound DNA, thus preventing biases due to PCR amplification.

Working with native nucleosomes preserves the mH2A1 epitopes and allows a very efficient ChIP ( , compare lanes 5, 6 and 7). Figure 3 The enrichment of mH2A in the immunoprecipitated (bound) fraction can be directly estimated by SDS gel electrophoresis and Western blotting of input and bound proteins. Firstly, Western blotting using the anti-mH2A1 antibody estimates the relative abundance of mH2A1 in the input and bound fractions (

). Secondly, using the same blot but with an anti-H2A antibody ( ) the relative abundance of Figure 3 Figure 3 H2A the input and bound fractions was estimated. The ratio between the mH2A1 and H2A signals is a measure of the enrichment of mH2A1 in the bound fraction. In the case of the bound fraction this ratio is much greater than 1, while for the input fraction the ratio was less than 1 ( , compare lane 5 with lanes 1 4). This analysis confirms that a very high enrichment of mH2A1 in the bound fraction was achieved. figure 3 -The mH2A1 and H2A signals of the Western blots of the input fractions ( , lanes 1 4) were used to generate calibration curves to allow figure 3 calculation of the enrichment. In the different experiments we found between 8 and 15 fold enrichment of mH2A1 in the bound fraction compared to the input material.

The analysis of the promoter tiling arrays after hybridization did not detect mH2A1 enrichment on specific promoters on female relative to male liver, except for a cluster of repeated genes belonging to the Ott family (

). With most probes within this area, the Ip/input ratio Figure 4A was consistently higher in the female than in the male. The Ott family corresponds to a clustered X-specific intrachromosomal repeat and most of the oligonucleotide probes within this region hybridized with a perfect match from 10 to 15 times to sequences repeated in close proximity on this portion of the X chromosome. As a consequence, the signal obtained with these probes was amplified, which could have allowed us to detect a weak and rather uniform mH2A1 enrichment that could have remained below detectable levels with the probes corresponding to single copy sequence. To detect such a weak enrichment, we compared the distribution of the signals obtained with all X chromosome probes with that of autosomal probes. When the immunoprecipitated over the input ratio for each probe of the female liver chromatin is divided by that of the male liver chromatin, the distribution of these ratios between the X and other autosomes can be directly compared using a Box plot representation (

). This comparison revealed that there was a weak, but statistically highly significant mH2A1 enrichment (p<10 Figure 4B 230 using a t-test) on the female Xs compared to the male one. This enrichment was observed when the X was compared to any autosomes or to all autosomes together, whereas comparison of any autosome pair did not show such a difference (data not shown). Thus, indeed our interpretation that the repeated Ott cluster allowed to reveal a minor global enrichment of mH2A on the female X chromosomes appeared valid. Throughout the Ott cluster, we have not detected a higher enrichment at some specific positions relative to the transcription start site of the genes, suggesting that the mH2A enrichment at promoters is more global than specifically associated to promoter function.

Because the dynamic of the signal measured on microarrays tend to be always smaller than in the initial nucleic acid population, we aimed at obtaining an estimation of the enrichment factor of mH2A1 on the female X by comparing the enrichment ratio detected on the female to male bound/input ratio to that of the female to male input ratio normalized to the overall signal (

). Since the X to autosome ratio in Figure 4B the female is twice that in the male, and the mH2A1 enrichment observed in the female is half the value observed for the normalized input, we estimate that there was about 1.5 fold higher levels of mH2A1 on the female Xs than on the male X. Assuming that the enrichment is due solely to the inactive X in the female, we estimate that there is at most twice more mH2A1 on the inactive X than on the active X.

Distribution of mH2A1 along the whole inactive X chromosome

Because we do not detect enrichment on specific promoter regions we next asked how mH2A1 is distributed along the inactive X chromosome. We have carried out a ChiP on Chip experiment using DNA tiling microarrays covering the entire mouse X chromosome (Figure ). In order to be able to compare between different samples, particularly between males and female samples, we have included 15 of the 5 % probes on the array from chromosome 17. Assuming that macroH2A1 distribution is similar or invariant on chromosome 17 between the sexes, we normalized and scaled the data within and between arrays using these chromosome 17 probes (

). We observe a low, but rather Figure 5 uniform chromosome-wide enrichment of macroH2A1 on the female X chromosome, while the male X chromosome appears slightly depleted of macroH2A1 relative to chromosome 17 (

). The low levels of enrichment may be in part because of the female cell has an active Figure 5A,C as well as an inactive chromosome, and presumably the active X of females is slightly depleted of macroH2A1 as in the single male X, thereby pulling down the averaged signal obtained from the inactive X. Some regions of the female X chromosome do not show the enrichment (Fig 5C ). These regions correspond to rodent-specific regions that are not conserved in other mammals ( ), suggesting that they http://genome.ucsc.edu/ may have been acquired during evolution after establishment of the mechanism allowing mH2A enrichment. To note is that a relatively strong enrichment along the pseudoautosomal region (PAR) is observed in both sexes (

). Figure 5D

DISCUSSION

In this work we have studied the origin of the higher staining of Xi with anti-mH2A1 antibody and the distribution of mH2A1 along the whole length of Xi by using quantitative fluorescence and ChIP on Chip approaches. The GFP-and immunofluorescence measurements show that the intensity of the mH2A1 staining of the Xi was ~twice stronger that this of the autosomes. This was associated with the higher condensation of the Xi as well as with an enrichment of mH2A1 in Xi, both effects exhibiting very similar contributions, i.e. about 50 of the % enhanced staining was due to the Xi higher compaction and the remaining 50 reflected the preferential association of mH2A1 with the Xi.

%

The ChIP on Chip experiments demonstrated that a higher proportion of mH2A1 was associated with the X chromosomes in female than in male liver along the whole length of the Xs, including promoters. This enrichment was most likely specific to the Xi based on the fluorescence analysis. Our quantitative analyses using these two types of approaches consistently revealed a 1.5 to 2 fold enrichment throughout the whole chromosome. Note that the antibody used showed a very low crossreactivity (not exceeding 10 15 ) with mH2A2 and thus, the estimated -% higher amount of mH2A reflected only the enrichment of mH2A1 in Xi.

Since the function of mH2A is not well understood we could only hypothesize, at least for the moment, the meaning of our findings. mH2A appeared to be involved in transcriptional regulation.

( ) and ( ) experiments pointed to an inhibitory role of mH2A in In vitro 14 ex vivo 2 transcription. The depletion of mH2A1 in mice might regulate the expression of some genes ( ) and appeared to be important for the silencing 9

of endogenous murine leukemia viruses ( ). The stable chromosome X inactivation requires, however, mH2A1 ( ). Since no specific 10 18 enrichment of mH2A1 on the promoter regions of the Xi genes was observed, the potential role of mH2A1 in Xi silencing should not involve a positioned nucleosome on the promoters as it was the case of B cells ( ). Instead, we speculate that a mH2A1-dependent chromatin structure 2 above the nucleosomal level could be involved in the X chromosome inactivation. The number of nucleosomes containing mH2A was estimated to be around 3 of the total number of nucleosomes and thus, bearing in mind the enrichment of mH2A1 on the Xi (the data % presented in this work), close to 4 6 of the Xi nucleosomes should contain mH2A1. Thus, each 15 to 25 Xi nucleosome is a mH2A -% th th nucleosome. These mH2A nucleosomes, which are uniformly distributed on the Xi, could interact with some other factors and form some " coating around the Xi and assist in its compaction and the maintenance of its inactive state. A potential candidate might be PARP-1. Indeed, " PARP-1 was found associated in vivo with mH2A nucleosomes ( , ) and it was shown that the association of PARP-1 promotes its 24 25 in vitro condensation ( ). 36

To note is that we have measured an enrichment of mH2A1 on the pseudoautosomal region (PAR) of both inactive and active chromosome X. This enrichment was higher than the bulk enrichment of mH2A1 on Xi. The PAR is the region where the X and Y chromosomes are homologous and homologous pairing of the XY body takes place during meiosis. This suggests that mH2A1 might be implicated in homologous recombination during meiosis. The assumption is that the small PAR of mice needs to generate one cross-over per meiosis and thus might have been selected for high recombination efficiency. Consequently, mH2A could be part of the machinery to silence these hyper-recombinogenic sequences to ensure genome stability in the soma. We predict that apart from gene regulation mH2A could be involved in suppressing chromosome recombination and thus serve a function in genomic stability.

Ackowledgements:

'

  determined from M values (log ChIP/Input) from chromosome 17 signals of each array and subtracted from all M values for normalization. 2 The mean absolute deviation of the M values across the normalized chromosome 17 signals in each array is used for scaling. A single array error model ( ) was applied to calculate the confidence values and a weighted average was used to combine replicas for males and females 19

  This work was supported by INSERM, CNRS and ANR Project no NT05-1_41978 and by the GEN-AU initiative of the Austrian ministry of science. S.D. acknowledges La Ligue Nationale contre le Cancer (Equipe labellis e La Ligue). We thank Drs. H. Fiegler and N.P. Carter for help é in the initial stage of this work.

The anti-mH2A1 immunopurified antibody recognizes a single band with about 42 kD (A) molecular mass within a HEK 293 cell extract. The same amount of HEK 293 whole cell extract was loaded on several wells of a 12 SDS gel. % After completion of the electrophoresis the gel was cut and one part of the gel was stained with Coomassie blue (lane 2), while the other part was used for western blotting with anti-mH2A antibodies (lane 3). Lane 1, protein molecular mass marker. To note is that the same high specificity of the anti-mH2A1 antibody was also observed when extract from mouse cells was used (not shown).

The mH2A1 antibody detects the inactive (B) X chromosome in HEK 293 cells at interphase. The top panel shows the nucleus of a HEK 293 cell stained with Hoechst and the low panel presents the immunostaining of the same cell with the mH2A1 antibody. ChIP of mH2A1 nucleosomes. Nuclei, prepared from liver of female mice, were digested with microccocal nuclease and mononucleosomes were purified on a sucrose gradient containing 0.6 M NaCl to remove linker histones. Mononucleosomes were immunoprecipitated by using anti-mH2A antibodies attached to protein-A agarose beads. Decreasing amounts of input nucleosomes (lanes 1 4, the nucleosome amounts of each successive lane is decreased twice), the bound (lane 5) and the unbound fractions (lane 6) were loaded on a 5 15 gradient polyacrylamide gel, containing -% SDS. On lane 7 were loaded the control beads, which did not contain anti-mH2A antibodies, but that were incubated with the nucleosomes. After completion of the electrophoresis the proteins were transferred to a nitrocellulose filter. The filter was first revealed with a mH2A antibody and then with an anti-H2A antibody. Note that mH2A gives a much higher signal than H2A in the bound fraction (lane 5). In contrast, the mH2A signals of the input (lanes, 1 4) and the unbound (lane 6) fractions are much less than the respective signals for H2A.

-

Figure 4

MacroH2A1 enrichment on the promoters of the X chromosome of female compared to male in mouse liver. Chromatin from both female and male mouse liver was immunoprecipitated with immunopurified anti-mH2A.1 antibody, and the input and bound DNA was used without amplification for hybridization on tiling arrays containing probes covering 5kb (about 4000 to 1000) of 24,939 mouse promoters. box plot analysis of the distribution of the mH2A enrichment levels in female relative to male on the different chromosomes. Both the female to male bound (Ip) to input ratio and the female to male normalized input ratio are represented (indicated at left and right side, respectively). Data from all pooled autosomes (Auto) are compared to that from the X alone. Very similar distributions are observed when any individual autosomes are analyzed.

Figure 5

MacroH2A1 enrichment on the whole length of the X chromosome of female compared to male in mouse liver. Chromatin from both female and male mouse liver was immunoprecipitated with immunopurified anti-mH2A1 antibody, and the input and bound DNA (without PCR amplification) was used for hybridization on tiling arrays containing probes from the entire X chromosome and part of chromosome 17. M values (log IP/Input) were normalized to chromosome 17 using a weighted average (Tukey s biweight function). Arrays were scaled using mean absolute chromosome. MacroH2A1 enrichment is seen mainly across the entire female X compared to the male X. It should be noted that the signal on the female X is average of the contributions from both the active and the inactive X. ( ) A high degree of macroH2A1 enrichment is seen in the D pseudoautosomal region ( ), starting from within the / gene (depicted with box, arrows show initiation sites of three annotated 28

Fxy Mid-1 transcripts) of both the male and female X chromosomes.


Yuzhao Yang
email: yuzhao.yang@irit.fr

Fatma Abdelhédi
email: fatma.abdelhedi@trimane.fr

Jérôme Darmont
email: jerome.darmont@univ-lyon2.fr

Franck Ravat
email: franck.ravat@irit.fr

Olivier Teste
email: olivier.teste@irit.fr

Internal Data Imputation in Data Warehouse Dimensions

Keywords: Data warehouses, Data imputation, Dimensions

Missing data occur commonly in data warehouses and may generate data usefulness problems. Thus, it is essential to address missing data to carry out a better analysis. There exists data imputation methods for missing data in fact tables, but not for dimension tables. Hence, we propose in this paper a data imputation method for data warehouse dimensions that is based on existing data and takes both intra-and inter-dimension relationships into account.

Introduction

Data warehouses (DWs) are widely used in companies and organizations to help building decision support systems. Data in DWs are usually modeled in a multidimensional way, which helps users consult and analyze aggregated data with On-Line Analytical Processing (OLAP). In a DW, there are non-NULL constraints on keys, but not always on the other attributes, so there may be missing data. Missing data may come from the DW's sources (operational data sources, data of other DWs) if not treated during the Extract-Transform-Load (ETL) process. We classify missing data in the DWs into factual missing data and dimensional missing data with respect to their occurrence in fact and dimension tables. Factual missing data are usually quantitative, making analysis results incomplete and preventing users from getting reliable aggregates. Dimensional missing data are usually qualitative, making aggregated data incomplete and making it hard to analyse them with respect to hierarchy levels. Therefore, it is significant to complete the missing data for the sake of a better data analysis.

Data imputation is the process of filling in missing data by plausible values based on information available in the dataset [START_REF] Li | Towards missing data imputation: A study of fuzzy k-means clustering method[END_REF]. Imputation of missing data focuses on factual data, with statistic-based [START_REF] Wu | Modeling and imputation of large incomplete multidimensional datasets[END_REF], K-Nearest Neighbour (KNN)based [START_REF] De S. Ribeiro | Complementing data in the etl process[END_REF], linear programming-based [START_REF] Bimonte | A linear programming-based framework for handling missing data in multi-granular data warehouses[END_REF] and hybrid (KNN and constraint programming) [START_REF] Amanzougarene | Predicting missing values in a data warehouse by combining constraint programming and knn[END_REF] methods. There is no research about dimensional missing data.

However, dimensional data are mostly qualitative and there are methods for qualitative data imputation. Some methods replace missing values through business rules [START_REF] Fan | Towards certain fixes with editing rules and master data[END_REF][START_REF] Song | Enriching data imputation with extensive similarity neighbors[END_REF] or association rules [START_REF] Wu | Using association rules for completing missing data[END_REF][START_REF] Shen | Combined association rules for dealing with missing values[END_REF]. Yet business rules are not always available in practice, and association rules require to define support and confidence thresholds, which is not always easy. External sources can also be employed, e.g., through crowdsourcing [START_REF] Lofi | Skyline queries over incomplete data-error models for focused crowd-sourcing[END_REF] or taking advantage of Web information [START_REF] Yakout | Infogather: Entity augmentation and attribute discovery by holistic matching with web tables[END_REF]. Yet, suitable external sources may be difficult to find. Eventually, data imputation in DWs should consider the different structural elements in an OLAP systems, such as dimensions and hierarchies. As a result, we propose in this article an internal, i.e., based on existing data, data imputation method for dimensional missing data in DWs, by considering inter-and intra-dimension relationships.

The rest of the paper is organized as follow. In Section 2, we formalize the OLAP model. In Section 3, we detail our imputation method and provide the corresponding algorithms. In Section 4, we validate our proposal through a series of experiments. Finally, in Section 5, we conclude the paper.

Preliminaries

We introduce here the multidimensional DW concepts and notations used in this paper [START_REF] Ravat | Algebraic and graphic languages for olap manipulations[END_REF].

Internal Data Imputation for Dimensions

Internal data imputation consists in replacing missing data in dimensions with the aid of existing data. Existing data imputation is convincible because we use accurate data and not predictions or otherwise computed values. Imputation can be achieved through intra-and inter-dimensional relationships. Let us introduce these two types of data imputation.

Intra-dimensional Imputation Intra-dimension imputation relies on data from the same dimension. There are indeed functional dependencies between attributes in the same hierarchy. If an attribute is a parameter, its values depend on the values of lower-granularity parameters. Our intra-dimension imputation method is presented in Algorithm 1. We first check each parameter in hierarchies of the DW. If there exists missing data for this parameter (Lines 1-2), we search for an instance with value in a lower-granularity parameter and whose value exists (Lines 3-4). Then, we can then fill in the missing data with this value (Line 5).

Algorithm 1: Intra-dimension Imputation

1 for each p H v ∈ P aram H , where H ∈ H D , D ∈ D DW do 2 for each i D e ∈ I D , where i D e .p H v is null do 3 while p H v 2 ∈ P aram H ∧ p H v 2 H p H v do 4 if ∃i D e 2 ∈ I D , i D e 2 .p H v 2 = i D e .p H v 2 ∧ i D e 2 .p H v is not null then 5 i D e .p H v ← i D e 2 .p H v 2 6
for each i D e 3 ∈ I D , where i D e 3 .w

p H v y is null, w p H v y ∈ W eak H [p H v ] do 7 while p H v 3 ∈ P aram H ∧ (p H v 3 H p H v ∨ p H v 3 = p H v )) do 8 if ∃i D e 4 ∈ I D , i D e 4 .p H v 3 = i D e 3 .p H v 3 ∧ i D e 4 .p H v is not null then 9 i D e 3 .w p H v y ← i D e 4 .w p H v y
The value of a weak attribute depends on the values of its parameter. Then, for each weak attribute of the parameter we check, if there are missing data (Line 6), we search for the instance that has the same value of its parameter or a lower-granularity parameter whose value exists (Lines 7-8). The missing weak attribute data can then be supplied by this value (Line 9). It is important to note that, since the parameter sets of hierarchy are ordered sets, checking parameters is sequential (from the lowest-granularity to the highest-granularity parameter). This ensures that imputation is maximal, as the value of a higher-granularity parameter depends on its lower-granularity parameters.

Inter-dimensional Imputation In a DW, there may be attributes that are common to different dimensions. Therefore, we can replace missing data with such inter-dimensional common attributes. The main idea of inter-dimension imputation is similar to intra-dimension imputation's, except that instead of searching for parameters in the same hierarchy, we search for common parameters of hierarchies in other dimensions (Algorithm 2, Lines 3-4 and 9-10). When performing the imputation of weak attributes, we must make sure that, in the searched dimension, the searched parameter is semantically identical with the parameter of the weak attribute to be completed; and that it bears a semantically identical weak attribute (Lines 10-11). We say "semantically identical" because in a DW, common attributes may be presented differently in different dimensions. Since in a DW, the designer would normally not use two vocabularies to describe a same entity, but may use the different prefixes or suffixes to distinguish the same entity in different dimensions, we must therefore use string similarity to match attribute names.

Algorithm 2: Inter-dimension Imputation

H2 ∈ H D 2 , D2 ∈ D DW ∧ D2 = D do 4 if p H 2 v 2 ≃ p H v then 5 while p H 2 v 3 ∈ P aram H 2 ∧ p H 2 v 3 H 2 p H 2 v 2 do 6 if ∃i D 2 e 2 ∈ I D 2 , i D 2 e 2 .p H v 3 = i D e .p H v 3 ∧ i D 2 e 2 .p H 2 v 2 is not null then 7 i D e .p H v ← i D 2 e 2 .p H 2 v 2 8
for each i D e 3 ∈ I D , where w

p H v y ∈ W eak H [p H v ], i D e 3 .w p H v y is null do 9 for each p H 3 v 4 ∈ H3, where H3 ∈ H D 3 , D3 ∈ D DW ∧ D3 = D do 10 if p H 3 v 4 ≃ p H v ∧ ∃w p H 3 v 4 y 2 ∈ W eak H 3 [p H 3 v 4 ], w p H 3 v 4 y 2 ≃ w p H v y then 11 while p H 3 v 4 ∈ P aram H 3 ∧ (p H 3 v 5 H 3 p H v ∨ p H 3 v 5 ≃ p H v ) do 12 if ∃i D 3 e 4 ∈ I D 3 , i D 3 e 4 .p H 3 v 5 = i D e 3 .p H 3 v 5 ∧ i D 3 e 4 .w p H 3 v 4 y 2 is not null then 13 i D e 3 .w p H v y ← i D 3 e 4 .w p H 3 v 4 y 2

Experimental Assessment

We implement our algorithms 4 and conduct experiments with different datasets.

Our code is developed in Python 3.7 and is executed on a Intel(R) Core(TM) i5-10210U 1.60 GHz CPU with a 16 GB RAM. Data are integrated in R-OLAP format with Oracle 11g.

Datasets and Experimental Method

Our experiments are based on one benchmark dataset and three real-world datasets. The TPC-H benchmark (TPCH) provides a relational schema5 with 8 tables and a data generator we use to produce 100 MB of data. The first realworld dataset is a customer-centric dataset (GlobalStore) of a global super store 6 . It contains the order data of different customers and products. The second real world dataset is a regional sale dataset (RegionalSales) storing sales data for a company across US regions 7 . The third dataset (GeoFrance) contains information about French cities, departments and regions from the French government open data site 8 . We create a DW for each real-world dataset.

In our experiments, the parameter of the first granularity level in dimension hierarchies is the primary key of the dimension table. Its values are not repetitive, so weak attributes of the first granularity level and parameters of the second granularity level cannot be completed. Therefore, we generate missing data for parameters from the third granularity level of dimension hierarchies and for weak attributes from the second granularity level. Moreover, we apply different missing rates (1%, 5%, 10%, 20%, 30%, 40% and 50%). To generate a certain percentage of missing data for an attribute, we sort randomly all the tuples and remove attribute data of the first certain percentage of tuples. For each dataset, we carry out 20 tests and get the average imputation rate, accuracy and runtime. Imputation rate is the number of replaced values divided by the number of missing values. Accuracy is the number of correctly replaced values divided by the number of all replaced values.

Intra-dimensional Imputation Experiments

The datasets TPCH, GlobalStore and RegionalSales are employed in this experiment intra-dimensional imputation experiment. The imputation rate ranges between 61.73% and 100%; the accuracy between 97.08% and 100%; and missing rate between 1% and 50%.

Imputation Rate In Figure 1, imputation rates (X-axis) vary with respect to missing rates (Y-axis). We observe that, for dataset TPCH, the imputation rate is always 100%, while the imputation rates of the other datasets decrease when the missing rate increases. The imputation rate of RegionalSales is much lower than the two others. Since missing data are replaced by the tuple having the same value on a lower-granularity parameter, the imputation rate of an attribute depends on the ratio of the distinct values and the coefficient of variation of each distinct value of its lower-granilarity parameters. For example, in the dimension P art of TPCH, imputation rate and ratio are 0.125% and 0.027 for the second granularity level parameter, respectively; while in dimension StoreLocation of RegionalSales, they are 62.13% and 1.1, respectively. Accuracy We can see in Figure 1 that the accuracy of TPCH is always 100%, while the accuracy of the two other datasets is always less than 100%. Since our imputation method is based on the hierarchy relationships, non-strict and incomplete hierarchies may impact accuracy. By analysing the data, we find that there are non-strict hierarchies in these datasets GlobalStore and Regional-Sales, i.e., in the dimension Customer of GlobalStore, there are some tuples whose City values are the same, but they belong to different States. There is a similar case in dimension StoreLocation of RegionalSales.

Runtime The evolution of runtime with respect to missing rate is linear (Figure 1), which is in line with the complexity of Algorithm 1, which is O(n), where n is the missing rate.

Inter-dimensional Imputation Experiments

We use TPCH and GeoFrance in this inter-dimensional imputation experiment. There are two TPCH dimensions, Customer and Supplier, which have same geographical attributes. In GeoFrance, we create two dimensions and randomly divide the original data into two partitions with the same number of tuples. Then, we load the each partition into one of the dimensions. The imputation rate ranges between 48.67% and 100%. The accuracy always remain at 100% with respect to missing rate.

Imputation Rate Yet again, the imputation rate of TPCH is always 100% (Figure 2), for the same same reason as intra-dimensional imputation. Ge-oFrance's imputation rate is low when the missing rate is very low, then it increases with the missing rate. After analysing the data, we find that there is a tuple where the values of RegionCode and RegioN ame are originally missing. The lower-granularity parameter DepartmentCode being unique, RegionCode and RegionN ame missing data cannot be imputed. When the missing rate is low, the number of total missing data is low, too. Thus, the missing data in this tuple account for a large proportion of total missing data, which can explain why GeoFrance's imputation rate is low when the missing rate is very low.

Fig. 2. Inter-dimensional imputation experiment results

Accuracy There is no incomplete nor non-strict hierarchy in TPCH's and GeoFrance's DWs. Hence, the accuracy for these two datasets is always 100% (Figure 2). Runtime Again, the evolution of runtime with respect to missing rate is linear (Figure 2), which is in line with the complexity of Algorithm 2, which is O(n), where n is the missing rate.

Conclusion and future work

In this article, we propose an internal data imputation method for dimensional missing data in DWs. Our method is based on the existing data found in both intra-and inter-dimensional relationships. We take in charge the imputation of both parameters and weak attributes. The solutions are formalized as algorithms and are actually implemented. Our method is validated by a series of experiments with the different percentages of missing data of the different attributes. However, not all missing data can be completed by the existing data, thus in the future we will also combine our method with web-based methods to achieve a better imputation

Definition 1 .

 1 A data warehouse, denoted DW , is defined as (N DW , F DW , D DW , Star DW ), where N DW is the data warehouse's name, F DW = {F DW 1 , ..., F DW m } is a set of facts, D DW = {D DW 1 , ..., D DW n } is a set of dimensions and Star DW : F DW → D DW is a mapping associating each fact to its linked dimensions. Definition 2. A dimension, denoted D ∈ D C , is defined as (N D , A D , H D , I D ), where N D is the dimension's name, A D = {a D 1 , .

Fig. 1 .

 1 Fig. 1. Intra-dimensional imputation experiment results

https://github.com/BI4PEOPLE/Internal-Data-Imputationin-Data-Warehouse-Dimensions/

http://tpc.org/tpc documents current versions/pdf/tpc-h v2.18.0.pdf

https://data.world/vikas-0731/global-super-store

https://data.world/dataman-udit/us-regional-sales-data

https://www.data.gouv.fr/fr/datasets/communes-de-france-base-des-codes-postaux/

Acknowledgement

This research is funded by the French National Research Agency (ANR), project ANR-19-CE23-0005 BI4people (Business Intelligence for the people).