Jennie Andersen
email: jennie.andersen@insa-lyon.fr

Sylvie Cazalens
email: sylvie.cazalens@insa-lyon.fr

Philippe Lamarre
email: philippe.lamarre@insa-lyon.fr

Pierre Maillot
email: pierre.maillot@inria.fr

A Framework to Assess Knowledge Graphs Accountability

Keywords: Dataset accountability, RDF graphs, Evaluation Framework, Data Quality I. INTRODUCTION

Knowledge Graphs (KGs), and Linked Open Data in particular, enable the generation and exchange of more and more information on the Web. In order to use and reuse these data properly, the presence of accountability information is essential. Accountability requires specific and accurate information about people's responsibilities and actions. In this article, we define KGAcc, a framework dedicated to the assessment of RDF graphs accountability. It consists of accountability requirements and a measure of accountability for KGs. Then, we evaluate KGs from the LOD cloud and describe the results obtained. Finally, we compare our approach with data quality and FAIR assessment frameworks to highlight the differences.

Therefore, every KG holding personal information, such as Wikidata, should provide contact information of this controller, i.e. a person responsible for the data, and ideally allow users to access it directly via its SPARQL endpoint. As another example, to avoid misinterpretation and to improve the (re)use of the data, it is often necessary to know for what purpose they were created, and for whom the data are intended. For instance, in some database mainly dedicated to teaching purposes, such as the MONDIAL Database2 , some inaccuracies can be tolerated (or even desired). However, it cannot be reused without precaution for other purposes. Therefore, it should indicate its intended audience or its expected usage. However, when querying its SPARQL endpoint, this information is not available. Accountability ensures that this kind of information of major interest is effectively available. Several studies are already looking for meta-information, either as some particular aspects of data quality [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF], [START_REF] Zaveri | Quality assessment for linked data: A survey[END_REF], or as some requirements of the FAIR principles (Findability, Accessibility, Interoperability, Reproducibility) [START_REF] Amdouni | O'FAIRe: Ontology FAIRness evaluator in the agroportal semantic resource repository[END_REF], [START_REF] Devaraju | An automated solution for measuring the progress toward fair research data[END_REF], [START_REF] Rosnet | FAIR-checker -supporting the findability and reusability of digital life science resources[END_REF], [START_REF] Wilkinson | The FAIR guiding principles for scientific data management and stewardship[END_REF]. Yet, they neither take into account the information used in the two previous examples nor several other accountability information. This highlights the importance of accountability as a specific and distinct characteristic of RDF datasets and the importance of their evaluation w.r.t. this aspect.

Hence, in this paper, we propose a new framework, KGAcc, dedicated to the assessment of RDF graphs accountability. It consists of organized accountability requirements and a measure of accountability. We experiment it on many KGs offering a publicly available SPARQL endpoint. Our accountability measure gives an indication of the accountability of KGs to dataset users and providers. It aims to guide users in their choice of one KG rather than another and to help providers to identify ways to improve their datasets.

To define such a measure, several questions arise, such as what meta-information is required? How to evaluate heterogeneous KGs? First, to define requirements, we rely on the LiQuID metadata model which focuses on dataset accountability [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF] in general. It provides an explicit list of accountability requirements expressed in natural language. The problem, then, is to adapt this model to the specificities of knowledge graphs and to define the requirements in terms of SPARQL queries. To evaluate the KGs, we use the SPARQL-based test suite of the IndeGx framework [START_REF] Maillot | IndeGx: A model and a framework for indexing RDF knowledge graphs with SPARQL-based test suits[END_REF]. We observe that most of them do not provide any easily accessible accountability information. However, as some KGs do answer some questions, it shows that our demand is reasonable and that KGs have a lot of room for improvement. In addition, to illustrate the specificities of this measure, we compare it with several assessment frameworks for data quality and FAIRness.

The rest of the article is organized as follows. Section II describes the state of the art. We define the KGAcc framework in Section III. Then, Section IV is devoted to the description of the methodology for evaluating RDF graphs and the results obtained. We then compare our accountability measure with the existing assessments of knowledge graphs in Section V. Finally, we conclude in the last section.

II. RELATED WORK

Generally speaking, accountability requires that there is sufficient information to describe the data [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF], the actions on the data, from its creation [START_REF] Rowe | Assessing trust: Contextual accountability[END_REF] to its use [START_REF] Weitzner | Information accountability[END_REF], and the people responsible for these data as well as these actions [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF], [START_REF] Weitzner | Information accountability[END_REF]. It may concern different levels of the information system, such as information accountability [START_REF] Weitzner | Information accountability[END_REF], [START_REF] Rowe | Assessing trust: Contextual accountability[END_REF], systems [START_REF] Naja | A semantic framework to support ai system accountability and audit[END_REF], and dataset accountability [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF]. To evaluate the accountability of knowledge graphs, we focus on this latter point. The accountability of knowledge graphs may be considered as part of their data quality, in the broad sense. These last years, several studies have highlighted the many facets of the notion [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF], [START_REF] Zaveri | Quality assessment for linked data: A survey[END_REF]. In addition, general monitoring tools such as SPARQLES [START_REF] Vandenbussche | Sparqles: Monitoring public sparql endpoints[END_REF] and YummyData [START_REF] Yamamoto | Yummydata: providing high-quality open life science data[END_REF] have been proposed, enabling to assess and draw profiles of SPARQL endpoints.

As a matter of fact, measuring the accountability of KGs is a special case of assessing metadata completeness, which is defined as "the degree to which metadata properties and values are not missing in a dataset for a given task" [START_REF] Issa | Knowledge graph completeness: A systematic literature review[END_REF]. Many works consider the presence of meta-information to evaluate knowledge graphs. Studies about the data quality of KGs [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF], [START_REF] Zaveri | Quality assessment for linked data: A survey[END_REF] include many different metrics, among which a few focus on meta-information. For instance, provenance information is required by a metric on trustworthiness. The FAIR principles [START_REF] Wilkinson | The FAIR guiding principles for scientific data management and stewardship[END_REF] are also interested in meta-information. One of the principles of findability states that "data [must be] described with rich metadata", and reusability requires that "meta(data) are richly described with a plurality of accurate and relevant attributes", including a license, and provenance information. Therefore, the required meta-information may overlap between accountability, data quality and FAIRness while having their own specificities. Because of the high variability of the actual implementations of these metrics and principles, we confront them with our own requirements at the scale of the RDF properties in section V.

In order to define the KGAcc framework to measure the accountability of KG, we base our work on the LiQuID metadata model [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF] which considers datasets in general. It offers a way for datasets to represent accountability meta-information throughout their life cycle. The model has been validated based on a real-world workload that relies on existing regulations (such as the GDPR) and an expert survey. To our knowledge, it is the only one to provide such a precise and explicit list of accountability requirements, presented in the form of questions that describe the model. Our framework adapts the hierarchy and the associated questions of LiQuID, taking into account the expressiveness of the most common vocabularies. It provides the requirements as a set of SPARQL queries corresponding to the questions. Our very first experiments are shortly reported in [START_REF] Andersen | Assessing knowledge graphs accountability[END_REF]. The work described in this paper relies on (i) new experiments that enable to distinguish between each dataset of a SPARQL endpoint, and ii) improved queries, taking into account more vocabularies. In addition, we provide a thorough comparison with other evaluation frameworks [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF], [START_REF] Zaveri | Quality assessment for linked data: A survey[END_REF], [START_REF] Amdouni | O'FAIRe: Ontology FAIRness evaluator in the agroportal semantic resource repository[END_REF], [START_REF] Rosnet | FAIR-checker -supporting the findability and reusability of digital life science resources[END_REF].

Finally, in order to conduct our experiments and to query KGs with our own set of queries, several frameworks can be used. Luzzu [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF] and Sieve [START_REF] Mendes | Sieve: linked data quality assessment and fusion[END_REF] enable users to choose metrics among those defined and to declare new ones. Monitoring tools, such as SPARQLES [START_REF] Vandenbussche | Sparqles: Monitoring public sparql endpoints[END_REF], also enable assessing some quality aspects. Instead of these, we choose the IndeGx framework [START_REF] Maillot | IndeGx: A model and a framework for indexing RDF knowledge graphs with SPARQL-based test suits[END_REF] because it relies entirely on SPARQL queries, unlike Sieve and Luzzu, and is easily extendable. The IndeGx framework enables querying many KGs, with multiple queries, and storing the results in RDF. Its primary use case is to build an index of KGs and thus to extract and compute various information about them using a SPARQL-based test suite. To evaluate KG accountability, we use it as an engine to submit our own queries to KGs and to store the evaluation results in RDF.

III. ACCOUNTABILITY REQUIREMENTS AND METRIC

In this section, we define the KGAcc framework. We define the requirements of knowledge graphs accountability, i.e. the precise information that KGs must contain. To be as unambiguous as possible, we go one step further in expressing these requirements using SPARQL queries. Finally, we formally define the metric of accountability. Our proposal is based on the LiQuID metadata model [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF] that enables the representation of information related to the accountability of datasets. To illustrate the use of their model, they provide precise questions that a dataset must answer to be considered accountable. LiQuID is not specific to any type of dataset, so it is necessary to adapt it.

A. The LiQuID Metadata Model of Accountability

The LiQuID metadata model relies on a hierarchical structure. First, it covers all steps of a dataset's life cycle: data collection, processing, maintenance and usage. Then, each life cycle step is structured according to different question types: why, who, when, where, how and what. Finally, each question type is divided into different fields of information level: description, explanation, legal and ethical considerations and limitations. The authors provide an exhaustive list of questions to describe each aspect of this hierarchy. For instance, for "data In what physical location can the KG be used? 1

processing", question type "when", the question associated with the field "description" is "On what date(s) or time frame(s) has the data been processed?". The LiQuID approach proceeds in a very systematic way and requires a large amount of very detailed information, representing what data sources should expose to be as accountable as possible.

B. Adaptation of LiQuID for Knowledge Graphs

Ideally, to assess the accountability of a KG, we should consider all LiQuID questions. However, it is not possible for all questions to be adapted for KGs and translated into SPARQL queries.

Indeed, as shown by Oppold and Herschel [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF], the two general metadata models Dublin Core 3 and PROV [START_REF] Lebo | PROV-O: The PROV Ontology[END_REF], cannot cover all the fields proposed by LiQuID. According to them, both models "contain few fields, some of them too general to be mapped to specific LiQuID fields". We make the same observation with other general metadata models used in KGs, especially if the task is not to provide the information required by the model, but to query it. As a consequence of this lack of expressiveness, some questions cannot be translated into queries. As an example, some fields of the information level require too specific information, such as "Why is it lawful to collect this kind of data?", which, to our knowledge, cannot be expressed in a KG using existing vocabularies. As another example, two questions result in the same query for different steps of the life cycle, this is in particular the case for the collection and processing steps.

Faced with these difficulties, we opt for a soft strategy in which the maximum score of accountability seems attainable to us. It consists in keeping only questions compatible with the 3 https://dublincore.org/specifications/dublin-core/dcmi-terms/ most common vocabularies of the semantic web. Therefore, we make the following adaptations: (i) only the field "description" of the information level is considered, (ii) the data processing step of the life cycle level is merged into the data collection step, (iii) the question types "why", "what" in "data collection" and "what" in "data maintenance" are not considered, and (iv) two questions concerning the exact methods and tools used for creation and maintenance are not considered in favor of more flexible questions concerning the methodology or procedure only. The resulting hierarchy is shown in Figure 1. As for the rest of the paper, we omit the last level, as it only contains the "description" element.

This definition of the accountability requirements, guided by the desire to ask reasonable questions, leads to a core set of 23 LiQuID questions (out of 207). We then define the KGAcc requirements by adapting these questions to the context of KGs. We make them more precise, and divide them into smaller parts, so they focus on only one element each. This precision is made as faithfully as possible, with the aforementioned limitations. Table I illustrates this adaptation. Therefore, the KGAcc framework results in 30 questions: 5 for Data Collection, 5 for Data Maintenance, and 20 for Data Usage. The totality of the questions is available on GitHub4 .

C. SPARQL Implementation of the Questions

Once the questions have been defined, each of them is translated into a SPARQL query or a succession of SPARQL queries. We use more than ten vocabularies of reference, chosen regarding their relevance to describe datasets and concepts around: VoID [START_REF] Alexander | Describing linked datasets with the VoID vocabulary[END_REF] is used to express metadata about RDF datasets. DCAT 5 and DataID6 allow the description of datasets and catalogs of datasets. SPARQL-SD [START_REF] Williams | Sparql 1.1 service description[END_REF] enables to describe SPARQL endpoints. These vocabularies rely on other general vocabularies, the Dublin Core, FOAF 7 and SKOS 8 . We also use PROV-O and PAV [START_REF] Ciccarese | Pav ontology: provenance, authoring and versioning[END_REF] for provenance issues. DQV 9 is used to describe the quality of datasets. Finally, we use schema.org a very general and widely used vocabulary, and some specific vocabularies for licenses, such as Creative Commons 10 . Each query uses all coherent properties and classes of these vocabularies to be as complete as possible. Listing 1 shows an example of a question translated into a query, where ?kg must be replaced by the IRI of the knowledge graph at hand. As queries are associated with questions requiring answers, they are "ASK" queries. The answer TRUE is considered a success, as it means that the KG contains the desired information. On the opposite, the answer FALSE or an error (e.g., timeout exception) is a failure, as it means the KG is unable to provide the wanted information.

Finally, notice that to express our precise requirements, we can either use the queries in their extended version, including all possible ways of expressing the required information, as in Listing 1. Alternatively, we can express the requirements in the form of a compact query, as in Listing 2, completed with a set of equivalences between properties (and between more complex graph patterns if necessary).

Listing 2. Compact query associated with "Who publishes this dataset?" PREFIX dct: <http://purl.org/dc/terms/> ASK { ?kg dct:publisher ?publisher . }

D. Definition of the Metric

First, we define the score obtained for each question. Then it is possible to determine the score of each node of the KGAcc hierarchy defined in Figure 1, from the bottom to the top. The score at the top of the hierarchy is the overall accountability score.

A successful query gives a score of 1 to its associated question, while a failure gives 0. The score of a question associated with a succession of queries is the average of the score given by each query. The accountability score of a leaf of the KGAcc hierarchy (e.g. "data usage -who") is the weighted average of the scores obtained for its associated questions. Notice that LiQuID does not weight its questions, which suggests they are of equal importance. To stay close to this, we use to the following rule. When m (m ≥ 1) KGAcc questions come from a same LiQuID question, a weight of 1/m is associated to each of them. Table I illustrates these weights. For instance, "data usage -who" has three questions, coming from two LiQuID questions. The first leads to one question, so its weight is 1, and the second leads to two questions, therefore their weight is 1/2 each. The accountability score of "data usage -who" is the weighted average of these three questions, with the weights of 1, 1/2, and 1/2. For the other elements of the hierarchy, we determine their score by computing the (nonweighted) average of the scores of the elements underneath.

Formally, let g be a knowledge graph, ℓ a leaf node of the KGAcc hierarchy (e.g. "data usage -who"), and let Q(ℓ) denote all questions associated with ℓ. With score a function giving the score of g for a given question q, w q the weight of question q, the accountability score of g w.r.t. ℓ is:

accountability(g, ℓ) = q∈Q(ℓ) w q • score(g, q) q∈Q(ℓ) w q (1)
and the score of a given node n of the KGAcc hierarchy which is not a leaf is:

accountability(g, n) = n ′ child of n accountability(g, n ′ ) number of children of n (2)
In particular, the global accountability score is the score for the upper node in the hierarchy.

IV. EXPERIMENTATION AND RESULTS

In this section, we describe our experiments. First, we detail the method employed to conduct an evaluation campaign of several KGs. Then, we discuss two aspects of the results. First, we examine the capabilities of knowledge graphs with regard to accountability. Second, we discuss the measure itself and the relevance of the KGAcc questions. All our queries and results are publicly available on our GitHub repository 11 .

A. Processing and Tool

To evaluate a knowledge graph, we first need to identify its IRI within its own data. Then, we proceed in several stages to evaluate how the KG answers the queries defined in the previous section.

An important prerequisite of all our queries is to identify the IRI that the studied KG uses to refer to itself, or more precisely, the IRIs of the datasets it contains. Indeed, this IRI is the subject of at least one triple in all our queries, as illustrated in Listing 1. Therefore, a query looking for the IRI is defined and presented in Listing 3, where $rawEndpointUrl is replaced by the URL of the endpoint during evaluation. If the KG does not provide an answer to this query, it will not answer any of our queries. In order to reduce the complexity of the queries sent to KGs, we focus on the accountability requirements in their compact form (cf. Listing 2). So, we proceed according to the following steps. For each KG, we first extract the triples corresponding to its metadata. As explained before, we use queries that begin with the lines described in Listing 3 to identify them. Then, we saturate this description of the KG by adding equivalent properties and classes, as defined by the requirements. Finally, we evaluate a KG according to this saturated metadata, using compact queries.

To carry out all these steps, we use the framework IndeGx 12 . It relies on a SPARQL-based test suite and can pre-process some steps for a better scalability. To use it, we provide SPARQL queries and configure the actions to be taken based on their results, i.e. which triples to write or update in the resulting RDF graph. So, we embed a set of queries into the framework, following the steps previously detailed, and declare how to store the result (True or False) for each evaluation query and for each KG using the DQV Vocabulary.

B. Querying of the SPARQL Endpoints

Our experiments query the 336 SPARQL endpoints already identified by IndeGx, extracted from LOD Cloud, Wikidata, SPARQLES, Yummy Data, and Linked Wiki in February 2023. These endpoints were queried at three different time points in June 2023. For each endpoint, only the results of an experiment for which it was available are kept. In this way, KGs are not penalized if they were unavailable at a given time. All endpoints not succeeding the query of Listing 3 are assigned an accountability score of 0, as no triple concerning its KG could be extracted.

Finally, given the results obtained for each query and thus each question, the accountability score can be computed. As defined in subsection III-D, an average is used to calculate the score for each aspect of the KGAcc hierarchy of Figure 1, until the overall accountability score is obtained.

C. Analysis of the Results

Among the 336 endpoints tested, only 26 successfully provide accountability information (Listing 3). The others were unavailable or did not provide easily accessible 12 https://github.com/Wimmics/dekalog meta-information within their data. Among the 26 endpoints, 166 different datasets were identified (in the sense of dcat:Dataset or void:Dataset. . . ), with accountability scores varying between 3.1% and 59%, with an average score of 26%. Even though most of the KGs do not provide any accountability information, the distribution of the values shows that this measure allows to discriminate between the datasets and the 26 endpoints left. On average, KGs are more accountable concerning "data usage" (41%) than "data collection" (25%), and twice better on "data collection" than on "data maintenance" (12%).

All URLs start with http(s):// and, except for *, end with /sparql. Figure 2 shows the accountability score of the best dataset of each endpoint. This score is divided according to the three life cycle steps "data collection", "data maintenance" and "data usage". It is possible to compare two datasets in more detail. As an example, Figure 3 shows the strengths and weaknesses of the main dataset of http://caligraph.org/sparql and of http: //wasabi.inria.fr/sparql according to the life cycle steps (3a) and more precisely on the question types of the "data usage" step (3b). The small number of KGs having a non-zero accountability score is not surprising. This observation is in line with other results [START_REF] Maillot | KartoGraphI: Drawing a Map of Linked Data[END_REF] showing that less than 10% of KGs provide selfdescriptions within their data. However, for some KGs, it is possible that some meta-information may be present outside of the KG itself, for instance on their web page, or inside the KG but not findable in the way shown in Listing 3. While not taking them into account may penalize some KGs, it points out the fact that they are less transparent because the information is less accessible.

Several reasons may explain the scores obtained on the different life cycle steps. The "data usage" step covers general description elements that are widely used such as a description, a publisher, or a license, that more than half of the 26 endpoints provide. Furthermore, it encompasses all questions involving VoID vocabulary, which are each answered at least once by more than 50% of the endpoints on average. "Data usage" also requires a link to the endpoint or a dump, so having an answer to this question is expected considering how we identify the IRI of the KG. "Data maintenance" usually has bad scores. This may be due to the fact that half of the questions have only one possible property, with no alternative. For instance, the modification frequency can only be obtained with the property accrualPeriodicity from the Dublin Core vocabulary. This lack of alternative solutions to express this concept makes it more difficult to answer the query and highlights the fact that the question is more unusual. "Data creation" has various results with very common requirements, such as the creator and the creation date, and more difficult questions to answer such as the creation method.

D. Discussion about the KGAcc Framework

As far as the framework is concerned, at least two questions can be asked: are the requirements relevant? Are they too demanding? Figure 4 provides some answers. It represents the distribution of the values of accountability of the best dataset of each endpoint w.r.t. each aspect of the KGAcc hierarchy. Each box represents the first quartile (Q1), the median, and the third quartile (Q3) of the values obtained on the different aspects and the whiskers indicate the minimum and the maximum values obtained. It shows that the question types of "data usage" usually have good values in the different KGs. It also shows that half of the aspects can be fully covered, including "data collection -who", "data collection -when" and "data collection -how" for instance.

On the one hand, as many of the aspects sometimes get the maximum score, it shows that these queries are relevant and that KGs have a good margin to improve themselves. On the other hand, some of the low scores observed on that figure may be explained by too demanding queries. Indeed, it is important to notice that 6 out of 30 queries never succeed. For instance, in "data usage -when" the end date of availability of the dataset may be difficult for providers to specify, as they may consider that their KGs will be available indefinitely. Other questions concerning locations may not be in line with the current practices. Indeed, they are especially important for KGs that hold private information, which is generally not the case for public SPARQL endpoints. As other frameworks, depending on the context, KGAcc may be discussed and improved with experts and KG providers.

V. COMPARISON WITH SOME EVALUATION FRAMEWORKS

To take the analysis of our framework a step further, we compare it in detail with several data quality and FAIRness assessment frameworks. The comparison is made at the level of the required properties: we aim to verify to what extent other studies require the properties demanded by the KGAcc framework. To do so, we focus on studies that consider RDF properties and RDF datasets, and that either provide an open access implementation or that describe the metrics in sufficient detail to allow comparison. This is why works such as F-UJI [START_REF] Devaraju | An automated solution for measuring the progress toward fair research data[END_REF] or Sieve [START_REF] Mendes | Sieve: linked data quality assessment and fusion[END_REF] are not considered.

Concerning data quality, Zaveri et al. [START_REF] Zaveri | Quality assessment for linked data: A survey[END_REF] provide an organized list of metrics obtained by a systematic literature review. This work is theoretical and does not implement these metrics, therefore, we do not take it into account. However, we focus on two major studies of data quality inspired by Zaveri et al. First, Färber et al. [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF] evaluate the data quality of five crossdomain KGs, namely DBpedia, Freebase, OpenCyc, Wikidata, and YAGO. While the implementation of their metrics is not available, each metric is richly described. Secondly, Debattista et al. [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF] provide a more generic set of data quality metrics enabling the evaluation of any KG. Their implementation is available online but the article [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF] describing them is more detailed and understandable. Therefore, for all these studies, we base our comparison solely on the referenced article.

For FAIRness, FAIR-checker [START_REF] Rosnet | FAIR-checker -supporting the findability and reusability of digital life science resources[END_REF] is interested in RDF triples as embedded metadata in web pages. For comparison, we rely on the specifications provided by the online tool 13 when evaluating a resource. We also consider O'FAIRe [START_REF] Amdouni | O'FAIRe: Ontology FAIRness evaluator in the agroportal semantic resource repository[END_REF] which focuses on RDF ontologies. It provides an online tool 14 to see the results obtained by a list of ontologies. To compare with them, we consider the complete list of questions and their required properties 15 . In total, this leads us to consider two data quality studies and two FAIRness ones.

Table II summarizes our comparative study. For each KGAcc query, if one of its required properties is also required in a data quality or FAIR metric, a mark is indicated in the table. If this property must not necessarily concern the KG (e.g. the creator of a resource instead of the creator of the dataset), then the mark is ≈, showing that the FAIR or data quality metric is not really related to dataset accountability. Otherwise, if this property is mandatory to obtain a maximum score on the data quality or FAIR metric, the mark is ✓. If the property is listed among other properties and only one or two or n of these properties are necessary for success, then the mark is ⊂. For instance, in O'FAIRe the third question for principle F2 states that to obtain the maximum score, six properties should be used from a list of 37 properties, whatever those six properties may be. Therefore, unlike the ✓ mark, a ⊂ mark does not guarantee that passing the FAIR metric ensures passing the accountability query. This table highlights several elements concerning data quality metrics. First, as part of the measure of accessibility, all these evaluations require a license to be present using properties such as dcterms:licence [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF]. They also demand some particular provenance information: the creators or the publishers of the KG [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF], or other information not specifically related to the KG such as the source of some data to enhance trustworthiness [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], their modification dates [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF], or traceability of the data [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF]. Some other meta-information is expected to be provided, such as the serialization formats [START_REF] Debattista | Evaluating the quality of the lod cloud: An empirical investigation[END_REF]. Finally, Färber et al. [START_REF] Färber | Linked data quality of dbpedia, freebase, opencyc, wikidata, and yago[END_REF] request the provision of KG metadata citing as an example the URI of the SPARQL endpoint or the RDF export URL to indicate where to access the data.

Concerning FAIR metrics, only two metrics are related to accountability in FAIR-checker. The first one measures the 'R1.1' principle that requires a license. The second one measures the provisioning of provenance information (R1.2) by checking that at least one of the 23 listed properties is found (such as prov:wasDerivedFrom, pav:createdBy, etc.). O'FAIRe offers more similarities with our work. There are mainly two different kinds of metrics of interest compared to our queries. First, the metrics concerning the reusability principles focus on one information each and are mostly also required by accountability (creator, contributor, source, method, periodicity, license and rights). Secondly, some metrics of findability require that the ontology uses some well-known properties. Indeed, two questions of the principle 'F2' cover properties required by at least 11 accountability queries (such as dct:created, void:dataDump...).

As a result, both data quality and FAIRness share common interests with accountability. Therefore, improving them may have a positive impact on the assessment of accountability and vice versa. However, neither data quality nor FAIRness focuses specifically on accountability as a whole and does not take into account all the elements it requires. The general studies on data quality only slightly overlap with accountability. FAIRness has more similarities, particularly with regard to the steps of data collection and maintenance as it is mainly interested in questions of provenance. In particular, O'FAIRe seems to have many similarities. However, most of them result solely from the two findability metrics, which are not very informative about the type of metadata present, since they cover no more than 11 of our queries. Therefore, the measure of accountability is much more detailed, precise, and focused than O'FAIRe on our point of interest. And as the result of each query is available, the former provides a much more relevant view of accountability.

VI. CONCLUSION

In order to evaluate the accountability of RDF graphs, we proposed : (i) the KGAcc framework defining requirements concerning the metadata that the KGs should expose and an associated metric, (ii) the evaluation of a large set of endpoints, (iii) a comparison of our approach with other frameworks that assess data quality or compliance to the FAIR principles.

The KGAcc requirements are expressed as SPARQL queries. They are obtained through a meticulous adaptation of an existing hierarchy of natural language questions, proposed for datasets in general [START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF], to the specific context of KGs. Indeed, the dedicated vocabularies make easy stating some requirements. But their lack of expressiveness makes some questions collapse into a same query or prevents from considering demanding and precise questions about ethical and legal questions. This is why we end up with a relatively small set of queries.

The evaluation of many RDF graphs reveals that most of them do not provide any of the required information within their data, even though some of the required information is very commonly requested. However, there are RDF graphs that provide some of the expected information, showing our demands are reasonable. Our comparative study shows in particular that O'FAIRe is the framework considering the most properties common to accountability. However, it is not so demanding in terms of accountability and cannot be considered as a framework dedicated to this aspect.

In future works, to improve our measure, we will introduce some weights to aggregate the results differently, and we will propose an online visualization of the results. Finally, it could be interesting to automate some tasks, such as defining the equivalences.

Fig. 1 .

 1 Fig.1. The KGAcc Hierarchy of Requirements of Accountability, adapted from LiQuID[START_REF] Oppold | Accountable data analytics start with accountable data: The LiQuID metadata model[END_REF] to Fit the Context of Knowledge Graphs

Listing 3 .

 3 Query to identify the IRI of the studied KG SELECT ?kg WHERE { ?kg ?endpointLink $rawEndpointUrl . { ?kg a dcat:Dataset } UNION { ?kg a void:Dataset } UNION { ?kg a dcmitype:Dataset } UNION { ?kg a schema:Dataset } UNION { ?kg a sd:Dataset } UNION { ?kg a dataid:Dataset } }

Fig. 2 .

 2 Fig. 2. Accountability Score Obtained by the Best Dataset of Each Evaluated Endpoint, Detailed according to the Life Cycle Steps.

Fig. 3 .

 3 Fig. 3. Accountability of Two KGs w.r.t. Different Elements of the Hierarchy

W

TABLE I ACCOUNTABILITY

 I REQUIREMENTS CONCERNING DATA USAGE: ORIGINAL QUESTIONS FROM LIQUID AND THE ADAPTED ONES IN THE KGACC FRAMEWORK

		Questions from LiQuID	KGAcc Questions	Weight
		Who publishes this data set?	Who publishes this KG?	1
	Usage. Who	Who has used/ can use the published data set?	Who has the right to use the published KG? Who is intended to use the published KG?	1/2 1/2
		When can/ was the published data set be used? Since when was the KG available?	1
	Usage. When	When is it available?	Until when is the KG available?	1
		Until what point in time is it valid?	Until when is the KG valid?	1
	Usage. Where	Where is the data set published/ available?	allowing to gain access to it? What is the webpage presenting the KG and/or	1/2
			Where to access the KG (either through a dump	1/2
			or a SPARQL endpoint)?

Where (place, geographically) can the published data set be used?

https://www.semwebtech.org/mondial/10/

https://github.com/Jendersen/KG accountability/tree/v2.0/docs

https://www.w3.org/ns/dcat

http://dataid.dbpedia.org/ns/core

http://xmlns.com/foaf/spec/

https://www.w3.org/TR/skos-reference/

https://www.w3.org/TR/vocab-dqv/

http://creativecommons.org/ns

https://github.com/Jendersen/KG accountability/tree/v2.0

fair-checker.france-bioinformatique.fr/check Accessed: 10 April 2023

agroportal.lirmm.fr/landscape#fairness assessment

https://github.com/agroportal/fairness/blob/master/doc/results/ FAIR-questions.md Accessed: 10 April 2023

This work is supported by the ANR DeKaloG (Decentralized Knowledge Graphs) project, ANR-19-CE23-0014, CE23 -Intelligence artificielle.

1 https://eur-lex.europa.eu/eli/reg/2016/679/2016-05-04


Amine Mohamed

Rouane Hacene

Yannick Toussaint

Petko Valtchev

Mohamed Rouane-Hacene

Mining Safety Signals in Spontaneous Report Database using Concept Analysis

In pharmacovigilance, linking the adverse reactions by patients to drugs they took is a key activity typically based on the analysis of patient reports. Yet generating potentially interesting pairs (drug, reaction) from a record database is a complex task, especially when many drugs are involved. To limit the generation effort, we exploit the frequently occurring patterns in the database and form association rules on top of them. Moreover, only rules of minimal premise are considered as output by concept analysis tools, which are then filtered through standard measures for statistical significance. We illustrate the process on a small database of anti-hiv drugs involved in the haart therapy while larger-scope validation within the database of the French Medicines Agency is also reported.

Introduction

Pharmacovigilance (pv) aims at, first, studying and, then, preventing the adverse reactions to drugs (adr) based on the data collected by spontaneous reporting systems (srs) and stored in case report databases (db). srs db comprises a collection of reports each capturing the patient characteristics including demographic data (age, race, gender, etc.), the suspected drugs and a description of the observed adr. Table 1 depicts a set of case reports on aids patients and antiretroviral drugs, i.e., treating infection by retroviruses such as hiv.

In pv, drug-reaction combinations, known as safety signals, help devising a drug therapy, hence the importance of their detection. For instance, in hiv treatment, the caregivers are interested in the response of various classes of patients to the haart therapy in order to adapt the overall anti-hiv therapy. Their prime target is an appropriate combination of antiretroviral drugs that, while effective, limits the adr: e.g., older patients with hiv infection have robust responses to haart with no increased risk of metabolic disorders or other adr. Beside safety signals, i.e., (drug, adr) pairs, further meaningful combinations from the srs db involve several drugs for a single adr. These are potential drug interactions (higher-order signals).

Signal detection has been approached with a variety of analysis tools [START_REF] Hauben | The role of data mining in pharmacovigilance[END_REF] including statistical methods for disproportionality assessment, deviation detection, etc. However, none of these proposes a way, both automated and feasible, for generating all potential signals from the srs db. Moreover, even with an expertprovided potential signal, the underlying approaches would consider all drugreaction combinations that can be derived from the signal, including many spurious ones. For instance, consider the anti-hiv drugs Lopinavir and Tenofovir in Table 1 and the adr HairLoss and Oedema. A proportionate approach would suggest the study of signals (Lopinavir, Oedema), (Lopinavir, HairLoss), (Tenofovir, Oedema), and (Tenofovir, HairLoss). Yet the only sensible combination to study is ({Lopinavir, Tenofovir}, {HairLoss, Oedema}) as, given the dataset, the four combine to a maximal pattern. In summary, because of the large size of most srs db, the computation of all combinations is strongly combinatorial, hence their test may prove infeasible. Instead, a more careful approach would track the frequently occurring patterns in the records and use these as prototypes. Patterns comprised of two sets, a premise and a conclusion, called associations, have been successfully applied to a variety of practical problems involving co-occurrencies of phenomena and seem to fit well the pv context. Yet a notorious problem of association miners is the huge number of potentially useful associations that may be extracted from even a small db. Formal concept analysis (fca) [START_REF] Ganter | Formal Concept Analysis[END_REF] provides the theoretical foundation for association rule bases that only withhold a tiny proportion of all valid associations while keeping the total of the information. Hence we propose an fca-based method for signal detection which, by examining a minimal set of association rules extracted from the srs db helps minimize the number of (drug, adr) pairs to be statistically analyzed.

Here, we examine the detection of safety signals and drug-drug interactions by means of fca and a set of disproportionality measures to discard statistically non significant associations. Our approach is illustrated on a set of case reports on aids patients and antiretroviral drugs. A validation thereof involving the srs db of the French Medicines Agency is also reported.

The paper starts by a short presentation of concept lattices and association rules (Sect. 2). Follows the description of the proposed method (Sect. 3). Sect. 4 presents the results of the preliminary experiments. Related work is summarised in Sect. 5 while further research directions are given in Sect. 6.

2 Background on concept lattices and association rules

Concept lattices

Formal concept analysis (fca) [START_REF] Ganter | Formal Concept Analysis[END_REF] is a method for designing concepts and conceptual hierarchies from collections of individuals (formal objects) described by properties (formal attributes). To apply fca to pv data as presented in Table 1, the latter must first be encoded in standard format. The format, a binary context K = (O, A, I), (see

Daffy × × × × × × × Farley × × × × × × × × × × Lane × × × × × × × × × Shana × × × × × × × Trudy × × × × × × × × ×
Table 2. Binary context encoding aids patients with their drugs and adr.

Two derivation operators, both denoted ′ link objects and attributes [START_REF] Ganter | Formal Concept Analysis[END_REF]. Let

X ⊆ O, Y ⊆ A: X ′ = {a ∈ A|∀o ∈ X, oIa}, Y ′ = {o ∈ O|∀a ∈ Y, oIa}. For example, following Table 2, {Daffy, Trudy}' = {Adult, Nausea, Vomiting}. The compound operators ′′ are closure operators over 2 O and 2 A , respectively. A set Y ⊆ A is closed if Y = Y ′′
which means the objects sharing Y , i.e., Y ′ , share no other attribute (i.e., from A/Y ). A pair of sets corresponding to one-another through ′ is called a (formal

) concept: c = (X, Y ) ∈ ℘(O) × ℘(A) is a concept of K iff X ′ = Y and Y ′ = X (
here X and Y are called the extent and the intent of c, respectively). For instance, ({Farley, Shana}, {HairLoss, Oedema, Lopinavir, Tenofovir}) is a concept (c 6 in Fig. 1).

Furthermore, the set C K of all concepts of the context K is partially ordered by extent inclusion (intent containment). The structure L = C K , ≤ K is a complete lattice, called the concept lattice. Fig. 1 shows the lattice of the context in Table 2, whereby a simplified labeling scheme is used where each object/attribute appears only once in the diagram. The extent of a concept is made of all objects whose labels can be reached from the concept on a downward-heading path while intent is recovered in a dual way. For example, the extent of the concept with the attribute label Bleeding is {Lane, Trudy} while its intent is {Bleeding, Fatigue}. Fig. 1. Concept lattice of case reports given in Table 1.

Within the lattice L = C K , ≤ K , concepts have a unique greatest lower bound termed meet ( ) that is defined as follows:

k i=1 (X i , Y i ) = ( k i=1 X i , ( k i=1 Y i ) ′′ )
For instance, in Fig. 1, the meet of c #19 = ({Daffy, Trudy}, {Adult, Vomiting, Nausea}) and concept c #20 =({Daffy, Lane}, {Adult, Female, Hives, Efavirenz}) is c #22 =({Daffy}, {Adult, Female, Efavirenz,Vomiting, Hives, Nausea, Vomiting, Lopinavir}). In addition, the function µ : A → C K maps an attribute a into the maximal concept in the lattice having that attribute (µ(a) = (a ′ , a ′′ )). For instance, in Fig. 1, µ(HeartFailure)=c #11 .

The lattice in Fig. 1 provides the analyst with a variety of insights into the data such as the profile of the aids patients under study, the different anti-hiv treatments and the respective most common adr. For instance, the concept c #20 = ({Daffy, Lane}, {Female, Adult, Hives}) represents adult female patients under anti-hiv drug regimen containing NNRTIs 2 , including Efavirenz, and experiencing Hives. In summary, the lattice of case reports provides an overview of drug-reaction combinations to be explored for pharmacological associations detection. In many cases, too specific concepts are not relevant. To only keep those having extents of certain size, the support of a concept is defined as its relative extent size, σ(c) = X O . The corresponding sub-order of the lattice, i.e., its upper part induced by threshold α in ]0, 1], is Lα = Cα , ≤ K where Cα = {c |c ∈ C, σ(c) ≥ α}. Lα is called the iceberg lattice [START_REF] Stumme | Computing iceberg concept lattices with TITANIC[END_REF]. In fca, mining association rules from a db consists in: (i) extracting all frequent closed itemsets, i.e., concept intents from the db, with support above α, (ii) generating all valid association rules, i.e., rules whose confidence exceeds a user-defined minimum threshold. The first step presents a greater challenge as the set of frequent itemsets may grow exponentially with the size of A while the second step is relatively straightforward. Moreover, several fca-based algorithms [START_REF] Bastide | Mining minimal non-redundant association rules using fci[END_REF] generate non-redundant bases of association rules. These bases are minimal with respect to the number of rules whereas the contained rules are informative, i.e., with minimal antecedents and maximal consequents. To extract a tractable number of association rules from pv data, we have used the Informative Generic Basis (igb) [START_REF] Bastide | Mining minimal non-redundant association rules using fci[END_REF] as it has been shown that this type of association rules conveys the maximum of useful knowledge, without information loss. Moreover, our igb contains exact (versus approximative) associations rules, i.e., rules whose confidence is equal to 1 (as opposed to confidence < 1). Table 3 illustrates some of the drug-reaction associations from the igb extracted out of data in Table 1.

Detecting safety signals using FCA

The outline of our mining method is as follows: First, srs data is encoded into a binary context, where formal objects represent case reports while formal attributes are either taken drugs or the observed reactions (see Table 2). Then, fca is used to derive both the lattice and the corresponding igb. For instance, in the case of anti-hiv drugs Lopinavir and Tenofovir and the two adr HairLoss and Oedema, the method will consider only the pair ({Lopinavir, Tenofovir}, {HairLoss, Oedema}) since it represents the only combination where the four elements appear (concept c 6 in Fig. 1).

Rules of the basis are split into three groups. Pure association have both antecedent and consequent made exclusively of drugs and reactions respectively. Semi-pure associations, in contrast, admit only non-reaction items in their consequent that are further removed for analysis purposes. Finaly, biaised associations admit non-drug items in their antecedents as well. Their components are filtered to fit the drugs -→ reactions rule scheme. Later, statistical filters are applied to detect statistically significant candidates for each of the two types of pharmacological associations, i.e., signals and drug-drug interactions.

In order to discard statistically non significant concepts, we use some of the measures of disproportionality [START_REF] Van Puijenbroek | Application of quantitative signal detection in the dutch spontaneous reporting system for adverse drug reactions[END_REF] that are currently applied in various reporting centers, e.g., the British Medicines and Healthcare products Regulatory Agency Such measures for a suspected adr of a drug of interest are calculated from the following variables: (a) reports including the drug of interest and the suspected reaction, (b) reports with the drug of interest and no reference to the suspected reaction, (c) reports where the suspected reaction appears without the drug of interest, (d) reports where neither the drug of interest nor the suspected reaction appear. The adopted measures are the proportional adr reporting ratio (prr), reporting odds ratio (ror), and χ 2 test.

For instance, the prr is the proportion of the suspected adr versus all adr reported for the drug of interest devided by the corresponding proportion for other drugs. It can be expressed as prr = a×(c+d) c×(a+b) . Fig. 2 shows how the various cells of the drug-adr contingency table are calculated using a drug-reaction concept lattice. Hence, every meet concept ∧ m,r in the lattice L P , for a given pair of a medicine m and a reaction r is the source of a drug-reaction contingency table.

For instance, the calculation of prr for the anti-hiv drug Lopinavir and the suspected adr HairLoss using the concept lattice of Fig. 1 is as follows:

a = |Ext(( Lopinavir,HairLoss )| = |Ext(c #6 )| = 2, b = |Ext(µ(Lopinavir))|- |Ext( Lopinavir,HairLoss )|= |Ext(c #17 )|-|Ext(c #6 )| = 1, c=|Ext(µ(HairLoss))|- |Ext( Lopinavir,HairLoss )|=|Ext(c #4 )| -|Ext(c #6 )|=1, d=|O|-(|Ext(µ(Lopinavir)) ∪ Ext(µ(HairLoss))|) = 5-|Ext(c #17 ) ∪ Ext(c #4 )|=1, prr = 2×(1+1)
1×(2+1) . The obtained value of prr is 1.33 ≤ 2. Hence, the assumption stating that Lopinavir causes HairLoss is statistically non significant.

The detection of higher-order drug-reaction associations, such as drug interactions, has been carried out so far by logistic regression modelling [START_REF] Hauben | The role of data mining in pharmacovigilance[END_REF] where concomitant drugs (resp. reactions) are considered as covariates and the suspected reaction (resp. drug) as dependent variable. For instance, in our running pv data, the logistic model predicting whether Nausea reaction is a result of possible interaction between Lopinavir and Efavirenz would look like:

N = β 0 + β 1 × L + β 2 × E + β 3 × L * E
The variables L and E are exposure variables (or predictors) representing risk factors associated with concomitant drugs Lopinavir and Efavirenz, respectively, while L * E is the interaction term. The intercept β 0 represents the value of the dependent variable Nausea (N ) in a patient with no risk factors, while logistic (or logit) coefficients β 1 , β 2 , and β 3 basically quantify the expected variation in N associated with a unit change in the binary predictor variables Lopinavir, Efavirenz, and the interaction term, respectively.

Maximum likelihood estimation (MLE) can be used to calculate logistic coefficients. In the case of Nausea, Lopinavir and Efavirenz, calculating logit coefficients using the hypothetical contingency table depicted in left-hand side of Fig. 3 and R package yields N = -1.609 -0.993 × L + 0.226 × E + 2.337 × L × E with the p-values depicted in right-hand side of Fig. 3. The interpretation would be that the interaction is statistically significant as the p-value for the interaction term is 0.0381, a value that is less than the usually accepted threshold of 0.05. SignalMiner 3 , is an open source tool dedicated to mining significant drugreaction associations. The tool is coupled with, on the one hand, Galicia open-source platform 4 for handling fca data including the input contexts, concept/iceberg lattices and rule basis, and on the other hand, the open-source statistical computing and graphics environment R5 for data pre-processing and multivariate statistics including logistic regression analysis. In addition, Sig-nalMiner performs a wide range of standard calculations, e.g., prr, ror, χ 2 (with Yates correction), etc. The srs db of the French Medicines Agency (Afssaps) was used for the validating experiments. We have tested the proposed method on several moderatesize subsets of the dataset. For instance, for a pool of 3249 case reports containing 527 drugs and 639 adr. The obtained lattice comprises 13178 concepts while the corresponding rule basis contains 28117 rules among them only 1165 represent candidates for pharmacological associations. These candidates are further distilled by SignalMiner to identify pure, semi-pure or biaised associations as illustrated in Table 4. Thus, the 1165 suggested association candidates (Table 4) are further filtered, on the one hand, by focusing potential safety signals satisfying the above MHRA 'interestingness' criteria, and on the other hand, by focusing drug interactions that have been revealed significant using regression analysis. The minimum criteria for raising hypotheses regarding safety signals are as follows: number of reports (patients) ≥ 3, prr ≥ 2, and χ 2 ≥ 4 (with Yates correction).

Among 834 candidates representing safety signals (Table 4), we have found that 63 candidates are statisticaly significant safety signals including 36 known signals (57%), e.g., {Abciximab, Thrombopenia}, 16 new signals warranting further investigations, e.g., {Lamivudine, Arthralgia}, while the remaining potential signals are either association where the drug appears as an innocent bystander, e.g., {Ritonavir, Hypophosphatemia}, or non-interpretable association, e.g., {Bupivacaine, decrease of the therapeutic effect}. In addition, among 331 associations representing candidates for drug interactions (Table 4), 10 candidates are revealed to be statistically interesting. In a previous work [START_REF] Bousquet | A review of potential signals generated by an automated method on 3324 pharmacovigilance case reports[END_REF][START_REF] Estacio-Moreno | Mining for adverse drug events with formal concept analysis[END_REF], disproportinality measures extracted 523 and 360 statistically significant {drug, adr} couples, respectively. Our approach returns a smaller set of drugreaction associations to be further investigated.

Related work

Several studies from the literature address the use of dma to identify drugreaction associations. In [START_REF] Estacio-Moreno | Mining for adverse drug events with formal concept analysis[END_REF], the use of fca in signal detection is briefely addressed. To assess the strength of the association between a target drug and suspected adr, disproportionality approach introduces several parameters such as, the prr [5], χ 2 that is often coupled with the prr, and the ror [START_REF] Van Puijenbroek | Application of quantitative signal detection in the dutch spontaneous reporting system for adverse drug reactions[END_REF], whereas Bayesian approach consists of the Multi-item Gamma Poisson Shrinker (MGPS) algorithm [START_REF] Szarfman | Use of screening algorithms and computer systems to efficiently signal higher-than-expected combinations of drugs and events in the us fdas reports database[END_REF] and the Bayesian Confidence Propagation Neural Network (BCPNN) [START_REF] Bate | A bayesian neural network method for adverse drug reaction signal generation[END_REF].

In [START_REF] Pogel | Contingency structures and concept analysis[END_REF], an interpretation of mathematical structures from fca into epidemiology is described. A comprehensive survey of state-of-the-art in statistical modused by a various dma of pv data is proposed in [START_REF] Hauben | The role of data mining in pharmacovigilance[END_REF]. However, to the best of our knowledge, none of them supports automatic detection of pharmacological associations involving several drugs and/or reactions.

Discussion

fca has been applied in combination with statistical metrics to the detection of several types of statistically significant pharmacological associations, e.g., safety signals and drug interactions. Compared to the classical dma-based detection, the proposed fca method improves the quantity and quality of extracted pharmacological associations, including those involving several drugs and/or reactions. Indeed, the amount of extracted associations is reduced by targeting basis of association rules using fca framework, yet relevant associations with respect to the referred population of case reports, thereby saving investments in time and money that would be spent in further clinial trials.

In the future, we intent to reformulate drug-reaction analysis so that detecting pharmacological association is mapped to a relational data mining problem [START_REF] Huchard | Relational concept discovery in structured datasets[END_REF]. Moreover, because drug-reaction analysis deals with a dynamic db that comprises high volume of data, the reconstruction -from scratch-of a new concept lattice for every change in the srs db is so computationally expensive that it is prohibitive. We shall address the on-line analysis of pharmacovigilance data using the incremental maintenance of concept lattice [START_REF] Valtchev | A generic scheme for the design of efficient on-line algorithms for lattices[END_REF] and the respective association basis.

2. 2

 2 FCA-based association rule designfca framework is widely-used in mining patterns from db, including association rules that express the co-ocurrences among attribute sets (called itemsets). An association rule is a pair of sets 'antecedent -→ consequent' with no claim of causality. A ruleB -→ D (B, D ⊆ A) has a support σ(B -→ D) = σ(B ∪ D)and a confidence that is the ratio of the rule support to the support of the antecedent (γ(B -→ D) = σ(B-→D)

Fig. 2 .

 2 Fig. 2. Left: Drug-concept and adr-concept in the drug-reaction concept lattice LP . Right: The two-by-two contingency table for target drug m and a suspected adr r.

Fig. 3 .

 3 Fig. 3. Left : 2 × 2 × 2 contingency table of reports for the regression of Nausea (N) on two exposure level Lopinavir (L), Efavirenz (E) and their interaction term L * E. Right : The corresponding logit coefficients provided by the R package.

Table 1 .

 1 A fragment 1 of srs db.

	Patient Age Gender Prescribed drugs	Observed adverse drug reactions
	Daffy 24 Female Lopinavir,	Nausea, Hives , Vomiting
		Efavirenz
	Farley 63 Male Lopinavir,	Oedema, Hives, Headache, Nausea,
		Tenofovir	Heart failure, Hair loss
	Lane	27 Female Maraviroc,	Fatigue, Oedema, Hives, Hair loss,
		Efavirenz	Bleeding
	Shana 15 Female Tenofovir,	Fatigue, Oedema, Hair loss
		Lopinavir
	Trudy 41 Male Raltegravir	Fatigue, Breath disorder, Nausea,
			Heart failure, Bleeding, Vomiting

Table 2 )

 2 involves a set of objects O, a set of attributes A and an incidence relation I ⊆ A × O (oIa stand for "object o has the attribute a"). For instance, in Table2, objects are patients and attributes demographic informations, drugs or reactions.

	Demographic data		Adverse reactions			Drugs
	Young	Adult	Senior	Male	Female	Fatigue	Oedema	BreathDisorder	Hives	Headache	Nausea	HeartFailure	HairLoss	Bleeding	Vomiting	Raltegravir	Lopinavir	Tenofovir	Maraviroc	Efavirenz

Table 3 .

 3 Drug-reaction associations derived from the srs data depicted in Table1with the corresponding support.

Table 4 .

 4 Left: Candidates for pharmacological associations obtained from 3249 case reports containing 527 drugs and 639 adr. Right: Statistically significant candidates.

		# Pure	# Semi-pure	# Biaised		# Pure	# Semi-pure	# Biaised
	Signals	1 88 745 834	Signals	0 4 59 63
	Interactions 1 260 70 331	Interactions 0 0 10 10
		2 348 815 1165		0 4 69 73

Source : MedEffect, Canada vigilance online database.

Non-Nucleoside Reverse Transcriptase Inhibitors (NNRTIs) intervene in the early stages of the hiv replication cycle.

http://safetyseer.cvs.sourceforge.net/signalminer/

http://www.iro.umontreal.ca/ ∼ galicia

http://www.r-project.org/

Acknowledgments

This work was supported partially by project grant (Ref. ANR-07-TecSan) from the French Agence Nationale de la Recherche, Biologie et Santé and Caisse Nationale de Solidarité pour l'Autonomie, and a discovery grant of the Natural Sciences and Engineering Research Council of Canada.


F Doumenc

B Guerrier

Self patterning induced by a solutal Marangoni effect in a receding drying meniscus

Keywords: 40, 47, 54, -r -Pattern selection; pattern formation 40, 47, 15gm -Thin film flows 40, 47, 55, np -Contact lines 40, 47, 57, Ng -Polymers and polymer solutions

This paper examines through numerical simulations the impact of a solutal Marangoni effect on the deposit obtained from a polymer solution. A hydrodynamical model with lubrication approximation is used to describe the liquid phase in a dip-coating-like configuration. The studied case considers evaporation in stagnant air (diffusion-limited evaporation), which results in a coupling between the liquid and gas phases. Viscosity, surface tension, and saturated vapor pressure depend on the solute concentration. In the evaporative regime, when the surface tension increases with the polymer concentration, the Marangoni effect induces a periodic regime. This results in a self-organized periodic patterning of the dried film in certain control parameter ranges. A morphological phase diagram as well as meniscus and dry deposit shapes are provided as a function of the substrate velocity and bulk solute concentration.

Introduction. -Recent years have seen important developments in studies dedicated to patterning induced by convective self-assembly during the drying of solutions or dispersions. For geometries such as sessile droplets or dip-coating-like configurations, the system may develop regular patterns induced by a periodic movement of the contact line. The contact line is pinned, or slows down compared to the mean velocity, and then speeds up (slip event) until the next pinning event [1,2]. A remarkable aspect of this phenomenon is its universality: it can be observed for different geometries (sessile droplet [3], liquid bridge [4], capillary tube [5], dip-coating [6] or similar geometry [7,8]) and different solutes (colloids [9], polymers [10], small molecules [11], etc.).

Despite the large number of experimental and theoretical studies published in the last ten years, we are still lacking a complete understanding of the mechanisms responsible for the appearance of a periodic regime (see Frastia et al. [12] for a recent and complete review). A very promising approach, which motivated the present work, consists in capturing a stick-slip phenomenon through a hydrodynamical model. Such models were developed to describe (a) E-mail: doumenc@fast.u-psud.fr the evaporation of dewetting liquid layers (Warner et al. [13], Frastia et al. [12,14]), of droplets (Craster et al [15]), or the transfer of a surfactant monolayer over a moving substrate (Köpf et al [16]). All of these models are based on lubrication approximation and concern thin liquid layers in a situation of partial wetting (substrate wettability is taken into account through a disjoining pressure term). Evaporation is assumed to be phase transition-limited (a situation that occurs when the liquid is in contact with its pure vapor); the dynamic in the gas phase can therefore be disregarded (one-sided models). With the exception of [16], these models consider colloidal dispersions, which are characterized by strong variations of viscosity as a function of particle concentration (Krieger-Dougherty law, which diverges at the maximum particle packing concentration). Additionally, Warner et al. [13] and Köpf et al. [16] have studied the solutal Marangoni effect's influence on the pattern formation (due to the presence of a surfactant, which lowers the liquid surface tension). An advantageous feature shared by all of these models is their ability to predict the periodic patterning of the deposit without an artificial trigger. For instance, the periodic movement of the contact line can be produced by alternate motions of dewetting and drying fronts that are competing against each other [12,14].

In this study, we consider a polymer solution drying in stagnant air in a dip-coating-like geometry (a meniscus over a moving substrate). Because the substrate velocity is a control parameter, this set-up corresponds to an active geometry as defined in [12]. Our adopted approach is similar to the above-discussed models, although it includes specific features relevant to our studied problem. First, we consider that evaporation takes place in stagnant air (diffusion-limited evaporation), which requires us to take account of the diffusion dynamic in the gas phase. Secondly, surface tension is assumed to depend on the polymer concentration (solutal Marangoni effect). However, in contrast to the above-mentioned works, the non-volatile solute has a higher surface tension than the volatile solvent. Finally, we consider the saturated vapor pressure's dependence on the solvent concentration. The evaporation flux decreases with the solvent concentration, and the film thickness therefore remains large enough to maintain a negligible influence of substrate wettability, thus the disjoining pressure is disregarded in the model.

Previous results obtained for this same configuration have disregarded the Marangoni effect [17]. Although these previous simulations have confirmed the impact of local evaporation on the shape of the meniscus and predicted the deposit thickness, only flat deposits were observed. In this work, we demonstrate that the solutal Marangoni effect may be one of the mechanisms responsible for the onset of a periodic regime. Indeed, when the non-volatile solute has a higher surface tension than the solvent and for a certain range of substrate velocities and bulk concentrations, a stable steady solution does not exist, and the system spontaneously evolves toward a periodic solution.

The film/gas model. -This study examines a drying binary solution (one volatile solvent and one nonvolatile solute) in a meniscus. The free surface is in contact with air at atmospheric pressure and evaporation is limited by the diffusion of solvent vapor into stagnant air. Our conditions assume a local thermodynamic equilibrium at the interface at a constant temperature (isothermal problem). The solution is in contact with a moving, flat substrate with a no-slip boundary condition. The model is two-dimensional, and the hydrodynamics inside the solution are described in a lubrication approximation framework. Gravity is neglected, and a uniform concentration over the thickness is assumed in the liquid phase.

The direction parallel to the substrate (flow main direction) is denoted by x; the axis normal to the substrate is denoted by z. With the above-mentioned approximations and assuming a Newtonian fluid, Stokes equations produce the following standard result [18]:

Q(x, t) = V sub h + h 3 3η(φ) ∂ ∂x (γ ∂ 2 h ∂x 2 ) + h 2 2η(φ) dγ dφ ∂φ ∂x , (1)
where V sub is the substrate velocity, h is the liquid height, η is the dynamic viscosity, γ is the surface tension, and φ is the polymer volume fraction. Q(x, t) is the liquid volumic flux (by unit of width) at abscissa x and time t over a cross-section normal to x,

Q(x, t) = h(x) 0 u(x, z) dz, (2)
where u(x, z) is the velocity component in the x direction.

The first term on the right-hand side of eq. ( 1) is the flow produced by the substrate motion; the second term is the flow induced by capillary pressure; the last term describes the flow driven by the surface tension gradient (Marangoni effect). In the following, these three terms are denoted by Q sub , Q cap , and Q M a , respectively. The global mass conservation and the non-volatile solute mass conservation respectively read as follows:

∂h ∂t + ∂Q ∂x = -v ev (x, t) (3)
∂(φh) ∂t + ∂(φQ) ∂x = ∂ ∂x (Dh ∂φ ∂x ), (4)
where v ev (x, t) is the local evaporation velocity (positive for evaporation), and D is the mutual diffusion coefficient of the binary system. At x = 0 (inlet of the computational domain) we impose the liquid height h 0 , the curvature C 0 , and the bulk solute volume fraction φ 0 :

at x = 0, h = h 0 , ∂ 2 h ∂x 2 = C 0 , φ = φ 0 . (5)
Considering, for instance, a capillary rise between two plates separated by a gap d, C 0 is the curvature of a static meniscus deduced from the gap d between the plates (C 0 = 2/d). The height h 0 is an arbitrary cut-off; it must be small enough to ensure the validity of a small slope approximation. Imposing h 0 and C 0 at x = 0 creates a meniscus section of static length L st ∼ h 0 /C 0 . Variations of curvature and height at x = 0, produced by the evaporation or the substrate motion, are neglected in this approach.

For the outlet conditions at x = W , far away from the bulk, we assume a zero concentration gradient:

at x = W, ∂φ ∂x = 0. ( 6
)
In the evaporative regime (cf. next section) the film is dry at the outlet and we consider φ(W, t) ∼ 1, which results in a very large viscosity close to the outlet. We can therefore infer that eq. ( 1) reduces to Q(x, t) ≃ V sub h in that region, thus eq. ( 3) turns into an advection equation of order 1 in space, which does not require any boundary conditions at x = W . In the Landau-Levich regime we assume a zero slope and curvature at the outlet. The local evaporation velocity v ev (x, t) in eq. ( 3) is determined by solving a diffusion problem in the gas phase for a domain of length W and height H (H would roughly correspond to the boundary layer thickness for a process with a forced air-flow above the free surface). Because H is considerably larger than h 0 , we assume a rectangular domain for the gas phase. The liquid thickness variations are therefore neglected in the computation of the mass transfer in the gas phase. The bottom boundary of this domain corresponding to the liquid-gas interface is thus: z = 0 and 0 < x < W . The diffusion equation in the gas phase reads as follows:

∂c g ∂t = D g ( ∂ 2 c g ∂x 2 + ∂ 2 c g ∂z 2 ), for 0 < x < W and 0 < z < H , (7)
where c g is the solvent vapor concentration in the air, and D g is the vapor diffusion coefficient. The vertical walls are assumed to be impermeable. A Dirichlet condition with a zero solvent vapor concentration is imposed at the top. We thus obtain the following boundary conditions for the gas domain (see fig. 1):

∂c g ∂x = 0 for (x = 0 or x = W ) and 0 < z < H (8)
c g = 0 for 0 ≤ x ≤ W and z = H (9)
The next boundary condition corresponds to the coupling between the liquid and the gas phases. The solvent activity in a polymer solution is given by the classical Flory-Huggins theory [START_REF] Flory | Principles of polymer chemistry[END_REF]:

a = (1 -φ)exp(φ + χφ 2 )
, where χ is the polymer-solvent interaction parameter. Given the assumption that the vapor behaves as an ideal gas, the local thermodynamic equilibrium at the interface implies a = P vs /P vs0 , where P vs and P vs0 are the saturated vapor pressure above the solution and the pure solvent, respectively. The vapor solvent concentration at the interface can be deduced from the solvent activity and the ideal gas law:

c g = a(φ, T )P vs0 (T ) M s RT for 0 ≤ x ≤ W and z = 0, (10)
where M s is the solvent molar mass, R is the ideal gas constant, and T is the temperature. Equation (10) neglects Kelvin effect. The validity of this assumptions has been confirmed a posteriori by inspection of the numerical results. Our final equation concerns the mass flux conservation across the interface:

ρv ev = -D g ∂c g ∂z , ( 11
)
where ρ is the liquid solvent density. In agreement with [17], the above set of equations (1 to 11) is solved through finite differences (using a pure implicit scheme of order 1 in time and 2 in space and an adaptive spatial mesh to increase the density of nodes in the high concentration gradient region). Results of a previous calculus for a close configuration provided the initial conditions. In the following, we focus on the long term behavior, and the initial transient regimes are not shown.

H

Gas phase

(air + solvent vapor)

W

Liquid phase

Evaporation z x x=0 x=W

Dirichlet boundary condition, eq. ( 9)

Liquid free surface, eq. (10-11) 0 h Impermeable surface, eq. ( 8)

Fig. 1: Geometry and boundary conditions of the gas domain.

The solution provides the meniscus shape, the local evaporation flux, the concentration field in the gas, and the concentration and velocity fields in the solution (cf. [17] for details of a configuration without the Marangoni effect). The following values apply to all simulations: H = 3 mm, W = 1 mm, C 0 = 2 mm -1 , h 0 = 0.1 mm, and T = 25 o C for the physico-chemical properties of the Polyisobutylene (PIB)/toluene system [17]. The toluene saturated vapor pressure, the molar mass and the diffusion coefficient in the gas phase are P vs0 = 3792 Pa, M s = 92.14 g.mol -1 , and D g = 8.6 × 10 -6 m 2 .s -1 , respectively. The solution density and the diffusion coefficient are assumed to be constant: ρ = 900 kg.m -3 and D = 10 -10 m 2 .s -1 . The surface tension γ is assumed to increase linearly with the solute volume fraction from γ = 28 × 10 -3 N.m -1 (pure toluene) to γ = 34 × 10 -3 N.m -1 (pure PIB). The viscosity η exhibits a strong increase with the solute volume fraction (12 orders of magnitude from pure toluene to pure PIB for a PIB molar mass of M W = 500 kg.mol -1 ). The following empirical law gives η in Pa.s: Y = 8.22 + 13.2X + 5.2X 2 + 0.70X 3 , where Y = log 10 (η) and X = log 10 (φ). Gravimetric experiments [START_REF] Doumenc | [END_REF] have measured the PIB-toluene interaction parameter as follows: χ = 0.45 + 0.30φ at T = 25 o C.

Results and discussion. -Fig. 2 illustrates the solutions obtained for different substrate velocities at φ 0 = 0.01. A steady regime is always observed for the reference configuration without the Marangoni effect (dγ/dφ = 0, γ = γ(φ 0 ), black dashed curves). Previous studies have shown that evaporation at the meniscus significantly impacts the flow [17] for this range of substrate velocities (10 µm.s -1 ≤ V sub ≤ 100 µm.s -1 ). The deposit thickness h d can be obtained through simple mass balances [11,17,21,22]:

h d = F ev φ 0 /V sub , (12)
where F ev is the integral of the evaporation velocity v ev over the whole meniscus. The dry film thickness in this evaporative regime, where most of the evaporation takes place in the meniscus, corresponds to the left branch in fig. 3. At higher substrate velocity, the right branch corre- sponds to the Landau-Levich regime, where viscous forces drag a film onto the substrate; this film subsequently dries [11,23]. The deposit thickness is proportional to

V 2/3
sub in this regime, as expected. When the Marangoni effect is considered, complex behaviors are observable in the evaporative regime. First, because the surface tension of the solute is higher than that of the solvent, the concentration gradient causes the meniscus to be stretched compared with the case without the Marangoni effect (solid lines v. dashed lines in fig. 2). The formation of a stationary bump in the sub-regime (c), corresponding to the velocity range 37 µm.s -1 < V sub ≤ 85 µm.s -1 , is a significant fact. The bump size decreases when V sub increases, and a monotonic profile is recovered for V sub > 85 µm.s -1 (sub-regime (d)). Poulard and Damman [25] have experimentally observed such a bump, induced by a solutal Marangoni flow, during the drying of a polymer solution droplet. For a simpler case (pure liquid and a uniform surface tension gradient imposed by heating the substrate), Carles and Cazabat [24] have advanced an elegant discussion to explain the bump formation using simple hydrodynamical arguments based on mass conservation in a steady state (cf. [24] for details). Our study considers a more complex configuration because the meniscus shape is the result of a complex interplay between the three components of the volumic flux and the variable viscosity. However similar arguments can be put forward to qualitatively understand the origin of the stationary bump. Indeed, to ensure mass conservation in the steady state (eq. ( 3) with ∂h ∂t = 0), the Marangoni flux Q M a must be balanced by a modification of the capillary flux Q cap . This is illustrated in fig. 4, which shows the three components (Q sub , Q cap , and Q M a ) of the liquid volumic flux Q(x). Q M a is always positive but nonmonotonic. The capillary term changes its sign to ensure 12) (evaporative regime). Dashed line: slope 2/3 (Landau-Levich regime). For the sub-regime case (b) (red circles), the thickness is averaged over one period.

mass conservation, and so does the third derivative of the height h(x), which results in the bump formation. Below a given substrate velocity (V sub ≤ 37 µm.s -1 in our example), a stationary solution is no longer achievable and the numerical simulation converges toward a periodic solution, leading to a regularly patterned deposit (sub-regime (b) in fig. 2). The time evolution of the liquid height profile is detailed over one period in fig. 5, where the black arrow indicates the bump top. The dotted vertical line is the drying front corresponding to the limit of the "frozen" region, where the liquid viscosity is so large that the liquid film is simply advected at the substrate velocity. In practice, we consider the drying front to be located at the abscissa

x f defined by (Q(x f , t) -Q sub (x f , t))/Q sub (x f , t) < 1%.
In this periodic regime, the bump initially grows upward while simultaneously moving to the right, preceded by the drying front; both of them move away from the meniscus. After a certain time, the drying front recedes, causing the bump to dry with a dramatic increase in viscosity. The bump is then advected at the substrate velocity, and a new bump is formed closer to the meniscus, and so on. Finally, for a lower substrate velocity (V sub < 19.5 µm.s -1 in our example), we again observe a steady regime with a monotonic liquid height profile (sub-regime (a) in fig. 2 ). It is noteworthy that, while the meniscus shape is strongly sensitive to the Marangoni effect, the dry deposit thicknesses (averaged over one period for the periodic regime case) are recovered without significant changes compared with the simulations without the Marangoni effect (cf. fig. 3). It follows that the global mass balances are not affected by the development of the flow induced by the surface tension gradient.

Fig. 6 depicts a morphological phase diagram of the different regimes as a function of V sub and φ 0 , illustrating that the periodic regime occurs in a relatively small range of substrate velocities and disappears for bulk concentrations larger than about 0.03.

Concerning the periodic sub-regime (b), fig. 7 illustrates wavelengths and amplitudes of the periodic patterns as a Fig. 4: Relation between meniscus profile and liquid fluxes for V sub = 40µm.s -1 and φ0 = 0.01 (steady state, zoom on the bump region). Top: liquid height. Bottom: total liquid volumic flux Q (thick black line), Q sub (thin green line), Qcap (dashed-dot blue line) and QMa (dashed red line). Dotted vertical line: position of the drying front corresponding to the abscissa x f , so that (Q

(x f , t) -Q sub (x f , t))/Q sub (x f , t) < 1%.
function of the substrate velocity and for two bulk concentrations. Note that these results correspond to the morphology of the film outside of the meniscus, where the system gels due to the very high viscosity of the solution. Therefore, in that region, the periodic pattern is simply translated at the substrate velocity V sub . We use the period τ to obtain the wavelength λ = τ V sub ; the pattern amplitude refers to the dry deposit thickness h d = hφ. Qualitatively, fig. 7 shows two types of transitions from flat to patterned deposit: (α) at low velocity, a divergence of the wavelength for a finite value of V sub occurs whereas the amplitude retains a quasi-constant value; (β) at high velocity, a decrease of the pattern amplitude is observed. For both cases, small domains of hysteresis are observed close to the transition regions. Indeed the substrate velocity corresponding to the transition from a flat to a patterned deposit can be slightly shifted (less than 1µm/s) by changing the initial condition (flat deposit limits shown in fig. 7 correspond to a decreasing substrate velocity). Li et al. [26] have also observed a divergence of the wavelength when the substrate velocity was decreased (numerical simulations of Langmuir-Blodgett transfer), and it is worth noting that behaviors (α) and (β) have already been reported by Frastia et al [12], although their study was based on a different situation (numerical simulations of a dewetting thin film with a passive geometry). As suggested by these authors, one may infer that, most likely, behavior (α) corresponds to a homoclinic bifurcation and behavior (β) corresponds to a subcritical Hopf bifurcation. A more precise description would require the definition of a reduced model and a subsequent analysis within the framework of bifurcation theory; this was performed, for instance, by Köpf et al. [27] for Langmuir-Blodgett transfer. Fig. 8 illustrates the complex behavior of the system for Fig. 5: Periodic time evolution of the meniscus (the region from x = 0 to x = 300 µm is not shown). V sub = 30 µm.s -1 , φ0 = 0.01. From top to bottom: t = 0, t = 0.25τ , t = 0.5τ , t = 0.75τ , t = τ , where the period τ = 8.69s. The black arrow indicates the bump top. The dotted vertical line is the position of the drying front corresponding to the abscissa x f , so that

(Q(x f , t) -Q sub (x f , t))/Q sub (x f , t) < 1%.
a step-by-step decrease of V sub at φ 0 = 0.01. Starting from a steady state (V sub = 38 µm/s, flat deposit), we obtain periodic regimes at V sub = 37, 36.5 and 36 µm/s (fig. 8-(1-3)), with a doubling of the wavelength between the last two velocities. After passing through an aperiodic regime (V sub = 35.75µm/s, fig. 8-4), a new periodic regime is reached, characterized by a larger wavelength and a significant change in the amplitude and deposit shape (V sub = 35.5 µm/s, fig. 8-5). The decrease of the pattern amplitude with an increasing substrate velocity has already been experimentally observed [7]. However, in these experiments, which were performed with colloidal suspensions, the wavelengths have remained proportional to V -1 sub for over a decade, suggesting that mechanisms other than the solutal Marangoni effect may be involved and should therefore be investigated. The study of two dimensional patterns offers another interesting perspective. Indeed, it is well known that the liquid bump observed in these simulations is subject to the Rayleigh-Plateau instability [25,28], which has the potential to produce a rich variety of different patterns. * * *

Fig. 2 :

 2 Fig.2: Liquid height for different substrate velocities, φ0 = 0.01. Dashed lines: constant surface tension (no Marangoni effect). Solid lines: variable surface tension (Marangoni effect). (a)V sub = 10µm/s (steady sub-regime, monotonic profile), (b)V sub = 30µm/s (periodic sub-regime, moving bump), (c)V sub = 55µm/s (steady sub-regime, stationary bump), (d)V sub = 100µm/s (steady sub-regime, monotonic profile).

Fig. 3 :

 3 Fig.3: Dry film thickness divided by evaporation flux for φ0 = 0.01. Solid line: eq. (12) (evaporative regime). Dashed line: slope 2/3 (Landau-Levich regime). For the sub-regime case (b) (red circles), the thickness is averaged over one period.

Fig. 8 -

 8 (1)(2)(3) and fig.8-5 correspond to the fourth righthandmost circles in fig.7. The aperiodic regime observed in fig.8-4is not represented in fig.7(undefined wavelength).

Fig. 6 :Fig. 7 :

 67 Fig.6: Morphological phase diagram of meniscus shape, in the plane spanned by the substrate velocity V sub and the bulk polymer volume fraction φ0.

Fig. 8 :

 8 Fig. 8: Transition from flat to patterned deposit for φ = 0.01 and decreasing substrate velocity, starting from steady state at V sub = 38µm/s (flat deposit, not shown). (1) V sub = 37µm/s, λ = 78.4µm ; (2) V sub = 36.5µm/s, λ = 82.1µm ; (3) V sub = 36µm/s, λ = 175µm ; (4) V sub = 35.75µm/s, aperiodic ; (5) V sub = 35.5µm/s, λ = 245µm.

This work received support from the EU through the ITN MULTIFLOW (PITN-GA-2008-214919).